From 5173a9e6f8b3e74d03b7aa5ae79f8af85a118057 Mon Sep 17 00:00:00 2001
From: Cory <cory@balaton.dev>
Date: Sun, 8 Oct 2023 17:14:46 +0200
Subject: [PATCH 01/26] Implement simulate method

---
 include/PenningTrap.hpp |  22 +++++----
 src/PenningTrap.cpp     | 102 ++++++++++++++++++++++++++++------------
 2 files changed, 86 insertions(+), 38 deletions(-)

diff --git a/include/PenningTrap.hpp b/include/PenningTrap.hpp
index 3601634..1c7d56c 100644
--- a/include/PenningTrap.hpp
+++ b/include/PenningTrap.hpp
@@ -18,8 +18,12 @@
 #include "Particle.hpp"
 #include "constants.hpp"
 
-#pragma omp declare reduction( + : arma::vec : omp_out += omp_in ) \
-  initializer( omp_priv = omp_orig )
+typedef std::vector<arma::vec::fixed<3>> sim_cols;
+typedef std::vector<arma::vec::fixed<3>> sim_rows;
+typedef std::vector<sim_cols> sim_arr;
+
+#pragma omp declare reduction(+ : arma::vec : omp_out += omp_in)               \
+    initializer(omp_priv = omp_orig)
 
 /** @brief A class that simulates a Penning trap.
  *
@@ -28,15 +32,15 @@
  * */
 class PenningTrap {
 private:
-    double B_0; ///< Magnetic field strength
-    double V_0; ///< Applied potential
-    double d; ///< Characteristic dimension
+    double B_0;                      ///< Magnetic field strength
+    double V_0;                      ///< Applied potential
+    double d;                        ///< Characteristic dimension
     std::vector<Particle> particles; ///< The particles in the Penning trap
 
 public:
     /** @brief Set B_0, V_0 and d.
      * */
-    PenningTrap(double B_0 = T, double V_0 = 25.*V/1000., double d = 500.);
+    PenningTrap(double B_0 = T, double V_0 = 25. * V / 1000., double d = 500.);
 
     /** @brief Add a particle to the system
      * */
@@ -52,7 +56,7 @@ public:
 
     /** @brief Calculate the force between 2 particles.
      *
-     *  @details Calculate the force exhibited on particle p_i from 
+     *  @details Calculate the force exhibited on particle p_i from
      *  particle p_j.
      * */
     arma::vec force_on_particle(int i, int j);
@@ -69,7 +73,7 @@ public:
     arma::vec total_force_particles(int i);
 
     /** @brief calculate the total force on a particle.
-     * */ 
+     * */
     arma::vec total_force(int i);
 
     /** @brief Go forward one timestep using the RK4 method
@@ -80,6 +84,8 @@ public:
      * */
     void evolve_forward_euler(double dt);
 
+    sim_arr simulate(double time, int steps, std::string method = "rk4");
+
     arma::vec get_particle(int i);
 
     double get_d();
diff --git a/src/PenningTrap.cpp b/src/PenningTrap.cpp
index 5d9a16b..c4fea93 100644
--- a/src/PenningTrap.cpp
+++ b/src/PenningTrap.cpp
@@ -16,6 +16,7 @@
 #include "PenningTrap.hpp"
 #include "constants.hpp"
 #include "utils.hpp"
+#include <cstdlib>
 
 PenningTrap::PenningTrap(double B_0, double V_0, double d)
 {
@@ -104,64 +105,72 @@ arma::vec PenningTrap::total_force(int i)
 void PenningTrap::evolve_RK4(double dt)
 {
     std::vector<Particle> tmp_particles = this->particles;
-    
-    arma::vec::fixed<3> *k_v = new arma::vec::fixed<3>[this->particles.size()*4];
-    arma::vec::fixed<3> *k_r = new arma::vec::fixed<3>[this->particles.size()*4];
+
+    arma::vec::fixed<3> *k_v =
+        new arma::vec::fixed<3>[this->particles.size() * 4];
+    arma::vec::fixed<3> *k_r =
+        new arma::vec::fixed<3>[this->particles.size() * 4];
 
     int size = this->particles.size();
 
-    for (int i=0; i<size; i++) {
-        k_v[i] = this->total_force(i)/this->particles.at(i).m;
+    for (int i = 0; i < size; i++) {
+        k_v[i] = this->total_force(i) / this->particles.at(i).m;
         k_r[i] = this->particles.at(i).v_vec;
     }
 
-    for (int i=0; i<size; i++) {
+    for (int i = 0; i < size; i++) {
         Particle *p = &this->particles.at(i);
 
-        p->v_vec = tmp_particles.at(i).v_vec + (dt/2)*k_v[i];
-        p->r_vec = tmp_particles.at(i).r_vec + (dt/2)*k_r[i];
+        p->v_vec = tmp_particles.at(i).v_vec + (dt / 2) * k_v[i];
+        p->r_vec = tmp_particles.at(i).r_vec + (dt / 2) * k_r[i];
     }
 
-
-    for (int i=0; i<size; i++) {
-        k_v[1*size + i] = this->total_force(i)/this->particles.at(i).m;
-        k_r[1*size + i] = this->particles.at(i).v_vec;
+    for (int i = 0; i < size; i++) {
+        k_v[1 * size + i] = this->total_force(i) / this->particles.at(i).m;
+        k_r[1 * size + i] = this->particles.at(i).v_vec;
     }
 
-    for (int i=0; i<size; i++) {
+    for (int i = 0; i < size; i++) {
         Particle *p = &this->particles.at(i);
 
-        p->v_vec = tmp_particles.at(i).v_vec + (dt/2)*k_v[1*size + i];
-        p->r_vec = tmp_particles.at(i).r_vec + (dt/2)*k_r[1*size + i];
+        p->v_vec = tmp_particles.at(i).v_vec + (dt / 2) * k_v[1 * size + i];
+        p->r_vec = tmp_particles.at(i).r_vec + (dt / 2) * k_r[1 * size + i];
     }
 
-    for (int i=0; i<size; i++) {
-        k_v[2*size + i] = this->total_force(i)/this->particles.at(i).m;
-        k_r[2*size + i] = this->particles.at(i).v_vec;
+    for (int i = 0; i < size; i++) {
+        k_v[2 * size + i] = this->total_force(i) / this->particles.at(i).m;
+        k_r[2 * size + i] = this->particles.at(i).v_vec;
     }
 
-    for (int i=0; i<size; i++) {
+    for (int i = 0; i < size; i++) {
         Particle *p = &this->particles.at(i);
 
-        p->v_vec = tmp_particles.at(i).v_vec + dt*k_v[2*size + i];
-        p->r_vec = tmp_particles.at(i).r_vec + dt*k_r[2*size + i];
+        p->v_vec = tmp_particles.at(i).v_vec + dt * k_v[2 * size + i];
+        p->r_vec = tmp_particles.at(i).r_vec + dt * k_r[2 * size + i];
     }
 
-
-    for (int i=0; i<size; i++) {
-        k_v[3*size + i] = this->total_force(i)/this->particles.at(i).m;
-        k_r[3*size + i] = this->particles.at(i).v_vec;
+    for (int i = 0; i < size; i++) {
+        k_v[3 * size + i] = this->total_force(i) / this->particles.at(i).m;
+        k_r[3 * size + i] = this->particles.at(i).v_vec;
     }
 
-    for (int i=0; i<size; i++) {
+    for (int i = 0; i < size; i++) {
         Particle *p = &this->particles.at(i);
 
-        p->v_vec = tmp_particles.at(i).v_vec + dt*(k_v[i] + k_v[size + i] + k_v[2*size + i] + k_v[3*size + i])/6;
-        p->r_vec = tmp_particles.at(i).r_vec + dt*(k_r[i] + k_r[size + i] + k_r[2*size + i] + k_r[3*size + i])/6;
+        p->v_vec = tmp_particles.at(i).v_vec +
+                   dt *
+                       (k_v[i] + k_v[size + i] + k_v[2 * size + i] +
+                        k_v[3 * size + i]) /
+                       6;
+        p->r_vec = tmp_particles.at(i).r_vec +
+                   dt *
+                       (k_r[i] + k_r[size + i] + k_r[2 * size + i] +
+                        k_r[3 * size + i]) /
+                       6;
     }
 
-    delete [] k_v;
-    delete [] k_r;
+    delete[] k_v;
+    delete[] k_r;
 }
 
 void PenningTrap::evolve_forward_euler(double dt)
@@ -180,6 +189,39 @@ void PenningTrap::evolve_forward_euler(double dt)
     this->particles = new_state;
 }
 
+sim_arr PenningTrap::simulate(double time, int steps, std::string method)
+{
+    double dt = time / (double)steps;
+    sim_arr res(this->particles.size(), sim_cols(steps));
+
+    std::function<void(double)> func;
+    if (method == "rk4") {
+        func = [this](double dt) {
+            this->evolve_RK4(dt);
+        };
+    }
+    else if(method == "euler") {
+        func = [this](double dt) {
+            this->evolve_forward_euler(dt);
+        };
+    }
+    else {
+        std::cout << "Not a valid method!" << std::endl;
+        abort();
+    }
+
+    int size = this->particles.size();
+
+    for (int j=0; j<steps; j++) {
+        for (int i=0;i<size;i++) {
+            res[i][j] = this->particles[i].r_vec;
+        }
+        func(dt); 
+    }
+
+    return res;
+}
+
 arma::vec PenningTrap::get_particle(int i)
 {
     return this->particles.at(i).r_vec;

From 51a381e672681b14448c67db22a1f6708c0f1093 Mon Sep 17 00:00:00 2001
From: Cory <cory@balaton.dev>
Date: Sun, 8 Oct 2023 17:15:04 +0200
Subject: [PATCH 02/26] Use simulate method instead of own code

---
 src/main.cpp | 103 +++++++++++++++++++++++++++++++++++++++++++--------
 1 file changed, 87 insertions(+), 16 deletions(-)

diff --git a/src/main.cpp b/src/main.cpp
index 1c55279..b6d83c7 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -21,6 +21,89 @@
 #define CHARGE 1.
 #define MASS 40. // unit: amu
 
+Particle p1(1., 40., arma::vec{20., 0., 20.}, arma::vec{0., 25., 0.});
+Particle p2(1., 40., arma::vec{25., 25., 0.}, arma::vec{0., 40., 5.});
+
+void simulate_single_particle()
+{
+    PenningTrap trap;
+
+    trap.add_particle(p1);
+
+    double time = 50.; // microseconds
+    double dt = time / (double)N;
+    
+    auto res = new arma::vec::fixed<3>[N];
+
+    for (int i=0; i<N;i++) {
+        res[i] = trap.get_particle(0);
+        trap.evolve_RK4(dt);
+    }
+
+    mkdir("output", 0777);
+    mkdir("output/simulate_single_particle", 0777);
+
+    std::ofstream ofile;
+
+    ofile.open("output/simulate_single_particle/out.txt");
+    for (int i=0; i<N;i++) {
+        arma::vec p = res[i];
+        ofile << p(0) << "," << p(1) << "," << p(3) << "\n";
+    }
+    ofile.close();
+    delete [] res;
+}
+
+void simulate_two_particles()
+{
+    PenningTrap trap;
+
+    trap.add_particle(p1);
+    trap.add_particle(p2);
+
+    double time = 50.; // microseconds
+    double dt = time / (double)N;
+
+    auto res = new arma::vec::fixed<3>[2][N];
+
+
+    int counter = 0;
+
+    // Get the path of all particles
+    for (int j = 0; j < N; j++) {
+#pragma omp parallel for
+        for (int i = 0; i < 2; i++) {
+            res[i][j] = trap.get_particle(i);
+        }
+        trap.evolve_RK4(dt);
+    }
+
+    std::cout << counter << std::endl;
+
+    arma::vec::fixed<3> *cur_row;
+    arma::vec::fixed<3> cur_elem;
+
+    mkdir("output", 0777);
+    mkdir("output/simulate_2_particles", 0777);
+
+    std::ofstream ofile;
+
+// Write particle paths to file
+#pragma omp parallel for private(cur_row, cur_elem, ofile)
+    for (int i = 0; i < 2; i++) {
+        cur_row = res[i];
+        ofile.open("output/simulate_100_particles/p" + std::to_string(i) +
+                   ".txt");
+        for (int j = 0; j < N; j++) {
+            cur_elem = cur_row[j];
+            ofile << cur_elem(0) << "," << cur_elem(1) << "," << cur_elem(2)
+                  << "\n";
+        }
+        ofile.close();
+    }
+
+}
+
 void simulate_100_particles()
 {
     PenningTrap trap;
@@ -37,22 +120,9 @@ void simulate_100_particles()
     double time = 50.; // microseconds
     double dt = time / (double)N;
 
-    auto res = new arma::vec::fixed<3>[PARTICLES][N];
+    sim_arr res = trap.simulate(time, N);
 
-    int counter = 0;
-
-    // Get the path of all particles
-    for (int j = 0; j < N; j++) {
-#pragma omp parallel for
-        for (int i = 0; i < PARTICLES; i++) {
-            res[i][j] = trap.get_particle(i);
-        }
-        trap.evolve_RK4(dt);
-    }
-
-    std::cout << counter << std::endl;
-
-    arma::vec::fixed<3> *cur_row;
+    sim_rows cur_row;
     arma::vec::fixed<3> cur_elem;
 
     mkdir("output", 0777);
@@ -64,7 +134,8 @@ void simulate_100_particles()
 #pragma omp parallel for private(cur_row, cur_elem, ofile)
     for (int i = 0; i < PARTICLES; i++) {
         cur_row = res[i];
-        ofile.open("output/simulate_100_particles/p" + std::to_string(i) + ".txt");
+        ofile.open("output/simulate_100_particles/p" + std::to_string(i) +
+                   ".txt");
         for (int j = 0; j < N; j++) {
             cur_elem = cur_row[j];
             ofile << cur_elem(0) << "," << cur_elem(1) << "," << cur_elem(2)

From 0b52008d4d71577a4dbeb71deea5aefdbf439159 Mon Sep 17 00:00:00 2001
From: Cory <cory@balaton.dev>
Date: Sun, 8 Oct 2023 17:25:43 +0200
Subject: [PATCH 03/26] Overload constructor and format

---
 include/PenningTrap.hpp |  6 ++++++
 src/PenningTrap.cpp     | 40 ++++++++++++++++++++++++++++++----------
 2 files changed, 36 insertions(+), 10 deletions(-)

diff --git a/include/PenningTrap.hpp b/include/PenningTrap.hpp
index 1c7d56c..50874f8 100644
--- a/include/PenningTrap.hpp
+++ b/include/PenningTrap.hpp
@@ -42,6 +42,12 @@ public:
      * */
     PenningTrap(double B_0 = T, double V_0 = 25. * V / 1000., double d = 500.);
 
+    PenningTrap(int i, double B_0 = T, double V_0 = 25. * V / 1000.,
+                double d = 500.);
+
+    PenningTrap(std::vector<Particle> particles, double B_0 = T,
+                double V_0 = 25. * V / 1000., double d = 500.);
+
     /** @brief Add a particle to the system
      * */
     void add_particle(Particle particle);
diff --git a/src/PenningTrap.cpp b/src/PenningTrap.cpp
index c4fea93..6dce7b0 100644
--- a/src/PenningTrap.cpp
+++ b/src/PenningTrap.cpp
@@ -17,6 +17,7 @@
 #include "constants.hpp"
 #include "utils.hpp"
 #include <cstdlib>
+#include <vector>
 
 PenningTrap::PenningTrap(double B_0, double V_0, double d)
 {
@@ -25,6 +26,29 @@ PenningTrap::PenningTrap(double B_0, double V_0, double d)
     this->d = d;
 }
 
+PenningTrap::PenningTrap(int i, double B_0, double V_0, double d)
+{
+    this->B_0 = B_0;
+    this->V_0 = V_0;
+    this->d = d;
+
+    arma::vec r, v;
+    for (int j = 0; j < i; j++) {
+        r = arma::vec(3).randn() * .1 * this->d;
+        v = arma::vec(3).randn() * .1 * this->d;
+        this->add_particle(Particle(1., 40., r, v));
+    }
+}
+
+PenningTrap::PenningTrap(std::vector<Particle> particles, double B_0,
+                         double V_0, double d)
+{
+    this->B_0 = B_0;
+    this->V_0 = V_0;
+    this->d = d;
+    this->particles = particles;
+}
+
 void PenningTrap::add_particle(Particle particle)
 {
     this->particles.push_back(particle);
@@ -196,14 +220,10 @@ sim_arr PenningTrap::simulate(double time, int steps, std::string method)
 
     std::function<void(double)> func;
     if (method == "rk4") {
-        func = [this](double dt) {
-            this->evolve_RK4(dt);
-        };
+        func = [this](double dt) { this->evolve_RK4(dt); };
     }
-    else if(method == "euler") {
-        func = [this](double dt) {
-            this->evolve_forward_euler(dt);
-        };
+    else if (method == "euler") {
+        func = [this](double dt) { this->evolve_forward_euler(dt); };
     }
     else {
         std::cout << "Not a valid method!" << std::endl;
@@ -212,11 +232,11 @@ sim_arr PenningTrap::simulate(double time, int steps, std::string method)
 
     int size = this->particles.size();
 
-    for (int j=0; j<steps; j++) {
-        for (int i=0;i<size;i++) {
+    for (int j = 0; j < steps; j++) {
+        for (int i = 0; i < size; i++) {
             res[i][j] = this->particles[i].r_vec;
         }
-        func(dt); 
+        func(dt);
     }
 
     return res;

From 2fd0ab9875f8e62300f3310e9657aa5b224ee2e0 Mon Sep 17 00:00:00 2001
From: Cory <cory@balaton.dev>
Date: Sun, 8 Oct 2023 17:26:46 +0200
Subject: [PATCH 04/26] Remove redundant methods

---
 include/PenningTrap.hpp | 4 ----
 src/PenningTrap.cpp     | 8 --------
 2 files changed, 12 deletions(-)

diff --git a/include/PenningTrap.hpp b/include/PenningTrap.hpp
index 50874f8..3831eb4 100644
--- a/include/PenningTrap.hpp
+++ b/include/PenningTrap.hpp
@@ -91,10 +91,6 @@ public:
     void evolve_forward_euler(double dt);
 
     sim_arr simulate(double time, int steps, std::string method = "rk4");
-
-    arma::vec get_particle(int i);
-
-    double get_d();
 };
 
 #endif
diff --git a/src/PenningTrap.cpp b/src/PenningTrap.cpp
index 6dce7b0..694b2fd 100644
--- a/src/PenningTrap.cpp
+++ b/src/PenningTrap.cpp
@@ -242,12 +242,4 @@ sim_arr PenningTrap::simulate(double time, int steps, std::string method)
     return res;
 }
 
-arma::vec PenningTrap::get_particle(int i)
-{
-    return this->particles.at(i).r_vec;
-}
 
-double PenningTrap::get_d()
-{
-    return this->d;
-}

From bb0bd8f6a01a77d3c31f4324a43d68865ef97c7b Mon Sep 17 00:00:00 2001
From: Cory <cory@balaton.dev>
Date: Sun, 8 Oct 2023 20:26:28 +0200
Subject: [PATCH 05/26] Modify path

---
 src/animate_100_particles.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/animate_100_particles.py b/src/animate_100_particles.py
index 19f10ca..3e2f3ff 100644
--- a/src/animate_100_particles.py
+++ b/src/animate_100_particles.py
@@ -32,7 +32,7 @@ def animate():
     fig = plt.figure()
     ax = fig.add_subplot(projection="3d")
 
-    arr = get_data([f"output/simulate_100_particles/p{i}.txt" for i in range(100)])
+    arr = get_data([f"output/simulate_100_particles/particle_{i}.txt" for i in range(100)])
 
     arr = arr[:, :, ::10]
 

From d2047e43e084d4a8ef1dc8fa46c357ebe8517496 Mon Sep 17 00:00:00 2001
From: Cory <cory@balaton.dev>
Date: Sun, 8 Oct 2023 20:27:51 +0200
Subject: [PATCH 06/26] Implement mkpath

---
 include/utils.hpp |  2 ++
 src/utils.cpp     | 28 ++++++++++++++++++++++++++++
 2 files changed, 30 insertions(+)

diff --git a/include/utils.hpp b/include/utils.hpp
index 7a03149..2210880 100644
--- a/include/utils.hpp
+++ b/include/utils.hpp
@@ -118,4 +118,6 @@ static inline std::string methodName(const std::string& prettyFunction)
     return prettyFunction.substr(begin,end) + "()";
 }
 
+bool mkpath(std::string path, int mode = 0777);
+
 #endif
diff --git a/src/utils.cpp b/src/utils.cpp
index b55fa34..934e50f 100644
--- a/src/utils.cpp
+++ b/src/utils.cpp
@@ -9,6 +9,9 @@
  *
  *  @bug No known bugs
  * */
+
+#include <sys/stat.h>
+
 #include "utils.hpp"
 
 std::string scientific_format(double d, int width, int prec)
@@ -69,3 +72,28 @@ bool arma_vector_close_to(arma::vec &a, arma::vec &b, double tol)
     }
     return true;
 }
+
+bool mkpath(std::string path, int mode)
+{
+    std::string cur_dir;
+    std::string::size_type pos = -1;
+    struct stat buf;
+
+    if (path.back() != '/') {
+        path += '/';
+    }
+    while (true) {
+        pos++;
+        pos = path.find('/', pos);
+        if (pos != std::string::npos) {
+            cur_dir = path.substr(0, pos);
+            if (mkdir(cur_dir.c_str(), mode) != 0 && stat(cur_dir.c_str(), &buf) != 0) {
+                return -1;
+            }
+        }
+        else {
+            break;
+        }
+    }
+    return 0;
+}

From 8df35f90f5d15b3bf88639569a22846fbfab99a8 Mon Sep 17 00:00:00 2001
From: Cory <cory@balaton.dev>
Date: Sun, 8 Oct 2023 20:29:41 +0200
Subject: [PATCH 07/26] Add particle_interaction parameter

---
 include/PenningTrap.hpp | 11 ++++--
 src/PenningTrap.cpp     | 75 +++++++++++++++++++++++++++++++++++------
 2 files changed, 72 insertions(+), 14 deletions(-)

diff --git a/include/PenningTrap.hpp b/include/PenningTrap.hpp
index 3831eb4..bd88c7f 100644
--- a/include/PenningTrap.hpp
+++ b/include/PenningTrap.hpp
@@ -84,13 +84,18 @@ public:
 
     /** @brief Go forward one timestep using the RK4 method
      * */
-    void evolve_RK4(double dt);
+    void evolve_RK4(double dt, bool particle_interaction = true);
 
     /** @brief Go forward one timestep using the forward Euler method
      * */
-    void evolve_forward_euler(double dt);
+    void evolve_forward_euler(double dt, bool particle_interaction = true);
 
-    sim_arr simulate(double time, int steps, std::string method = "rk4");
+    sim_arr simulate(double time, int steps, std::string method = "rk4",
+                     bool particle_interaction = true);
+
+    void write_simulation_to_dir(std::string path, double time, int steps,
+                                 std::string method = "rk4",
+                                 bool particle_interaction = true);
 };
 
 #endif
diff --git a/src/PenningTrap.cpp b/src/PenningTrap.cpp
index 694b2fd..62c608a 100644
--- a/src/PenningTrap.cpp
+++ b/src/PenningTrap.cpp
@@ -17,6 +17,8 @@
 #include "constants.hpp"
 #include "utils.hpp"
 #include <cstdlib>
+#include <functional>
+#include <string>
 #include <vector>
 
 PenningTrap::PenningTrap(double B_0, double V_0, double d)
@@ -126,10 +128,23 @@ arma::vec PenningTrap::total_force(int i)
     return this->total_force_external(i) - this->total_force_particles(i);
 }
 
-void PenningTrap::evolve_RK4(double dt)
+void PenningTrap::evolve_RK4(double dt, bool particle_interaction)
 {
+
     std::vector<Particle> tmp_particles = this->particles;
 
+    std::function<arma::vec(int)> force;
+    if (particle_interaction) {
+        force = [this](int i) {
+            return this->total_force(i);
+        };
+    }
+    else {
+        force = [this](int i) {
+            return this->total_force_external(i);
+        };
+    }
+
     arma::vec::fixed<3> *k_v =
         new arma::vec::fixed<3>[this->particles.size() * 4];
     arma::vec::fixed<3> *k_r =
@@ -197,49 +212,87 @@ void PenningTrap::evolve_RK4(double dt)
     delete[] k_r;
 }
 
-void PenningTrap::evolve_forward_euler(double dt)
+void PenningTrap::evolve_forward_euler(double dt, bool particle_interaction)
 {
     std::vector<Particle> new_state = this->particles;
 
     Particle *p;
 
+    std::function<arma::vec(int)> force;
+    if (particle_interaction) {
+        force = [this](int i) { return this->total_force(i); };
+    }
+    else {
+        force = [this](int i) { return this->total_force_external(i); };
+    }
+
 #pragma omp parallel for private(p)
     for (int i = 0; i < this->particles.size(); i++) {
         p = &new_state.at(i);
-        p->v_vec += dt * this->total_force(i) / new_state.at(i).m;
+        p->v_vec += dt * force(i) / new_state.at(i).m;
         p->r_vec += dt * this->particles.at(i).v_vec;
     }
 
     this->particles = new_state;
 }
 
-sim_arr PenningTrap::simulate(double time, int steps, std::string method)
+sim_arr PenningTrap::simulate(double time, int steps, std::string method,
+                              bool particle_interaction)
 {
     double dt = time / (double)steps;
     sim_arr res(this->particles.size(), sim_cols(steps));
 
-    std::function<void(double)> func;
+    std::function<void(double, bool)> func;
     if (method == "rk4") {
-        func = [this](double dt) { this->evolve_RK4(dt); };
+        func = [this](double dt, bool particle_interaction) {
+            this->evolve_RK4(dt, particle_interaction);
+        };
     }
     else if (method == "euler") {
-        func = [this](double dt) { this->evolve_forward_euler(dt); };
+        func = [this](double dt, bool particle_interaction) {
+            this->evolve_forward_euler(dt, particle_interaction);
+        };
     }
     else {
         std::cout << "Not a valid method!" << std::endl;
         abort();
     }
 
-    int size = this->particles.size();
-
     for (int j = 0; j < steps; j++) {
-        for (int i = 0; i < size; i++) {
+        for (int i = 0; i < this->particles.size(); i++) {
             res[i][j] = this->particles[i].r_vec;
         }
-        func(dt);
+        func(dt, particle_interaction);
     }
 
     return res;
 }
 
+void PenningTrap::write_simulation_to_dir(std::string path, double time,
+                                          int steps, std::string method,
+                                          bool particle_interaction)
+{
+    if (path.back() != '/') {
+        path += '/';
+    }
+    if (mkpath(path, 0777) != 0) {
+        std::cout << "Hello" << std::endl;
+        return;
+    }
 
+    sim_arr res = this->simulate(time, steps, method, particle_interaction);
+
+    int number_of_particles = this->particles.size();
+
+    std::ofstream ofile;
+    sim_rows row;
+
+    for (int i = 0; i < number_of_particles; i++) {
+        row = res[i];
+        ofile.open(path + "particle_" + std::to_string(i) + ".txt");
+        for (arma::vec vector : row) {
+            ofile << vector(0) << "," << vector(1) << "," << vector(2) << "\n";
+        }
+        ofile.close();
+    }
+}

From 13c662c148c6976266265712c4e79792771cddc0 Mon Sep 17 00:00:00 2001
From: Cory <cory@balaton.dev>
Date: Fri, 13 Oct 2023 00:51:33 +0200
Subject: [PATCH 08/26] Use new constructors and methods

---
 src/main.cpp | 133 ++++++++++++++-------------------------------------
 1 file changed, 37 insertions(+), 96 deletions(-)

diff --git a/src/main.cpp b/src/main.cpp
index b6d83c7..2930784 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -12,143 +12,84 @@
 
 #include <fstream>
 #include <omp.h>
+#include <string>
 #include <sys/stat.h>
+#include <vector>
 
 #include "PenningTrap.hpp"
+#include "utils.hpp"
 
 #define PARTICLES 100
 #define N 10000
 #define CHARGE 1.
 #define MASS 40. // unit: amu
 
-Particle p1(1., 40., arma::vec{20., 0., 20.}, arma::vec{0., 25., 0.});
-Particle p2(1., 40., arma::vec{25., 25., 0.}, arma::vec{0., 40., 5.});
+Particle p1(CHARGE, MASS, arma::vec{20., 0., 20.}, arma::vec{0., 25., 0.});
+Particle p2(CHARGE, MASS, arma::vec{25., 25., 0.}, arma::vec{0., 40., 5.});
 
 void simulate_single_particle()
 {
-    PenningTrap trap;
-
-    trap.add_particle(p1);
+    PenningTrap trap(std::vector<Particle>{p1});
 
     double time = 50.; // microseconds
-    double dt = time / (double)N;
-    
-    auto res = new arma::vec::fixed<3>[N];
 
-    for (int i=0; i<N;i++) {
-        res[i] = trap.get_particle(0);
-        trap.evolve_RK4(dt);
-    }
-
-    mkdir("output", 0777);
-    mkdir("output/simulate_single_particle", 0777);
-
-    std::ofstream ofile;
-
-    ofile.open("output/simulate_single_particle/out.txt");
-    for (int i=0; i<N;i++) {
-        arma::vec p = res[i];
-        ofile << p(0) << "," << p(1) << "," << p(3) << "\n";
-    }
-    ofile.close();
-    delete [] res;
+    trap.write_simulation_to_dir("output/simulate_single_particle", time, N);
 }
 
 void simulate_two_particles()
 {
-    PenningTrap trap;
-
-    trap.add_particle(p1);
-    trap.add_particle(p2);
+    PenningTrap trap_no_interaction(std::vector<Particle>{p1, p2});
+    PenningTrap trap_with_interaction(std::vector<Particle>{p1, p2});
 
     double time = 50.; // microseconds
-    double dt = time / (double)N;
 
-    auto res = new arma::vec::fixed<3>[2][N];
+    trap_no_interaction.write_simulation_to_dir(
+        "output/simulate_2_particles/no_interaction", time, N, "rk4", false);
+    trap_with_interaction.write_simulation_to_dir(
+        "output/simulate_2_particles/with_interaction", time, N);
+}
 
+void simulate_single_particle_with_different_steps()
+{
 
-    int counter = 0;
+    double time = 50; // microseconds
 
-    // Get the path of all particles
-    for (int j = 0; j < N; j++) {
-#pragma omp parallel for
-        for (int i = 0; i < 2; i++) {
-            res[i][j] = trap.get_particle(i);
-        }
-        trap.evolve_RK4(dt);
+    for (int i = 0; i < 4; i++) {
+        int steps = 4000 * (i + 1);
+        PenningTrap trap(std::vector<Particle>{p1});
+        trap.write_simulation_to_dir("output/N_steps/RK4/" + std::to_string(steps) +
+                                         "_steps",
+                                     time, steps, "rk4", false);
     }
 
-    std::cout << counter << std::endl;
-
-    arma::vec::fixed<3> *cur_row;
-    arma::vec::fixed<3> cur_elem;
-
-    mkdir("output", 0777);
-    mkdir("output/simulate_2_particles", 0777);
-
-    std::ofstream ofile;
-
-// Write particle paths to file
-#pragma omp parallel for private(cur_row, cur_elem, ofile)
-    for (int i = 0; i < 2; i++) {
-        cur_row = res[i];
-        ofile.open("output/simulate_100_particles/p" + std::to_string(i) +
-                   ".txt");
-        for (int j = 0; j < N; j++) {
-            cur_elem = cur_row[j];
-            ofile << cur_elem(0) << "," << cur_elem(1) << "," << cur_elem(2)
-                  << "\n";
-        }
-        ofile.close();
+    for (int i = 0; i < 4; i++) {
+        int steps = 4000 * (i + 1);
+        PenningTrap trap(std::vector<Particle>{p1});
+        trap.write_simulation_to_dir("output/N_steps/euler/" + std::to_string(steps) +
+                                         "_steps",
+                                     time, steps, "euler", false);
     }
-
 }
 
 void simulate_100_particles()
 {
-    PenningTrap trap;
-
-    // Add particles inside trap
-    for (int i = 0; i < PARTICLES; i++) {
-        arma::vec r = arma::vec(3).randn() * 0.1 *
-                      trap.get_d(); // random initial position
-        arma::vec v = arma::vec(3).randn() * 0.1 *
-                      trap.get_d(); // random initial velocity
-        trap.add_particle(Particle(CHARGE, MASS, r, v));
-    }
+    PenningTrap trap(100);
 
     double time = 50.; // microseconds
-    double dt = time / (double)N;
 
-    sim_arr res = trap.simulate(time, N);
-
-    sim_rows cur_row;
-    arma::vec::fixed<3> cur_elem;
-
-    mkdir("output", 0777);
-    mkdir("output/simulate_100_particles", 0777);
-
-    std::ofstream ofile;
-
-// Write particle paths to file
-#pragma omp parallel for private(cur_row, cur_elem, ofile)
-    for (int i = 0; i < PARTICLES; i++) {
-        cur_row = res[i];
-        ofile.open("output/simulate_100_particles/p" + std::to_string(i) +
-                   ".txt");
-        for (int j = 0; j < N; j++) {
-            cur_elem = cur_row[j];
-            ofile << cur_elem(0) << "," << cur_elem(1) << "," << cur_elem(2)
-                  << "\n";
-        }
-        ofile.close();
-    }
+    trap.write_simulation_to_dir("output/simulate_100_particles", time, N);
 }
 
 int main()
 {
     double start = omp_get_wtime();
 
+    simulate_single_particle();
+
+    simulate_two_particles();
+
+    simulate_single_particle_with_different_steps();
+
     simulate_100_particles();
 
     double end = omp_get_wtime();

From 720f1815d294c6d8db2fb99baa4597bc10d12c38 Mon Sep 17 00:00:00 2001
From: Cory <cory@balaton.dev>
Date: Fri, 13 Oct 2023 00:52:30 +0200
Subject: [PATCH 09/26] Implement methods to simulate and write to file

---
 include/PenningTrap.hpp      |   4 ++
 src/PenningTrap.cpp          | 134 +++++++++++++++--------------------
 src/animate_100_particles.py |   4 +-
 3 files changed, 63 insertions(+), 79 deletions(-)

diff --git a/include/PenningTrap.hpp b/include/PenningTrap.hpp
index bd88c7f..b3a32d1 100644
--- a/include/PenningTrap.hpp
+++ b/include/PenningTrap.hpp
@@ -36,6 +36,10 @@ private:
     double V_0;                      ///< Applied potential
     double d;                        ///< Characteristic dimension
     std::vector<Particle> particles; ///< The particles in the Penning trap
+    arma::vec::fixed<3> *k_v;
+    arma::vec::fixed<3> *k_r;
+    std::function<arma::vec(int, double)> v_funcs[4];
+    std::function<arma::vec(int, double)> r_funcs[4];
 
 public:
     /** @brief Set B_0, V_0 and d.
diff --git a/src/PenningTrap.cpp b/src/PenningTrap.cpp
index 62c608a..93ed3a6 100644
--- a/src/PenningTrap.cpp
+++ b/src/PenningTrap.cpp
@@ -26,28 +26,51 @@ PenningTrap::PenningTrap(double B_0, double V_0, double d)
     this->B_0 = B_0;
     this->V_0 = V_0;
     this->d = d;
+
+    v_funcs[0] = [this](int i, double dt) { return .5 * dt * this->k_v[i]; };
+    v_funcs[1] = [this](int i, double dt) {
+        return .5 * dt * this->k_v[this->particles.size() + i];
+    };
+    v_funcs[2] = [this](int i, double dt) {
+        return dt * this->k_v[2 * this->particles.size() + i];
+    };
+    v_funcs[3] = [this](int i, double dt) {
+        arma::vec res = this->k_v[i] + this->k_v[this->particles.size() + i] +
+                        this->k_v[2 * this->particles.size() + i] +
+                        this->k_v[3 * this->particles.size() + i];
+        return (dt / 6) * res;
+    };
+
+    r_funcs[0] = [this](int i, double dt) { return .5 * dt * this->k_r[i]; };
+    r_funcs[1] = [this](int i, double dt) {
+        return .5 * dt * this->k_r[this->particles.size() + i];
+    };
+    r_funcs[2] = [this](int i, double dt) {
+        return dt * this->k_r[2 * this->particles.size() + i];
+    };
+    r_funcs[3] = [this](int i, double dt) {
+        arma::vec res = this->k_r[i] + this->k_r[this->particles.size() + i] +
+                        this->k_r[2 * this->particles.size() + i] +
+                        this->k_r[3 * this->particles.size() + i];
+        return (dt / 6) * res;
+    };
 }
 
 PenningTrap::PenningTrap(int i, double B_0, double V_0, double d)
+    : PenningTrap::PenningTrap(B_0, V_0, d)
 {
-    this->B_0 = B_0;
-    this->V_0 = V_0;
-    this->d = d;
-
     arma::vec r, v;
     for (int j = 0; j < i; j++) {
-        r = arma::vec(3).randn() * .1 * this->d;
-        v = arma::vec(3).randn() * .1 * this->d;
+        r = arma::vec::fixed<3>().randn() * .1 * this->d;
+        v = arma::vec::fixed<3>().randn() * .1 * this->d;
         this->add_particle(Particle(1., 40., r, v));
     }
 }
 
 PenningTrap::PenningTrap(std::vector<Particle> particles, double B_0,
                          double V_0, double d)
+    : PenningTrap::PenningTrap(B_0, V_0, d)
 {
-    this->B_0 = B_0;
-    this->V_0 = V_0;
-    this->d = d;
     this->particles = particles;
 }
 
@@ -58,11 +81,8 @@ void PenningTrap::add_particle(Particle particle)
 
 arma::vec PenningTrap::external_E_field(arma::vec r)
 {
-    arma::vec::fixed<3> res;
+    arma::vec::fixed<3> res{r(0), r(1), -2. * r(2)};
     double f = this->V_0 / (this->d * this->d);
-    res(0) = r(0);
-    res(1) = r(1);
-    res(2) = -2. * r(2);
 
     return f * res;
 }
@@ -91,6 +111,10 @@ arma::vec PenningTrap::force_on_particle(int i, int j)
 
 arma::vec PenningTrap::total_force_external(int i)
 {
+    if (arma::norm(this->particles.at(i).r_vec) > this->d) {
+        return arma::vec::fixed<3>{0., 0., 0.};
+    }
+
     Particle p = this->particles.at(i);
 
     arma::vec::fixed<3> B = this->external_B_field(p.r_vec);
@@ -99,7 +123,8 @@ arma::vec PenningTrap::total_force_external(int i)
                                   p.v_vec(2) * B(0) - p.v_vec(0) * B(2),
                                   p.v_vec(0) * B(1) - p.v_vec(1) * B(0)};
 
-    arma::vec force = p.q * (this->external_E_field(p.r_vec) + v_cross_B);
+    arma::vec::fixed<3> force =
+        p.q * (this->external_E_field(p.r_vec) + v_cross_B);
 
     return force;
 }
@@ -108,7 +133,7 @@ arma::vec PenningTrap::total_force_particles(int i)
 {
     Particle p = this->particles.at(i);
 
-    arma::vec res(3);
+    arma::vec::fixed<3> res;
 
     for (int j = 0; j < this->particles.size(); j++) {
         if (i == j) {
@@ -131,81 +156,34 @@ arma::vec PenningTrap::total_force(int i)
 void PenningTrap::evolve_RK4(double dt, bool particle_interaction)
 {
 
+    std::vector<Particle> original_particles = this->particles;
     std::vector<Particle> tmp_particles = this->particles;
 
     std::function<arma::vec(int)> force;
     if (particle_interaction) {
-        force = [this](int i) {
-            return this->total_force(i);
-        };
+        force = [this](int i) { return this->total_force(i); };
     }
     else {
-        force = [this](int i) {
-            return this->total_force_external(i);
-        };
+        force = [this](int i) { return this->total_force_external(i); };
     }
 
-    arma::vec::fixed<3> *k_v =
-        new arma::vec::fixed<3>[this->particles.size() * 4];
-    arma::vec::fixed<3> *k_r =
-        new arma::vec::fixed<3>[this->particles.size() * 4];
-
     int size = this->particles.size();
 
-    for (int i = 0; i < size; i++) {
-        k_v[i] = this->total_force(i) / this->particles.at(i).m;
-        k_r[i] = this->particles.at(i).v_vec;
-    }
+    k_v = new arma::vec::fixed<3>[size * 4];
+    k_r = new arma::vec::fixed<3>[size * 4];
 
-    for (int i = 0; i < size; i++) {
-        Particle *p = &this->particles.at(i);
+    for (int i = 0; i < 4; i++) {
+#pragma omp parallel for
+        for (int j = 0; j < size; j++) {
+            k_v[i * size + j] = this->total_force(j) / this->particles.at(j).m;
+            k_r[i * size + j] = this->particles.at(j).v_vec;
 
-        p->v_vec = tmp_particles.at(i).v_vec + (dt / 2) * k_v[i];
-        p->r_vec = tmp_particles.at(i).r_vec + (dt / 2) * k_r[i];
-    }
+            Particle *p = &tmp_particles.at(j);
 
-    for (int i = 0; i < size; i++) {
-        k_v[1 * size + i] = this->total_force(i) / this->particles.at(i).m;
-        k_r[1 * size + i] = this->particles.at(i).v_vec;
-    }
-
-    for (int i = 0; i < size; i++) {
-        Particle *p = &this->particles.at(i);
-
-        p->v_vec = tmp_particles.at(i).v_vec + (dt / 2) * k_v[1 * size + i];
-        p->r_vec = tmp_particles.at(i).r_vec + (dt / 2) * k_r[1 * size + i];
-    }
-
-    for (int i = 0; i < size; i++) {
-        k_v[2 * size + i] = this->total_force(i) / this->particles.at(i).m;
-        k_r[2 * size + i] = this->particles.at(i).v_vec;
-    }
-
-    for (int i = 0; i < size; i++) {
-        Particle *p = &this->particles.at(i);
-
-        p->v_vec = tmp_particles.at(i).v_vec + dt * k_v[2 * size + i];
-        p->r_vec = tmp_particles.at(i).r_vec + dt * k_r[2 * size + i];
-    }
-
-    for (int i = 0; i < size; i++) {
-        k_v[3 * size + i] = this->total_force(i) / this->particles.at(i).m;
-        k_r[3 * size + i] = this->particles.at(i).v_vec;
-    }
-
-    for (int i = 0; i < size; i++) {
-        Particle *p = &this->particles.at(i);
-
-        p->v_vec = tmp_particles.at(i).v_vec +
-                   dt *
-                       (k_v[i] + k_v[size + i] + k_v[2 * size + i] +
-                        k_v[3 * size + i]) /
-                       6;
-        p->r_vec = tmp_particles.at(i).r_vec +
-                   dt *
-                       (k_r[i] + k_r[size + i] + k_r[2 * size + i] +
-                        k_r[3 * size + i]) /
-                       6;
+            p->v_vec = original_particles.at(j).v_vec + this->v_funcs[i](j, dt);
+            p->r_vec = original_particles.at(j).r_vec + this->r_funcs[i](j, dt);
+        }
+        this->particles = tmp_particles;
     }
 
     delete[] k_v;
@@ -259,6 +237,7 @@ sim_arr PenningTrap::simulate(double time, int steps, std::string method,
     }
 
     for (int j = 0; j < steps; j++) {
+        #pragma omp parallel for
         for (int i = 0; i < this->particles.size(); i++) {
             res[i][j] = this->particles[i].r_vec;
         }
@@ -287,6 +266,7 @@ void PenningTrap::write_simulation_to_dir(std::string path, double time,
     std::ofstream ofile;
     sim_rows row;
 
+#pragma omp parallel for private(ofile, row)
     for (int i = 0; i < number_of_particles; i++) {
         row = res[i];
         ofile.open(path + "particle_" + std::to_string(i) + ".txt");
diff --git a/src/animate_100_particles.py b/src/animate_100_particles.py
index 3e2f3ff..0fc0083 100644
--- a/src/animate_100_particles.py
+++ b/src/animate_100_particles.py
@@ -63,8 +63,8 @@ def animate():
         fig, update, N, fargs=(lines, arr), interval=1, blit=False
     )
 
-    ani.save("../images/100_particles.gif", writer=animation.FFMpegFileWriter(fps=50))
-    # plt.show()
+    # ani.save("../images/100_particles.gif", writer=animation.FFMpegFileWriter(fps=50))
+    plt.show()
 
 
 if __name__ == "__main__":

From ae7b437ac30d564104e8e36e5e798f1fba86627e Mon Sep 17 00:00:00 2001
From: Cory <cory@balaton.dev>
Date: Fri, 13 Oct 2023 15:36:52 +0200
Subject: [PATCH 10/26] Fix compiler warnings

---
 include/Particle.hpp    |  14 ++--
 include/PenningTrap.hpp |  31 +++++----
 include/typedefs.hpp    |  12 ++++
 src/PenningTrap.cpp     | 142 +++++++++++++++++-----------------------
 src/main.cpp            |   4 +-
 src/test_suite.cpp      |   2 +-
 src/utils.cpp           |   2 +-
 7 files changed, 99 insertions(+), 108 deletions(-)
 create mode 100644 include/typedefs.hpp

diff --git a/include/Particle.hpp b/include/Particle.hpp
index 29b4ccb..cf3232c 100644
--- a/include/Particle.hpp
+++ b/include/Particle.hpp
@@ -14,14 +14,16 @@
 
 #include <armadillo>
 
+#include "typedefs.hpp"
+
 /** @brief A class that holds attributes of a particle
  * */
 class Particle {
 private:
-    double q; ///< Charge
-    double m; ///< Mass
-    arma::vec::fixed<3> r_vec; ///< position
-    arma::vec::fixed<3> v_vec; ///< velocity
+    double q;     ///< Charge
+    double m;     ///< Mass
+    vec_3d r_vec; ///< position
+    vec_3d v_vec; ///< velocity
 
 public:
     /** @brief Initialize the particle.
@@ -29,9 +31,7 @@ public:
      *  @details Initialize the particle with a charge, mass, position and
      *  velocity.
      * */
-    Particle(double q, double m, 
-             arma::vec::fixed<3> r_vec, 
-             arma::vec::fixed<3> v_vec);
+    Particle(double q, double m, vec_3d r_vec, vec_3d v_vec);
 
     /** @brief Make private attributes available for PenningTrap.
      * */
diff --git a/include/PenningTrap.hpp b/include/PenningTrap.hpp
index b3a32d1..4a131aa 100644
--- a/include/PenningTrap.hpp
+++ b/include/PenningTrap.hpp
@@ -17,12 +17,10 @@
 
 #include "Particle.hpp"
 #include "constants.hpp"
+#include "typedefs.hpp"
 
-typedef std::vector<arma::vec::fixed<3>> sim_cols;
-typedef std::vector<arma::vec::fixed<3>> sim_rows;
-typedef std::vector<sim_cols> sim_arr;
 
-#pragma omp declare reduction(+ : arma::vec : omp_out += omp_in)               \
+#pragma omp declare reduction(+ : vec_3d : omp_out += omp_in)               \
     initializer(omp_priv = omp_orig)
 
 /** @brief A class that simulates a Penning trap.
@@ -36,10 +34,10 @@ private:
     double V_0;                      ///< Applied potential
     double d;                        ///< Characteristic dimension
     std::vector<Particle> particles; ///< The particles in the Penning trap
-    arma::vec::fixed<3> *k_v;
-    arma::vec::fixed<3> *k_r;
-    std::function<arma::vec(int, double)> v_funcs[4];
-    std::function<arma::vec(int, double)> r_funcs[4];
+    sim_arr k_v;
+    sim_arr k_r;
+    std::function<vec_3d(int, double)> v_funcs[4];
+    std::function<vec_3d(int, double)> r_funcs[4];
 
 public:
     /** @brief Set B_0, V_0 and d.
@@ -58,33 +56,33 @@ public:
 
     /** @brief Calculate E at point r
      * */
-    arma::vec external_E_field(arma::vec r);
+    vec_3d external_E_field(vec_3d r);
 
     /** @brief Calculate B at point r
      * */
-    arma::vec external_B_field(arma::vec r);
+    vec_3d external_B_field(vec_3d r);
 
     /** @brief Calculate the force between 2 particles.
      *
      *  @details Calculate the force exhibited on particle p_i from
      *  particle p_j.
      * */
-    arma::vec force_on_particle(int i, int j);
+    vec_3d force_on_particle(int i, int j);
 
     /** @brief Calculate the total external force on a particle.
      *
      *  @details Calculate the total amount of force that E and B exhibits
      *  on particle p_i.
      * */
-    arma::vec total_force_external(int i);
+    vec_3d total_force_external(int i);
 
     /** @brief Calculate the total force on a particle from other particles.
      * */
-    arma::vec total_force_particles(int i);
+    vec_3d total_force_particles(unsigned int i);
 
     /** @brief calculate the total force on a particle.
      * */
-    arma::vec total_force(int i);
+    vec_3d total_force(int i);
 
     /** @brief Go forward one timestep using the RK4 method
      * */
@@ -94,8 +92,9 @@ public:
      * */
     void evolve_forward_euler(double dt, bool particle_interaction = true);
 
-    sim_arr simulate(double time, int steps, std::string method = "rk4",
-                     bool particle_interaction = true);
+    sim_arr simulate(double time, unsigned int steps,
+                                              std::string method = "rk4",
+                                              bool particle_interaction = true);
 
     void write_simulation_to_dir(std::string path, double time, int steps,
                                  std::string method = "rk4",
diff --git a/include/typedefs.hpp b/include/typedefs.hpp
new file mode 100644
index 0000000..42c00bb
--- /dev/null
+++ b/include/typedefs.hpp
@@ -0,0 +1,12 @@
+#ifndef __TYPEDEFS__
+#define __TYPEDEFS__
+
+#include <vector>
+#include <armadillo>
+
+typedef std::vector<arma::vec::fixed<3>> sim_cols;
+typedef std::vector<arma::vec::fixed<3>> sim_rows;
+typedef std::vector<sim_cols> sim_arr;
+typedef arma::vec::fixed<3> vec_3d;
+
+#endif
diff --git a/src/PenningTrap.cpp b/src/PenningTrap.cpp
index 93ed3a6..93c6ed7 100644
--- a/src/PenningTrap.cpp
+++ b/src/PenningTrap.cpp
@@ -15,6 +15,7 @@
 
 #include "PenningTrap.hpp"
 #include "constants.hpp"
+#include "typedefs.hpp"
 #include "utils.hpp"
 #include <cstdlib>
 #include <functional>
@@ -27,42 +28,31 @@ PenningTrap::PenningTrap(double B_0, double V_0, double d)
     this->V_0 = V_0;
     this->d = d;
 
-    v_funcs[0] = [this](int i, double dt) { return .5 * dt * this->k_v[i]; };
-    v_funcs[1] = [this](int i, double dt) {
-        return .5 * dt * this->k_v[this->particles.size() + i];
-    };
-    v_funcs[2] = [this](int i, double dt) {
-        return dt * this->k_v[2 * this->particles.size() + i];
-    };
+    // Create lambda functions for each iteration in RK4
+    v_funcs[0] = [this](int i, double dt) { return .5 * dt * this->k_v[0][i]; };
+    v_funcs[1] = [this](int i, double dt) { return .5 * dt * this->k_v[1][i]; };
+    v_funcs[2] = [this](int i, double dt) { return dt * this->k_v[2][i]; };
     v_funcs[3] = [this](int i, double dt) {
-        arma::vec res = this->k_v[i] + this->k_v[this->particles.size() + i] +
-                        this->k_v[2 * this->particles.size() + i] +
-                        this->k_v[3 * this->particles.size() + i];
-        return (dt / 6) * res;
+        return (dt / 6) * (this->k_v[0][i].eval() + this->k_v[1][i].eval() +
+                           this->k_v[2][i].eval() + this->k_v[3][i].eval());
     };
 
-    r_funcs[0] = [this](int i, double dt) { return .5 * dt * this->k_r[i]; };
-    r_funcs[1] = [this](int i, double dt) {
-        return .5 * dt * this->k_r[this->particles.size() + i];
-    };
-    r_funcs[2] = [this](int i, double dt) {
-        return dt * this->k_r[2 * this->particles.size() + i];
-    };
+    r_funcs[0] = [this](int i, double dt) { return .5 * dt * this->k_r[0][i]; };
+    r_funcs[1] = [this](int i, double dt) { return .5 * dt * this->k_r[0][i]; };
+    r_funcs[2] = [this](int i, double dt) { return dt * this->k_r[2][i]; };
     r_funcs[3] = [this](int i, double dt) {
-        arma::vec res = this->k_r[i] + this->k_r[this->particles.size() + i] +
-                        this->k_r[2 * this->particles.size() + i] +
-                        this->k_r[3 * this->particles.size() + i];
-        return (dt / 6) * res;
+        return (dt / 6) * (this->k_r[0][i].eval() + this->k_r[1][i].eval() +
+                           this->k_r[2][i].eval() + this->k_r[3][i].eval());
     };
 }
 
 PenningTrap::PenningTrap(int i, double B_0, double V_0, double d)
     : PenningTrap::PenningTrap(B_0, V_0, d)
 {
-    arma::vec r, v;
+    vec_3d r, v;
     for (int j = 0; j < i; j++) {
-        r = arma::vec::fixed<3>().randn() * .1 * this->d;
-        v = arma::vec::fixed<3>().randn() * .1 * this->d;
+        r = vec_3d().randn() * .1 * this->d;
+        v = vec_3d().randn() * .1 * this->d;
         this->add_particle(Particle(1., 40., r, v));
     }
 }
@@ -79,63 +69,60 @@ void PenningTrap::add_particle(Particle particle)
     this->particles.push_back(particle);
 }
 
-arma::vec PenningTrap::external_E_field(arma::vec r)
+vec_3d PenningTrap::external_E_field(vec_3d r)
 {
-    arma::vec::fixed<3> res{r(0), r(1), -2. * r(2)};
+    r(2) *= -2.;
     double f = this->V_0 / (this->d * this->d);
 
-    return f * res;
+    return f * r;
 }
 
-arma::vec PenningTrap::external_B_field(arma::vec r)
+vec_3d PenningTrap::external_B_field(vec_3d r)
 {
-    arma::vec::fixed<3> res{0., 0., this->B_0};
-
-    return res;
+    return vec_3d{0.,0.,this->B_0};
 }
 
-arma::vec PenningTrap::force_on_particle(int i, int j)
+vec_3d PenningTrap::force_on_particle(int i, int j)
 {
     // Calculate the difference between the particles' position
-    arma::vec::fixed<3> res =
-        this->particles.at(i).r_vec - this->particles.at(j).r_vec;
+    vec_3d res = this->particles[i].r_vec - this->particles[j].r_vec;
 
     // Get the distance between the particles
     double norm = arma::norm(res);
 
     // Multiply res with p_j's charge divided by the norm cubed
-    res *= this->particles.at(j).q / (norm * norm * norm);
+    res *= this->particles[j].q / (norm * norm * norm);
 
     return res;
 }
 
-arma::vec PenningTrap::total_force_external(int i)
+vec_3d PenningTrap::total_force_external(int i)
 {
-    if (arma::norm(this->particles.at(i).r_vec) > this->d) {
-        return arma::vec::fixed<3>{0., 0., 0.};
+    Particle p = this->particles[i];
+
+    if (arma::norm(p.r_vec) > this->d) {
+        return vec_3d{0., 0., 0.};
     }
 
-    Particle p = this->particles.at(i);
+    vec_3d B = this->external_B_field(p.r_vec);
 
-    arma::vec::fixed<3> B = this->external_B_field(p.r_vec);
+    vec_3d v_cross_B{p.v_vec(1) * B(2) - p.v_vec(2) * B(1),
+                     p.v_vec(2) * B(0) - p.v_vec(0) * B(2),
+                     p.v_vec(0) * B(1) - p.v_vec(1) * B(0)};
 
-    arma::vec::fixed<3> v_cross_B{p.v_vec(1) * B(2) - p.v_vec(2) * B(1),
-                                  p.v_vec(2) * B(0) - p.v_vec(0) * B(2),
-                                  p.v_vec(0) * B(1) - p.v_vec(1) * B(0)};
-
-    arma::vec::fixed<3> force =
-        p.q * (this->external_E_field(p.r_vec) + v_cross_B);
+    vec_3d force = p.q * (this->external_E_field(p.r_vec) + v_cross_B);
 
     return force;
 }
 
-arma::vec PenningTrap::total_force_particles(int i)
+vec_3d PenningTrap::total_force_particles(unsigned int i)
 {
-    Particle p = this->particles.at(i);
+    Particle p = this->particles[i];
 
-    arma::vec::fixed<3> res;
+    vec_3d res;
+    size_t size = this->particles.size();
 
-    for (int j = 0; j < this->particles.size(); j++) {
+    for (size_t j = 0; j < size; j++) {
         if (i == j) {
             continue;
         }
@@ -148,7 +135,7 @@ arma::vec PenningTrap::total_force_particles(int i)
     return res;
 }
 
-arma::vec PenningTrap::total_force(int i)
+vec_3d PenningTrap::total_force(int i)
 {
     return this->total_force_external(i) - this->total_force_particles(i);
 }
@@ -159,7 +146,7 @@ void PenningTrap::evolve_RK4(double dt, bool particle_interaction)
     std::vector<Particle> original_particles = this->particles;
     std::vector<Particle> tmp_particles = this->particles;
 
-    std::function<arma::vec(int)> force;
+    std::function<vec_3d(int)> force;
     if (particle_interaction) {
         force = [this](int i) { return this->total_force(i); };
     }
@@ -169,25 +156,22 @@ void PenningTrap::evolve_RK4(double dt, bool particle_interaction)
 
     int size = this->particles.size();
 
-    k_v = new arma::vec::fixed<3>[size * 4];
-    k_r = new arma::vec::fixed<3>[size * 4];
+    this->k_v = sim_arr(4, sim_cols(size));
+    this->k_r = sim_arr(4, sim_cols(size));
 
     for (int i = 0; i < 4; i++) {
 #pragma omp parallel for
         for (int j = 0; j < size; j++) {
-            k_v[i * size + j] = this->total_force(j) / this->particles.at(j).m;
-            k_r[i * size + j] = this->particles.at(j).v_vec;
+            this->k_v[i][j] = this->total_force(j) / this->particles[j].m;
+            this->k_r[i][j] = this->particles[j].v_vec;
 
-            Particle *p = &tmp_particles.at(j);
+            Particle *p = &tmp_particles[j];
 
-            p->v_vec = original_particles.at(j).v_vec + this->v_funcs[i](j, dt);
-            p->r_vec = original_particles.at(j).r_vec + this->r_funcs[i](j, dt);
+            p->v_vec = original_particles[j].v_vec + this->v_funcs[i](j, dt);
+            p->r_vec = original_particles[j].r_vec + this->r_funcs[i](j, dt);
         }
         this->particles = tmp_particles;
     }
-
-    delete[] k_v;
-    delete[] k_r;
 }
 
 void PenningTrap::evolve_forward_euler(double dt, bool particle_interaction)
@@ -196,7 +180,7 @@ void PenningTrap::evolve_forward_euler(double dt, bool particle_interaction)
 
     Particle *p;
 
-    std::function<arma::vec(int)> force;
+    std::function<vec_3d(int)> force;
     if (particle_interaction) {
         force = [this](int i) { return this->total_force(i); };
     }
@@ -205,19 +189,20 @@ void PenningTrap::evolve_forward_euler(double dt, bool particle_interaction)
     }
 
 #pragma omp parallel for private(p)
-    for (int i = 0; i < this->particles.size(); i++) {
-        p = &new_state.at(i);
-        p->v_vec += dt * force(i) / new_state.at(i).m;
-        p->r_vec += dt * this->particles.at(i).v_vec;
+    for (size_t i = 0; i < this->particles.size(); i++) {
+        p = &new_state[i];
+        p->v_vec += dt * force(i) / p->m;
+        p->r_vec += dt * this->particles[i].v_vec;
     }
 
     this->particles = new_state;
 }
 
-sim_arr PenningTrap::simulate(double time, int steps, std::string method,
-                              bool particle_interaction)
+sim_arr PenningTrap::simulate(double time, unsigned int steps,
+                              std::string method, bool particle_interaction)
 {
     double dt = time / (double)steps;
+
     sim_arr res(this->particles.size(), sim_cols(steps));
 
     std::function<void(double, bool)> func;
@@ -236,9 +221,8 @@ sim_arr PenningTrap::simulate(double time, int steps, std::string method,
         abort();
     }
 
-    for (int j = 0; j < steps; j++) {
-        #pragma omp parallel for
-        for (int i = 0; i < this->particles.size(); i++) {
+    for (size_t j = 0; j < steps; j++) {
+        for (size_t i = 0; i < this->particles.size(); i++) {
             res[i][j] = this->particles[i].r_vec;
         }
         func(dt, particle_interaction);
@@ -261,17 +245,13 @@ void PenningTrap::write_simulation_to_dir(std::string path, double time,
 
     sim_arr res = this->simulate(time, steps, method, particle_interaction);
 
-    int number_of_particles = this->particles.size();
-
     std::ofstream ofile;
-    sim_rows row;
 
-#pragma omp parallel for private(ofile, row)
-    for (int i = 0; i < number_of_particles; i++) {
-        row = res[i];
+#pragma omp parallel for private(ofile)
+    for (size_t i = 0; i < this->particles.size(); i++) {
         ofile.open(path + "particle_" + std::to_string(i) + ".txt");
-        for (arma::vec vector : row) {
-            ofile << vector(0) << "," << vector(1) << "," << vector(2) << "\n";
+        for (vec_3d &vec : res[i]) {
+            ofile << vec(0) << "," << vec(1) << "," << vec(2) << "\n";
         }
         ofile.close();
     }
diff --git a/src/main.cpp b/src/main.cpp
index 2930784..cd72d0c 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -24,8 +24,8 @@
 #define CHARGE 1.
 #define MASS 40. // unit: amu
 
-Particle p1(CHARGE, MASS, arma::vec{20., 0., 20.}, arma::vec{0., 25., 0.});
-Particle p2(CHARGE, MASS, arma::vec{25., 25., 0.}, arma::vec{0., 40., 5.});
+Particle p1(CHARGE, MASS, vec_3d{20., 0., 20.}, vec_3d{0., 25., 0.});
+Particle p2(CHARGE, MASS, vec_3d{25., 25., 0.}, vec_3d{0., 40., 5.});
 
 void simulate_single_particle()
 {
diff --git a/src/test_suite.cpp b/src/test_suite.cpp
index 81ea5c1..cd422c5 100644
--- a/src/test_suite.cpp
+++ b/src/test_suite.cpp
@@ -44,7 +44,7 @@ public:
         arma::vec result;
         arma::vec v;
         std::stringstream msg;
-        for (int i = 0; i < tests.size(); i++) {
+        for (size_t i = 0; i < tests.size(); i++) {
             v = tests.at(i).first;
             result = trap.external_E_field(v);
 
diff --git a/src/utils.cpp b/src/utils.cpp
index 934e50f..14670f0 100644
--- a/src/utils.cpp
+++ b/src/utils.cpp
@@ -65,7 +65,7 @@ bool arma_vector_close_to(arma::vec &a, arma::vec &b, double tol)
         return false;
     }
 
-    for (int i = 0; i < a.n_elem; i++) {
+    for (size_t i = 0; i < a.n_elem; i++) {
         if (std::abs(a(i) - b(i)) >= tol) {
             return false;
         }

From 11757e5e28c5093b13e0332e63d811cbdccc009c Mon Sep 17 00:00:00 2001
From: Cory <cory@balaton.dev>
Date: Fri, 13 Oct 2023 15:37:26 +0200
Subject: [PATCH 11/26] Add profiling flag

---
 src/Makefile | 15 +++++++++++----
 1 file changed, 11 insertions(+), 4 deletions(-)

diff --git a/src/Makefile b/src/Makefile
index 52c16b7..69f309e 100644
--- a/src/Makefile
+++ b/src/Makefile
@@ -8,7 +8,7 @@ CLASSOBJS=$(CLASSSRCS:.cpp=.o)
 
 INCLUDE=../include
 
-CFLAGS=-larmadillo -llapack -std=c++11 -O2
+CFLAGS=-Wall -larmadillo -llapack -std=c++11 -O3
 OPENMP=-fopenmp
 
 # Add a debug flag when compiling (For the DEBUG macro in utils.hpp)
@@ -19,20 +19,27 @@ else
 	DBGFLAG=
 endif
 
+PROFILE ?= 0
+ifeq ($(PROFILE), 1)
+	PROFFLAG=-pg
+else
+	PROFFLAG=
+endif
+
 .PHONY: clean
 
 all: test_suite main
 
 # Rules for executables
 main: main.o $(LIBOBJS) $(CLASSOBJS)
-	$(CC) $^ -o $@ $(CFLAGS) $(DBGFLAG) -I$(INCLUDE) $(OPENMP)
+	$(CC) $^ -o $@ $(CFLAGS) $(DBGFLAG) $(PROFFLAG) -I$(INCLUDE) $(OPENMP)
 
 test_suite: test_suite.o $(LIBOBJS) $(CLASSOBJS)
-	$(CC) $^ -o $@ $(CFLAGS) $(DBGFLAG) -I$(INCLUDE) $(OPENMP)
+	$(CC) $^ -o $@ $(CFLAGS) $(DBGFLAG) $(PROFFLAG) -I$(INCLUDE) $(OPENMP)
 
 # Rule for object files
 %.o: %.cpp
-	$(CC) -c $^ -o $@ $(CFLAGS) $(DBGFLAG) -I$(INCLUDE) $(OPENMP)
+	$(CC) -c $^ -o $@ $(CFLAGS) $(DBGFLAG) $(PROFFLAG) -I$(INCLUDE) $(OPENMP)
 
 clean:
 	rm *.o

From 69491d1c02b79c35534bd2e0829c6f77e165a0a2 Mon Sep 17 00:00:00 2001
From: Cory <cory@balaton.dev>
Date: Fri, 13 Oct 2023 16:53:17 +0200
Subject: [PATCH 12/26] Some changes

---
 include/PenningTrap.hpp |  4 +--
 src/PenningTrap.cpp     | 55 ++++++++++++++++++++++++++++++-----------
 src/main.cpp            |  7 ++++++
 3 files changed, 50 insertions(+), 16 deletions(-)

diff --git a/include/PenningTrap.hpp b/include/PenningTrap.hpp
index 4a131aa..74759e2 100644
--- a/include/PenningTrap.hpp
+++ b/include/PenningTrap.hpp
@@ -36,8 +36,8 @@ private:
     std::vector<Particle> particles; ///< The particles in the Penning trap
     sim_arr k_v;
     sim_arr k_r;
-    std::function<vec_3d(int, double)> v_funcs[4];
-    std::function<vec_3d(int, double)> r_funcs[4];
+    std::function<vec_3d(int, double)>* v_funcs;
+    std::function<vec_3d(int, double)>* r_funcs;
 
 public:
     /** @brief Set B_0, V_0 and d.
diff --git a/src/PenningTrap.cpp b/src/PenningTrap.cpp
index 93c6ed7..4ab38e9 100644
--- a/src/PenningTrap.cpp
+++ b/src/PenningTrap.cpp
@@ -29,21 +29,31 @@ PenningTrap::PenningTrap(double B_0, double V_0, double d)
     this->d = d;
 
     // Create lambda functions for each iteration in RK4
-    v_funcs[0] = [this](int i, double dt) { return .5 * dt * this->k_v[0][i]; };
-    v_funcs[1] = [this](int i, double dt) { return .5 * dt * this->k_v[1][i]; };
-    v_funcs[2] = [this](int i, double dt) { return dt * this->k_v[2][i]; };
-    v_funcs[3] = [this](int i, double dt) {
-        return (dt / 6) * (this->k_v[0][i].eval() + this->k_v[1][i].eval() +
-                           this->k_v[2][i].eval() + this->k_v[3][i].eval());
+    this->v_funcs = new std::function<vec_3d(int, double)>[] {
+        [this](int i, double dt) {
+            DEBUG("Inside v_funcs");
+            return .5 * dt * this->k_v[0][i];
+        },
+        [this](int i, double dt) { return .5 * dt * this->k_v[1][i]; },
+        [this](int i, double dt) { return dt * this->k_v[2][i]; },
+        [this](int i, double dt) {
+            return (dt / 6) * (this->k_v[0][i].eval() + this->k_v[1][i].eval() +
+                               this->k_v[2][i].eval() + this->k_v[3][i].eval());
+        }
+    };
+    this->r_funcs = new std::function<vec_3d(int, double)>[] {
+        [this](int i, double dt) {
+            DEBUG("Inside v_funcs");
+            return .5 * dt * this->k_r[0][i];
+        },
+        [this](int i, double dt) { return .5 * dt * this->k_r[1][i]; },
+        [this](int i, double dt) { return dt * this->k_r[2][i]; },
+        [this](int i, double dt) {
+            return (dt / 6) * (this->k_r[0][i].eval() + this->k_r[1][i].eval() +
+                               this->k_r[2][i].eval() + this->k_r[3][i].eval());
+        }
     };
 
-    r_funcs[0] = [this](int i, double dt) { return .5 * dt * this->k_r[0][i]; };
-    r_funcs[1] = [this](int i, double dt) { return .5 * dt * this->k_r[0][i]; };
-    r_funcs[2] = [this](int i, double dt) { return dt * this->k_r[2][i]; };
-    r_funcs[3] = [this](int i, double dt) {
-        return (dt / 6) * (this->k_r[0][i].eval() + this->k_r[1][i].eval() +
-                           this->k_r[2][i].eval() + this->k_r[3][i].eval());
-    };
 }
 
 PenningTrap::PenningTrap(int i, double B_0, double V_0, double d)
@@ -79,7 +89,7 @@ vec_3d PenningTrap::external_E_field(vec_3d r)
 
 vec_3d PenningTrap::external_B_field(vec_3d r)
 {
-    return vec_3d{0.,0.,this->B_0};
+    return vec_3d{0., 0., this->B_0};
 }
 
 vec_3d PenningTrap::force_on_particle(int i, int j)
@@ -143,9 +153,11 @@ vec_3d PenningTrap::total_force(int i)
 void PenningTrap::evolve_RK4(double dt, bool particle_interaction)
 {
 
+    DEBUG("Inside RK4");
     std::vector<Particle> original_particles = this->particles;
     std::vector<Particle> tmp_particles = this->particles;
 
+    DEBUG("Choose force func");
     std::function<vec_3d(int)> force;
     if (particle_interaction) {
         force = [this](int i) { return this->total_force(i); };
@@ -154,22 +166,28 @@ void PenningTrap::evolve_RK4(double dt, bool particle_interaction)
         force = [this](int i) { return this->total_force_external(i); };
     }
 
+    DEBUG("Create k_v and k_r");
     int size = this->particles.size();
 
     this->k_v = sim_arr(4, sim_cols(size));
     this->k_r = sim_arr(4, sim_cols(size));
 
+    DEBUG("Loop");
     for (int i = 0; i < 4; i++) {
+        DEBUG("Inside outer loop");
 #pragma omp parallel for
         for (int j = 0; j < size; j++) {
+            DEBUG("Set k_v and k_r");
             this->k_v[i][j] = this->total_force(j) / this->particles[j].m;
             this->k_r[i][j] = this->particles[j].v_vec;
 
             Particle *p = &tmp_particles[j];
 
+            DEBUG("Update v and r");
             p->v_vec = original_particles[j].v_vec + this->v_funcs[i](j, dt);
             p->r_vec = original_particles[j].r_vec + this->r_funcs[i](j, dt);
         }
+        DEBUG("After inner loop");
         this->particles = tmp_particles;
     }
 }
@@ -201,13 +219,16 @@ void PenningTrap::evolve_forward_euler(double dt, bool particle_interaction)
 sim_arr PenningTrap::simulate(double time, unsigned int steps,
                               std::string method, bool particle_interaction)
 {
+    DEBUG("Inside simulate");
     double dt = time / (double)steps;
 
     sim_arr res(this->particles.size(), sim_cols(steps));
 
+    DEBUG("Choose function to use");
     std::function<void(double, bool)> func;
     if (method == "rk4") {
         func = [this](double dt, bool particle_interaction) {
+            DEBUG("Inside RK4 lambda");
             this->evolve_RK4(dt, particle_interaction);
         };
     }
@@ -221,10 +242,13 @@ sim_arr PenningTrap::simulate(double time, unsigned int steps,
         abort();
     }
 
+    DEBUG("Loop");
     for (size_t j = 0; j < steps; j++) {
+        DEBUG("Inside outer loop");
         for (size_t i = 0; i < this->particles.size(); i++) {
             res[i][j] = this->particles[i].r_vec;
         }
+        DEBUG("After inner loop");
         func(dt, particle_interaction);
     }
 
@@ -235,6 +259,7 @@ void PenningTrap::write_simulation_to_dir(std::string path, double time,
                                           int steps, std::string method,
                                           bool particle_interaction)
 {
+    DEBUG("Inside write to dir");
     if (path.back() != '/') {
         path += '/';
     }
@@ -243,10 +268,12 @@ void PenningTrap::write_simulation_to_dir(std::string path, double time,
         return;
     }
 
+    DEBUG("Create sim_arr");
     sim_arr res = this->simulate(time, steps, method, particle_interaction);
 
     std::ofstream ofile;
 
+    DEBUG("Loop");
 #pragma omp parallel for private(ofile)
     for (size_t i = 0; i < this->particles.size(); i++) {
         ofile.open(path + "particle_" + std::to_string(i) + ".txt");
diff --git a/src/main.cpp b/src/main.cpp
index cd72d0c..35ec896 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -29,10 +29,12 @@ Particle p2(CHARGE, MASS, vec_3d{25., 25., 0.}, vec_3d{0., 40., 5.});
 
 void simulate_single_particle()
 {
+    DEBUG("Inside single particle sim");
     PenningTrap trap(std::vector<Particle>{p1});
 
     double time = 50.; // microseconds
 
+    DEBUG("Write to dir");
     trap.write_simulation_to_dir("output/simulate_single_particle", time, N);
 }
 
@@ -82,14 +84,19 @@ void simulate_100_particles()
 
 int main()
 {
+    DEBUG("Start");
     double start = omp_get_wtime();
 
+    DEBUG("Single particle");
     simulate_single_particle();
 
+    DEBUG("Two particles");
     simulate_two_particles();
 
+    DEBUG("Single particle with different steps");
     simulate_single_particle_with_different_steps();
 
+    DEBUG("100 particles");
     simulate_100_particles();
 
     double end = omp_get_wtime();

From c4aa6f2179537e92a6b88f37d316f6fdd56f6821 Mon Sep 17 00:00:00 2001
From: Cory <cory@balaton.dev>
Date: Fri, 13 Oct 2023 20:32:32 +0200
Subject: [PATCH 13/26] Change lambda to method

---
 include/PenningTrap.hpp |  5 ++--
 src/PenningTrap.cpp     | 66 ++++++++++++++++++++++++-----------------
 2 files changed, 41 insertions(+), 30 deletions(-)

diff --git a/include/PenningTrap.hpp b/include/PenningTrap.hpp
index 74759e2..eb7bff7 100644
--- a/include/PenningTrap.hpp
+++ b/include/PenningTrap.hpp
@@ -36,8 +36,9 @@ private:
     std::vector<Particle> particles; ///< The particles in the Penning trap
     sim_arr k_v;
     sim_arr k_r;
-    std::function<vec_3d(int, double)>* v_funcs;
-    std::function<vec_3d(int, double)>* r_funcs;
+
+    vec_3d v_func(int, int, double);
+    vec_3d r_func(int, int, double);
 
 public:
     /** @brief Set B_0, V_0 and d.
diff --git a/src/PenningTrap.cpp b/src/PenningTrap.cpp
index 4ab38e9..0c50836 100644
--- a/src/PenningTrap.cpp
+++ b/src/PenningTrap.cpp
@@ -28,32 +28,6 @@ PenningTrap::PenningTrap(double B_0, double V_0, double d)
     this->V_0 = V_0;
     this->d = d;
 
-    // Create lambda functions for each iteration in RK4
-    this->v_funcs = new std::function<vec_3d(int, double)>[] {
-        [this](int i, double dt) {
-            DEBUG("Inside v_funcs");
-            return .5 * dt * this->k_v[0][i];
-        },
-        [this](int i, double dt) { return .5 * dt * this->k_v[1][i]; },
-        [this](int i, double dt) { return dt * this->k_v[2][i]; },
-        [this](int i, double dt) {
-            return (dt / 6) * (this->k_v[0][i].eval() + this->k_v[1][i].eval() +
-                               this->k_v[2][i].eval() + this->k_v[3][i].eval());
-        }
-    };
-    this->r_funcs = new std::function<vec_3d(int, double)>[] {
-        [this](int i, double dt) {
-            DEBUG("Inside v_funcs");
-            return .5 * dt * this->k_r[0][i];
-        },
-        [this](int i, double dt) { return .5 * dt * this->k_r[1][i]; },
-        [this](int i, double dt) { return dt * this->k_r[2][i]; },
-        [this](int i, double dt) {
-            return (dt / 6) * (this->k_r[0][i].eval() + this->k_r[1][i].eval() +
-                               this->k_r[2][i].eval() + this->k_r[3][i].eval());
-        }
-    };
-
 }
 
 PenningTrap::PenningTrap(int i, double B_0, double V_0, double d)
@@ -74,6 +48,42 @@ PenningTrap::PenningTrap(std::vector<Particle> particles, double B_0,
     this->particles = particles;
 }
 
+vec_3d PenningTrap::v_func(int i, int j, double dt)
+{
+    switch (i) {
+    case 0:
+        return .5 * dt * this->k_v[0][j];
+    case 1:
+        return .5 * dt * this->k_v[1][j];
+    case 2:
+        return dt * this->k_v[2][j];
+    case 3:
+        return (dt / 6.) * (this->k_v[0][j].eval() + this->k_v[1][j].eval() +
+                            this->k_v[2][j].eval() + this->k_v[3][j].eval());
+    default:
+        std::cout << "Not valid!" << std::endl;
+        abort();
+    }
+}
+
+vec_3d PenningTrap::r_func(int i, int j, double dt)
+{
+    switch (i) {
+    case 0:
+        return .5 * dt * this->k_r[0][j];
+    case 1:
+        return .5 * dt * this->k_r[1][j];
+    case 2:
+        return dt * this->k_r[2][j];
+    case 3:
+        return (dt / 6.) * (this->k_r[0][j].eval() + this->k_r[1][j].eval() +
+                            this->k_r[2][j].eval() + this->k_r[3][j].eval());
+    default:
+        std::cout << "Not valid!" << std::endl;
+        abort();
+    }
+}
+
 void PenningTrap::add_particle(Particle particle)
 {
     this->particles.push_back(particle);
@@ -184,8 +194,8 @@ void PenningTrap::evolve_RK4(double dt, bool particle_interaction)
             Particle *p = &tmp_particles[j];
 
             DEBUG("Update v and r");
-            p->v_vec = original_particles[j].v_vec + this->v_funcs[i](j, dt);
-            p->r_vec = original_particles[j].r_vec + this->r_funcs[i](j, dt);
+            p->v_vec = original_particles[j].v_vec + this->v_func(i, j, dt);
+            p->r_vec = original_particles[j].r_vec + this->r_func(i, j, dt);
         }
         DEBUG("After inner loop");
         this->particles = tmp_particles;

From 22c8b9707db7b854c4823005ab95c43e992b29be Mon Sep 17 00:00:00 2001
From: Cory <cory@balaton.dev>
Date: Sat, 14 Oct 2023 03:11:43 +0200
Subject: [PATCH 14/26] Update docs

---
 docs/100_particles.gif                        | Bin 1503631 -> 117798 bytes
 docs/Particle_8cpp.html                       |   2 +-
 docs/Particle_8cpp_source.html                |  34 +-
 docs/Particle_8hpp.html                       |   1 +
 docs/Particle_8hpp_source.html                |  44 +-
 docs/PenningTrap_8cpp.html                    |   6 +-
 docs/PenningTrap_8cpp_source.html             | 476 +++++++----
 docs/PenningTrap_8hpp.html                    |   1 +
 docs/PenningTrap_8hpp_source.html             | 149 ++--
 docs/animate__100__particles_8py_source.html  | 113 +--
 docs/bug.html                                 |  14 +-
 docs/classParticle-members.html               |   6 +-
 docs/classParticle.html                       |  63 +-
 docs/classParticle.js                         |   6 +-
 docs/classPenningTrap-members.html            |  34 +-
 docs/classPenningTrap.html                    | 800 +++++++++++++++---
 docs/classPenningTrap.js                      |  30 +-
 .../dir_68267d1309a1af8e8297ef4c3efbcdba.html |   2 +
 docs/dir_68267d1309a1af8e8297ef4c3efbcdba.js  |   1 +
 .../dir_d44c64559bbebec7f509842c48db8b23.html |   3 +
 docs/dir_d44c64559bbebec7f509842c48db8b23.js  |   1 +
 docs/files.html                               |  18 +-
 docs/functions.html                           |  34 +-
 docs/functions_func.html                      |  25 +-
 docs/functions_vars.html                      |   9 +-
 docs/globals.html                             |   6 +
 docs/globals_defs.html                        |   1 +
 docs/globals_func.html                        |   1 +
 docs/globals_type.html                        | 116 +++
 docs/main_8cpp.html                           | 116 ++-
 docs/main_8cpp_source.html                    | 206 +++--
 docs/menudata.js                              |   1 +
 docs/navtreedata.js                           |   2 +-
 docs/navtreeindex0.js                         | 156 ++--
 docs/pages.html                               |   1 -
 docs/plot__particles__left_8py_source.html    | 147 ++++
 docs/search/all_0.js                          |   4 +-
 docs/search/all_1.js                          |   5 +-
 docs/search/all_10.js                         |   4 +
 docs/search/all_2.js                          |   3 +-
 docs/search/all_3.js                          |   3 +-
 docs/search/all_4.js                          |   6 +-
 docs/search/all_5.js                          |   5 +-
 docs/search/all_6.js                          |   3 +-
 docs/search/all_7.js                          |   6 +-
 docs/search/all_8.js                          |  13 +-
 docs/search/all_9.js                          |  10 +-
 docs/search/all_a.js                          |   2 +-
 docs/search/all_b.js                          |   3 +-
 docs/search/all_c.js                          |  11 +-
 docs/search/all_d.js                          |   9 +-
 docs/search/all_e.js                          |   5 +-
 docs/search/all_f.js                          |   8 +
 docs/search/defines_0.js                      |   2 +-
 docs/search/defines_1.js                      |   2 +-
 docs/search/defines_2.js                      |   2 +-
 docs/search/defines_3.js                      |   2 +-
 docs/search/defines_4.js                      |   2 +-
 docs/search/defines_5.js                      |   4 +
 docs/search/files_3.js                        |   3 +-
 docs/search/functions_1.js                    |   8 +-
 docs/search/functions_2.js                    |   3 +-
 docs/search/functions_3.js                    |   3 +-
 docs/search/functions_4.js                    |   4 +-
 docs/search/functions_5.js                    |   2 +-
 docs/search/functions_6.js                    |   5 +-
 docs/search/functions_7.js                    |   6 +
 docs/search/functions_8.js                    |   4 +
 docs/search/functions_9.js                    |   4 +
 docs/search/searchdata.js                     |  27 +-
 docs/search/typedefs_0.js                     |   6 +
 docs/search/typedefs_1.js                     |   4 +
 docs/search/variables_2.js                    |   3 +-
 docs/search/variables_3.js                    |   2 +-
 docs/search/variables_4.js                    |   2 +-
 docs/search/variables_5.js                    |   2 +-
 docs/search/variables_6.js                    |   3 +-
 docs/search/variables_7.js                    |   4 +
 docs/search/variables_8.js                    |   5 +
 docs/test__suite_8cpp.html                    |   2 +-
 docs/test__suite_8cpp_source.html             |  34 +-
 docs/typedefs_8hpp.html                       | 222 +++++
 docs/typedefs_8hpp.js                         |   7 +
 docs/typedefs_8hpp_source.html                | 134 +++
 docs/utils_8cpp.html                          |  66 +-
 docs/utils_8cpp.js                            |   1 +
 docs/utils_8cpp_source.html                   | 152 ++--
 docs/utils_8hpp.html                          |  73 +-
 docs/utils_8hpp.js                            |   2 +
 docs/utils_8hpp_source.html                   |  68 +-
 man_pages/man3/Particle.3                     |  43 +-
 man_pages/man3/Particle.cpp.3                 |   4 +-
 man_pages/man3/Particle.hpp.3                 |   4 +-
 man_pages/man3/PenningTrap.3                  | 408 +++++++--
 man_pages/man3/PenningTrap.cpp.3              |  14 +-
 man_pages/man3/PenningTrap.hpp.3              |   4 +-
 man_pages/man3/PenningTrapTest.3              |   2 +-
 man_pages/man3/bug.3                          |   8 +-
 man_pages/man3/constants.hpp.3                |   2 +-
 man_pages/man3/main.cpp.3                     |  60 +-
 man_pages/man3/test_suite.cpp.3               |   2 +-
 man_pages/man3/todo.3                         |   2 +-
 man_pages/man3/typedefs.hpp.3                 |  92 ++
 man_pages/man3/utils.cpp.3                    |  46 +-
 man_pages/man3/utils.hpp.3                    |  49 +-
 105 files changed, 3315 insertions(+), 1025 deletions(-)
 create mode 100644 docs/globals_type.html
 create mode 100644 docs/plot__particles__left_8py_source.html
 create mode 100644 docs/search/all_10.js
 create mode 100644 docs/search/all_f.js
 create mode 100644 docs/search/defines_5.js
 create mode 100644 docs/search/functions_7.js
 create mode 100644 docs/search/functions_8.js
 create mode 100644 docs/search/functions_9.js
 create mode 100644 docs/search/typedefs_0.js
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 create mode 100644 docs/search/variables_8.js
 create mode 100644 docs/typedefs_8hpp.html
 create mode 100644 docs/typedefs_8hpp.js
 create mode 100644 docs/typedefs_8hpp_source.html
 create mode 100644 man_pages/man3/typedefs.hpp.3

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diff --git a/docs/Particle_8cpp.html b/docs/Particle_8cpp.html
index 98aaf8d..b3fd0e9 100644
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 <dd>
 Janita Ovidie Sandtrøen Willumsen (janitaws)</dd></dl>
 <dl class="section version"><dt>Version</dt><dd>0.1</dd></dl>
-<dl class="bug"><dt><b><a class="el" href="bug.html#_bug000006">Bug:</a></b></dt><dd>No known bugs</dd></dl>
+<dl class="bug"><dt><b><a class="el" href="bug.html#_bug000007">Bug:</a></b></dt><dd>No known bugs </dd></dl>
 
 <p class="definition">Definition in file <a class="el" href="Particle_8cpp_source.html">Particle.cpp</a>.</p>
 </div></div><!-- contents -->
diff --git a/docs/Particle_8cpp_source.html b/docs/Particle_8cpp_source.html
index 2eaf72e..13c1950 100644
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 <div class="contents">
 <a href="Particle_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span> </div>
-<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span><span class="preprocessor">#include &quot;<a class="code" href="Particle_8hpp.html">Particle.hpp</a>&quot;</span></div>
-<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span> </div>
-<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"><a class="line" href="classParticle.html#a00e108823877a25513ccae7cac011b4c">   16</a></span><a class="code hl_function" href="classParticle.html#a00e108823877a25513ccae7cac011b4c">Particle::Particle</a>(<span class="keywordtype">double</span> q, <span class="keywordtype">double</span> m,</div>
-<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span>                   arma::vec::fixed&lt;3&gt; r_vec,</div>
-<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span>                   arma::vec::fixed&lt;3&gt; v_vec)</div>
-<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span>{</div>
-<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span>    <span class="comment">// Giving the particle its properties</span></div>
-<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span>    this-&gt;q = <a class="code hl_variable" href="classParticle.html#a566dcc1de4bdc01251776948798ea8e1">q</a>;</div>
-<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span>    this-&gt;m = <a class="code hl_variable" href="classParticle.html#aedcc7e1bc53b0e2b1a4a07c9a1b47563">m</a>;</div>
-<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span>    this-&gt;r_vec = <a class="code hl_variable" href="classParticle.html#acf1a0f3c978b06d76df5bb4279594467">r_vec</a>;</div>
-<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span>    this-&gt;v_vec = <a class="code hl_variable" href="classParticle.html#a4a5d22c7aeca66f67d083f270cba25df">v_vec</a>;</div>
-<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span>}</div>
+<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span><span class="preprocessor">#include &quot;<a class="code" href="Particle_8hpp.html">Particle.hpp</a>&quot;</span></div>
+<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span> </div>
+<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"><a class="line" href="classParticle.html#a7af9f8d1fef63dd7643b06629ac7bef4">   15</a></span><a class="code hl_function" href="classParticle.html#a7af9f8d1fef63dd7643b06629ac7bef4">Particle::Particle</a>(<span class="keywordtype">double</span> q, <span class="keywordtype">double</span> m,</div>
+<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span>                   arma::vec::fixed&lt;3&gt; r_vec,</div>
+<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span>                   arma::vec::fixed&lt;3&gt; v_vec)</div>
+<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span>{</div>
+<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span>    <span class="comment">// Giving the particle its properties</span></div>
+<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span>    this-&gt;q = <a class="code hl_variable" href="classParticle.html#a566dcc1de4bdc01251776948798ea8e1">q</a>;</div>
+<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span>    this-&gt;m = <a class="code hl_variable" href="classParticle.html#aedcc7e1bc53b0e2b1a4a07c9a1b47563">m</a>;</div>
+<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span>    this-&gt;r_vec = <a class="code hl_variable" href="classParticle.html#af9497cd8f2dcad0fad54f571ddb383e6">r_vec</a>;</div>
+<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span>    this-&gt;v_vec = <a class="code hl_variable" href="classParticle.html#a879692772803d6ab65fa4993b54aea6e">v_vec</a>;</div>
+<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span>}</div>
 <div class="ttc" id="aParticle_8hpp_html"><div class="ttname"><a href="Particle_8hpp.html">Particle.hpp</a></div><div class="ttdoc">A class that holds the properties of a particle.</div></div>
-<div class="ttc" id="aclassParticle_html_a00e108823877a25513ccae7cac011b4c"><div class="ttname"><a href="classParticle.html#a00e108823877a25513ccae7cac011b4c">Particle::Particle</a></div><div class="ttdeci">Particle(double q, double m, arma::vec::fixed&lt; 3 &gt; r_vec, arma::vec::fixed&lt; 3 &gt; v_vec)</div><div class="ttdoc">Initialize the particle.</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8cpp_source.html#l00016">Particle.cpp:16</a></div></div>
-<div class="ttc" id="aclassParticle_html_a4a5d22c7aeca66f67d083f270cba25df"><div class="ttname"><a href="classParticle.html#a4a5d22c7aeca66f67d083f270cba25df">Particle::v_vec</a></div><div class="ttdeci">arma::vec::fixed&lt; 3 &gt; v_vec</div><div class="ttdoc">velocity</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00024">Particle.hpp:24</a></div></div>
-<div class="ttc" id="aclassParticle_html_a566dcc1de4bdc01251776948798ea8e1"><div class="ttname"><a href="classParticle.html#a566dcc1de4bdc01251776948798ea8e1">Particle::q</a></div><div class="ttdeci">double q</div><div class="ttdoc">Charge.</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00021">Particle.hpp:21</a></div></div>
-<div class="ttc" id="aclassParticle_html_acf1a0f3c978b06d76df5bb4279594467"><div class="ttname"><a href="classParticle.html#acf1a0f3c978b06d76df5bb4279594467">Particle::r_vec</a></div><div class="ttdeci">arma::vec::fixed&lt; 3 &gt; r_vec</div><div class="ttdoc">position</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00023">Particle.hpp:23</a></div></div>
-<div class="ttc" id="aclassParticle_html_aedcc7e1bc53b0e2b1a4a07c9a1b47563"><div class="ttname"><a href="classParticle.html#aedcc7e1bc53b0e2b1a4a07c9a1b47563">Particle::m</a></div><div class="ttdeci">double m</div><div class="ttdoc">Mass.</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00022">Particle.hpp:22</a></div></div>
+<div class="ttc" id="aclassParticle_html_a566dcc1de4bdc01251776948798ea8e1"><div class="ttname"><a href="classParticle.html#a566dcc1de4bdc01251776948798ea8e1">Particle::q</a></div><div class="ttdeci">double q</div><div class="ttdoc">Charge.</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00023">Particle.hpp:23</a></div></div>
+<div class="ttc" id="aclassParticle_html_a7af9f8d1fef63dd7643b06629ac7bef4"><div class="ttname"><a href="classParticle.html#a7af9f8d1fef63dd7643b06629ac7bef4">Particle::Particle</a></div><div class="ttdeci">Particle(double q, double m, vec_3d r_vec, vec_3d v_vec)</div><div class="ttdoc">Initialize the particle.</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8cpp_source.html#l00015">Particle.cpp:15</a></div></div>
+<div class="ttc" id="aclassParticle_html_a879692772803d6ab65fa4993b54aea6e"><div class="ttname"><a href="classParticle.html#a879692772803d6ab65fa4993b54aea6e">Particle::v_vec</a></div><div class="ttdeci">vec_3d v_vec</div><div class="ttdoc">velocity</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00026">Particle.hpp:26</a></div></div>
+<div class="ttc" id="aclassParticle_html_aedcc7e1bc53b0e2b1a4a07c9a1b47563"><div class="ttname"><a href="classParticle.html#aedcc7e1bc53b0e2b1a4a07c9a1b47563">Particle::m</a></div><div class="ttdeci">double m</div><div class="ttdoc">Mass.</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00024">Particle.hpp:24</a></div></div>
+<div class="ttc" id="aclassParticle_html_af9497cd8f2dcad0fad54f571ddb383e6"><div class="ttname"><a href="classParticle.html#af9497cd8f2dcad0fad54f571ddb383e6">Particle::r_vec</a></div><div class="ttdeci">vec_3d r_vec</div><div class="ttdoc">position</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00025">Particle.hpp:25</a></div></div>
 </div><!-- fragment --></div><!-- contents -->
 </div><!-- doc-content -->
 <!-- start footer part -->
diff --git a/docs/Particle_8hpp.html b/docs/Particle_8hpp.html
index 3516260..00fc0e2 100644
--- a/docs/Particle_8hpp.html
+++ b/docs/Particle_8hpp.html
@@ -107,6 +107,7 @@ $(document).ready(function(){initNavTree('Particle_8hpp.html',''); initResizable
 <p>A class that holds the properties of a particle.  
 <a href="#details">More...</a></p>
 <div class="textblock"><code>#include &lt;armadillo&gt;</code><br />
+<code>#include &quot;<a class="el" href="typedefs_8hpp_source.html">typedefs.hpp</a>&quot;</code><br />
 </div>
 <p><a href="Particle_8hpp_source.html">Go to the source code of this file.</a></p>
 <table class="memberdecls">
diff --git a/docs/Particle_8hpp_source.html b/docs/Particle_8hpp_source.html
index dbb28de..f3339f5 100644
--- a/docs/Particle_8hpp_source.html
+++ b/docs/Particle_8hpp_source.html
@@ -107,28 +107,30 @@ $(document).ready(function(){initNavTree('Particle_8hpp_source.html',''); initRe
 <div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span> </div>
 <div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span><span class="preprocessor">#include &lt;armadillo&gt;</span></div>
 <div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span> </div>
-<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"><a class="line" href="classParticle.html">   19</a></span><span class="keyword">class </span><a class="code hl_class" href="classParticle.html">Particle</a> {</div>
-<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span><span class="keyword">private</span>:</div>
-<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"><a class="line" href="classParticle.html#a566dcc1de4bdc01251776948798ea8e1">   21</a></span>    <span class="keywordtype">double</span> <a class="code hl_variable" href="classParticle.html#a566dcc1de4bdc01251776948798ea8e1">q</a>; </div>
-<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"><a class="line" href="classParticle.html#aedcc7e1bc53b0e2b1a4a07c9a1b47563">   22</a></span>    <span class="keywordtype">double</span> <a class="code hl_variable" href="classParticle.html#aedcc7e1bc53b0e2b1a4a07c9a1b47563">m</a>; </div>
-<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"><a class="line" href="classParticle.html#acf1a0f3c978b06d76df5bb4279594467">   23</a></span>    arma::vec::fixed&lt;3&gt; <a class="code hl_variable" href="classParticle.html#acf1a0f3c978b06d76df5bb4279594467">r_vec</a>; </div>
-<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"><a class="line" href="classParticle.html#a4a5d22c7aeca66f67d083f270cba25df">   24</a></span>    arma::vec::fixed&lt;3&gt; <a class="code hl_variable" href="classParticle.html#a4a5d22c7aeca66f67d083f270cba25df">v_vec</a>; </div>
-<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span> </div>
-<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span><span class="keyword">public</span>:</div>
-<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>    <a class="code hl_class" href="classParticle.html">Particle</a>(<span class="keywordtype">double</span> <a class="code hl_variable" href="classParticle.html#a566dcc1de4bdc01251776948798ea8e1">q</a>, <span class="keywordtype">double</span> <a class="code hl_variable" href="classParticle.html#aedcc7e1bc53b0e2b1a4a07c9a1b47563">m</a>, </div>
-<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>             arma::vec::fixed&lt;3&gt; <a class="code hl_variable" href="classParticle.html#acf1a0f3c978b06d76df5bb4279594467">r_vec</a>, </div>
-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>             arma::vec::fixed&lt;3&gt; <a class="code hl_variable" href="classParticle.html#a4a5d22c7aeca66f67d083f270cba25df">v_vec</a>);</div>
-<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span> </div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"><a class="line" href="classParticle.html#aa797d319549dc2a0beb06cdbfd430232">   38</a></span>    <span class="keyword">friend</span> <span class="keyword">class </span><a class="code hl_class" href="classPenningTrap.html">PenningTrap</a>;</div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>};</div>
+<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span><span class="preprocessor">#include &quot;<a class="code" href="typedefs_8hpp.html">typedefs.hpp</a>&quot;</span></div>
+<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span> </div>
+<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"><a class="line" href="classParticle.html">   21</a></span><span class="keyword">class </span><a class="code hl_class" href="classParticle.html">Particle</a> {</div>
+<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span><span class="keyword">private</span>:</div>
+<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"><a class="line" href="classParticle.html#a566dcc1de4bdc01251776948798ea8e1">   23</a></span>    <span class="keywordtype">double</span> <a class="code hl_variable" href="classParticle.html#a566dcc1de4bdc01251776948798ea8e1">q</a>;     </div>
+<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"><a class="line" href="classParticle.html#aedcc7e1bc53b0e2b1a4a07c9a1b47563">   24</a></span>    <span class="keywordtype">double</span> <a class="code hl_variable" href="classParticle.html#aedcc7e1bc53b0e2b1a4a07c9a1b47563">m</a>;     </div>
+<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"><a class="line" href="classParticle.html#af9497cd8f2dcad0fad54f571ddb383e6">   25</a></span>    <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> <a class="code hl_variable" href="classParticle.html#af9497cd8f2dcad0fad54f571ddb383e6">r_vec</a>; </div>
+<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"><a class="line" href="classParticle.html#a879692772803d6ab65fa4993b54aea6e">   26</a></span>    <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> <a class="code hl_variable" href="classParticle.html#a879692772803d6ab65fa4993b54aea6e">v_vec</a>; </div>
+<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span> </div>
+<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span><span class="keyword">public</span>:</div>
+<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>    <a class="code hl_class" href="classParticle.html">Particle</a>(<span class="keywordtype">double</span> <a class="code hl_variable" href="classParticle.html#a566dcc1de4bdc01251776948798ea8e1">q</a>, <span class="keywordtype">double</span> <a class="code hl_variable" href="classParticle.html#aedcc7e1bc53b0e2b1a4a07c9a1b47563">m</a>, <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> <a class="code hl_variable" href="classParticle.html#af9497cd8f2dcad0fad54f571ddb383e6">r_vec</a>, <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> <a class="code hl_variable" href="classParticle.html#a879692772803d6ab65fa4993b54aea6e">v_vec</a>);</div>
 <div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span> </div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span><span class="preprocessor">#endif</span></div>
-<div class="ttc" id="aclassParticle_html"><div class="ttname"><a href="classParticle.html">Particle</a></div><div class="ttdoc">A class that holds attributes of a particle.</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00019">Particle.hpp:19</a></div></div>
-<div class="ttc" id="aclassParticle_html_a4a5d22c7aeca66f67d083f270cba25df"><div class="ttname"><a href="classParticle.html#a4a5d22c7aeca66f67d083f270cba25df">Particle::v_vec</a></div><div class="ttdeci">arma::vec::fixed&lt; 3 &gt; v_vec</div><div class="ttdoc">velocity</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00024">Particle.hpp:24</a></div></div>
-<div class="ttc" id="aclassParticle_html_a566dcc1de4bdc01251776948798ea8e1"><div class="ttname"><a href="classParticle.html#a566dcc1de4bdc01251776948798ea8e1">Particle::q</a></div><div class="ttdeci">double q</div><div class="ttdoc">Charge.</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00021">Particle.hpp:21</a></div></div>
-<div class="ttc" id="aclassParticle_html_acf1a0f3c978b06d76df5bb4279594467"><div class="ttname"><a href="classParticle.html#acf1a0f3c978b06d76df5bb4279594467">Particle::r_vec</a></div><div class="ttdeci">arma::vec::fixed&lt; 3 &gt; r_vec</div><div class="ttdoc">position</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00023">Particle.hpp:23</a></div></div>
-<div class="ttc" id="aclassParticle_html_aedcc7e1bc53b0e2b1a4a07c9a1b47563"><div class="ttname"><a href="classParticle.html#aedcc7e1bc53b0e2b1a4a07c9a1b47563">Particle::m</a></div><div class="ttdeci">double m</div><div class="ttdoc">Mass.</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00022">Particle.hpp:22</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html"><div class="ttname"><a href="classPenningTrap.html">PenningTrap</a></div><div class="ttdoc">A class that simulates a Penning trap.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00029">PenningTrap.hpp:29</a></div></div>
+<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"><a class="line" href="classParticle.html#aa797d319549dc2a0beb06cdbfd430232">   43</a></span>    <span class="keyword">friend</span> <span class="keyword">class </span><a class="code hl_class" href="classPenningTrap.html">PenningTrap</a>;</div>
+<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>};</div>
+<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span> </div>
+<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span><span class="preprocessor">#endif</span></div>
+<div class="ttc" id="aclassParticle_html"><div class="ttname"><a href="classParticle.html">Particle</a></div><div class="ttdoc">A class that holds attributes of a particle.</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00021">Particle.hpp:21</a></div></div>
+<div class="ttc" id="aclassParticle_html_a566dcc1de4bdc01251776948798ea8e1"><div class="ttname"><a href="classParticle.html#a566dcc1de4bdc01251776948798ea8e1">Particle::q</a></div><div class="ttdeci">double q</div><div class="ttdoc">Charge.</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00023">Particle.hpp:23</a></div></div>
+<div class="ttc" id="aclassParticle_html_a879692772803d6ab65fa4993b54aea6e"><div class="ttname"><a href="classParticle.html#a879692772803d6ab65fa4993b54aea6e">Particle::v_vec</a></div><div class="ttdeci">vec_3d v_vec</div><div class="ttdoc">velocity</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00026">Particle.hpp:26</a></div></div>
+<div class="ttc" id="aclassParticle_html_aedcc7e1bc53b0e2b1a4a07c9a1b47563"><div class="ttname"><a href="classParticle.html#aedcc7e1bc53b0e2b1a4a07c9a1b47563">Particle::m</a></div><div class="ttdeci">double m</div><div class="ttdoc">Mass.</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00024">Particle.hpp:24</a></div></div>
+<div class="ttc" id="aclassParticle_html_af9497cd8f2dcad0fad54f571ddb383e6"><div class="ttname"><a href="classParticle.html#af9497cd8f2dcad0fad54f571ddb383e6">Particle::r_vec</a></div><div class="ttdeci">vec_3d r_vec</div><div class="ttdoc">position</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00025">Particle.hpp:25</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html"><div class="ttname"><a href="classPenningTrap.html">PenningTrap</a></div><div class="ttdoc">A class that simulates a Penning trap.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00030">PenningTrap.hpp:30</a></div></div>
+<div class="ttc" id="atypedefs_8hpp_html"><div class="ttname"><a href="typedefs_8hpp.html">typedefs.hpp</a></div><div class="ttdoc">Useful typedefs for cleaner code.</div></div>
+<div class="ttc" id="atypedefs_8hpp_html_a9f33f4962c8fb62cc5ccd0e4e039a8df"><div class="ttname"><a href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a></div><div class="ttdeci">arma::vec::fixed&lt; 3 &gt; vec_3d</div><div class="ttdoc">Typedef for a fixed 3d arma vector.</div><div class="ttdef"><b>Definition:</b> <a href="typedefs_8hpp_source.html#l00036">typedefs.hpp:36</a></div></div>
 </div><!-- fragment --></div><!-- contents -->
 </div><!-- doc-content -->
 <!-- start footer part -->
diff --git a/docs/PenningTrap_8cpp.html b/docs/PenningTrap_8cpp.html
index 62355e1..5817ff6 100644
--- a/docs/PenningTrap_8cpp.html
+++ b/docs/PenningTrap_8cpp.html
@@ -106,6 +106,7 @@ $(document).ready(function(){initNavTree('PenningTrap_8cpp.html',''); initResiza
 <a href="#details">More...</a></p>
 <div class="textblock"><code>#include &quot;<a class="el" href="PenningTrap_8hpp_source.html">PenningTrap.hpp</a>&quot;</code><br />
 <code>#include &quot;<a class="el" href="constants_8hpp_source.html">constants.hpp</a>&quot;</code><br />
+<code>#include &quot;<a class="el" href="typedefs_8hpp_source.html">typedefs.hpp</a>&quot;</code><br />
 <code>#include &quot;<a class="el" href="utils_8hpp_source.html">utils.hpp</a>&quot;</code><br />
 </div>
 <p><a href="PenningTrap_8cpp_source.html">Go to the source code of this file.</a></p>
@@ -115,10 +116,7 @@ $(document).ready(function(){initNavTree('PenningTrap_8cpp.html',''); initResiza
 <dd>
 Janita Ovidie Sandtrøen Willumsen (janitaws)</dd></dl>
 <dl class="section version"><dt>Version</dt><dd>0.1</dd></dl>
-<dl class="bug"><dt><b><a class="el" href="bug.html#_bug000007">Bug:</a></b></dt><dd>No known bugs</dd></dl>
-<dl class="todo"><dt><b><a class="el" href="todo.html#_todo000001">Todo:</a></b></dt><dd><p class="startdd">Implement evolve_RK4 </p>
-<p class="enddd">Implement evolve_forward_euler </p>
-</dd></dl>
+<dl class="bug"><dt><b><a class="el" href="bug.html#_bug000008">Bug:</a></b></dt><dd>No known bugs </dd></dl>
 
 <p class="definition">Definition in file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
 </div></div><!-- contents -->
diff --git a/docs/PenningTrap_8cpp_source.html b/docs/PenningTrap_8cpp_source.html
index 993de8e..282e5c2 100644
--- a/docs/PenningTrap_8cpp_source.html
+++ b/docs/PenningTrap_8cpp_source.html
@@ -102,205 +102,311 @@ $(document).ready(function(){initNavTree('PenningTrap_8cpp_source.html',''); ini
 </div><!--header-->
 <div class="contents">
 <a href="PenningTrap_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span> </div>
-<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span><span class="preprocessor">#include &quot;<a class="code" href="PenningTrap_8hpp.html">PenningTrap.hpp</a>&quot;</span></div>
-<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span><span class="preprocessor">#include &quot;<a class="code" href="constants_8hpp.html">constants.hpp</a>&quot;</span></div>
-<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span><span class="preprocessor">#include &quot;<a class="code" href="utils_8hpp.html">utils.hpp</a>&quot;</span></div>
-<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span> </div>
-<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a81add5063bd5f29d77f0b5c299c6c560">   20</a></span><a class="code hl_function" href="classPenningTrap.html#a81add5063bd5f29d77f0b5c299c6c560">PenningTrap::PenningTrap</a>(<span class="keywordtype">double</span> B_0, <span class="keywordtype">double</span> V_0, <span class="keywordtype">double</span> d)</div>
-<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span>{</div>
-<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span>    this-&gt;B_0 = <a class="code hl_variable" href="classPenningTrap.html#a0cac3509aa96e71a26d3b2c902e27716">B_0</a>;</div>
-<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span>    this-&gt;V_0 = <a class="code hl_variable" href="classPenningTrap.html#a715329844d75ec4c04f8391421fb4e89">V_0</a>;</div>
-<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span>    this-&gt;d = <a class="code hl_variable" href="classPenningTrap.html#a66dfe89c68716b9502927b97f59c27d2">d</a>;</div>
+<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span><span class="preprocessor">#include &quot;<a class="code" href="PenningTrap_8hpp.html">PenningTrap.hpp</a>&quot;</span></div>
+<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span><span class="preprocessor">#include &quot;<a class="code" href="constants_8hpp.html">constants.hpp</a>&quot;</span></div>
+<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span><span class="preprocessor">#include &quot;<a class="code" href="typedefs_8hpp.html">typedefs.hpp</a>&quot;</span></div>
+<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span><span class="preprocessor">#include &quot;<a class="code" href="utils_8hpp.html">utils.hpp</a>&quot;</span></div>
+<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span> </div>
+<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"><a class="line" href="classPenningTrap.html#ae670d7de621acdb343b01af098086f63">   18</a></span><a class="code hl_function" href="classPenningTrap.html#ae670d7de621acdb343b01af098086f63">PenningTrap::PenningTrap</a>(<span class="keywordtype">double</span> B_0, std::function&lt;<span class="keywordtype">double</span>(<span class="keywordtype">double</span>)&gt; V_0,</div>
+<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span>                         <span class="keywordtype">double</span> d, <span class="keywordtype">double</span> t)</div>
+<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span>{</div>
+<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span>    this-&gt;B_0 = <a class="code hl_variable" href="classPenningTrap.html#a0cac3509aa96e71a26d3b2c902e27716">B_0</a>;</div>
+<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span>    this-&gt;<a class="code hl_variable" href="classPenningTrap.html#aaf105828121c4a33cc2b217453c20317">V_0</a> = <a class="code hl_variable" href="classPenningTrap.html#aaf105828121c4a33cc2b217453c20317">V_0</a>;</div>
+<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span>    this-&gt;d = <a class="code hl_variable" href="classPenningTrap.html#a66dfe89c68716b9502927b97f59c27d2">d</a>;</div>
+<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span>    this-&gt;t = <a class="code hl_variable" href="classPenningTrap.html#a8ca4e21291f60fde619c14099d8c4e8e">t</a>;</div>
 <div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span>}</div>
 <div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span> </div>
-<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a6e9776ff5b149f01080800716455d7c8">   27</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classPenningTrap.html#a6e9776ff5b149f01080800716455d7c8">PenningTrap::add_particle</a>(<a class="code hl_class" href="classParticle.html">Particle</a> particle)</div>
-<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span>{</div>
-<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>    this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>.push_back(particle);</div>
-<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span>}</div>
-<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span> </div>
-<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a978a2e2026a4b5308d5184712f81704b">   32</a></span>arma::vec <a class="code hl_function" href="classPenningTrap.html#a978a2e2026a4b5308d5184712f81704b">PenningTrap::external_E_field</a>(arma::vec r)</div>
-<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>{</div>
-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>    arma::vec::fixed&lt;3&gt; res;</div>
-<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>    <span class="keywordtype">double</span> f = this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a715329844d75ec4c04f8391421fb4e89">V_0</a> / (this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a66dfe89c68716b9502927b97f59c27d2">d</a> * this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a66dfe89c68716b9502927b97f59c27d2">d</a>);</div>
-<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>    res(0) = r(0);</div>
-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>    res(1) = r(1);</div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>    res(2) = -2. * r(2);</div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span> </div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>    <span class="keywordflow">return</span> f * res;</div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>}</div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span> </div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a2a3e7f480ba52e9f24d4c50c3981a784">   43</a></span>arma::vec <a class="code hl_function" href="classPenningTrap.html#a2a3e7f480ba52e9f24d4c50c3981a784">PenningTrap::external_B_field</a>(arma::vec r)</div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>{</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>    arma::vec::fixed&lt;3&gt; res{0., 0., this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0cac3509aa96e71a26d3b2c902e27716">B_0</a>};</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span> </div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>    <span class="keywordflow">return</span> res;</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>}</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span> </div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a4790f41e4fbc6ede4991aa7bbda92182">   50</a></span>arma::vec <a class="code hl_function" href="classPenningTrap.html#a4790f41e4fbc6ede4991aa7bbda92182">PenningTrap::force_on_particle</a>(<span class="keywordtype">int</span> i, <span class="keywordtype">int</span> j)</div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>{</div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>    <span class="comment">// Calculate the difference between the particles&#39; position</span></div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>    arma::vec::fixed&lt;3&gt; res =</div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>        this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>.at(i).r_vec - this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>.at(j).r_vec;</div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span> </div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>    <span class="comment">// Get the distance between the particles</span></div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>    <span class="keywordtype">double</span> norm = arma::norm(res);</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span> </div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    <span class="comment">// Multiply res with p_j&#39;s charge divided by the norm cubed</span></div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>    res *= this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>.at(j).q / (norm * norm * norm);</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span> </div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>    <span class="keywordflow">return</span> res;</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>}</div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span> </div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a045adb85e97a8e0c38fb36d2fd74eeee">   65</a></span>arma::vec <a class="code hl_function" href="classPenningTrap.html#a045adb85e97a8e0c38fb36d2fd74eeee">PenningTrap::total_force_external</a>(<span class="keywordtype">int</span> i)</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>{</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    <a class="code hl_class" href="classParticle.html">Particle</a> p = this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>.at(i);</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span> </div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>    arma::vec::fixed&lt;3&gt; B = this-&gt;<a class="code hl_function" href="classPenningTrap.html#a2a3e7f480ba52e9f24d4c50c3981a784">external_B_field</a>(p.<a class="code hl_variable" href="classParticle.html#acf1a0f3c978b06d76df5bb4279594467">r_vec</a>);</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span> </div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>    arma::vec::fixed&lt;3&gt; v_cross_B{p.<a class="code hl_variable" href="classParticle.html#a4a5d22c7aeca66f67d083f270cba25df">v_vec</a>(1) * B(2) - p.<a class="code hl_variable" href="classParticle.html#a4a5d22c7aeca66f67d083f270cba25df">v_vec</a>(2) * B(1),</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>                                  p.<a class="code hl_variable" href="classParticle.html#a4a5d22c7aeca66f67d083f270cba25df">v_vec</a>(2) * B(0) - p.<a class="code hl_variable" href="classParticle.html#a4a5d22c7aeca66f67d083f270cba25df">v_vec</a>(0) * B(2),</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>                                  p.<a class="code hl_variable" href="classParticle.html#a4a5d22c7aeca66f67d083f270cba25df">v_vec</a>(0) * B(1) - p.<a class="code hl_variable" href="classParticle.html#a4a5d22c7aeca66f67d083f270cba25df">v_vec</a>(1) * B(0)};</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span> </div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>    arma::vec force = p.<a class="code hl_variable" href="classParticle.html#a566dcc1de4bdc01251776948798ea8e1">q</a> * (this-&gt;<a class="code hl_function" href="classPenningTrap.html#a978a2e2026a4b5308d5184712f81704b">external_E_field</a>(p.<a class="code hl_variable" href="classParticle.html#acf1a0f3c978b06d76df5bb4279594467">r_vec</a>) + v_cross_B);</div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span> </div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    <span class="keywordflow">return</span> force;</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>}</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span> </div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a135db7d991d9b88b00fde4edee71f78d">   80</a></span>arma::vec <a class="code hl_function" href="classPenningTrap.html#a135db7d991d9b88b00fde4edee71f78d">PenningTrap::total_force_particles</a>(<span class="keywordtype">int</span> i)</div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>{</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>    <a class="code hl_class" href="classParticle.html">Particle</a> p = this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>.at(i);</div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span> </div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    arma::vec res(3);</div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span> </div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>.size(); j++) {</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>        <span class="keywordflow">if</span> (i == j) {</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>            <span class="keywordflow">continue</span>;</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>        }</div>
-<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span> </div>
-<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>        res += this-&gt;<a class="code hl_function" href="classPenningTrap.html#a4790f41e4fbc6ede4991aa7bbda92182">force_on_particle</a>(i, j);</div>
-<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>    }</div>
-<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span> </div>
-<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>    res *= <a class="code hl_define" href="constants_8hpp.html#a4e451456ad7e9276ed0afa42826e7ccb">K_E</a> * (p.<a class="code hl_variable" href="classParticle.html#a566dcc1de4bdc01251776948798ea8e1">q</a> / p.<a class="code hl_variable" href="classParticle.html#aedcc7e1bc53b0e2b1a4a07c9a1b47563">m</a>);</div>
-<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span> </div>
-<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>    <span class="keywordflow">return</span> res;</div>
-<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>}</div>
-<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span> </div>
-<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a83cc7a04dae009ed8e75453c38fdf8be">   99</a></span>arma::vec <a class="code hl_function" href="classPenningTrap.html#a83cc7a04dae009ed8e75453c38fdf8be">PenningTrap::total_force</a>(<span class="keywordtype">int</span> i)</div>
-<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>{</div>
-<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    <span class="keywordflow">return</span> this-&gt;<a class="code hl_function" href="classPenningTrap.html#a045adb85e97a8e0c38fb36d2fd74eeee">total_force_external</a>(i) - this-&gt;<a class="code hl_function" href="classPenningTrap.html#a135db7d991d9b88b00fde4edee71f78d">total_force_particles</a>(i);</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>}</div>
-<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span> </div>
-<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"><a class="line" href="classPenningTrap.html#ab891b839c40eeb38d8a2a636c70090a9">  104</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classPenningTrap.html#ab891b839c40eeb38d8a2a636c70090a9">PenningTrap::evolve_RK4</a>(<span class="keywordtype">double</span> dt)</div>
-<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>{</div>
-<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>    std::vector&lt;Particle&gt; tmp_particles = this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>;</div>
-<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    </div>
-<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    arma::vec::fixed&lt;3&gt; *k_v = <span class="keyword">new</span> arma::vec::fixed&lt;3&gt;[this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>.size()*4];</div>
-<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    arma::vec::fixed&lt;3&gt; *k_r = <span class="keyword">new</span> arma::vec::fixed&lt;3&gt;[this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>.size()*4];</div>
+<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a763700316b502d5900e587c1f61e6bf1">   27</a></span><a class="code hl_function" href="classPenningTrap.html#ae670d7de621acdb343b01af098086f63">PenningTrap::PenningTrap</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i, <span class="keywordtype">double</span> B_0,</div>
+<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span>                         std::function&lt;<span class="keywordtype">double</span>(<span class="keywordtype">double</span>)&gt; V_0, <span class="keywordtype">double</span> d, <span class="keywordtype">double</span> t)</div>
+<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>    : <a class="code hl_class" href="classPenningTrap.html">PenningTrap</a>::<a class="code hl_class" href="classPenningTrap.html">PenningTrap</a>(B_0, V_0, d)</div>
+<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span>{</div>
+<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span>    <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> r, v;</div>
+<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; i; j++) {</div>
+<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>        r = <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a>().randn() * .1 * this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a66dfe89c68716b9502927b97f59c27d2">d</a>;</div>
+<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>        v = <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a>().randn() * .1 * this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a66dfe89c68716b9502927b97f59c27d2">d</a>;</div>
+<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>        this-&gt;<a class="code hl_function" href="classPenningTrap.html#a6e9776ff5b149f01080800716455d7c8">add_particle</a>(<a class="code hl_class" href="classParticle.html">Particle</a>(1., 40., r, v));</div>
+<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>    }</div>
+<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>}</div>
+<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span> </div>
+<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a67139e04ef69c0bcffde8f30f67cbf73">   39</a></span><a class="code hl_function" href="classPenningTrap.html#ae670d7de621acdb343b01af098086f63">PenningTrap::PenningTrap</a>(std::vector&lt;Particle&gt; particles, <span class="keywordtype">double</span> B_0,</div>
+<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>                         std::function&lt;<span class="keywordtype">double</span>(<span class="keywordtype">double</span>)&gt; V_0, <span class="keywordtype">double</span> d, <span class="keywordtype">double</span> t)</div>
+<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>    : <a class="code hl_class" href="classPenningTrap.html">PenningTrap</a>::<a class="code hl_class" href="classPenningTrap.html">PenningTrap</a>(B_0, V_0, d)</div>
+<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>{</div>
+<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>    this-&gt;particles = <a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>;</div>
+<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>}</div>
+<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span> </div>
+<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"><a class="line" href="classPenningTrap.html#af98a720da60b0e1a62aefa5f5cb37c1e">   46</a></span><a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> <a class="code hl_function" href="classPenningTrap.html#af98a720da60b0e1a62aefa5f5cb37c1e">PenningTrap::v_func</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j, <span class="keywordtype">double</span> dt)</div>
+<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>{</div>
+<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>    <span class="keywordflow">switch</span> (i) {</div>
+<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>    <span class="keywordflow">case</span> 0:</div>
+<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>        <span class="keywordflow">return</span> .5 * dt * this-&gt;<a class="code hl_variable" href="classPenningTrap.html#ae9b5afdaa5cd366e94bd294452a1eed4">k_v</a>[0][j];</div>
+<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>    <span class="keywordflow">case</span> 1:</div>
+<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>        <span class="keywordflow">return</span> .5 * dt * this-&gt;k_v[1][j];</div>
+<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>    <span class="keywordflow">case</span> 2:</div>
+<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>        <span class="keywordflow">return</span> dt * this-&gt;k_v[2][j];</div>
+<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>    <span class="keywordflow">case</span> 3:</div>
+<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>        <span class="keywordflow">return</span> (dt / 6.) * (this-&gt;k_v[0][j].eval() + this-&gt;k_v[1][j].eval() +</div>
+<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>                            this-&gt;k_v[2][j].eval() + this-&gt;k_v[3][j].eval());</div>
+<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    <span class="keywordflow">default</span>:</div>
+<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>        std::cout &lt;&lt; <span class="stringliteral">&quot;Not valid!&quot;</span> &lt;&lt; std::endl;</div>
+<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>        abort();</div>
+<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>    }</div>
+<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>}</div>
+<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span> </div>
+<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a43e74792ab4b3f9299f35cb64bdb2648">   64</a></span><a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> <a class="code hl_function" href="classPenningTrap.html#a43e74792ab4b3f9299f35cb64bdb2648">PenningTrap::r_func</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j, <span class="keywordtype">double</span> dt)</div>
+<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>{</div>
+<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    <span class="keywordflow">switch</span> (i) {</div>
+<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    <span class="keywordflow">case</span> 0:</div>
+<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>        <span class="keywordflow">return</span> .5 * dt * this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a2f168622587709b9e3c49077f0b9a640">k_r</a>[0][j];</div>
+<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>    <span class="keywordflow">case</span> 1:</div>
+<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>        <span class="keywordflow">return</span> .5 * dt * this-&gt;k_r[1][j];</div>
+<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>    <span class="keywordflow">case</span> 2:</div>
+<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>        <span class="keywordflow">return</span> dt * this-&gt;k_r[2][j];</div>
+<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>    <span class="keywordflow">case</span> 3:</div>
+<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>        <span class="keywordflow">return</span> (dt / 6.) * (this-&gt;k_r[0][j].eval() + this-&gt;k_r[1][j].eval() +</div>
+<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>                            this-&gt;k_r[2][j].eval() + this-&gt;k_r[3][j].eval());</div>
+<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>    <span class="keywordflow">default</span>:</div>
+<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>        std::cout &lt;&lt; <span class="stringliteral">&quot;Not valid!&quot;</span> &lt;&lt; std::endl;</div>
+<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>        abort();</div>
+<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    }</div>
+<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>}</div>
+<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span> </div>
+<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a6e9776ff5b149f01080800716455d7c8">   82</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classPenningTrap.html#a6e9776ff5b149f01080800716455d7c8">PenningTrap::add_particle</a>(<a class="code hl_class" href="classParticle.html">Particle</a> particle)</div>
+<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>{</div>
+<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    this-&gt;particles.push_back(particle);</div>
+<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>}</div>
+<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span> </div>
+<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a1d58feaa2c9e34cbf26b1c5ed75ca9d9">   87</a></span><a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> <a class="code hl_function" href="classPenningTrap.html#a1d58feaa2c9e34cbf26b1c5ed75ca9d9">PenningTrap::external_E_field</a>(<a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> r)</div>
+<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>{</div>
+<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>    r(2) *= -2.;</div>
+<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>    <span class="keywordtype">double</span> f = this-&gt;<a class="code hl_variable" href="classPenningTrap.html#aaf105828121c4a33cc2b217453c20317">V_0</a>(this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a8ca4e21291f60fde619c14099d8c4e8e">t</a>) / (this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a66dfe89c68716b9502927b97f59c27d2">d</a> * this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a66dfe89c68716b9502927b97f59c27d2">d</a>);</div>
+<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span> </div>
+<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>    <span class="keywordflow">return</span> f * r;</div>
+<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>}</div>
+<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span> </div>
+<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"><a class="line" href="classPenningTrap.html#acbf065c9c125682329ad82a8d166554c">   95</a></span><a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> <a class="code hl_function" href="classPenningTrap.html#acbf065c9c125682329ad82a8d166554c">PenningTrap::external_B_field</a>(<a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> r)</div>
+<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>{</div>
+<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>    <span class="keywordflow">return</span> <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a>{0., 0., this-&gt;B_0};</div>
+<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>}</div>
+<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span> </div>
+<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a9ae34ad740a230e667e96bc6ee8730ce">  100</a></span><a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> <a class="code hl_function" href="classPenningTrap.html#a9ae34ad740a230e667e96bc6ee8730ce">PenningTrap::force_on_particle</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j)</div>
+<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>{</div>
+<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>    <a class="code hl_class" href="classParticle.html">Particle</a> p_j = this-&gt;particles[j];</div>
+<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>    <span class="comment">// Calculate the difference between the particles&#39; position</span></div>
+<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> res = this-&gt;particles[i].<a class="code hl_variable" href="classParticle.html#af9497cd8f2dcad0fad54f571ddb383e6">r_vec</a> - p_j.<a class="code hl_variable" href="classParticle.html#af9497cd8f2dcad0fad54f571ddb383e6">r_vec</a>;</div>
+<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span> </div>
+<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>    <span class="comment">// Get the distance between the particles</span></div>
+<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    <span class="keywordtype">double</span> norm = arma::norm(res, 2);</div>
+<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span> </div>
+<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    <span class="comment">// Multiply res with p_j&#39;s charge divided by the norm cubed</span></div>
 <div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span> </div>
-<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    <span class="keywordtype">int</span> size = this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>.size();</div>
-<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span> </div>
-<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=0; i&lt;size; i++) {</div>
-<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>        k_v[i] = this-&gt;<a class="code hl_function" href="classPenningTrap.html#a83cc7a04dae009ed8e75453c38fdf8be">total_force</a>(i)/this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>.at(i).m;</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>        k_r[i] = this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>.at(i).v_vec;</div>
-<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>    }</div>
+<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    <span class="keywordflow">return</span> <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a>(res * p_j.<a class="code hl_variable" href="classParticle.html#a566dcc1de4bdc01251776948798ea8e1">q</a> / (norm * norm * norm));</div>
+<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>}</div>
+<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span> </div>
+<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"><a class="line" href="classPenningTrap.html#ae72d203b0bfa1b9e72bea28cb2863c56">  114</a></span><a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> <a class="code hl_function" href="classPenningTrap.html#ae72d203b0bfa1b9e72bea28cb2863c56">PenningTrap::total_force_external</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i)</div>
+<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>{</div>
+<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>    <a class="code hl_class" href="classParticle.html">Particle</a> p = this-&gt;particles[i];</div>
 <div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span> </div>
-<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=0; i&lt;size; i++) {</div>
-<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>        <a class="code hl_class" href="classParticle.html">Particle</a> *p = &amp;this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>.at(i);</div>
-<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span> </div>
-<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>        p-&gt;<a class="code hl_variable" href="classParticle.html#a4a5d22c7aeca66f67d083f270cba25df">v_vec</a> = tmp_particles.at(i).v_vec + (dt/2)*k_v[i];</div>
-<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>        p-&gt;<a class="code hl_variable" href="classParticle.html#acf1a0f3c978b06d76df5bb4279594467">r_vec</a> = tmp_particles.at(i).r_vec + (dt/2)*k_r[i];</div>
-<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>    }</div>
-<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span> </div>
+<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>    <span class="keywordflow">if</span> (arma::norm(p.<a class="code hl_variable" href="classParticle.html#af9497cd8f2dcad0fad54f571ddb383e6">r_vec</a>) &gt; this-&gt;d) {</div>
+<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>        <span class="keywordflow">return</span> <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a>{0., 0., 0.};</div>
+<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    }</div>
+<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span> </div>
+<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>    <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> force =</div>
+<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>        p.<a class="code hl_variable" href="classParticle.html#a566dcc1de4bdc01251776948798ea8e1">q</a> * (this-&gt;<a class="code hl_function" href="classPenningTrap.html#a1d58feaa2c9e34cbf26b1c5ed75ca9d9">external_E_field</a>(p.<a class="code hl_variable" href="classParticle.html#af9497cd8f2dcad0fad54f571ddb383e6">r_vec</a>) +</div>
+<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>               arma::cross(p.<a class="code hl_variable" href="classParticle.html#a879692772803d6ab65fa4993b54aea6e">v_vec</a>, this-&gt;external_B_field(p.<a class="code hl_variable" href="classParticle.html#af9497cd8f2dcad0fad54f571ddb383e6">r_vec</a>)));</div>
 <div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span> </div>
-<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=0; i&lt;size; i++) {</div>
-<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>        k_v[1*size + i] = this-&gt;<a class="code hl_function" href="classPenningTrap.html#a83cc7a04dae009ed8e75453c38fdf8be">total_force</a>(i)/this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>.at(i).m;</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>        k_r[1*size + i] = this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>.at(i).v_vec;</div>
-<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>    }</div>
-<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span> </div>
-<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=0; i&lt;size; i++) {</div>
-<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>        <a class="code hl_class" href="classParticle.html">Particle</a> *p = &amp;this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>.at(i);</div>
-<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span> </div>
-<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>        p-&gt;<a class="code hl_variable" href="classParticle.html#a4a5d22c7aeca66f67d083f270cba25df">v_vec</a> = tmp_particles.at(i).v_vec + (dt/2)*k_v[1*size + i];</div>
-<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>        p-&gt;<a class="code hl_variable" href="classParticle.html#acf1a0f3c978b06d76df5bb4279594467">r_vec</a> = tmp_particles.at(i).r_vec + (dt/2)*k_r[1*size + i];</div>
-<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>    }</div>
-<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span> </div>
-<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=0; i&lt;size; i++) {</div>
-<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>        k_v[2*size + i] = this-&gt;<a class="code hl_function" href="classPenningTrap.html#a83cc7a04dae009ed8e75453c38fdf8be">total_force</a>(i)/this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>.at(i).m;</div>
-<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>        k_r[2*size + i] = this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>.at(i).v_vec;</div>
+<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>    <span class="keywordflow">return</span> force;</div>
+<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>}</div>
+<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span> </div>
+<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a46a954a0946def199e30fb300ba1c47b">  129</a></span><a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> <a class="code hl_function" href="classPenningTrap.html#a46a954a0946def199e30fb300ba1c47b">PenningTrap::total_force_particles</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i)</div>
+<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>{</div>
+<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>    <a class="code hl_class" href="classParticle.html">Particle</a> p = this-&gt;particles[i];</div>
+<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span> </div>
+<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>    <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> res;</div>
+<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span> </div>
+<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; this-&gt;particles.size(); j++) {</div>
+<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>        <span class="keywordflow">if</span> (i == j) {</div>
+<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>            <span class="keywordflow">continue</span>;</div>
+<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>        }</div>
+<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span> </div>
+<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>        res += this-&gt;<a class="code hl_function" href="classPenningTrap.html#a9ae34ad740a230e667e96bc6ee8730ce">force_on_particle</a>(i, j);</div>
 <div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>    }</div>
 <div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span> </div>
-<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=0; i&lt;size; i++) {</div>
-<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>        <a class="code hl_class" href="classParticle.html">Particle</a> *p = &amp;this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>.at(i);</div>
+<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>    <span class="keywordflow">return</span> <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a>(res * <a class="code hl_define" href="constants_8hpp.html#a4e451456ad7e9276ed0afa42826e7ccb">K_E</a> * (p.<a class="code hl_variable" href="classParticle.html#a566dcc1de4bdc01251776948798ea8e1">q</a> / p.<a class="code hl_variable" href="classParticle.html#aedcc7e1bc53b0e2b1a4a07c9a1b47563">m</a>));</div>
+<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>}</div>
 <div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span> </div>
-<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>        p-&gt;<a class="code hl_variable" href="classParticle.html#a4a5d22c7aeca66f67d083f270cba25df">v_vec</a> = tmp_particles.at(i).v_vec + dt*k_v[2*size + i];</div>
-<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>        p-&gt;<a class="code hl_variable" href="classParticle.html#acf1a0f3c978b06d76df5bb4279594467">r_vec</a> = tmp_particles.at(i).r_vec + dt*k_r[2*size + i];</div>
-<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>    }</div>
-<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span> </div>
+<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a1f668c4433421136ad51741741aa1bc8">  146</a></span><a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> <a class="code hl_function" href="classPenningTrap.html#a1f668c4433421136ad51741741aa1bc8">PenningTrap::total_force</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i)</div>
+<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>{</div>
+<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>    <span class="keywordflow">return</span> this-&gt;<a class="code hl_function" href="classPenningTrap.html#ae72d203b0bfa1b9e72bea28cb2863c56">total_force_external</a>(i) - this-&gt;<a class="code hl_function" href="classPenningTrap.html#a46a954a0946def199e30fb300ba1c47b">total_force_particles</a>(i);</div>
+<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>}</div>
 <div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span> </div>
-<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=0; i&lt;size; i++) {</div>
-<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>        k_v[3*size + i] = this-&gt;<a class="code hl_function" href="classPenningTrap.html#a83cc7a04dae009ed8e75453c38fdf8be">total_force</a>(i)/this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>.at(i).m;</div>
-<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>        k_r[3*size + i] = this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>.at(i).v_vec;</div>
-<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>    }</div>
-<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span> </div>
-<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=0; i&lt;size; i++) {</div>
-<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>        <a class="code hl_class" href="classParticle.html">Particle</a> *p = &amp;this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>.at(i);</div>
-<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span> </div>
-<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>        p-&gt;<a class="code hl_variable" href="classParticle.html#a4a5d22c7aeca66f67d083f270cba25df">v_vec</a> = tmp_particles.at(i).v_vec + dt*(k_v[i] + k_v[size + i] + k_v[2*size + i] + k_v[3*size + i])/6;</div>
-<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>        p-&gt;<a class="code hl_variable" href="classParticle.html#acf1a0f3c978b06d76df5bb4279594467">r_vec</a> = tmp_particles.at(i).r_vec + dt*(k_r[i] + k_r[size + i] + k_r[2*size + i] + k_r[3*size + i])/6;</div>
-<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>    }</div>
-<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span> </div>
-<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>    <span class="keyword">delete</span> [] k_v;</div>
-<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>    <span class="keyword">delete</span> [] k_r;</div>
-<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>}</div>
+<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a36946152fd951b1f7c346c51ff900d8e">  151</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classPenningTrap.html#a36946152fd951b1f7c346c51ff900d8e">PenningTrap::evolve_RK4</a>(<span class="keywordtype">double</span> dt, <span class="keywordtype">bool</span> particle_interaction)</div>
+<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>{</div>
+<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span> </div>
+<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>    std::vector&lt;Particle&gt; original_particles = this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>;</div>
+<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>    std::vector&lt;Particle&gt; tmp_particles = this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>;</div>
+<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span> </div>
+<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>    <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> (<a class="code hl_class" href="classPenningTrap.html">PenningTrap</a>::*force)(<span class="keywordtype">unsigned</span> int);</div>
+<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>    <span class="keywordflow">if</span> (particle_interaction) {</div>
+<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>        force = &amp;<a class="code hl_function" href="classPenningTrap.html#a1f668c4433421136ad51741741aa1bc8">PenningTrap::total_force</a>;</div>
+<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>    }</div>
+<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>    <span class="keywordflow">else</span> {</div>
+<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>        force = &amp;<a class="code hl_function" href="classPenningTrap.html#ae72d203b0bfa1b9e72bea28cb2863c56">PenningTrap::total_force_external</a>;</div>
+<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>    }</div>
+<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span> </div>
+<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>    <span class="keywordtype">size_t</span> size = this-&gt;particles.size();</div>
 <div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span> </div>
-<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a56544b6f4befb42984e9650cf2a40965">  167</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classPenningTrap.html#a56544b6f4befb42984e9650cf2a40965">PenningTrap::evolve_forward_euler</a>(<span class="keywordtype">double</span> dt)</div>
-<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>{</div>
-<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>    std::vector&lt;Particle&gt; new_state = this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>;</div>
-<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span> </div>
-<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>    <a class="code hl_class" href="classParticle.html">Particle</a> *p;</div>
-<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span> </div>
-<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span><span class="preprocessor">#pragma omp parallel for private(p)</span></div>
-<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>.size(); i++) {</div>
-<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>        p = &amp;new_state.at(i);</div>
-<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>        p-&gt;<a class="code hl_variable" href="classParticle.html#a4a5d22c7aeca66f67d083f270cba25df">v_vec</a> += dt * this-&gt;<a class="code hl_function" href="classPenningTrap.html#a83cc7a04dae009ed8e75453c38fdf8be">total_force</a>(i) / new_state.at(i).m;</div>
-<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>        p-&gt;<a class="code hl_variable" href="classParticle.html#acf1a0f3c978b06d76df5bb4279594467">r_vec</a> += dt * this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>.at(i).v_vec;</div>
-<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>    }</div>
-<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span> </div>
-<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>    this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a> = new_state;</div>
-<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>}</div>
-<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span> </div>
-<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>arma::vec PenningTrap::get_particle(<span class="keywordtype">int</span> i)</div>
-<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>{</div>
-<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>    <span class="keywordflow">return</span> this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>.at(i).r_vec;</div>
-<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>}</div>
-<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span> </div>
-<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span><span class="keywordtype">double</span> PenningTrap::get_d()</div>
-<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>{</div>
-<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>    <span class="keywordflow">return</span> this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a66dfe89c68716b9502927b97f59c27d2">d</a>;</div>
-<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>}</div>
+<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>    this-&gt;<a class="code hl_variable" href="classPenningTrap.html#ae9b5afdaa5cd366e94bd294452a1eed4">k_v</a> = <a class="code hl_typedef" href="typedefs_8hpp.html#aec69d34220fff45de238b9e01f2686af">sim_arr</a>(4, <a class="code hl_typedef" href="typedefs_8hpp.html#a7c2dfa854274262c4e00e4ef0ab2ce23">sim_cols</a>(size));</div>
+<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>    this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a2f168622587709b9e3c49077f0b9a640">k_r</a> = <a class="code hl_typedef" href="typedefs_8hpp.html#aec69d34220fff45de238b9e01f2686af">sim_arr</a>(4, <a class="code hl_typedef" href="typedefs_8hpp.html#a7c2dfa854274262c4e00e4ef0ab2ce23">sim_cols</a>(size));</div>
+<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span> </div>
+<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; 4; i++) {</div>
+<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span><span class="preprocessor">#pragma omp parallel for</span></div>
+<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; this-&gt;particles.size(); j++) {</div>
+<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>            this-&gt;<a class="code hl_variable" href="classPenningTrap.html#ae9b5afdaa5cd366e94bd294452a1eed4">k_v</a>[i][j] = (this-&gt;*force)(j) / this-&gt;particles[j].m;</div>
+<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>            this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a2f168622587709b9e3c49077f0b9a640">k_r</a>[i][j] = this-&gt;particles[j].v_vec;</div>
+<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span> </div>
+<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>            <a class="code hl_class" href="classParticle.html">Particle</a> *p = &amp;tmp_particles[j];</div>
+<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span> </div>
+<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>            p-&gt;<a class="code hl_variable" href="classParticle.html#a879692772803d6ab65fa4993b54aea6e">v_vec</a> = original_particles[j].v_vec + this-&gt;<a class="code hl_function" href="classPenningTrap.html#af98a720da60b0e1a62aefa5f5cb37c1e">v_func</a>(i, j, dt);</div>
+<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>            p-&gt;<a class="code hl_variable" href="classParticle.html#af9497cd8f2dcad0fad54f571ddb383e6">r_vec</a> = original_particles[j].r_vec + this-&gt;<a class="code hl_function" href="classPenningTrap.html#a43e74792ab4b3f9299f35cb64bdb2648">r_func</a>(i, j, dt);</div>
+<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>        }</div>
+<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>        this-&gt;particles = tmp_particles;</div>
+<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>    }</div>
+<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>    this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a8ca4e21291f60fde619c14099d8c4e8e">t</a> += dt;</div>
+<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>}</div>
+<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span> </div>
+<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"><a class="line" href="classPenningTrap.html#ab9ea97a406534bbe621a95215144875e">  186</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classPenningTrap.html#ab9ea97a406534bbe621a95215144875e">PenningTrap::evolve_forward_euler</a>(<span class="keywordtype">double</span> dt, <span class="keywordtype">bool</span> particle_interaction)</div>
+<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>{</div>
+<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>    std::vector&lt;Particle&gt; new_state = this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>;</div>
+<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span> </div>
+<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>    <a class="code hl_class" href="classParticle.html">Particle</a> *p;</div>
+<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span> </div>
+<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>    <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> (<a class="code hl_class" href="classPenningTrap.html">PenningTrap</a>::*force)(<span class="keywordtype">unsigned</span> int);</div>
+<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>    <span class="keywordflow">if</span> (particle_interaction) {</div>
+<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>        force = &amp;<a class="code hl_function" href="classPenningTrap.html#a1f668c4433421136ad51741741aa1bc8">PenningTrap::total_force</a>;</div>
+<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>    }</div>
+<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>    <span class="keywordflow">else</span> {</div>
+<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>        force = &amp;<a class="code hl_function" href="classPenningTrap.html#ae72d203b0bfa1b9e72bea28cb2863c56">PenningTrap::total_force_external</a>;</div>
+<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>    }</div>
+<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span> </div>
+<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span><span class="preprocessor">#pragma omp parallel for private(p)</span></div>
+<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; this-&gt;particles.size(); i++) {</div>
+<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>        p = &amp;new_state[i];</div>
+<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>        p-&gt;<a class="code hl_variable" href="classParticle.html#a879692772803d6ab65fa4993b54aea6e">v_vec</a> += dt * (this-&gt;*force)(i) / p-&gt;<a class="code hl_variable" href="classParticle.html#aedcc7e1bc53b0e2b1a4a07c9a1b47563">m</a>;</div>
+<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>        p-&gt;<a class="code hl_variable" href="classParticle.html#af9497cd8f2dcad0fad54f571ddb383e6">r_vec</a> += dt * this-&gt;particles[i].v_vec;</div>
+<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>    }</div>
+<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span> </div>
+<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>    this-&gt;particles = new_state;</div>
+<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>    this-&gt;<a class="code hl_variable" href="classPenningTrap.html#a8ca4e21291f60fde619c14099d8c4e8e">t</a> += dt;</div>
+<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>}</div>
+<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span> </div>
+<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a5331837e6dd7bce807a99edd2ba7e854">  211</a></span><a class="code hl_typedef" href="typedefs_8hpp.html#aec69d34220fff45de238b9e01f2686af">sim_arr</a> <a class="code hl_function" href="classPenningTrap.html#a5331837e6dd7bce807a99edd2ba7e854">PenningTrap::simulate</a>(<span class="keywordtype">double</span> time, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> steps,</div>
+<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>                              std::string method, <span class="keywordtype">bool</span> particle_interaction)</div>
+<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>{</div>
+<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>    <span class="keywordtype">double</span> dt = time / (double)steps;</div>
+<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span> </div>
+<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>    <a class="code hl_typedef" href="typedefs_8hpp.html#aec69d34220fff45de238b9e01f2686af">sim_arr</a> res(this-&gt;particles.size(), <a class="code hl_typedef" href="typedefs_8hpp.html#a7c2dfa854274262c4e00e4ef0ab2ce23">sim_cols</a>(steps));</div>
+<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span> </div>
+<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>    void (<a class="code hl_class" href="classPenningTrap.html">PenningTrap</a>::*func)(double, bool);</div>
+<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>    <span class="keywordflow">if</span> (method == <span class="stringliteral">&quot;rk4&quot;</span>) {</div>
+<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>        func = &amp;<a class="code hl_function" href="classPenningTrap.html#a36946152fd951b1f7c346c51ff900d8e">PenningTrap::evolve_RK4</a>;</div>
+<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>    }</div>
+<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (method == <span class="stringliteral">&quot;euler&quot;</span>) {</div>
+<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>        func = &amp;<a class="code hl_function" href="classPenningTrap.html#ab9ea97a406534bbe621a95215144875e">PenningTrap::evolve_forward_euler</a>;</div>
+<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>    }</div>
+<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>    <span class="keywordflow">else</span> {</div>
+<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>        std::cout &lt;&lt; <span class="stringliteral">&quot;Not a valid method!&quot;</span> &lt;&lt; std::endl;</div>
+<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>        abort();</div>
+<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>    }</div>
+<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span> </div>
+<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; steps; j++) {</div>
+<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; this-&gt;particles.size(); i++) {</div>
+<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>            res[i][j] = this-&gt;particles[i].r_vec;</div>
+<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>        }</div>
+<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>        (this-&gt;*func)(dt, particle_interaction);</div>
+<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>    }</div>
+<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span> </div>
+<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>    <span class="keywordflow">return</span> res;</div>
+<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>}</div>
+<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span> </div>
+<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"><a class="line" href="classPenningTrap.html#abbb832a85139b1a56ebde57d7b8f9a57">  240</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classPenningTrap.html#abbb832a85139b1a56ebde57d7b8f9a57">PenningTrap::write_simulation_to_dir</a>(std::string path, <span class="keywordtype">double</span> time,</div>
+<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span>                                          <span class="keywordtype">int</span> steps, std::string method,</div>
+<div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span>                                          <span class="keywordtype">bool</span> particle_interaction)</div>
+<div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span>{</div>
+<div class="line"><a id="l00244" name="l00244"></a><span class="lineno">  244</span>    <span class="keywordflow">if</span> (path.back() != <span class="charliteral">&#39;/&#39;</span>) {</div>
+<div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span>        path += <span class="charliteral">&#39;/&#39;</span>;</div>
+<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>    }</div>
+<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>    <span class="keywordflow">if</span> (<a class="code hl_function" href="utils_8hpp.html#a6fdd7217b750aff5b6295ece7cbdeffa">mkpath</a>(path, 0777) != 0) {</div>
+<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>        std::cout &lt;&lt; <span class="stringliteral">&quot;Hello&quot;</span> &lt;&lt; std::endl;</div>
+<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>        <span class="keywordflow">return</span>;</div>
+<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>    }</div>
+<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span> </div>
+<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>    <a class="code hl_typedef" href="typedefs_8hpp.html#aec69d34220fff45de238b9e01f2686af">sim_arr</a> res = this-&gt;<a class="code hl_function" href="classPenningTrap.html#a5331837e6dd7bce807a99edd2ba7e854">simulate</a>(time, steps, method, particle_interaction);</div>
+<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span> </div>
+<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>    std::ofstream ofile;</div>
+<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span> </div>
+<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span><span class="preprocessor">#pragma omp parallel for private(ofile)</span></div>
+<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; this-&gt;particles.size(); i++) {</div>
+<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>        ofile.open(path + <span class="stringliteral">&quot;particle_&quot;</span> + std::to_string(i) + <span class="stringliteral">&quot;.txt&quot;</span>);</div>
+<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>        <span class="keywordflow">for</span> (<a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> &amp;vec : res[i]) {</div>
+<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>            ofile &lt;&lt; vec(0) &lt;&lt; <span class="stringliteral">&quot;,&quot;</span> &lt;&lt; vec(1) &lt;&lt; <span class="stringliteral">&quot;,&quot;</span> &lt;&lt; vec(2) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span>        }</div>
+<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>        ofile.close();</div>
+<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>    }</div>
+<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span>}</div>
+<div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span> </div>
+<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a0194be61c956a9259c747c23e4163c5b">  266</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="classPenningTrap.html#a0194be61c956a9259c747c23e4163c5b">PenningTrap::fraction_of_particles_left</a>(<span class="keywordtype">double</span> time, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> steps, std::string method, <span class="keywordtype">bool</span> particle_interaction)</div>
+<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>{</div>
+<div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span>    <a class="code hl_typedef" href="typedefs_8hpp.html#aec69d34220fff45de238b9e01f2686af">sim_arr</a> res = this-&gt;<a class="code hl_function" href="classPenningTrap.html#a5331837e6dd7bce807a99edd2ba7e854">simulate</a>(time, steps, method, particle_interaction);</div>
+<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span> </div>
+<div class="line"><a id="l00270" name="l00270"></a><span class="lineno">  270</span>    <span class="keywordtype">int</span> particles_left = 0;</div>
+<div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span> </div>
+<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>    <span class="keywordflow">for</span> (<a class="code hl_class" href="classParticle.html">Particle</a> p : this-&gt;particles) {</div>
+<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span>        <span class="keywordflow">if</span> (arma::norm(p.r_vec) &lt; this-&gt;d) {</div>
+<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>            particles_left++;</div>
+<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>        }</div>
+<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>    }</div>
+<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span> </div>
+<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>    <span class="keywordflow">return</span> (<span class="keywordtype">double</span>) particles_left / (double) this-&gt;particles.size();</div>
+<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span>}</div>
+<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span> </div>
 <div class="ttc" id="aPenningTrap_8hpp_html"><div class="ttname"><a href="PenningTrap_8hpp.html">PenningTrap.hpp</a></div><div class="ttdoc">A class for simulating a Penning trap.</div></div>
-<div class="ttc" id="aclassParticle_html"><div class="ttname"><a href="classParticle.html">Particle</a></div><div class="ttdoc">A class that holds attributes of a particle.</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00019">Particle.hpp:19</a></div></div>
-<div class="ttc" id="aclassParticle_html_a4a5d22c7aeca66f67d083f270cba25df"><div class="ttname"><a href="classParticle.html#a4a5d22c7aeca66f67d083f270cba25df">Particle::v_vec</a></div><div class="ttdeci">arma::vec::fixed&lt; 3 &gt; v_vec</div><div class="ttdoc">velocity</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00024">Particle.hpp:24</a></div></div>
-<div class="ttc" id="aclassParticle_html_a566dcc1de4bdc01251776948798ea8e1"><div class="ttname"><a href="classParticle.html#a566dcc1de4bdc01251776948798ea8e1">Particle::q</a></div><div class="ttdeci">double q</div><div class="ttdoc">Charge.</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00021">Particle.hpp:21</a></div></div>
-<div class="ttc" id="aclassParticle_html_acf1a0f3c978b06d76df5bb4279594467"><div class="ttname"><a href="classParticle.html#acf1a0f3c978b06d76df5bb4279594467">Particle::r_vec</a></div><div class="ttdeci">arma::vec::fixed&lt; 3 &gt; r_vec</div><div class="ttdoc">position</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00023">Particle.hpp:23</a></div></div>
-<div class="ttc" id="aclassParticle_html_aedcc7e1bc53b0e2b1a4a07c9a1b47563"><div class="ttname"><a href="classParticle.html#aedcc7e1bc53b0e2b1a4a07c9a1b47563">Particle::m</a></div><div class="ttdeci">double m</div><div class="ttdoc">Mass.</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00022">Particle.hpp:22</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a0112525d9e79a472e761f8ef402a339f"><div class="ttname"><a href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">PenningTrap::particles</a></div><div class="ttdeci">std::vector&lt; Particle &gt; particles</div><div class="ttdoc">The particles in the Penning trap.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00034">PenningTrap.hpp:34</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a045adb85e97a8e0c38fb36d2fd74eeee"><div class="ttname"><a href="classPenningTrap.html#a045adb85e97a8e0c38fb36d2fd74eeee">PenningTrap::total_force_external</a></div><div class="ttdeci">arma::vec total_force_external(int i)</div><div class="ttdoc">Calculate the total external force on a particle.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00065">PenningTrap.cpp:65</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a0cac3509aa96e71a26d3b2c902e27716"><div class="ttname"><a href="classPenningTrap.html#a0cac3509aa96e71a26d3b2c902e27716">PenningTrap::B_0</a></div><div class="ttdeci">double B_0</div><div class="ttdoc">Magnetic field strength.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00031">PenningTrap.hpp:31</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a135db7d991d9b88b00fde4edee71f78d"><div class="ttname"><a href="classPenningTrap.html#a135db7d991d9b88b00fde4edee71f78d">PenningTrap::total_force_particles</a></div><div class="ttdeci">arma::vec total_force_particles(int i)</div><div class="ttdoc">Calculate the total force on a particle from other particles.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00080">PenningTrap.cpp:80</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a2a3e7f480ba52e9f24d4c50c3981a784"><div class="ttname"><a href="classPenningTrap.html#a2a3e7f480ba52e9f24d4c50c3981a784">PenningTrap::external_B_field</a></div><div class="ttdeci">arma::vec external_B_field(arma::vec r)</div><div class="ttdoc">Calculate B at point r.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00043">PenningTrap.cpp:43</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a4790f41e4fbc6ede4991aa7bbda92182"><div class="ttname"><a href="classPenningTrap.html#a4790f41e4fbc6ede4991aa7bbda92182">PenningTrap::force_on_particle</a></div><div class="ttdeci">arma::vec force_on_particle(int i, int j)</div><div class="ttdoc">Calculate the force between 2 particles.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00050">PenningTrap.cpp:50</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a56544b6f4befb42984e9650cf2a40965"><div class="ttname"><a href="classPenningTrap.html#a56544b6f4befb42984e9650cf2a40965">PenningTrap::evolve_forward_euler</a></div><div class="ttdeci">void evolve_forward_euler(double dt)</div><div class="ttdoc">Go forward one timestep using the forward Euler method.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00167">PenningTrap.cpp:167</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a66dfe89c68716b9502927b97f59c27d2"><div class="ttname"><a href="classPenningTrap.html#a66dfe89c68716b9502927b97f59c27d2">PenningTrap::d</a></div><div class="ttdeci">double d</div><div class="ttdoc">Characteristic dimension.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00033">PenningTrap.hpp:33</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a6e9776ff5b149f01080800716455d7c8"><div class="ttname"><a href="classPenningTrap.html#a6e9776ff5b149f01080800716455d7c8">PenningTrap::add_particle</a></div><div class="ttdeci">void add_particle(Particle particle)</div><div class="ttdoc">Add a particle to the system.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00027">PenningTrap.cpp:27</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a715329844d75ec4c04f8391421fb4e89"><div class="ttname"><a href="classPenningTrap.html#a715329844d75ec4c04f8391421fb4e89">PenningTrap::V_0</a></div><div class="ttdeci">double V_0</div><div class="ttdoc">Applied potential.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00032">PenningTrap.hpp:32</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a81add5063bd5f29d77f0b5c299c6c560"><div class="ttname"><a href="classPenningTrap.html#a81add5063bd5f29d77f0b5c299c6c560">PenningTrap::PenningTrap</a></div><div class="ttdeci">PenningTrap(double B_0=T, double V_0=25.*V/1000., double d=500.)</div><div class="ttdoc">Set B_0, V_0 and d.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00020">PenningTrap.cpp:20</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a83cc7a04dae009ed8e75453c38fdf8be"><div class="ttname"><a href="classPenningTrap.html#a83cc7a04dae009ed8e75453c38fdf8be">PenningTrap::total_force</a></div><div class="ttdeci">arma::vec total_force(int i)</div><div class="ttdoc">calculate the total force on a particle.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00099">PenningTrap.cpp:99</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a978a2e2026a4b5308d5184712f81704b"><div class="ttname"><a href="classPenningTrap.html#a978a2e2026a4b5308d5184712f81704b">PenningTrap::external_E_field</a></div><div class="ttdeci">arma::vec external_E_field(arma::vec r)</div><div class="ttdoc">Calculate E at point r.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00032">PenningTrap.cpp:32</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_ab891b839c40eeb38d8a2a636c70090a9"><div class="ttname"><a href="classPenningTrap.html#ab891b839c40eeb38d8a2a636c70090a9">PenningTrap::evolve_RK4</a></div><div class="ttdeci">void evolve_RK4(double dt)</div><div class="ttdoc">Go forward one timestep using the RK4 method.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00104">PenningTrap.cpp:104</a></div></div>
+<div class="ttc" id="aclassParticle_html"><div class="ttname"><a href="classParticle.html">Particle</a></div><div class="ttdoc">A class that holds attributes of a particle.</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00021">Particle.hpp:21</a></div></div>
+<div class="ttc" id="aclassParticle_html_a566dcc1de4bdc01251776948798ea8e1"><div class="ttname"><a href="classParticle.html#a566dcc1de4bdc01251776948798ea8e1">Particle::q</a></div><div class="ttdeci">double q</div><div class="ttdoc">Charge.</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00023">Particle.hpp:23</a></div></div>
+<div class="ttc" id="aclassParticle_html_a879692772803d6ab65fa4993b54aea6e"><div class="ttname"><a href="classParticle.html#a879692772803d6ab65fa4993b54aea6e">Particle::v_vec</a></div><div class="ttdeci">vec_3d v_vec</div><div class="ttdoc">velocity</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00026">Particle.hpp:26</a></div></div>
+<div class="ttc" id="aclassParticle_html_aedcc7e1bc53b0e2b1a4a07c9a1b47563"><div class="ttname"><a href="classParticle.html#aedcc7e1bc53b0e2b1a4a07c9a1b47563">Particle::m</a></div><div class="ttdeci">double m</div><div class="ttdoc">Mass.</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00024">Particle.hpp:24</a></div></div>
+<div class="ttc" id="aclassParticle_html_af9497cd8f2dcad0fad54f571ddb383e6"><div class="ttname"><a href="classParticle.html#af9497cd8f2dcad0fad54f571ddb383e6">Particle::r_vec</a></div><div class="ttdeci">vec_3d r_vec</div><div class="ttdoc">position</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00025">Particle.hpp:25</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html"><div class="ttname"><a href="classPenningTrap.html">PenningTrap</a></div><div class="ttdoc">A class that simulates a Penning trap.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00030">PenningTrap.hpp:30</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a0112525d9e79a472e761f8ef402a339f"><div class="ttname"><a href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">PenningTrap::particles</a></div><div class="ttdeci">std::vector&lt; Particle &gt; particles</div><div class="ttdoc">The particles in the Penning trap.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00036">PenningTrap.hpp:36</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a0194be61c956a9259c747c23e4163c5b"><div class="ttname"><a href="classPenningTrap.html#a0194be61c956a9259c747c23e4163c5b">PenningTrap::fraction_of_particles_left</a></div><div class="ttdeci">double fraction_of_particles_left(double time, unsigned int steps, std::string method=&quot;rk4&quot;, bool particle_interaction=true)</div><div class="ttdoc">Simulate and calculate what fraction of particles are still left inside the Penning trap after the si...</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00266">PenningTrap.cpp:266</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a0cac3509aa96e71a26d3b2c902e27716"><div class="ttname"><a href="classPenningTrap.html#a0cac3509aa96e71a26d3b2c902e27716">PenningTrap::B_0</a></div><div class="ttdeci">double B_0</div><div class="ttdoc">Magnetic field strength.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00032">PenningTrap.hpp:32</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a1d58feaa2c9e34cbf26b1c5ed75ca9d9"><div class="ttname"><a href="classPenningTrap.html#a1d58feaa2c9e34cbf26b1c5ed75ca9d9">PenningTrap::external_E_field</a></div><div class="ttdeci">vec_3d external_E_field(vec_3d r)</div><div class="ttdoc">Calculate E at point r.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00087">PenningTrap.cpp:87</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a1f668c4433421136ad51741741aa1bc8"><div class="ttname"><a href="classPenningTrap.html#a1f668c4433421136ad51741741aa1bc8">PenningTrap::total_force</a></div><div class="ttdeci">vec_3d total_force(unsigned int i)</div><div class="ttdoc">calculate the total force on a particle p_i.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00146">PenningTrap.cpp:146</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a2f168622587709b9e3c49077f0b9a640"><div class="ttname"><a href="classPenningTrap.html#a2f168622587709b9e3c49077f0b9a640">PenningTrap::k_r</a></div><div class="ttdeci">sim_arr k_r</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00039">PenningTrap.hpp:39</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a36946152fd951b1f7c346c51ff900d8e"><div class="ttname"><a href="classPenningTrap.html#a36946152fd951b1f7c346c51ff900d8e">PenningTrap::evolve_RK4</a></div><div class="ttdeci">void evolve_RK4(double dt, bool particle_interaction=true)</div><div class="ttdoc">Go forward one timestep using the RK4 method.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00151">PenningTrap.cpp:151</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a43e74792ab4b3f9299f35cb64bdb2648"><div class="ttname"><a href="classPenningTrap.html#a43e74792ab4b3f9299f35cb64bdb2648">PenningTrap::r_func</a></div><div class="ttdeci">vec_3d r_func(unsigned int i, unsigned int j, double dt)</div><div class="ttdoc">Helper for evolve_RK4 when calculating  values.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00064">PenningTrap.cpp:64</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a46a954a0946def199e30fb300ba1c47b"><div class="ttname"><a href="classPenningTrap.html#a46a954a0946def199e30fb300ba1c47b">PenningTrap::total_force_particles</a></div><div class="ttdeci">vec_3d total_force_particles(unsigned int i)</div><div class="ttdoc">Calculate the total force on a particle p_i from other particles.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00129">PenningTrap.cpp:129</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a5331837e6dd7bce807a99edd2ba7e854"><div class="ttname"><a href="classPenningTrap.html#a5331837e6dd7bce807a99edd2ba7e854">PenningTrap::simulate</a></div><div class="ttdeci">sim_arr simulate(double time, unsigned int steps, std::string method=&quot;rk4&quot;, bool particle_interaction=true)</div><div class="ttdoc">Simulate the particle system inside the Penning trap over a certain amount of time.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00211">PenningTrap.cpp:211</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a66dfe89c68716b9502927b97f59c27d2"><div class="ttname"><a href="classPenningTrap.html#a66dfe89c68716b9502927b97f59c27d2">PenningTrap::d</a></div><div class="ttdeci">double d</div><div class="ttdoc">Characteristic dimension.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00034">PenningTrap.hpp:34</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a6e9776ff5b149f01080800716455d7c8"><div class="ttname"><a href="classPenningTrap.html#a6e9776ff5b149f01080800716455d7c8">PenningTrap::add_particle</a></div><div class="ttdeci">void add_particle(Particle particle)</div><div class="ttdoc">Add a particle to the system.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00082">PenningTrap.cpp:82</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a8ca4e21291f60fde619c14099d8c4e8e"><div class="ttname"><a href="classPenningTrap.html#a8ca4e21291f60fde619c14099d8c4e8e">PenningTrap::t</a></div><div class="ttdeci">double t</div><div class="ttdoc">Current time.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00035">PenningTrap.hpp:35</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a9ae34ad740a230e667e96bc6ee8730ce"><div class="ttname"><a href="classPenningTrap.html#a9ae34ad740a230e667e96bc6ee8730ce">PenningTrap::force_on_particle</a></div><div class="ttdeci">vec_3d force_on_particle(unsigned int i, unsigned int j)</div><div class="ttdoc">Calculate the force between 2 particles.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00100">PenningTrap.cpp:100</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_aaf105828121c4a33cc2b217453c20317"><div class="ttname"><a href="classPenningTrap.html#aaf105828121c4a33cc2b217453c20317">PenningTrap::V_0</a></div><div class="ttdeci">std::function&lt; double(double)&gt; V_0</div><div class="ttdoc">Applied potential.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00033">PenningTrap.hpp:33</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_ab9ea97a406534bbe621a95215144875e"><div class="ttname"><a href="classPenningTrap.html#ab9ea97a406534bbe621a95215144875e">PenningTrap::evolve_forward_euler</a></div><div class="ttdeci">void evolve_forward_euler(double dt, bool particle_interaction=true)</div><div class="ttdoc">Go forward one timestep using the forward Euler method.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00186">PenningTrap.cpp:186</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_abbb832a85139b1a56ebde57d7b8f9a57"><div class="ttname"><a href="classPenningTrap.html#abbb832a85139b1a56ebde57d7b8f9a57">PenningTrap::write_simulation_to_dir</a></div><div class="ttdeci">void write_simulation_to_dir(std::string path, double time, unsigned int steps, std::string method=&quot;rk4&quot;, bool particle_interaction=true)</div><div class="ttdoc">Simulate and write the displacement of all particles to files.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00240">PenningTrap.cpp:240</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_acbf065c9c125682329ad82a8d166554c"><div class="ttname"><a href="classPenningTrap.html#acbf065c9c125682329ad82a8d166554c">PenningTrap::external_B_field</a></div><div class="ttdeci">vec_3d external_B_field(vec_3d r)</div><div class="ttdoc">Calculate B at point r.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00095">PenningTrap.cpp:95</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_ae670d7de621acdb343b01af098086f63"><div class="ttname"><a href="classPenningTrap.html#ae670d7de621acdb343b01af098086f63">PenningTrap::PenningTrap</a></div><div class="ttdeci">PenningTrap(double B_0=T, std::function&lt; double(double)&gt; V_0=[](double t) { return 25. *V/1000.;}, double d=500., double t=0.)</div><div class="ttdoc">Constructor for the PenningTrap class.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00018">PenningTrap.cpp:18</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_ae72d203b0bfa1b9e72bea28cb2863c56"><div class="ttname"><a href="classPenningTrap.html#ae72d203b0bfa1b9e72bea28cb2863c56">PenningTrap::total_force_external</a></div><div class="ttdeci">vec_3d total_force_external(unsigned int i)</div><div class="ttdoc">Calculate the total external force on a particle.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00114">PenningTrap.cpp:114</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_ae9b5afdaa5cd366e94bd294452a1eed4"><div class="ttname"><a href="classPenningTrap.html#ae9b5afdaa5cd366e94bd294452a1eed4">PenningTrap::k_v</a></div><div class="ttdeci">sim_arr k_v</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00037">PenningTrap.hpp:37</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_af98a720da60b0e1a62aefa5f5cb37c1e"><div class="ttname"><a href="classPenningTrap.html#af98a720da60b0e1a62aefa5f5cb37c1e">PenningTrap::v_func</a></div><div class="ttdeci">vec_3d v_func(unsigned int i, unsigned int j, double dt)</div><div class="ttdoc">Helper for evolve_RK4 when calculating  values.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00046">PenningTrap.cpp:46</a></div></div>
 <div class="ttc" id="aconstants_8hpp_html"><div class="ttname"><a href="constants_8hpp.html">constants.hpp</a></div><div class="ttdoc">Library of constants.</div></div>
 <div class="ttc" id="aconstants_8hpp_html_a4e451456ad7e9276ed0afa42826e7ccb"><div class="ttname"><a href="constants_8hpp.html#a4e451456ad7e9276ed0afa42826e7ccb">K_E</a></div><div class="ttdeci">#define K_E</div><div class="ttdoc">Coulomb constant. unit: .</div><div class="ttdef"><b>Definition:</b> <a href="constants_8hpp_source.html#l00015">constants.hpp:15</a></div></div>
+<div class="ttc" id="atypedefs_8hpp_html"><div class="ttname"><a href="typedefs_8hpp.html">typedefs.hpp</a></div><div class="ttdoc">Useful typedefs for cleaner code.</div></div>
+<div class="ttc" id="atypedefs_8hpp_html_a7c2dfa854274262c4e00e4ef0ab2ce23"><div class="ttname"><a href="typedefs_8hpp.html#a7c2dfa854274262c4e00e4ef0ab2ce23">sim_cols</a></div><div class="ttdeci">std::vector&lt; arma::vec::fixed&lt; 3 &gt; &gt; sim_cols</div><div class="ttdoc">Typedef for the column of the result vector from simulating particles.</div><div class="ttdef"><b>Definition:</b> <a href="typedefs_8hpp_source.html#l00024">typedefs.hpp:24</a></div></div>
+<div class="ttc" id="atypedefs_8hpp_html_a9f33f4962c8fb62cc5ccd0e4e039a8df"><div class="ttname"><a href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a></div><div class="ttdeci">arma::vec::fixed&lt; 3 &gt; vec_3d</div><div class="ttdoc">Typedef for a fixed 3d arma vector.</div><div class="ttdef"><b>Definition:</b> <a href="typedefs_8hpp_source.html#l00036">typedefs.hpp:36</a></div></div>
+<div class="ttc" id="atypedefs_8hpp_html_aec69d34220fff45de238b9e01f2686af"><div class="ttname"><a href="typedefs_8hpp.html#aec69d34220fff45de238b9e01f2686af">sim_arr</a></div><div class="ttdeci">std::vector&lt; sim_cols &gt; sim_arr</div><div class="ttdoc">Typedef for the result of the simulate method.</div><div class="ttdef"><b>Definition:</b> <a href="typedefs_8hpp_source.html#l00032">typedefs.hpp:32</a></div></div>
 <div class="ttc" id="autils_8hpp_html"><div class="ttname"><a href="utils_8hpp.html">utils.hpp</a></div><div class="ttdoc">Function prototypes and macros that are useful.</div></div>
+<div class="ttc" id="autils_8hpp_html_a6fdd7217b750aff5b6295ece7cbdeffa"><div class="ttname"><a href="utils_8hpp.html#a6fdd7217b750aff5b6295ece7cbdeffa">mkpath</a></div><div class="ttdeci">bool mkpath(std::string path, int mode=0777)</div><div class="ttdoc">Make path given.</div><div class="ttdef"><b>Definition:</b> <a href="utils_8cpp_source.html#l00076">utils.cpp:76</a></div></div>
 </div><!-- fragment --></div><!-- contents -->
 </div><!-- doc-content -->
 <!-- start footer part -->
diff --git a/docs/PenningTrap_8hpp.html b/docs/PenningTrap_8hpp.html
index 306bc89..5f6ee45 100644
--- a/docs/PenningTrap_8hpp.html
+++ b/docs/PenningTrap_8hpp.html
@@ -110,6 +110,7 @@ $(document).ready(function(){initNavTree('PenningTrap_8hpp.html',''); initResiza
 <code>#include &lt;omp.h&gt;</code><br />
 <code>#include &quot;<a class="el" href="Particle_8hpp_source.html">Particle.hpp</a>&quot;</code><br />
 <code>#include &quot;<a class="el" href="constants_8hpp_source.html">constants.hpp</a>&quot;</code><br />
+<code>#include &quot;<a class="el" href="typedefs_8hpp_source.html">typedefs.hpp</a>&quot;</code><br />
 </div>
 <p><a href="PenningTrap_8hpp_source.html">Go to the source code of this file.</a></p>
 <table class="memberdecls">
diff --git a/docs/PenningTrap_8hpp_source.html b/docs/PenningTrap_8hpp_source.html
index 02b2aed..dfdddbe 100644
--- a/docs/PenningTrap_8hpp_source.html
+++ b/docs/PenningTrap_8hpp_source.html
@@ -110,63 +110,106 @@ $(document).ready(function(){initNavTree('PenningTrap_8hpp_source.html',''); ini
 <div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span> </div>
 <div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span><span class="preprocessor">#include &quot;<a class="code" href="Particle_8hpp.html">Particle.hpp</a>&quot;</span></div>
 <div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span><span class="preprocessor">#include &quot;<a class="code" href="constants_8hpp.html">constants.hpp</a>&quot;</span></div>
-<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span> </div>
-<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span><span class="preprocessor">#pragma omp declare reduction( + : arma::vec : omp_out += omp_in ) \</span></div>
-<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span><span class="preprocessor">  initializer( omp_priv = omp_orig )</span></div>
-<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span> </div>
-<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"><a class="line" href="classPenningTrap.html">   29</a></span><span class="keyword">class </span><a class="code hl_class" href="classPenningTrap.html">PenningTrap</a> {</div>
-<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span><span class="keyword">private</span>:</div>
-<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a0cac3509aa96e71a26d3b2c902e27716">   31</a></span>    <span class="keywordtype">double</span> <a class="code hl_variable" href="classPenningTrap.html#a0cac3509aa96e71a26d3b2c902e27716">B_0</a>; </div>
-<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a715329844d75ec4c04f8391421fb4e89">   32</a></span>    <span class="keywordtype">double</span> <a class="code hl_variable" href="classPenningTrap.html#a715329844d75ec4c04f8391421fb4e89">V_0</a>; </div>
-<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a66dfe89c68716b9502927b97f59c27d2">   33</a></span>    <span class="keywordtype">double</span> <a class="code hl_variable" href="classPenningTrap.html#a66dfe89c68716b9502927b97f59c27d2">d</a>; </div>
-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">   34</a></span>    std::vector&lt;Particle&gt; <a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>; </div>
-<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span> </div>
-<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span><span class="keyword">public</span>:</div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>    <a class="code hl_class" href="classPenningTrap.html">PenningTrap</a>(<span class="keywordtype">double</span> <a class="code hl_variable" href="classPenningTrap.html#a0cac3509aa96e71a26d3b2c902e27716">B_0</a> = <a class="code hl_define" href="constants_8hpp.html#a0acb682b8260ab1c60b918599864e2e5">T</a>, <span class="keywordtype">double</span> <a class="code hl_variable" href="classPenningTrap.html#a715329844d75ec4c04f8391421fb4e89">V_0</a> = 25.*<a class="code hl_define" href="constants_8hpp.html#af40a326b23c68a27cebe60f16634a2cb">V</a>/1000., <span class="keywordtype">double</span> <a class="code hl_variable" href="classPenningTrap.html#a66dfe89c68716b9502927b97f59c27d2">d</a> = 500.);</div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span> </div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classPenningTrap.html#a6e9776ff5b149f01080800716455d7c8">add_particle</a>(<a class="code hl_class" href="classParticle.html">Particle</a> particle);</div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span> </div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>    arma::vec <a class="code hl_function" href="classPenningTrap.html#a978a2e2026a4b5308d5184712f81704b">external_E_field</a>(arma::vec r);</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span> </div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>    arma::vec <a class="code hl_function" href="classPenningTrap.html#a2a3e7f480ba52e9f24d4c50c3981a784">external_B_field</a>(arma::vec r);</div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span> </div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    arma::vec <a class="code hl_function" href="classPenningTrap.html#a4790f41e4fbc6ede4991aa7bbda92182">force_on_particle</a>(<span class="keywordtype">int</span> i, <span class="keywordtype">int</span> j);</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span> </div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    arma::vec <a class="code hl_function" href="classPenningTrap.html#a045adb85e97a8e0c38fb36d2fd74eeee">total_force_external</a>(<span class="keywordtype">int</span> i);</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span> </div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>    arma::vec <a class="code hl_function" href="classPenningTrap.html#a135db7d991d9b88b00fde4edee71f78d">total_force_particles</a>(<span class="keywordtype">int</span> i);</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span> </div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>    arma::vec <a class="code hl_function" href="classPenningTrap.html#a83cc7a04dae009ed8e75453c38fdf8be">total_force</a>(<span class="keywordtype">int</span> i);</div>
-<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span> </div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classPenningTrap.html#ab891b839c40eeb38d8a2a636c70090a9">evolve_RK4</a>(<span class="keywordtype">double</span> dt);</div>
-<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span> </div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classPenningTrap.html#a56544b6f4befb42984e9650cf2a40965">evolve_forward_euler</a>(<span class="keywordtype">double</span> dt);</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span> </div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>    arma::vec get_particle(<span class="keywordtype">int</span> i);</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span> </div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>    <span class="keywordtype">double</span> get_d();</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>};</div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span> </div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span><span class="preprocessor">#endif</span></div>
+<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span><span class="preprocessor">#include &quot;<a class="code" href="typedefs_8hpp.html">typedefs.hpp</a>&quot;</span></div>
+<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span> </div>
+<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span><span class="preprocessor">#pragma omp declare reduction(+ : vec_3d : omp_out += omp_in)                  \</span></div>
+<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span><span class="preprocessor">    initializer(omp_priv = omp_orig)</span></div>
+<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span> </div>
+<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"><a class="line" href="classPenningTrap.html">   30</a></span><span class="keyword">class </span><a class="code hl_class" href="classPenningTrap.html">PenningTrap</a> {</div>
+<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span><span class="keyword">private</span>:</div>
+<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a0cac3509aa96e71a26d3b2c902e27716">   32</a></span>    <span class="keywordtype">double</span> <a class="code hl_variable" href="classPenningTrap.html#a0cac3509aa96e71a26d3b2c902e27716">B_0</a>;                        </div>
+<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"><a class="line" href="classPenningTrap.html#aaf105828121c4a33cc2b217453c20317">   33</a></span>    std::function&lt;double(<span class="keywordtype">double</span>)&gt; <a class="code hl_variable" href="classPenningTrap.html#aaf105828121c4a33cc2b217453c20317">V_0</a>; </div>
+<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a66dfe89c68716b9502927b97f59c27d2">   34</a></span>    <span class="keywordtype">double</span> <a class="code hl_variable" href="classPenningTrap.html#a66dfe89c68716b9502927b97f59c27d2">d</a>;                          </div>
+<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a8ca4e21291f60fde619c14099d8c4e8e">   35</a></span>    <span class="keywordtype">double</span> <a class="code hl_variable" href="classPenningTrap.html#a8ca4e21291f60fde619c14099d8c4e8e">t</a>;                          </div>
+<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">   36</a></span>    std::vector&lt;Particle&gt; <a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>;   </div>
+<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"><a class="line" href="classPenningTrap.html#ae9b5afdaa5cd366e94bd294452a1eed4">   37</a></span>    <a class="code hl_typedef" href="typedefs_8hpp.html#aec69d34220fff45de238b9e01f2686af">sim_arr</a> <a class="code hl_variable" href="classPenningTrap.html#ae9b5afdaa5cd366e94bd294452a1eed4">k_v</a>; </div>
+<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"><a class="line" href="classPenningTrap.html#a2f168622587709b9e3c49077f0b9a640">   39</a></span>    <a class="code hl_typedef" href="typedefs_8hpp.html#aec69d34220fff45de238b9e01f2686af">sim_arr</a> <a class="code hl_variable" href="classPenningTrap.html#a2f168622587709b9e3c49077f0b9a640">k_r</a>; </div>
+<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span> </div>
+<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>    <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> <a class="code hl_function" href="classPenningTrap.html#af98a720da60b0e1a62aefa5f5cb37c1e">v_func</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j, <span class="keywordtype">double</span> dt);</div>
+<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span> </div>
+<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>    <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> <a class="code hl_function" href="classPenningTrap.html#a43e74792ab4b3f9299f35cb64bdb2648">r_func</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j, <span class="keywordtype">double</span> dt);</div>
+<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span> </div>
+<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span><span class="keyword">public</span>:</div>
+<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>    <a class="code hl_class" href="classPenningTrap.html">PenningTrap</a>(</div>
+<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>        <span class="keywordtype">double</span> <a class="code hl_variable" href="classPenningTrap.html#a0cac3509aa96e71a26d3b2c902e27716">B_0</a> = <a class="code hl_define" href="constants_8hpp.html#a0acb682b8260ab1c60b918599864e2e5">T</a>,</div>
+<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>        std::function&lt;<span class="keywordtype">double</span>(<span class="keywordtype">double</span>)&gt; <a class="code hl_variable" href="classPenningTrap.html#aaf105828121c4a33cc2b217453c20317">V_0</a> =</div>
+<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>            [](<span class="keywordtype">double</span> <a class="code hl_variable" href="classPenningTrap.html#a8ca4e21291f60fde619c14099d8c4e8e">t</a>) { <span class="keywordflow">return</span> 25. * <a class="code hl_define" href="constants_8hpp.html#af40a326b23c68a27cebe60f16634a2cb">V</a> / 1000.; },</div>
+<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>        <span class="keywordtype">double</span> <a class="code hl_variable" href="classPenningTrap.html#a66dfe89c68716b9502927b97f59c27d2">d</a> = 500., <span class="keywordtype">double</span> <a class="code hl_variable" href="classPenningTrap.html#a8ca4e21291f60fde619c14099d8c4e8e">t</a> = 0.);</div>
+<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span> </div>
+<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>    <a class="code hl_class" href="classPenningTrap.html">PenningTrap</a>(</div>
+<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>        <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i, <span class="keywordtype">double</span> <a class="code hl_variable" href="classPenningTrap.html#a0cac3509aa96e71a26d3b2c902e27716">B_0</a> = <a class="code hl_define" href="constants_8hpp.html#a0acb682b8260ab1c60b918599864e2e5">T</a>,</div>
+<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>        std::function&lt;<span class="keywordtype">double</span>(<span class="keywordtype">double</span>)&gt; <a class="code hl_variable" href="classPenningTrap.html#aaf105828121c4a33cc2b217453c20317">V_0</a> =</div>
+<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>            [](<span class="keywordtype">double</span> <a class="code hl_variable" href="classPenningTrap.html#a8ca4e21291f60fde619c14099d8c4e8e">t</a>) { <span class="keywordflow">return</span> 25. * <a class="code hl_define" href="constants_8hpp.html#af40a326b23c68a27cebe60f16634a2cb">V</a> / 1000.; },</div>
+<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>        <span class="keywordtype">double</span> <a class="code hl_variable" href="classPenningTrap.html#a66dfe89c68716b9502927b97f59c27d2">d</a> = 500., <span class="keywordtype">double</span> <a class="code hl_variable" href="classPenningTrap.html#a8ca4e21291f60fde619c14099d8c4e8e">t</a> = 0.);</div>
+<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span> </div>
+<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>    <a class="code hl_class" href="classPenningTrap.html">PenningTrap</a>(</div>
+<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>        std::vector&lt;Particle&gt; <a class="code hl_variable" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a>, <span class="keywordtype">double</span> <a class="code hl_variable" href="classPenningTrap.html#a0cac3509aa96e71a26d3b2c902e27716">B_0</a> = <a class="code hl_define" href="constants_8hpp.html#a0acb682b8260ab1c60b918599864e2e5">T</a>,</div>
+<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>        std::function&lt;<span class="keywordtype">double</span>(<span class="keywordtype">double</span>)&gt; <a class="code hl_variable" href="classPenningTrap.html#aaf105828121c4a33cc2b217453c20317">V_0</a> =</div>
+<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>            [](<span class="keywordtype">double</span> <a class="code hl_variable" href="classPenningTrap.html#a8ca4e21291f60fde619c14099d8c4e8e">t</a>) { <span class="keywordflow">return</span> 25. * <a class="code hl_define" href="constants_8hpp.html#af40a326b23c68a27cebe60f16634a2cb">V</a> / 1000.; },</div>
+<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>        <span class="keywordtype">double</span> <a class="code hl_variable" href="classPenningTrap.html#a66dfe89c68716b9502927b97f59c27d2">d</a> = 500., <span class="keywordtype">double</span> <a class="code hl_variable" href="classPenningTrap.html#a8ca4e21291f60fde619c14099d8c4e8e">t</a> = 0.);</div>
+<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span> </div>
+<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classPenningTrap.html#a6e9776ff5b149f01080800716455d7c8">add_particle</a>(<a class="code hl_class" href="classParticle.html">Particle</a> particle);</div>
+<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span> </div>
+<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> <a class="code hl_function" href="classPenningTrap.html#a1d58feaa2c9e34cbf26b1c5ed75ca9d9">external_E_field</a>(<a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> r);</div>
+<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span> </div>
+<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>    <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> <a class="code hl_function" href="classPenningTrap.html#acbf065c9c125682329ad82a8d166554c">external_B_field</a>(<a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> r);</div>
+<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span> </div>
+<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>    <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> <a class="code hl_function" href="classPenningTrap.html#a9ae34ad740a230e667e96bc6ee8730ce">force_on_particle</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j);</div>
+<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span> </div>
+<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>    <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> <a class="code hl_function" href="classPenningTrap.html#ae72d203b0bfa1b9e72bea28cb2863c56">total_force_external</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i);</div>
+<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span> </div>
+<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>    <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> <a class="code hl_function" href="classPenningTrap.html#a46a954a0946def199e30fb300ba1c47b">total_force_particles</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i);</div>
+<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span> </div>
+<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>    <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> <a class="code hl_function" href="classPenningTrap.html#a1f668c4433421136ad51741741aa1bc8">total_force</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i);</div>
+<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span> </div>
+<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classPenningTrap.html#a36946152fd951b1f7c346c51ff900d8e">evolve_RK4</a>(<span class="keywordtype">double</span> dt, <span class="keywordtype">bool</span> particle_interaction = <span class="keyword">true</span>);</div>
+<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span> </div>
+<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classPenningTrap.html#ab9ea97a406534bbe621a95215144875e">evolve_forward_euler</a>(<span class="keywordtype">double</span> dt, <span class="keywordtype">bool</span> particle_interaction = <span class="keyword">true</span>);</div>
+<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span> </div>
+<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>    <a class="code hl_typedef" href="typedefs_8hpp.html#aec69d34220fff45de238b9e01f2686af">sim_arr</a> <a class="code hl_function" href="classPenningTrap.html#a5331837e6dd7bce807a99edd2ba7e854">simulate</a>(<span class="keywordtype">double</span> time, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> steps,</div>
+<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>                     std::string method = <span class="stringliteral">&quot;rk4&quot;</span>,</div>
+<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>                     <span class="keywordtype">bool</span> particle_interaction = <span class="keyword">true</span>);</div>
+<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span> </div>
+<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classPenningTrap.html#abbb832a85139b1a56ebde57d7b8f9a57">write_simulation_to_dir</a>(std::string path, <span class="keywordtype">double</span> time,</div>
+<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>                                 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> steps, std::string method = <span class="stringliteral">&quot;rk4&quot;</span>,</div>
+<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>                                 <span class="keywordtype">bool</span> particle_interaction = <span class="keyword">true</span>);</div>
+<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span> </div>
+<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>    <span class="keywordtype">double</span> <a class="code hl_function" href="classPenningTrap.html#a0194be61c956a9259c747c23e4163c5b">fraction_of_particles_left</a>(<span class="keywordtype">double</span> time, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> steps,</div>
+<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>                                      std::string method = <span class="stringliteral">&quot;rk4&quot;</span>,</div>
+<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>                                      <span class="keywordtype">bool</span> particle_interaction = <span class="keyword">true</span>);</div>
+<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>};</div>
+<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span> </div>
+<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span><span class="preprocessor">#endif</span></div>
 <div class="ttc" id="aParticle_8hpp_html"><div class="ttname"><a href="Particle_8hpp.html">Particle.hpp</a></div><div class="ttdoc">A class that holds the properties of a particle.</div></div>
-<div class="ttc" id="aclassParticle_html"><div class="ttname"><a href="classParticle.html">Particle</a></div><div class="ttdoc">A class that holds attributes of a particle.</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00019">Particle.hpp:19</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html"><div class="ttname"><a href="classPenningTrap.html">PenningTrap</a></div><div class="ttdoc">A class that simulates a Penning trap.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00029">PenningTrap.hpp:29</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a0112525d9e79a472e761f8ef402a339f"><div class="ttname"><a href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">PenningTrap::particles</a></div><div class="ttdeci">std::vector&lt; Particle &gt; particles</div><div class="ttdoc">The particles in the Penning trap.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00034">PenningTrap.hpp:34</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a045adb85e97a8e0c38fb36d2fd74eeee"><div class="ttname"><a href="classPenningTrap.html#a045adb85e97a8e0c38fb36d2fd74eeee">PenningTrap::total_force_external</a></div><div class="ttdeci">arma::vec total_force_external(int i)</div><div class="ttdoc">Calculate the total external force on a particle.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00065">PenningTrap.cpp:65</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a0cac3509aa96e71a26d3b2c902e27716"><div class="ttname"><a href="classPenningTrap.html#a0cac3509aa96e71a26d3b2c902e27716">PenningTrap::B_0</a></div><div class="ttdeci">double B_0</div><div class="ttdoc">Magnetic field strength.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00031">PenningTrap.hpp:31</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a135db7d991d9b88b00fde4edee71f78d"><div class="ttname"><a href="classPenningTrap.html#a135db7d991d9b88b00fde4edee71f78d">PenningTrap::total_force_particles</a></div><div class="ttdeci">arma::vec total_force_particles(int i)</div><div class="ttdoc">Calculate the total force on a particle from other particles.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00080">PenningTrap.cpp:80</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a2a3e7f480ba52e9f24d4c50c3981a784"><div class="ttname"><a href="classPenningTrap.html#a2a3e7f480ba52e9f24d4c50c3981a784">PenningTrap::external_B_field</a></div><div class="ttdeci">arma::vec external_B_field(arma::vec r)</div><div class="ttdoc">Calculate B at point r.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00043">PenningTrap.cpp:43</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a4790f41e4fbc6ede4991aa7bbda92182"><div class="ttname"><a href="classPenningTrap.html#a4790f41e4fbc6ede4991aa7bbda92182">PenningTrap::force_on_particle</a></div><div class="ttdeci">arma::vec force_on_particle(int i, int j)</div><div class="ttdoc">Calculate the force between 2 particles.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00050">PenningTrap.cpp:50</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a56544b6f4befb42984e9650cf2a40965"><div class="ttname"><a href="classPenningTrap.html#a56544b6f4befb42984e9650cf2a40965">PenningTrap::evolve_forward_euler</a></div><div class="ttdeci">void evolve_forward_euler(double dt)</div><div class="ttdoc">Go forward one timestep using the forward Euler method.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00167">PenningTrap.cpp:167</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a66dfe89c68716b9502927b97f59c27d2"><div class="ttname"><a href="classPenningTrap.html#a66dfe89c68716b9502927b97f59c27d2">PenningTrap::d</a></div><div class="ttdeci">double d</div><div class="ttdoc">Characteristic dimension.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00033">PenningTrap.hpp:33</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a6e9776ff5b149f01080800716455d7c8"><div class="ttname"><a href="classPenningTrap.html#a6e9776ff5b149f01080800716455d7c8">PenningTrap::add_particle</a></div><div class="ttdeci">void add_particle(Particle particle)</div><div class="ttdoc">Add a particle to the system.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00027">PenningTrap.cpp:27</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a715329844d75ec4c04f8391421fb4e89"><div class="ttname"><a href="classPenningTrap.html#a715329844d75ec4c04f8391421fb4e89">PenningTrap::V_0</a></div><div class="ttdeci">double V_0</div><div class="ttdoc">Applied potential.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00032">PenningTrap.hpp:32</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a83cc7a04dae009ed8e75453c38fdf8be"><div class="ttname"><a href="classPenningTrap.html#a83cc7a04dae009ed8e75453c38fdf8be">PenningTrap::total_force</a></div><div class="ttdeci">arma::vec total_force(int i)</div><div class="ttdoc">calculate the total force on a particle.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00099">PenningTrap.cpp:99</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a978a2e2026a4b5308d5184712f81704b"><div class="ttname"><a href="classPenningTrap.html#a978a2e2026a4b5308d5184712f81704b">PenningTrap::external_E_field</a></div><div class="ttdeci">arma::vec external_E_field(arma::vec r)</div><div class="ttdoc">Calculate E at point r.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00032">PenningTrap.cpp:32</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_ab891b839c40eeb38d8a2a636c70090a9"><div class="ttname"><a href="classPenningTrap.html#ab891b839c40eeb38d8a2a636c70090a9">PenningTrap::evolve_RK4</a></div><div class="ttdeci">void evolve_RK4(double dt)</div><div class="ttdoc">Go forward one timestep using the RK4 method.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00104">PenningTrap.cpp:104</a></div></div>
+<div class="ttc" id="aclassParticle_html"><div class="ttname"><a href="classParticle.html">Particle</a></div><div class="ttdoc">A class that holds attributes of a particle.</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00021">Particle.hpp:21</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html"><div class="ttname"><a href="classPenningTrap.html">PenningTrap</a></div><div class="ttdoc">A class that simulates a Penning trap.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00030">PenningTrap.hpp:30</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a0112525d9e79a472e761f8ef402a339f"><div class="ttname"><a href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">PenningTrap::particles</a></div><div class="ttdeci">std::vector&lt; Particle &gt; particles</div><div class="ttdoc">The particles in the Penning trap.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00036">PenningTrap.hpp:36</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a0194be61c956a9259c747c23e4163c5b"><div class="ttname"><a href="classPenningTrap.html#a0194be61c956a9259c747c23e4163c5b">PenningTrap::fraction_of_particles_left</a></div><div class="ttdeci">double fraction_of_particles_left(double time, unsigned int steps, std::string method=&quot;rk4&quot;, bool particle_interaction=true)</div><div class="ttdoc">Simulate and calculate what fraction of particles are still left inside the Penning trap after the si...</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00266">PenningTrap.cpp:266</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a0cac3509aa96e71a26d3b2c902e27716"><div class="ttname"><a href="classPenningTrap.html#a0cac3509aa96e71a26d3b2c902e27716">PenningTrap::B_0</a></div><div class="ttdeci">double B_0</div><div class="ttdoc">Magnetic field strength.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00032">PenningTrap.hpp:32</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a1d58feaa2c9e34cbf26b1c5ed75ca9d9"><div class="ttname"><a href="classPenningTrap.html#a1d58feaa2c9e34cbf26b1c5ed75ca9d9">PenningTrap::external_E_field</a></div><div class="ttdeci">vec_3d external_E_field(vec_3d r)</div><div class="ttdoc">Calculate E at point r.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00087">PenningTrap.cpp:87</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a1f668c4433421136ad51741741aa1bc8"><div class="ttname"><a href="classPenningTrap.html#a1f668c4433421136ad51741741aa1bc8">PenningTrap::total_force</a></div><div class="ttdeci">vec_3d total_force(unsigned int i)</div><div class="ttdoc">calculate the total force on a particle p_i.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00146">PenningTrap.cpp:146</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a2f168622587709b9e3c49077f0b9a640"><div class="ttname"><a href="classPenningTrap.html#a2f168622587709b9e3c49077f0b9a640">PenningTrap::k_r</a></div><div class="ttdeci">sim_arr k_r</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00039">PenningTrap.hpp:39</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a36946152fd951b1f7c346c51ff900d8e"><div class="ttname"><a href="classPenningTrap.html#a36946152fd951b1f7c346c51ff900d8e">PenningTrap::evolve_RK4</a></div><div class="ttdeci">void evolve_RK4(double dt, bool particle_interaction=true)</div><div class="ttdoc">Go forward one timestep using the RK4 method.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00151">PenningTrap.cpp:151</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a43e74792ab4b3f9299f35cb64bdb2648"><div class="ttname"><a href="classPenningTrap.html#a43e74792ab4b3f9299f35cb64bdb2648">PenningTrap::r_func</a></div><div class="ttdeci">vec_3d r_func(unsigned int i, unsigned int j, double dt)</div><div class="ttdoc">Helper for evolve_RK4 when calculating  values.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00064">PenningTrap.cpp:64</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a46a954a0946def199e30fb300ba1c47b"><div class="ttname"><a href="classPenningTrap.html#a46a954a0946def199e30fb300ba1c47b">PenningTrap::total_force_particles</a></div><div class="ttdeci">vec_3d total_force_particles(unsigned int i)</div><div class="ttdoc">Calculate the total force on a particle p_i from other particles.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00129">PenningTrap.cpp:129</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a5331837e6dd7bce807a99edd2ba7e854"><div class="ttname"><a href="classPenningTrap.html#a5331837e6dd7bce807a99edd2ba7e854">PenningTrap::simulate</a></div><div class="ttdeci">sim_arr simulate(double time, unsigned int steps, std::string method=&quot;rk4&quot;, bool particle_interaction=true)</div><div class="ttdoc">Simulate the particle system inside the Penning trap over a certain amount of time.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00211">PenningTrap.cpp:211</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a66dfe89c68716b9502927b97f59c27d2"><div class="ttname"><a href="classPenningTrap.html#a66dfe89c68716b9502927b97f59c27d2">PenningTrap::d</a></div><div class="ttdeci">double d</div><div class="ttdoc">Characteristic dimension.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00034">PenningTrap.hpp:34</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a6e9776ff5b149f01080800716455d7c8"><div class="ttname"><a href="classPenningTrap.html#a6e9776ff5b149f01080800716455d7c8">PenningTrap::add_particle</a></div><div class="ttdeci">void add_particle(Particle particle)</div><div class="ttdoc">Add a particle to the system.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00082">PenningTrap.cpp:82</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a8ca4e21291f60fde619c14099d8c4e8e"><div class="ttname"><a href="classPenningTrap.html#a8ca4e21291f60fde619c14099d8c4e8e">PenningTrap::t</a></div><div class="ttdeci">double t</div><div class="ttdoc">Current time.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00035">PenningTrap.hpp:35</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a9ae34ad740a230e667e96bc6ee8730ce"><div class="ttname"><a href="classPenningTrap.html#a9ae34ad740a230e667e96bc6ee8730ce">PenningTrap::force_on_particle</a></div><div class="ttdeci">vec_3d force_on_particle(unsigned int i, unsigned int j)</div><div class="ttdoc">Calculate the force between 2 particles.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00100">PenningTrap.cpp:100</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_aaf105828121c4a33cc2b217453c20317"><div class="ttname"><a href="classPenningTrap.html#aaf105828121c4a33cc2b217453c20317">PenningTrap::V_0</a></div><div class="ttdeci">std::function&lt; double(double)&gt; V_0</div><div class="ttdoc">Applied potential.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00033">PenningTrap.hpp:33</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_ab9ea97a406534bbe621a95215144875e"><div class="ttname"><a href="classPenningTrap.html#ab9ea97a406534bbe621a95215144875e">PenningTrap::evolve_forward_euler</a></div><div class="ttdeci">void evolve_forward_euler(double dt, bool particle_interaction=true)</div><div class="ttdoc">Go forward one timestep using the forward Euler method.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00186">PenningTrap.cpp:186</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_abbb832a85139b1a56ebde57d7b8f9a57"><div class="ttname"><a href="classPenningTrap.html#abbb832a85139b1a56ebde57d7b8f9a57">PenningTrap::write_simulation_to_dir</a></div><div class="ttdeci">void write_simulation_to_dir(std::string path, double time, unsigned int steps, std::string method=&quot;rk4&quot;, bool particle_interaction=true)</div><div class="ttdoc">Simulate and write the displacement of all particles to files.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00240">PenningTrap.cpp:240</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_acbf065c9c125682329ad82a8d166554c"><div class="ttname"><a href="classPenningTrap.html#acbf065c9c125682329ad82a8d166554c">PenningTrap::external_B_field</a></div><div class="ttdeci">vec_3d external_B_field(vec_3d r)</div><div class="ttdoc">Calculate B at point r.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00095">PenningTrap.cpp:95</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_ae72d203b0bfa1b9e72bea28cb2863c56"><div class="ttname"><a href="classPenningTrap.html#ae72d203b0bfa1b9e72bea28cb2863c56">PenningTrap::total_force_external</a></div><div class="ttdeci">vec_3d total_force_external(unsigned int i)</div><div class="ttdoc">Calculate the total external force on a particle.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00114">PenningTrap.cpp:114</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_ae9b5afdaa5cd366e94bd294452a1eed4"><div class="ttname"><a href="classPenningTrap.html#ae9b5afdaa5cd366e94bd294452a1eed4">PenningTrap::k_v</a></div><div class="ttdeci">sim_arr k_v</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00037">PenningTrap.hpp:37</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_af98a720da60b0e1a62aefa5f5cb37c1e"><div class="ttname"><a href="classPenningTrap.html#af98a720da60b0e1a62aefa5f5cb37c1e">PenningTrap::v_func</a></div><div class="ttdeci">vec_3d v_func(unsigned int i, unsigned int j, double dt)</div><div class="ttdoc">Helper for evolve_RK4 when calculating  values.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00046">PenningTrap.cpp:46</a></div></div>
 <div class="ttc" id="aconstants_8hpp_html"><div class="ttname"><a href="constants_8hpp.html">constants.hpp</a></div><div class="ttdoc">Library of constants.</div></div>
 <div class="ttc" id="aconstants_8hpp_html_a0acb682b8260ab1c60b918599864e2e5"><div class="ttname"><a href="constants_8hpp.html#a0acb682b8260ab1c60b918599864e2e5">T</a></div><div class="ttdeci">#define T</div><div class="ttdoc">1 Tesla. unit:</div><div class="ttdef"><b>Definition:</b> <a href="constants_8hpp_source.html#l00017">constants.hpp:17</a></div></div>
 <div class="ttc" id="aconstants_8hpp_html_af40a326b23c68a27cebe60f16634a2cb"><div class="ttname"><a href="constants_8hpp.html#af40a326b23c68a27cebe60f16634a2cb">V</a></div><div class="ttdeci">#define V</div><div class="ttdoc">1 Volt. unit:</div><div class="ttdef"><b>Definition:</b> <a href="constants_8hpp_source.html#l00019">constants.hpp:19</a></div></div>
+<div class="ttc" id="atypedefs_8hpp_html"><div class="ttname"><a href="typedefs_8hpp.html">typedefs.hpp</a></div><div class="ttdoc">Useful typedefs for cleaner code.</div></div>
+<div class="ttc" id="atypedefs_8hpp_html_a9f33f4962c8fb62cc5ccd0e4e039a8df"><div class="ttname"><a href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a></div><div class="ttdeci">arma::vec::fixed&lt; 3 &gt; vec_3d</div><div class="ttdoc">Typedef for a fixed 3d arma vector.</div><div class="ttdef"><b>Definition:</b> <a href="typedefs_8hpp_source.html#l00036">typedefs.hpp:36</a></div></div>
+<div class="ttc" id="atypedefs_8hpp_html_aec69d34220fff45de238b9e01f2686af"><div class="ttname"><a href="typedefs_8hpp.html#aec69d34220fff45de238b9e01f2686af">sim_arr</a></div><div class="ttdeci">std::vector&lt; sim_cols &gt; sim_arr</div><div class="ttdoc">Typedef for the result of the simulate method.</div><div class="ttdef"><b>Definition:</b> <a href="typedefs_8hpp_source.html#l00032">typedefs.hpp:32</a></div></div>
 </div><!-- fragment --></div><!-- contents -->
 </div><!-- doc-content -->
 <!-- start footer part -->
diff --git a/docs/animate__100__particles_8py_source.html b/docs/animate__100__particles_8py_source.html
index 80feb43..af734ca 100644
--- a/docs/animate__100__particles_8py_source.html
+++ b/docs/animate__100__particles_8py_source.html
@@ -103,68 +103,75 @@ $(document).ready(function(){initNavTree('animate__100__particles_8py_source.htm
 <div class="contents">
 <div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span><span class="keyword">import</span> matplotlib.pyplot <span class="keyword">as</span> plt</div>
 <div class="line"><a id="l00002" name="l00002"></a><span class="lineno">    2</span><span class="keyword">import</span> numpy <span class="keyword">as</span> np</div>
-<div class="line"><a id="l00003" name="l00003"></a><span class="lineno">    3</span><span class="keyword">from</span> mpl_toolkits.mplot3d <span class="keyword">import</span> Axes3D</div>
-<div class="line"><a id="l00004" name="l00004"></a><span class="lineno">    4</span><span class="keyword">from</span> matplotlib <span class="keyword">import</span> animation</div>
+<div class="line"><a id="l00003" name="l00003"></a><span class="lineno">    3</span><span class="keyword">from</span> matplotlib <span class="keyword">import</span> animation</div>
+<div class="line"><a id="l00004" name="l00004"></a><span class="lineno">    4</span><span class="keyword">from</span> mpl_toolkits.mplot3d <span class="keyword">import</span> Axes3D</div>
 <div class="line"><a id="l00005" name="l00005"></a><span class="lineno">    5</span> </div>
-<div class="line"><a id="l00006" name="l00006"></a><span class="lineno">    6</span><span class="keyword">def </span>get_data(files):</div>
-<div class="line"><a id="l00007" name="l00007"></a><span class="lineno">    7</span>    res = []</div>
-<div class="line"><a id="l00008" name="l00008"></a><span class="lineno">    8</span>    <span class="keywordflow">for</span> file <span class="keywordflow">in</span> files:</div>
-<div class="line"><a id="l00009" name="l00009"></a><span class="lineno">    9</span>        arr = [[], [], []]</div>
-<div class="line"><a id="l00010" name="l00010"></a><span class="lineno">   10</span>        <span class="keyword">with</span> open(file, encoding=<span class="stringliteral">&quot;utf8&quot;</span>) <span class="keyword">as</span> f:</div>
-<div class="line"><a id="l00011" name="l00011"></a><span class="lineno">   11</span>            lines = f.readlines()</div>
-<div class="line"><a id="l00012" name="l00012"></a><span class="lineno">   12</span> </div>
-<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span>            <span class="keywordflow">for</span> line <span class="keywordflow">in</span> lines:</div>
-<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span>                xi,yi,zi = map(float, line.strip().split(<span class="stringliteral">&quot;,&quot;</span>))</div>
-<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span>                arr[0].append(xi)</div>
-<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span>                arr[1].append(yi)</div>
-<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span>                arr[2].append(zi)</div>
-<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span>        res.append(arr)</div>
-<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span> </div>
-<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span>    <span class="keywordflow">return</span> np.array(res)</div>
-<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span> </div>
-<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span><span class="keyword">def </span>update(num, lines, arr):</div>
-<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span>    <span class="keywordflow">for</span> line, a <span class="keywordflow">in</span> zip(lines, arr):</div>
-<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span>        line.set_data(a[:2, num])</div>
-<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span>        line.set_3d_properties(a[2, num])</div>
-<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span>    </div>
-<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span> </div>
+<div class="line"><a id="l00006" name="l00006"></a><span class="lineno">    6</span> </div>
+<div class="line"><a id="l00007" name="l00007"></a><span class="lineno">    7</span><span class="keyword">def </span>get_data(files):</div>
+<div class="line"><a id="l00008" name="l00008"></a><span class="lineno">    8</span>    res = []</div>
+<div class="line"><a id="l00009" name="l00009"></a><span class="lineno">    9</span>    <span class="keywordflow">for</span> file <span class="keywordflow">in</span> files:</div>
+<div class="line"><a id="l00010" name="l00010"></a><span class="lineno">   10</span>        arr = [[], [], []]</div>
+<div class="line"><a id="l00011" name="l00011"></a><span class="lineno">   11</span>        <span class="keyword">with</span> open(file, encoding=<span class="stringliteral">&quot;utf8&quot;</span>) <span class="keyword">as</span> f:</div>
+<div class="line"><a id="l00012" name="l00012"></a><span class="lineno">   12</span>            lines = f.readlines()</div>
+<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span> </div>
+<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span>            <span class="keywordflow">for</span> line <span class="keywordflow">in</span> lines:</div>
+<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span>                xi, yi, zi = map(float, line.strip().split(<span class="stringliteral">&quot;,&quot;</span>))</div>
+<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span>                arr[0].append(xi)</div>
+<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span>                arr[1].append(yi)</div>
+<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span>                arr[2].append(zi)</div>
+<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span>        res.append(arr)</div>
+<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span> </div>
+<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span>    <span class="keywordflow">return</span> np.array(res)</div>
+<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span> </div>
+<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span> </div>
+<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span><span class="keyword">def </span>update(num, lines, arr):</div>
+<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span>    <span class="keywordflow">for</span> line, a <span class="keywordflow">in</span> zip(lines, arr):</div>
+<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span>        line.set_data(a[:2, num - 1 : num])</div>
+<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span>        line.set_3d_properties(a[2, num])</div>
 <div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span> </div>
-<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span><span class="keyword">def </span>animate():</div>
-<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span>    plt.style.use(<span class="stringliteral">&quot;dark_background&quot;</span>)</div>
-<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span>    fig = plt.figure()</div>
-<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>    ax = fig.add_subplot(projection=<span class="stringliteral">&quot;3d&quot;</span>)</div>
-<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span> </div>
+<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span> </div>
+<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span><span class="keyword">def </span>animate():</div>
+<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span>    plt.style.use(<span class="stringliteral">&quot;dark_background&quot;</span>)</div>
+<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>    fig = plt.figure()</div>
+<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>    ax = fig.add_subplot(projection=<span class="stringliteral">&quot;3d&quot;</span>)</div>
 <div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span> </div>
-<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>    arr = get_data([f<span class="stringliteral">&quot;output/p{i}_RK4.txt&quot;</span> <span class="keywordflow">for</span> i <span class="keywordflow">in</span> range(100)])</div>
+<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>    arr = get_data([f<span class="stringliteral">&quot;output/simulate_100_particles/particle_{i}.txt&quot;</span> <span class="keywordflow">for</span> i <span class="keywordflow">in</span> range(100)])</div>
 <div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span> </div>
-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>    arr = arr[:,:,::10]</div>
+<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>    arr = arr[:, :, ::10]</div>
 <div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span> </div>
 <div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>    N = len(arr[0][0])</div>
 <div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span> </div>
-<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>    lines = [ax.plot(*a[:,1], <span class="stringliteral">&quot;o&quot;</span>)[0] <span class="keywordflow">for</span> a <span class="keywordflow">in</span> arr]</div>
+<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>    lines = [ax.plot(*a[:, 1], <span class="stringliteral">&quot;o&quot;</span>)[0] <span class="keywordflow">for</span> a <span class="keywordflow">in</span> arr]</div>
 <div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span> </div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>    ax.set_xlim3d([-500.0, 500.0])</div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>    ax.set_xlabel(<span class="stringliteral">&#39;X&#39;</span>)</div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span> </div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>    ax.set_ylim3d([-500.0, 500.0])</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>    ax.set_ylabel(<span class="stringliteral">&#39;Y&#39;</span>)</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span> </div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>    ax.set_zlim3d([-500.0, 500.0])</div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>    ax.set_zlabel(<span class="stringliteral">&#39;Z&#39;</span>)  </div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span> </div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>    ani = animation.FuncAnimation(fig, update, N, fargs=(lines, arr), </div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>                                  interval=1,</div>
-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>                                  blit=<span class="keyword">False</span>)</div>
+<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>    ax.set_title(<span class="stringliteral">&quot;100 particles inside a Penning trap&quot;</span>)</div>
+<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>    plt.figtext(</div>
+<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>        0.5,</div>
+<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>        0.01,</div>
+<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>        <span class="stringliteral">&quot;100 randomly generated particles &quot;</span></div>
+<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>        <span class="stringliteral">&quot;evolving over a time of 50 microseconds.&quot;</span>,</div>
+<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>        fontsize=12,</div>
+<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>        horizontalalignment=<span class="stringliteral">&quot;center&quot;</span>,</div>
+<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>    )</div>
+<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span> </div>
+<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>    ax.set_xlim3d([-500.0, 500.0])</div>
+<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>    ax.set_xlabel(<span class="stringliteral">&quot;X (micrometers)&quot;</span>)</div>
 <div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span> </div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span> </div>
-<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>    ani.save(<span class="stringliteral">&quot;100_particles.gif&quot;</span>, writer=animation.FFMpegFileWriter(fps=30))</div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    plt.show()</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span> </div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span> </div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span><span class="keywordflow">if</span> __name__ == <span class="stringliteral">&quot;__main__&quot;</span>:</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>    animate()</div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span> </div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span> </div>
+<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>    ax.set_ylim3d([-500.0, 500.0])</div>
+<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>    ax.set_ylabel(<span class="stringliteral">&quot;Y (micrometers)&quot;</span>)</div>
+<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span> </div>
+<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    ax.set_zlim3d([-500.0, 500.0])</div>
+<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>    ax.set_zlabel(<span class="stringliteral">&quot;Z (micrometers)&quot;</span>)</div>
+<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span> </div>
+<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>    ani = animation.FuncAnimation(</div>
+<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>        fig, update, N, fargs=(lines, arr), interval=1, blit=<span class="keyword">False</span></div>
+<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>    )</div>
+<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span> </div>
+<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    <span class="comment"># ani.save(&quot;../images/100_particles.gif&quot;, writer=animation.FFMpegFileWriter(fps=50))</span></div>
+<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    plt.show()</div>
+<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span> </div>
+<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span> </div>
+<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span><span class="keywordflow">if</span> __name__ == <span class="stringliteral">&quot;__main__&quot;</span>:</div>
+<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>    animate()</div>
 </div><!-- fragment --></div><!-- contents -->
 </div><!-- doc-content -->
 <!-- start footer part -->
diff --git a/docs/bug.html b/docs/bug.html
index bbcbbea..8ed5241 100644
--- a/docs/bug.html
+++ b/docs/bug.html
@@ -105,21 +105,23 @@ $(document).ready(function(){initNavTree('bug.html',''); initResizable(); });
 <dt>File <a class="el" href="constants_8hpp.html">constants.hpp</a>  </dt>
 <dd><a class="anchor" id="_bug000001"></a>No known bugs  </dd>
 <dt>File <a class="el" href="main_8cpp.html">main.cpp</a>  </dt>
-<dd><a class="anchor" id="_bug000005"></a>No known bugs  </dd>
+<dd><a class="anchor" id="_bug000006"></a>No known bugs  </dd>
 <dt>File <a class="el" href="Particle_8cpp.html">Particle.cpp</a>  </dt>
-<dd><a class="anchor" id="_bug000006"></a>No known bugs </dd>
+<dd><a class="anchor" id="_bug000007"></a>No known bugs  </dd>
 <dt>File <a class="el" href="Particle_8hpp.html">Particle.hpp</a>  </dt>
 <dd><a class="anchor" id="_bug000002"></a>No known bugs  </dd>
 <dt>File <a class="el" href="PenningTrap_8cpp.html">PenningTrap.cpp</a>  </dt>
-<dd><a class="anchor" id="_bug000007"></a>No known bugs </dd>
+<dd><a class="anchor" id="_bug000008"></a>No known bugs  </dd>
 <dt>File <a class="el" href="PenningTrap_8hpp.html">PenningTrap.hpp</a>  </dt>
 <dd><a class="anchor" id="_bug000003"></a>No known bugs  </dd>
 <dt>File <a class="el" href="test__suite_8cpp.html">test_suite.cpp</a>  </dt>
-<dd><a class="anchor" id="_bug000008"></a>No known bugs  </dd>
-<dt>File <a class="el" href="utils_8cpp.html">utils.cpp</a>  </dt>
 <dd><a class="anchor" id="_bug000009"></a>No known bugs  </dd>
+<dt>File <a class="el" href="typedefs_8hpp.html">typedefs.hpp</a>  </dt>
+<dd><a class="anchor" id="_bug000004"></a>No known bugs  </dd>
+<dt>File <a class="el" href="utils_8cpp.html">utils.cpp</a>  </dt>
+<dd><a class="anchor" id="_bug000010"></a>No known bugs  </dd>
 <dt>File <a class="el" href="utils_8hpp.html">utils.hpp</a>  </dt>
-<dd><a class="anchor" id="_bug000004"></a>No known bugs </dd>
+<dd><a class="anchor" id="_bug000005"></a>No known bugs </dd>
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 </div></div><!-- contents -->
 </div><!-- PageDoc -->
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index 02f2b23..b3fc92b 100644
--- a/docs/classParticle-members.html
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@@ -105,11 +105,11 @@ $(document).ready(function(){initNavTree('classParticle.html',''); initResizable
 <p>This is the complete list of members for <a class="el" href="classParticle.html">Particle</a>, including all inherited members.</p>
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   <tr class="even"><td class="entry"><a class="el" href="classParticle.html#aedcc7e1bc53b0e2b1a4a07c9a1b47563">m</a></td><td class="entry"><a class="el" href="classParticle.html">Particle</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
-  <tr class="odd"><td class="entry"><a class="el" href="classParticle.html#a00e108823877a25513ccae7cac011b4c">Particle</a>(double q, double m, arma::vec::fixed&lt; 3 &gt; r_vec, arma::vec::fixed&lt; 3 &gt; v_vec)</td><td class="entry"><a class="el" href="classParticle.html">Particle</a></td><td class="entry"></td></tr>
+  <tr class="odd"><td class="entry"><a class="el" href="classParticle.html#a7af9f8d1fef63dd7643b06629ac7bef4">Particle</a>(double q, double m, vec_3d r_vec, vec_3d v_vec)</td><td class="entry"><a class="el" href="classParticle.html">Particle</a></td><td class="entry"></td></tr>
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   <tr class="odd"><td class="entry"><a class="el" href="classParticle.html#a566dcc1de4bdc01251776948798ea8e1">q</a></td><td class="entry"><a class="el" href="classParticle.html">Particle</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
-  <tr class="even"><td class="entry"><a class="el" href="classParticle.html#acf1a0f3c978b06d76df5bb4279594467">r_vec</a></td><td class="entry"><a class="el" href="classParticle.html">Particle</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
-  <tr class="odd"><td class="entry"><a class="el" href="classParticle.html#a4a5d22c7aeca66f67d083f270cba25df">v_vec</a></td><td class="entry"><a class="el" href="classParticle.html">Particle</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
+  <tr class="even"><td class="entry"><a class="el" href="classParticle.html#af9497cd8f2dcad0fad54f571ddb383e6">r_vec</a></td><td class="entry"><a class="el" href="classParticle.html">Particle</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
+  <tr class="odd"><td class="entry"><a class="el" href="classParticle.html#a879692772803d6ab65fa4993b54aea6e">v_vec</a></td><td class="entry"><a class="el" href="classParticle.html">Particle</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
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diff --git a/docs/classParticle.html b/docs/classParticle.html
index 997eb37..271a213 100644
--- a/docs/classParticle.html
+++ b/docs/classParticle.html
@@ -114,9 +114,9 @@ $(document).ready(function(){initNavTree('classParticle.html',''); initResizable
 <table class="memberdecls">
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-<tr class="memitem:a00e108823877a25513ccae7cac011b4c"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classParticle.html#a00e108823877a25513ccae7cac011b4c">Particle</a> (double <a class="el" href="classParticle.html#a566dcc1de4bdc01251776948798ea8e1">q</a>, double <a class="el" href="classParticle.html#aedcc7e1bc53b0e2b1a4a07c9a1b47563">m</a>, arma::vec::fixed&lt; 3 &gt; <a class="el" href="classParticle.html#acf1a0f3c978b06d76df5bb4279594467">r_vec</a>, arma::vec::fixed&lt; 3 &gt; <a class="el" href="classParticle.html#a4a5d22c7aeca66f67d083f270cba25df">v_vec</a>)</td></tr>
-<tr class="memdesc:a00e108823877a25513ccae7cac011b4c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Initialize the particle.  <br /></td></tr>
-<tr class="separator:a00e108823877a25513ccae7cac011b4c"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a7af9f8d1fef63dd7643b06629ac7bef4"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classParticle.html#a7af9f8d1fef63dd7643b06629ac7bef4">Particle</a> (double <a class="el" href="classParticle.html#a566dcc1de4bdc01251776948798ea8e1">q</a>, double <a class="el" href="classParticle.html#aedcc7e1bc53b0e2b1a4a07c9a1b47563">m</a>, <a class="el" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> <a class="el" href="classParticle.html#af9497cd8f2dcad0fad54f571ddb383e6">r_vec</a>, <a class="el" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> <a class="el" href="classParticle.html#a879692772803d6ab65fa4993b54aea6e">v_vec</a>)</td></tr>
+<tr class="memdesc:a7af9f8d1fef63dd7643b06629ac7bef4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Initialize the particle.  <br /></td></tr>
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-<tr class="memitem:acf1a0f3c978b06d76df5bb4279594467"><td class="memItemLeft" align="right" valign="top">arma::vec::fixed&lt; 3 &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classParticle.html#acf1a0f3c978b06d76df5bb4279594467">r_vec</a></td></tr>
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-<tr class="memdesc:a4a5d22c7aeca66f67d083f270cba25df"><td class="mdescLeft">&#160;</td><td class="mdescRight">velocity  <br /></td></tr>
-<tr class="separator:a4a5d22c7aeca66f67d083f270cba25df"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:af9497cd8f2dcad0fad54f571ddb383e6"><td class="memItemLeft" align="right" valign="top"><a class="el" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classParticle.html#af9497cd8f2dcad0fad54f571ddb383e6">r_vec</a></td></tr>
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+<tr class="memdesc:a879692772803d6ab65fa4993b54aea6e"><td class="mdescLeft">&#160;</td><td class="mdescRight">velocity  <br /></td></tr>
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@@ -142,10 +142,10 @@ Friends</h2></td></tr>
 <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
 <div class="textblock"><p>A class that holds attributes of a particle. </p>
 
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+<p class="definition">Definition at line <a class="el" href="Particle_8hpp_source.html#l00021">21</a> of file <a class="el" href="Particle_8hpp_source.html">Particle.hpp</a>.</p>
 </div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
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         <tr>
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-          <td class="paramtype">arma::vec::fixed&lt; 3 &gt;&#160;</td>
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 <p>Initialize the particle. </p>
-<p>Initialize the particle with a charge, mass, position and velocity. </p>
+<p>Initialize the particle with a charge, mass, position and velocity.</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">q</td><td>The charge of the particle </td></tr>
+    <tr><td class="paramname">m</td><td>The mass of the particle </td></tr>
+    <tr><td class="paramname">r_vec</td><td>The initial position of the particle </td></tr>
+    <tr><td class="paramname">v_vec</td><td>The initial velocity of the particle </td></tr>
+  </table>
+  </dd>
+</dl>
 
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+<p class="definition">Definition at line <a class="el" href="Particle_8cpp_source.html#l00015">15</a> of file <a class="el" href="Particle_8cpp_source.html">Particle.cpp</a>.</p>
 
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 <p>Make private attributes available for <a class="el" href="classPenningTrap.html" title="A class that simulates a Penning trap.">PenningTrap</a>. </p>
 
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+<p class="definition">Definition at line <a class="el" href="Particle_8hpp_source.html#l00043">43</a> of file <a class="el" href="Particle_8hpp_source.html">Particle.hpp</a>.</p>
 
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 <p>Mass. </p>
 
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+<p class="definition">Definition at line <a class="el" href="Particle_8hpp_source.html#l00024">24</a> of file <a class="el" href="Particle_8hpp_source.html">Particle.hpp</a>.</p>
 
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 <p>Charge. </p>
 
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+<p class="definition">Definition at line <a class="el" href="Particle_8hpp_source.html#l00023">23</a> of file <a class="el" href="Particle_8hpp_source.html">Particle.hpp</a>.</p>
 
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+<p class="definition">Definition at line <a class="el" href="Particle_8hpp_source.html#l00025">25</a> of file <a class="el" href="Particle_8hpp_source.html">Particle.hpp</a>.</p>
 
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+<p class="definition">Definition at line <a class="el" href="Particle_8hpp_source.html#l00026">26</a> of file <a class="el" href="Particle_8hpp_source.html">Particle.hpp</a>.</p>
 
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index 113132c..71255c1 100644
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-    [ "Particle", "classParticle.html#a00e108823877a25513ccae7cac011b4c", null ],
+    [ "Particle", "classParticle.html#a7af9f8d1fef63dd7643b06629ac7bef4", null ],
     [ "PenningTrap", "classParticle.html#aa797d319549dc2a0beb06cdbfd430232", null ],
     [ "m", "classParticle.html#aedcc7e1bc53b0e2b1a4a07c9a1b47563", null ],
     [ "q", "classParticle.html#a566dcc1de4bdc01251776948798ea8e1", null ],
-    [ "r_vec", "classParticle.html#acf1a0f3c978b06d76df5bb4279594467", null ],
-    [ "v_vec", "classParticle.html#a4a5d22c7aeca66f67d083f270cba25df", null ]
+    [ "r_vec", "classParticle.html#af9497cd8f2dcad0fad54f571ddb383e6", null ],
+    [ "v_vec", "classParticle.html#a879692772803d6ab65fa4993b54aea6e", null ]
 ];
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-  <tr class="odd"><td class="entry"><a class="el" href="classPenningTrap.html#a56544b6f4befb42984e9650cf2a40965">evolve_forward_euler</a>(double dt)</td><td class="entry"><a class="el" href="classPenningTrap.html">PenningTrap</a></td><td class="entry"></td></tr>
-  <tr class="even"><td class="entry"><a class="el" href="classPenningTrap.html#ab891b839c40eeb38d8a2a636c70090a9">evolve_RK4</a>(double dt)</td><td class="entry"><a class="el" href="classPenningTrap.html">PenningTrap</a></td><td class="entry"></td></tr>
-  <tr class="odd"><td class="entry"><a class="el" href="classPenningTrap.html#a2a3e7f480ba52e9f24d4c50c3981a784">external_B_field</a>(arma::vec r)</td><td class="entry"><a class="el" href="classPenningTrap.html">PenningTrap</a></td><td class="entry"></td></tr>
-  <tr class="even"><td class="entry"><a class="el" href="classPenningTrap.html#a978a2e2026a4b5308d5184712f81704b">external_E_field</a>(arma::vec r)</td><td class="entry"><a class="el" href="classPenningTrap.html">PenningTrap</a></td><td class="entry"></td></tr>
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+  <tr class="odd"><td class="entry"><a class="el" href="classPenningTrap.html#ab9ea97a406534bbe621a95215144875e">evolve_forward_euler</a>(double dt, bool particle_interaction=true)</td><td class="entry"><a class="el" href="classPenningTrap.html">PenningTrap</a></td><td class="entry"></td></tr>
+  <tr class="even"><td class="entry"><a class="el" href="classPenningTrap.html#a36946152fd951b1f7c346c51ff900d8e">evolve_RK4</a>(double dt, bool particle_interaction=true)</td><td class="entry"><a class="el" href="classPenningTrap.html">PenningTrap</a></td><td class="entry"></td></tr>
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+  <tr class="even"><td class="entry"><a class="el" href="classPenningTrap.html#a0194be61c956a9259c747c23e4163c5b">fraction_of_particles_left</a>(double time, unsigned int steps, std::string method=&quot;rk4&quot;, bool particle_interaction=true)</td><td class="entry"><a class="el" href="classPenningTrap.html">PenningTrap</a></td><td class="entry"></td></tr>
+  <tr class="odd"><td class="entry"><a class="el" href="classPenningTrap.html#a2f168622587709b9e3c49077f0b9a640">k_r</a></td><td class="entry"><a class="el" href="classPenningTrap.html">PenningTrap</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
+  <tr class="even"><td class="entry"><a class="el" href="classPenningTrap.html#ae9b5afdaa5cd366e94bd294452a1eed4">k_v</a></td><td class="entry"><a class="el" href="classPenningTrap.html">PenningTrap</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
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+  <tr class="odd"><td class="entry"><a class="el" href="classPenningTrap.html#a43e74792ab4b3f9299f35cb64bdb2648">r_func</a>(unsigned int i, unsigned int j, double dt)</td><td class="entry"><a class="el" href="classPenningTrap.html">PenningTrap</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
+  <tr class="even"><td class="entry"><a class="el" href="classPenningTrap.html#a5331837e6dd7bce807a99edd2ba7e854">simulate</a>(double time, unsigned int steps, std::string method=&quot;rk4&quot;, bool particle_interaction=true)</td><td class="entry"><a class="el" href="classPenningTrap.html">PenningTrap</a></td><td class="entry"></td></tr>
+  <tr class="odd"><td class="entry"><a class="el" href="classPenningTrap.html#a8ca4e21291f60fde619c14099d8c4e8e">t</a></td><td class="entry"><a class="el" href="classPenningTrap.html">PenningTrap</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
+  <tr class="even"><td class="entry"><a class="el" href="classPenningTrap.html#a1f668c4433421136ad51741741aa1bc8">total_force</a>(unsigned int i)</td><td class="entry"><a class="el" href="classPenningTrap.html">PenningTrap</a></td><td class="entry"></td></tr>
+  <tr class="odd"><td class="entry"><a class="el" href="classPenningTrap.html#ae72d203b0bfa1b9e72bea28cb2863c56">total_force_external</a>(unsigned int i)</td><td class="entry"><a class="el" href="classPenningTrap.html">PenningTrap</a></td><td class="entry"></td></tr>
+  <tr class="even"><td class="entry"><a class="el" href="classPenningTrap.html#a46a954a0946def199e30fb300ba1c47b">total_force_particles</a>(unsigned int i)</td><td class="entry"><a class="el" href="classPenningTrap.html">PenningTrap</a></td><td class="entry"></td></tr>
+  <tr class="odd"><td class="entry"><a class="el" href="classPenningTrap.html#aaf105828121c4a33cc2b217453c20317">V_0</a></td><td class="entry"><a class="el" href="classPenningTrap.html">PenningTrap</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
+  <tr class="even"><td class="entry"><a class="el" href="classPenningTrap.html#af98a720da60b0e1a62aefa5f5cb37c1e">v_func</a>(unsigned int i, unsigned int j, double dt)</td><td class="entry"><a class="el" href="classPenningTrap.html">PenningTrap</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
+  <tr class="odd"><td class="entry"><a class="el" href="classPenningTrap.html#abbb832a85139b1a56ebde57d7b8f9a57">write_simulation_to_dir</a>(std::string path, double time, unsigned int steps, std::string method=&quot;rk4&quot;, bool particle_interaction=true)</td><td class="entry"><a class="el" href="classPenningTrap.html">PenningTrap</a></td><td class="entry"></td></tr>
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index af62e25..9afb617 100644
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 <div class="header">
   <div class="summary">
 <a href="#pub-methods">Public Member Functions</a> &#124;
+<a href="#pri-methods">Private Member Functions</a> &#124;
 <a href="#pri-attribs">Private Attributes</a> &#124;
 <a href="classPenningTrap-members.html">List of all members</a>  </div>
   <div class="headertitle"><div class="title">PenningTrap Class Reference</div></div>
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 <table class="memberdecls">
 <tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pub-methods" name="pub-methods"></a>
 Public Member Functions</h2></td></tr>
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+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pri-methods" name="pri-methods"></a>
+Private Member Functions</h2></td></tr>
+<tr class="memitem:af98a720da60b0e1a62aefa5f5cb37c1e"><td class="memItemLeft" align="right" valign="top"><a class="el" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classPenningTrap.html#af98a720da60b0e1a62aefa5f5cb37c1e">v_func</a> (unsigned int i, unsigned int j, double dt)</td></tr>
+<tr class="memdesc:af98a720da60b0e1a62aefa5f5cb37c1e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Helper for evolve_RK4 when calculating \(k_{v,i,j}\) values.  <br /></td></tr>
+<tr class="separator:af98a720da60b0e1a62aefa5f5cb37c1e"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a43e74792ab4b3f9299f35cb64bdb2648"><td class="memItemLeft" align="right" valign="top"><a class="el" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classPenningTrap.html#a43e74792ab4b3f9299f35cb64bdb2648">r_func</a> (unsigned int i, unsigned int j, double dt)</td></tr>
+<tr class="memdesc:a43e74792ab4b3f9299f35cb64bdb2648"><td class="mdescLeft">&#160;</td><td class="mdescRight">Helper for evolve_RK4 when calculating \(k_{r,i,j}\) values.  <br /></td></tr>
+<tr class="separator:a43e74792ab4b3f9299f35cb64bdb2648"><td class="memSeparator" colspan="2">&#160;</td></tr>
 </table><table class="memberdecls">
 <tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pri-attribs" name="pri-attribs"></a>
 Private Attributes</h2></td></tr>
 <tr class="memitem:a0cac3509aa96e71a26d3b2c902e27716"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classPenningTrap.html#a0cac3509aa96e71a26d3b2c902e27716">B_0</a></td></tr>
 <tr class="memdesc:a0cac3509aa96e71a26d3b2c902e27716"><td class="mdescLeft">&#160;</td><td class="mdescRight">Magnetic field strength.  <br /></td></tr>
 <tr class="separator:a0cac3509aa96e71a26d3b2c902e27716"><td class="memSeparator" colspan="2">&#160;</td></tr>
-<tr class="memitem:a715329844d75ec4c04f8391421fb4e89"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classPenningTrap.html#a715329844d75ec4c04f8391421fb4e89">V_0</a></td></tr>
-<tr class="memdesc:a715329844d75ec4c04f8391421fb4e89"><td class="mdescLeft">&#160;</td><td class="mdescRight">Applied potential.  <br /></td></tr>
-<tr class="separator:a715329844d75ec4c04f8391421fb4e89"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:aaf105828121c4a33cc2b217453c20317"><td class="memItemLeft" align="right" valign="top">std::function&lt; double(double)&gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classPenningTrap.html#aaf105828121c4a33cc2b217453c20317">V_0</a></td></tr>
+<tr class="memdesc:aaf105828121c4a33cc2b217453c20317"><td class="mdescLeft">&#160;</td><td class="mdescRight">Applied potential.  <br /></td></tr>
+<tr class="separator:aaf105828121c4a33cc2b217453c20317"><td class="memSeparator" colspan="2">&#160;</td></tr>
 <tr class="memitem:a66dfe89c68716b9502927b97f59c27d2"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classPenningTrap.html#a66dfe89c68716b9502927b97f59c27d2">d</a></td></tr>
 <tr class="memdesc:a66dfe89c68716b9502927b97f59c27d2"><td class="mdescLeft">&#160;</td><td class="mdescRight">Characteristic dimension.  <br /></td></tr>
 <tr class="separator:a66dfe89c68716b9502927b97f59c27d2"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a8ca4e21291f60fde619c14099d8c4e8e"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classPenningTrap.html#a8ca4e21291f60fde619c14099d8c4e8e">t</a></td></tr>
+<tr class="memdesc:a8ca4e21291f60fde619c14099d8c4e8e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Current time.  <br /></td></tr>
+<tr class="separator:a8ca4e21291f60fde619c14099d8c4e8e"><td class="memSeparator" colspan="2">&#160;</td></tr>
 <tr class="memitem:a0112525d9e79a472e761f8ef402a339f"><td class="memItemLeft" align="right" valign="top">std::vector&lt; <a class="el" href="classParticle.html">Particle</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classPenningTrap.html#a0112525d9e79a472e761f8ef402a339f">particles</a></td></tr>
 <tr class="memdesc:a0112525d9e79a472e761f8ef402a339f"><td class="mdescLeft">&#160;</td><td class="mdescRight">The particles in the Penning trap.  <br /></td></tr>
 <tr class="separator:a0112525d9e79a472e761f8ef402a339f"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae9b5afdaa5cd366e94bd294452a1eed4"><td class="memItemLeft" align="right" valign="top"><a class="el" href="typedefs_8hpp.html#aec69d34220fff45de238b9e01f2686af">sim_arr</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classPenningTrap.html#ae9b5afdaa5cd366e94bd294452a1eed4">k_v</a></td></tr>
+<tr class="separator:ae9b5afdaa5cd366e94bd294452a1eed4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a2f168622587709b9e3c49077f0b9a640"><td class="memItemLeft" align="right" valign="top"><a class="el" href="typedefs_8hpp.html#aec69d34220fff45de238b9e01f2686af">sim_arr</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classPenningTrap.html#a2f168622587709b9e3c49077f0b9a640">k_r</a></td></tr>
+<tr class="separator:a2f168622587709b9e3c49077f0b9a640"><td class="memSeparator" colspan="2">&#160;</td></tr>
 </table>
 <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
 <div class="textblock"><p>A class that simulates a Penning trap. </p>
 <p>This class simulates a Penning trap. It can take in a number of particles and simulate how they would behave inside a Penning trap. </p>
 
-<p class="definition">Definition at line <a class="el" href="PenningTrap_8hpp_source.html#l00029">29</a> of file <a class="el" href="PenningTrap_8hpp_source.html">PenningTrap.hpp</a>.</p>
+<p class="definition">Definition at line <a class="el" href="PenningTrap_8hpp_source.html#l00030">30</a> of file <a class="el" href="PenningTrap_8hpp_source.html">PenningTrap.hpp</a>.</p>
 </div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
-<a id="a81add5063bd5f29d77f0b5c299c6c560" name="a81add5063bd5f29d77f0b5c299c6c560"></a>
-<h2 class="memtitle"><span class="permalink"><a href="#a81add5063bd5f29d77f0b5c299c6c560">&#9670;&#160;</a></span>PenningTrap()</h2>
+<a id="ae670d7de621acdb343b01af098086f63" name="ae670d7de621acdb343b01af098086f63"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae670d7de621acdb343b01af098086f63">&#9670;&#160;</a></span>PenningTrap() <span class="overload">[1/3]</span></h2>
 
 <div class="memitem">
 <div class="memproto">
@@ -184,14 +212,20 @@ Private Attributes</h2></td></tr>
         <tr>
           <td class="paramkey"></td>
           <td></td>
-          <td class="paramtype">double&#160;</td>
-          <td class="paramname"><em>V_0</em> = <code>25.*<a class="el" href="constants_8hpp.html#af40a326b23c68a27cebe60f16634a2cb">V</a>/1000.</code>, </td>
+          <td class="paramtype">std::function&lt; double(double)&gt;&#160;</td>
+          <td class="paramname"><em>V_0</em> = <code>[](double&#160;<a class="el" href="classPenningTrap.html#a8ca4e21291f60fde619c14099d8c4e8e">t</a>)&#160;{&#160;return&#160;25.&#160;*&#160;<a class="el" href="constants_8hpp.html#af40a326b23c68a27cebe60f16634a2cb">V</a>&#160;/&#160;1000.;&#160;}</code>, </td>
         </tr>
         <tr>
           <td class="paramkey"></td>
           <td></td>
           <td class="paramtype">double&#160;</td>
-          <td class="paramname"><em>d</em> = <code>500.</code>&#160;</td>
+          <td class="paramname"><em>d</em> = <code>500.</code>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>t</em> = <code>0.</code>&#160;</td>
         </tr>
         <tr>
           <td></td>
@@ -201,9 +235,138 @@ Private Attributes</h2></td></tr>
       </table>
 </div><div class="memdoc">
 
-<p>Set B_0, V_0 and d. </p>
+<p>Constructor for the <a class="el" href="classPenningTrap.html" title="A class that simulates a Penning trap.">PenningTrap</a> class. </p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">B_0</td><td>The magnetic field strength </td></tr>
+    <tr><td class="paramname">V_0</td><td>The time dependent applied potential </td></tr>
+    <tr><td class="paramname">d</td><td>The characteristic dimension </td></tr>
+    <tr><td class="paramname">t</td><td>The starting time </td></tr>
+  </table>
+  </dd>
+</dl>
 
-<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00020">20</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
+<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00018">18</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
+
+</div>
+</div>
+<a id="a763700316b502d5900e587c1f61e6bf1" name="a763700316b502d5900e587c1f61e6bf1"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a763700316b502d5900e587c1f61e6bf1">&#9670;&#160;</a></span>PenningTrap() <span class="overload">[2/3]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">PenningTrap::PenningTrap </td>
+          <td>(</td>
+          <td class="paramtype">unsigned int&#160;</td>
+          <td class="paramname"><em>i</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>B_0</em> = <code><a class="el" href="constants_8hpp.html#a0acb682b8260ab1c60b918599864e2e5">T</a></code>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">std::function&lt; double(double)&gt;&#160;</td>
+          <td class="paramname"><em>V_0</em> = <code>[](double&#160;<a class="el" href="classPenningTrap.html#a8ca4e21291f60fde619c14099d8c4e8e">t</a>)&#160;{&#160;return&#160;25.&#160;*&#160;<a class="el" href="constants_8hpp.html#af40a326b23c68a27cebe60f16634a2cb">V</a>&#160;/&#160;1000.;&#160;}</code>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>d</em> = <code>500.</code>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>t</em> = <code>0.</code>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p>Constructor for the <a class="el" href="classPenningTrap.html" title="A class that simulates a Penning trap.">PenningTrap</a> class. </p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">i</td><td>The number of particles to generate </td></tr>
+    <tr><td class="paramname">B_0</td><td>The magnetic field strength </td></tr>
+    <tr><td class="paramname">V_0</td><td>The time dependent applied potential </td></tr>
+    <tr><td class="paramname">d</td><td>The characteristic dimension </td></tr>
+    <tr><td class="paramname">t</td><td>The starting time </td></tr>
+  </table>
+  </dd>
+</dl>
+
+<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00027">27</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
+
+</div>
+</div>
+<a id="a67139e04ef69c0bcffde8f30f67cbf73" name="a67139e04ef69c0bcffde8f30f67cbf73"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a67139e04ef69c0bcffde8f30f67cbf73">&#9670;&#160;</a></span>PenningTrap() <span class="overload">[3/3]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">PenningTrap::PenningTrap </td>
+          <td>(</td>
+          <td class="paramtype">std::vector&lt; <a class="el" href="classParticle.html">Particle</a> &gt;&#160;</td>
+          <td class="paramname"><em>particles</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>B_0</em> = <code><a class="el" href="constants_8hpp.html#a0acb682b8260ab1c60b918599864e2e5">T</a></code>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">std::function&lt; double(double)&gt;&#160;</td>
+          <td class="paramname"><em>V_0</em> = <code>[](double&#160;<a class="el" href="classPenningTrap.html#a8ca4e21291f60fde619c14099d8c4e8e">t</a>)&#160;{&#160;return&#160;25.&#160;*&#160;<a class="el" href="constants_8hpp.html#af40a326b23c68a27cebe60f16634a2cb">V</a>&#160;/&#160;1000.;&#160;}</code>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>d</em> = <code>500.</code>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>t</em> = <code>0.</code>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p>Constructor for the <a class="el" href="classPenningTrap.html" title="A class that simulates a Penning trap.">PenningTrap</a> class. </p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">particles</td><td>The starting particles </td></tr>
+    <tr><td class="paramname">B_0</td><td>The magnetic field strength </td></tr>
+    <tr><td class="paramname">V_0</td><td>The time dependent applied potential </td></tr>
+    <tr><td class="paramname">d</td><td>The characteristic dimension </td></tr>
+    <tr><td class="paramname">t</td><td>The starting time </td></tr>
+  </table>
+  </dd>
+</dl>
+
+<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00039">39</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
 
 </div>
 </div>
@@ -225,13 +388,19 @@ Private Attributes</h2></td></tr>
 </div><div class="memdoc">
 
 <p>Add a particle to the system. </p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">particle</td><td>The particle to add to the Penning trap </td></tr>
+  </table>
+  </dd>
+</dl>
 
-<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00027">27</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
+<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00082">82</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
 
 </div>
 </div>
-<a id="a56544b6f4befb42984e9650cf2a40965" name="a56544b6f4befb42984e9650cf2a40965"></a>
-<h2 class="memtitle"><span class="permalink"><a href="#a56544b6f4befb42984e9650cf2a40965">&#9670;&#160;</a></span>evolve_forward_euler()</h2>
+<a id="ab9ea97a406534bbe621a95215144875e" name="ab9ea97a406534bbe621a95215144875e"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ab9ea97a406534bbe621a95215144875e">&#9670;&#160;</a></span>evolve_forward_euler()</h2>
 
 <div class="memitem">
 <div class="memproto">
@@ -240,20 +409,37 @@ Private Attributes</h2></td></tr>
           <td class="memname">void PenningTrap::evolve_forward_euler </td>
           <td>(</td>
           <td class="paramtype">double&#160;</td>
-          <td class="paramname"><em>dt</em></td><td>)</td>
+          <td class="paramname"><em>dt</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
           <td></td>
+          <td class="paramtype">bool&#160;</td>
+          <td class="paramname"><em>particle_interaction</em> = <code>true</code>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
         </tr>
       </table>
 </div><div class="memdoc">
 
 <p>Go forward one timestep using the forward Euler method. </p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">dt</td><td>The step length </td></tr>
+    <tr><td class="paramname">particle_interaction</td><td>Turn particle interactions on/off </td></tr>
+  </table>
+  </dd>
+</dl>
 
-<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00167">167</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
+<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00186">186</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
 
 </div>
 </div>
-<a id="ab891b839c40eeb38d8a2a636c70090a9" name="ab891b839c40eeb38d8a2a636c70090a9"></a>
-<h2 class="memtitle"><span class="permalink"><a href="#ab891b839c40eeb38d8a2a636c70090a9">&#9670;&#160;</a></span>evolve_RK4()</h2>
+<a id="a36946152fd951b1f7c346c51ff900d8e" name="a36946152fd951b1f7c346c51ff900d8e"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a36946152fd951b1f7c346c51ff900d8e">&#9670;&#160;</a></span>evolve_RK4()</h2>
 
 <div class="memitem">
 <div class="memproto">
@@ -262,28 +448,45 @@ Private Attributes</h2></td></tr>
           <td class="memname">void PenningTrap::evolve_RK4 </td>
           <td>(</td>
           <td class="paramtype">double&#160;</td>
-          <td class="paramname"><em>dt</em></td><td>)</td>
+          <td class="paramname"><em>dt</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
           <td></td>
+          <td class="paramtype">bool&#160;</td>
+          <td class="paramname"><em>particle_interaction</em> = <code>true</code>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
         </tr>
       </table>
 </div><div class="memdoc">
 
 <p>Go forward one timestep using the RK4 method. </p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">dt</td><td>The step length </td></tr>
+    <tr><td class="paramname">particle_interaction</td><td>Turn particle interactions on/off </td></tr>
+  </table>
+  </dd>
+</dl>
 
-<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00104">104</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
+<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00151">151</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
 
 </div>
 </div>
-<a id="a2a3e7f480ba52e9f24d4c50c3981a784" name="a2a3e7f480ba52e9f24d4c50c3981a784"></a>
-<h2 class="memtitle"><span class="permalink"><a href="#a2a3e7f480ba52e9f24d4c50c3981a784">&#9670;&#160;</a></span>external_B_field()</h2>
+<a id="acbf065c9c125682329ad82a8d166554c" name="acbf065c9c125682329ad82a8d166554c"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#acbf065c9c125682329ad82a8d166554c">&#9670;&#160;</a></span>external_B_field()</h2>
 
 <div class="memitem">
 <div class="memproto">
       <table class="memname">
         <tr>
-          <td class="memname">arma::vec PenningTrap::external_B_field </td>
+          <td class="memname"><a class="el" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> PenningTrap::external_B_field </td>
           <td>(</td>
-          <td class="paramtype">arma::vec&#160;</td>
+          <td class="paramtype"><a class="el" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a>&#160;</td>
           <td class="paramname"><em>r</em></td><td>)</td>
           <td></td>
         </tr>
@@ -291,21 +494,28 @@ Private Attributes</h2></td></tr>
 </div><div class="memdoc">
 
 <p>Calculate B at point r. </p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">r</td><td>The position where we want to calculate the B field</td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>vec_3d </dd></dl>
 
-<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00043">43</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
+<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00095">95</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
 
 </div>
 </div>
-<a id="a978a2e2026a4b5308d5184712f81704b" name="a978a2e2026a4b5308d5184712f81704b"></a>
-<h2 class="memtitle"><span class="permalink"><a href="#a978a2e2026a4b5308d5184712f81704b">&#9670;&#160;</a></span>external_E_field()</h2>
+<a id="a1d58feaa2c9e34cbf26b1c5ed75ca9d9" name="a1d58feaa2c9e34cbf26b1c5ed75ca9d9"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a1d58feaa2c9e34cbf26b1c5ed75ca9d9">&#9670;&#160;</a></span>external_E_field()</h2>
 
 <div class="memitem">
 <div class="memproto">
       <table class="memname">
         <tr>
-          <td class="memname">arma::vec PenningTrap::external_E_field </td>
+          <td class="memname"><a class="el" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> PenningTrap::external_E_field </td>
           <td>(</td>
-          <td class="paramtype">arma::vec&#160;</td>
+          <td class="paramtype"><a class="el" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a>&#160;</td>
           <td class="paramname"><em>r</em></td><td>)</td>
           <td></td>
         </tr>
@@ -313,27 +523,34 @@ Private Attributes</h2></td></tr>
 </div><div class="memdoc">
 
 <p>Calculate E at point r. </p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">r</td><td>The position where we want to calculate the E field</td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>vec_3d </dd></dl>
 
-<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00032">32</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
+<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00087">87</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
 
 </div>
 </div>
-<a id="a4790f41e4fbc6ede4991aa7bbda92182" name="a4790f41e4fbc6ede4991aa7bbda92182"></a>
-<h2 class="memtitle"><span class="permalink"><a href="#a4790f41e4fbc6ede4991aa7bbda92182">&#9670;&#160;</a></span>force_on_particle()</h2>
+<a id="a9ae34ad740a230e667e96bc6ee8730ce" name="a9ae34ad740a230e667e96bc6ee8730ce"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a9ae34ad740a230e667e96bc6ee8730ce">&#9670;&#160;</a></span>force_on_particle()</h2>
 
 <div class="memitem">
 <div class="memproto">
       <table class="memname">
         <tr>
-          <td class="memname">arma::vec PenningTrap::force_on_particle </td>
+          <td class="memname"><a class="el" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> PenningTrap::force_on_particle </td>
           <td>(</td>
-          <td class="paramtype">int&#160;</td>
+          <td class="paramtype">unsigned int&#160;</td>
           <td class="paramname"><em>i</em>, </td>
         </tr>
         <tr>
           <td class="paramkey"></td>
           <td></td>
-          <td class="paramtype">int&#160;</td>
+          <td class="paramtype">unsigned int&#160;</td>
           <td class="paramname"><em>j</em>&#160;</td>
         </tr>
         <tr>
@@ -345,83 +562,222 @@ Private Attributes</h2></td></tr>
 </div><div class="memdoc">
 
 <p>Calculate the force between 2 particles. </p>
-<p>Calculate the force exhibited on particle p_i from particle p_j. </p>
+<p>Calculate the force exhibited on particle p_i from particle p_j.</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">i</td><td>The index of particle p_i </td></tr>
+    <tr><td class="paramname">j</td><td>The index of particle p_j</td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>vec_3d </dd></dl>
 
-<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00050">50</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
+<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00100">100</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
 
 </div>
 </div>
-<a id="a85b6a231a3208963b46811776da7e580" name="a85b6a231a3208963b46811776da7e580"></a>
-<h2 class="memtitle"><span class="permalink"><a href="#a85b6a231a3208963b46811776da7e580">&#9670;&#160;</a></span>get_d()</h2>
+<a id="a0194be61c956a9259c747c23e4163c5b" name="a0194be61c956a9259c747c23e4163c5b"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a0194be61c956a9259c747c23e4163c5b">&#9670;&#160;</a></span>fraction_of_particles_left()</h2>
 
 <div class="memitem">
 <div class="memproto">
       <table class="memname">
         <tr>
-          <td class="memname">double PenningTrap::get_d </td>
+          <td class="memname">double PenningTrap::fraction_of_particles_left </td>
           <td>(</td>
-          <td class="paramname"></td><td>)</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>time</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
           <td></td>
+          <td class="paramtype">unsigned int&#160;</td>
+          <td class="paramname"><em>steps</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">std::string&#160;</td>
+          <td class="paramname"><em>method</em> = <code>&quot;rk4&quot;</code>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">bool&#160;</td>
+          <td class="paramname"><em>particle_interaction</em> = <code>true</code>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
         </tr>
       </table>
 </div><div class="memdoc">
 
-<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00188">188</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
+<p>Simulate and calculate what fraction of particles are still left inside the Penning trap after the simulation. </p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">time</td><td>The time to simulate in microseconds </td></tr>
+    <tr><td class="paramname">steps</td><td>The amount of steps for the whole simulation </td></tr>
+    <tr><td class="paramname">method</td><td>The method to use when moving forward a timestep </td></tr>
+    <tr><td class="paramname">particle_interaction</td><td>Turn particle interactions on/off</td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>double </dd></dl>
+
+<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00266">266</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
 
 </div>
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-<a id="a12b511e6903a0b033ba894c10b54d264" name="a12b511e6903a0b033ba894c10b54d264"></a>
-<h2 class="memtitle"><span class="permalink"><a href="#a12b511e6903a0b033ba894c10b54d264">&#9670;&#160;</a></span>get_particle()</h2>
+<a id="a43e74792ab4b3f9299f35cb64bdb2648" name="a43e74792ab4b3f9299f35cb64bdb2648"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a43e74792ab4b3f9299f35cb64bdb2648">&#9670;&#160;</a></span>r_func()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="el" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> PenningTrap::r_func </td>
+          <td>(</td>
+          <td class="paramtype">unsigned int&#160;</td>
+          <td class="paramname"><em>i</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">unsigned int&#160;</td>
+          <td class="paramname"><em>j</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>dt</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">private</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+
+<p>Helper for evolve_RK4 when calculating \(k_{r,i,j}\) values. </p>
+<p>Something</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">i</td><td>Index i for \(k_{r,i,j}\) </td></tr>
+    <tr><td class="paramname">j</td><td>Index j for \(k_{r,i,j}\) </td></tr>
+    <tr><td class="paramname">dt</td><td>the step length (delta time)</td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>vec_3d </dd></dl>
+
+<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00064">64</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
+
+</div>
+</div>
+<a id="a5331837e6dd7bce807a99edd2ba7e854" name="a5331837e6dd7bce807a99edd2ba7e854"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a5331837e6dd7bce807a99edd2ba7e854">&#9670;&#160;</a></span>simulate()</h2>
 
 <div class="memitem">
 <div class="memproto">
       <table class="memname">
         <tr>
-          <td class="memname">arma::vec PenningTrap::get_particle </td>
+          <td class="memname"><a class="el" href="typedefs_8hpp.html#aec69d34220fff45de238b9e01f2686af">sim_arr</a> PenningTrap::simulate </td>
           <td>(</td>
-          <td class="paramtype">int&#160;</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>time</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">unsigned int&#160;</td>
+          <td class="paramname"><em>steps</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">std::string&#160;</td>
+          <td class="paramname"><em>method</em> = <code>&quot;rk4&quot;</code>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">bool&#160;</td>
+          <td class="paramname"><em>particle_interaction</em> = <code>true</code>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p>Simulate the particle system inside the Penning trap over a certain amount of time. </p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">time</td><td>The time to simulate in microseconds </td></tr>
+    <tr><td class="paramname">steps</td><td>The amount of steps for the whole simulation </td></tr>
+    <tr><td class="paramname">method</td><td>The method to use when moving forward a timestep </td></tr>
+    <tr><td class="paramname">particle_interaction</td><td>Turn particle interactions on/off </td></tr>
+  </table>
+  </dd>
+</dl>
+
+<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00211">211</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
+
+</div>
+</div>
+<a id="a1f668c4433421136ad51741741aa1bc8" name="a1f668c4433421136ad51741741aa1bc8"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a1f668c4433421136ad51741741aa1bc8">&#9670;&#160;</a></span>total_force()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="el" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> PenningTrap::total_force </td>
+          <td>(</td>
+          <td class="paramtype">unsigned int&#160;</td>
           <td class="paramname"><em>i</em></td><td>)</td>
           <td></td>
         </tr>
       </table>
 </div><div class="memdoc">
 
-<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00183">183</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
+<p>calculate the total force on a particle p_i. </p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">i</td><td>The index of particle p_i</td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>vec_3d </dd></dl>
+
+<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00146">146</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
 
 </div>
 </div>
-<a id="a83cc7a04dae009ed8e75453c38fdf8be" name="a83cc7a04dae009ed8e75453c38fdf8be"></a>
-<h2 class="memtitle"><span class="permalink"><a href="#a83cc7a04dae009ed8e75453c38fdf8be">&#9670;&#160;</a></span>total_force()</h2>
+<a id="ae72d203b0bfa1b9e72bea28cb2863c56" name="ae72d203b0bfa1b9e72bea28cb2863c56"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae72d203b0bfa1b9e72bea28cb2863c56">&#9670;&#160;</a></span>total_force_external()</h2>
 
 <div class="memitem">
 <div class="memproto">
       <table class="memname">
         <tr>
-          <td class="memname">arma::vec PenningTrap::total_force </td>
+          <td class="memname"><a class="el" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> PenningTrap::total_force_external </td>
           <td>(</td>
-          <td class="paramtype">int&#160;</td>
-          <td class="paramname"><em>i</em></td><td>)</td>
-          <td></td>
-        </tr>
-      </table>
-</div><div class="memdoc">
-
-<p>calculate the total force on a particle. </p>
-
-<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00099">99</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
-
-</div>
-</div>
-<a id="a045adb85e97a8e0c38fb36d2fd74eeee" name="a045adb85e97a8e0c38fb36d2fd74eeee"></a>
-<h2 class="memtitle"><span class="permalink"><a href="#a045adb85e97a8e0c38fb36d2fd74eeee">&#9670;&#160;</a></span>total_force_external()</h2>
-
-<div class="memitem">
-<div class="memproto">
-      <table class="memname">
-        <tr>
-          <td class="memname">arma::vec PenningTrap::total_force_external </td>
-          <td>(</td>
-          <td class="paramtype">int&#160;</td>
+          <td class="paramtype">unsigned int&#160;</td>
           <td class="paramname"><em>i</em></td><td>)</td>
           <td></td>
         </tr>
@@ -429,31 +785,161 @@ Private Attributes</h2></td></tr>
 </div><div class="memdoc">
 
 <p>Calculate the total external force on a particle. </p>
-<p>Calculate the total amount of force that E and B exhibits on particle p_i. </p>
+<p>Calculate the total amount of force that E and B exhibits on particle p_i.</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">i</td><td>The index of particle p_i</td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>vec_3d </dd></dl>
 
-<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00065">65</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
+<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00114">114</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
 
 </div>
 </div>
-<a id="a135db7d991d9b88b00fde4edee71f78d" name="a135db7d991d9b88b00fde4edee71f78d"></a>
-<h2 class="memtitle"><span class="permalink"><a href="#a135db7d991d9b88b00fde4edee71f78d">&#9670;&#160;</a></span>total_force_particles()</h2>
+<a id="a46a954a0946def199e30fb300ba1c47b" name="a46a954a0946def199e30fb300ba1c47b"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a46a954a0946def199e30fb300ba1c47b">&#9670;&#160;</a></span>total_force_particles()</h2>
 
 <div class="memitem">
 <div class="memproto">
       <table class="memname">
         <tr>
-          <td class="memname">arma::vec PenningTrap::total_force_particles </td>
+          <td class="memname"><a class="el" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a> PenningTrap::total_force_particles </td>
           <td>(</td>
-          <td class="paramtype">int&#160;</td>
+          <td class="paramtype">unsigned int&#160;</td>
           <td class="paramname"><em>i</em></td><td>)</td>
           <td></td>
         </tr>
       </table>
 </div><div class="memdoc">
 
-<p>Calculate the total force on a particle from other particles. </p>
+<p>Calculate the total force on a particle p_i from other particles. </p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">i</td><td>The index of particle p_i</td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>vec_3d </dd></dl>
 
-<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00080">80</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
+<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00129">129</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
+
+</div>
+</div>
+<a id="af98a720da60b0e1a62aefa5f5cb37c1e" name="af98a720da60b0e1a62aefa5f5cb37c1e"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#af98a720da60b0e1a62aefa5f5cb37c1e">&#9670;&#160;</a></span>v_func()</h2>
+
+<div class="memitem">
+<div class="memproto">
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+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
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+          <td>(</td>
+          <td class="paramtype">unsigned int&#160;</td>
+          <td class="paramname"><em>i</em>, </td>
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+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">unsigned int&#160;</td>
+          <td class="paramname"><em>j</em>, </td>
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+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>dt</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">private</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+
+<p>Helper for evolve_RK4 when calculating \(k_{v,i,j}\) values. </p>
+<p>Something</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">i</td><td>Index i for \(k_{v,i,j}\) </td></tr>
+    <tr><td class="paramname">j</td><td>Index j for \(k_{v,i,j}\) </td></tr>
+    <tr><td class="paramname">dt</td><td>the step length (delta time)</td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>vec_3d </dd></dl>
+
+<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00046">46</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
+
+</div>
+</div>
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+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void PenningTrap::write_simulation_to_dir </td>
+          <td>(</td>
+          <td class="paramtype">std::string&#160;</td>
+          <td class="paramname"><em>path</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>time</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">unsigned int&#160;</td>
+          <td class="paramname"><em>steps</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">std::string&#160;</td>
+          <td class="paramname"><em>method</em> = <code>&quot;rk4&quot;</code>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">bool&#160;</td>
+          <td class="paramname"><em>particle_interaction</em> = <code>true</code>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p>Simulate and write the displacement of all particles to files. </p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">path</td><td>The directory to save the data </td></tr>
+    <tr><td class="paramname">time</td><td>The time to simulate in microseconds </td></tr>
+    <tr><td class="paramname">steps</td><td>The amount of steps for the whole simulation </td></tr>
+    <tr><td class="paramname">method</td><td>The method to use when moving forward a timestep </td></tr>
+    <tr><td class="paramname">particle_interaction</td><td>Turn particle interactions on/off </td></tr>
+  </table>
+  </dd>
+</dl>
+
+<p class="definition">Definition at line <a class="el" href="PenningTrap_8cpp_source.html#l00240">240</a> of file <a class="el" href="PenningTrap_8cpp_source.html">PenningTrap.cpp</a>.</p>
 
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 <p>Magnetic field strength. </p>
 
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+<p class="definition">Definition at line <a class="el" href="PenningTrap_8hpp_source.html#l00032">32</a> of file <a class="el" href="PenningTrap_8hpp_source.html">PenningTrap.hpp</a>.</p>
 
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 <p>Characteristic dimension. </p>
 
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+<p class="definition">Definition at line <a class="el" href="PenningTrap_8hpp_source.html#l00034">34</a> of file <a class="el" href="PenningTrap_8hpp_source.html">PenningTrap.hpp</a>.</p>
+
+</div>
+</div>
+<a id="a2f168622587709b9e3c49077f0b9a640" name="a2f168622587709b9e3c49077f0b9a640"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a2f168622587709b9e3c49077f0b9a640">&#9670;&#160;</a></span>k_r</h2>
+
+<div class="memitem">
+<div class="memproto">
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+  <tr>
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+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="el" href="typedefs_8hpp.html#aec69d34220fff45de238b9e01f2686af">sim_arr</a> PenningTrap::k_r</td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">private</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>A 2D vector containing all \(k_{i,j}\) where \(j\) is the index of a particle </p>
+
+<p class="definition">Definition at line <a class="el" href="PenningTrap_8hpp_source.html#l00039">39</a> of file <a class="el" href="PenningTrap_8hpp_source.html">PenningTrap.hpp</a>.</p>
+
+</div>
+</div>
+<a id="ae9b5afdaa5cd366e94bd294452a1eed4" name="ae9b5afdaa5cd366e94bd294452a1eed4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae9b5afdaa5cd366e94bd294452a1eed4">&#9670;&#160;</a></span>k_v</h2>
+
+<div class="memitem">
+<div class="memproto">
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+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="el" href="typedefs_8hpp.html#aec69d34220fff45de238b9e01f2686af">sim_arr</a> PenningTrap::k_v</td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">private</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>A 2D vector containing all \(k_{i,j}\) where \(j\) is the index of a particle </p>
+
+<p class="definition">Definition at line <a class="el" href="PenningTrap_8hpp_source.html#l00037">37</a> of file <a class="el" href="PenningTrap_8hpp_source.html">PenningTrap.hpp</a>.</p>
 
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 <p>The particles in the Penning trap. </p>
 
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+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
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+
+<p>Current time. </p>
+
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+
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-    [ "total_force_particles", "classPenningTrap.html#a135db7d991d9b88b00fde4edee71f78d", null ],
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+    [ "evolve_RK4", "classPenningTrap.html#a36946152fd951b1f7c346c51ff900d8e", null ],
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+    [ "force_on_particle", "classPenningTrap.html#a9ae34ad740a230e667e96bc6ee8730ce", null ],
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+    [ "r_func", "classPenningTrap.html#a43e74792ab4b3f9299f35cb64bdb2648", null ],
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+<li>write_simulation_to_dir()&#160;:&#160;<a class="el" href="classPenningTrap.html#abbb832a85139b1a56ebde57d7b8f9a57">PenningTrap</a></li>
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+<li>external_B_field()&#160;:&#160;<a class="el" href="classPenningTrap.html#acbf065c9c125682329ad82a8d166554c">PenningTrap</a></li>
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+<li>Particle()&#160;:&#160;<a class="el" href="classParticle.html#a7af9f8d1fef63dd7643b06629ac7bef4">Particle</a></li>
+<li>PenningTrap()&#160;:&#160;<a class="el" href="classPenningTrap.html#ae670d7de621acdb343b01af098086f63">PenningTrap</a></li>
+<li>r_func()&#160;:&#160;<a class="el" href="classPenningTrap.html#a43e74792ab4b3f9299f35cb64bdb2648">PenningTrap</a></li>
+<li>simulate()&#160;:&#160;<a class="el" href="classPenningTrap.html#a5331837e6dd7bce807a99edd2ba7e854">PenningTrap</a></li>
+<li>total_force()&#160;:&#160;<a class="el" href="classPenningTrap.html#a1f668c4433421136ad51741741aa1bc8">PenningTrap</a></li>
+<li>total_force_external()&#160;:&#160;<a class="el" href="classPenningTrap.html#ae72d203b0bfa1b9e72bea28cb2863c56">PenningTrap</a></li>
+<li>total_force_particles()&#160;:&#160;<a class="el" href="classPenningTrap.html#a46a954a0946def199e30fb300ba1c47b">PenningTrap</a></li>
+<li>v_func()&#160;:&#160;<a class="el" href="classPenningTrap.html#af98a720da60b0e1a62aefa5f5cb37c1e">PenningTrap</a></li>
+<li>write_simulation_to_dir()&#160;:&#160;<a class="el" href="classPenningTrap.html#abbb832a85139b1a56ebde57d7b8f9a57">PenningTrap</a></li>
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diff --git a/docs/functions_vars.html b/docs/functions_vars.html
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+<li>V_0&#160;:&#160;<a class="el" href="classPenningTrap.html#aaf105828121c4a33cc2b217453c20317">PenningTrap</a></li>
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 <p>The main program for this project.  
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-<div class="textblock"><code>#include &lt;fstream&gt;</code><br />
+<div class="textblock"><code>#include &lt;cmath&gt;</code><br />
+<code>#include &lt;fstream&gt;</code><br />
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+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p class="definition">Definition at line <a class="el" href="main_8cpp_source.html#l00031">31</a> of file <a class="el" href="main_8cpp_source.html">main.cpp</a>.</p>
+
+</div>
+</div>
+<a id="ac67e0d59227856c4d42e7d01c75e0ad2" name="ac67e0d59227856c4d42e7d01c75e0ad2"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ac67e0d59227856c4d42e7d01c75e0ad2">&#9670;&#160;</a></span>simulate_single_particle_with_different_steps()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void simulate_single_particle_with_different_steps </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p class="definition">Definition at line <a class="el" href="main_8cpp_source.html#l00055">55</a> of file <a class="el" href="main_8cpp_source.html">main.cpp</a>.</p>
+
+</div>
+</div>
+<a id="a783789519f97c6430081171cacb0ffb1" name="a783789519f97c6430081171cacb0ffb1"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a783789519f97c6430081171cacb0ffb1">&#9670;&#160;</a></span>simulate_two_particles()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void simulate_two_particles </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p class="definition">Definition at line <a class="el" href="main_8cpp_source.html#l00042">42</a> of file <a class="el" href="main_8cpp_source.html">main.cpp</a>.</p>
 
 </div>
 </div>
diff --git a/docs/main_8cpp_source.html b/docs/main_8cpp_source.html
index 5542b5a..d437689 100644
--- a/docs/main_8cpp_source.html
+++ b/docs/main_8cpp_source.html
@@ -102,87 +102,149 @@ $(document).ready(function(){initNavTree('main_8cpp_source.html',''); initResiza
 </div><!--header-->
 <div class="contents">
 <a href="main_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span> </div>
-<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span><span class="preprocessor">#include &lt;fstream&gt;</span></div>
-<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span><span class="preprocessor">#include &lt;omp.h&gt;</span></div>
-<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span><span class="preprocessor">#include &lt;sys/stat.h&gt;</span></div>
-<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span> </div>
-<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span><span class="preprocessor">#include &quot;<a class="code" href="PenningTrap_8hpp.html">PenningTrap.hpp</a>&quot;</span></div>
-<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span> </div>
-<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span><span class="preprocessor">#define PARTICLES 100</span></div>
-<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span><span class="preprocessor">#define N 10000</span></div>
-<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span><span class="preprocessor">#define CHARGE 1.</span></div>
-<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span><span class="preprocessor">#define MASS 40. </span><span class="comment">// unit: amu</span></div>
-<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span> </div>
-<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span><span class="keywordtype">void</span> simulate_100_particles()</div>
-<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span>{</div>
-<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span>    <a class="code hl_class" href="classPenningTrap.html">PenningTrap</a> trap;</div>
+<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span><span class="preprocessor">#include &lt;cmath&gt;</span></div>
+<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span><span class="preprocessor">#include &lt;fstream&gt;</span></div>
+<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span><span class="preprocessor">#include &lt;omp.h&gt;</span></div>
+<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span><span class="preprocessor">#include &lt;string&gt;</span></div>
+<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span><span class="preprocessor">#include &lt;sys/stat.h&gt;</span></div>
+<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span><span class="preprocessor">#include &lt;vector&gt;</span></div>
+<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span> </div>
+<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span><span class="preprocessor">#include &quot;<a class="code" href="PenningTrap_8hpp.html">PenningTrap.hpp</a>&quot;</span></div>
+<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span><span class="preprocessor">#include &quot;<a class="code" href="utils_8hpp.html">utils.hpp</a>&quot;</span></div>
+<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span> </div>
+<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span><span class="preprocessor">#define PARTICLES 100</span></div>
+<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span><span class="preprocessor">#define N 10000</span></div>
+<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span><span class="preprocessor">#define CHARGE 1.</span></div>
+<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span><span class="preprocessor">#define MASS 40. </span><span class="comment">// unit: amu</span></div>
 <div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span> </div>
-<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span>    <span class="comment">// Add particles inside trap</span></div>
-<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; PARTICLES; i++) {</div>
-<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span>        arma::vec r = arma::vec(3).randn() * 0.1 *</div>
-<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span>                      trap.get_d(); <span class="comment">// random initial position</span></div>
-<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>        arma::vec v = arma::vec(3).randn() * 0.1 *</div>
-<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>                      trap.get_d(); <span class="comment">// random initial velocity</span></div>
-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>        trap.<a class="code hl_function" href="classPenningTrap.html#a6e9776ff5b149f01080800716455d7c8">add_particle</a>(<a class="code hl_class" href="classParticle.html">Particle</a>(CHARGE, MASS, r, v));</div>
-<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>    }</div>
-<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span> </div>
-<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>    <span class="keywordtype">double</span> time = 50.; <span class="comment">// microseconds</span></div>
-<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>    <span class="keywordtype">double</span> dt = time / (double)N;</div>
-<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span> </div>
-<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>    <span class="keyword">auto</span> res = <span class="keyword">new</span> arma::vec::fixed&lt;3&gt;[PARTICLES][N];</div>
+<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span><a class="code hl_class" href="classParticle.html">Particle</a> p1(CHARGE, MASS, <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a>{20., 0., 20.}, <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a>{0., 25., 0.});</div>
+<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span><a class="code hl_class" href="classParticle.html">Particle</a> p2(CHARGE, MASS, <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a>{25., 25., 0.}, <a class="code hl_typedef" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a>{0., 40., 5.});</div>
+<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span> </div>
+<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span><span class="keywordtype">void</span> simulate_single_particle()</div>
+<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>{</div>
+<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>    <a class="code hl_define" href="utils_8hpp.html#aecc1f7a8a2493b9e021e5bff76a00a5b">DEBUG</a>(<span class="stringliteral">&quot;Inside single particle sim&quot;</span>);</div>
+<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>    <a class="code hl_class" href="classPenningTrap.html">PenningTrap</a> trap(std::vector&lt;Particle&gt;{p1});</div>
+<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span> </div>
+<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>    <span class="keywordtype">double</span> time = 50.; <span class="comment">// microseconds</span></div>
+<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span> </div>
+<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>    <a class="code hl_define" href="utils_8hpp.html#aecc1f7a8a2493b9e021e5bff76a00a5b">DEBUG</a>(<span class="stringliteral">&quot;Write to dir&quot;</span>);</div>
+<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>    trap.write_simulation_to_dir(<span class="stringliteral">&quot;output/simulate_single_particle&quot;</span>, time, N);</div>
+<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>}</div>
 <div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span> </div>
-<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>    <span class="keywordtype">int</span> counter = 0;</div>
-<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span> </div>
-<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>    <span class="comment">// Get the path of all particles</span></div>
-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; N; j++) {</div>
-<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span><span class="preprocessor">#pragma omp parallel for</span></div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; PARTICLES; i++) {</div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>            res[i][j] = trap.get_particle(i);</div>
-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>        }</div>
-<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>        trap.<a class="code hl_function" href="classPenningTrap.html#ab891b839c40eeb38d8a2a636c70090a9">evolve_RK4</a>(dt);</div>
-<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>    }</div>
-<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span> </div>
-<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>    std::cout &lt;&lt; counter &lt;&lt; std::endl;</div>
+<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span><span class="keywordtype">void</span> simulate_two_particles()</div>
+<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>{</div>
+<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>    <a class="code hl_class" href="classPenningTrap.html">PenningTrap</a> trap_no_interaction(std::vector&lt;Particle&gt;{p1, p2});</div>
+<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>    <a class="code hl_class" href="classPenningTrap.html">PenningTrap</a> trap_with_interaction(std::vector&lt;Particle&gt;{p1, p2});</div>
+<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span> </div>
+<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>    <span class="keywordtype">double</span> time = 50.; <span class="comment">// microseconds</span></div>
+<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span> </div>
+<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>    trap_no_interaction.<a class="code hl_function" href="classPenningTrap.html#abbb832a85139b1a56ebde57d7b8f9a57">write_simulation_to_dir</a>(</div>
+<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>        <span class="stringliteral">&quot;output/simulate_2_particles/no_interaction&quot;</span>, time, N, <span class="stringliteral">&quot;rk4&quot;</span>, <span class="keyword">false</span>);</div>
+<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>    trap_with_interaction.write_simulation_to_dir(</div>
+<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>        <span class="stringliteral">&quot;output/simulate_2_particles/with_interaction&quot;</span>, time, N);</div>
+<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>}</div>
 <div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span> </div>
-<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>    arma::vec::fixed&lt;3&gt; *cur_row;</div>
-<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>    arma::vec::fixed&lt;3&gt; cur_elem;</div>
+<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span><span class="keywordtype">void</span> simulate_single_particle_with_different_steps()</div>
+<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>{</div>
 <div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span> </div>
-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    mkdir(<span class="stringliteral">&quot;output&quot;</span>, 0777);</div>
-<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    mkdir(<span class="stringliteral">&quot;output/simulate_100_particles&quot;</span>, 0777);</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span> </div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>    std::ofstream ofile;</div>
-<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span> </div>
-<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span><span class="comment">// Write particle paths to file</span></div>
-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span><span class="preprocessor">#pragma omp parallel for private(cur_row, cur_elem, ofile)</span></div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; PARTICLES; i++) {</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        cur_row = res[i];</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>        ofile.open(<span class="stringliteral">&quot;output/simulate_100_particles/p&quot;</span> + std::to_string(i) + <span class="stringliteral">&quot;.txt&quot;</span>);</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; N; j++) {</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>            cur_elem = cur_row[j];</div>
-<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>            ofile &lt;&lt; cur_elem(0) &lt;&lt; <span class="stringliteral">&quot;,&quot;</span> &lt;&lt; cur_elem(1) &lt;&lt; <span class="stringliteral">&quot;,&quot;</span> &lt;&lt; cur_elem(2)</div>
-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>                  &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
-<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>        }</div>
-<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>        ofile.close();</div>
+<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    <span class="keywordtype">double</span> time = 50; <span class="comment">// microseconds</span></div>
+<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span> </div>
+<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 4; i++) {</div>
+<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>        <span class="keywordtype">int</span> steps = 4000 * (i + 1);</div>
+<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>        <a class="code hl_class" href="classPenningTrap.html">PenningTrap</a> trap(std::vector&lt;Particle&gt;{p1});</div>
+<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>        trap.<a class="code hl_function" href="classPenningTrap.html#abbb832a85139b1a56ebde57d7b8f9a57">write_simulation_to_dir</a>(<span class="stringliteral">&quot;output/N_steps/RK4/&quot;</span> +</div>
+<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>                                         std::to_string(steps) + <span class="stringliteral">&quot;_steps&quot;</span>,</div>
+<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>                                     time, steps, <span class="stringliteral">&quot;rk4&quot;</span>, <span class="keyword">false</span>);</div>
+<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    }</div>
+<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span> </div>
+<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 4; i++) {</div>
+<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>        <span class="keywordtype">int</span> steps = 4000 * (i + 1);</div>
+<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>        <a class="code hl_class" href="classPenningTrap.html">PenningTrap</a> trap(std::vector&lt;Particle&gt;{p1});</div>
+<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>        trap.<a class="code hl_function" href="classPenningTrap.html#abbb832a85139b1a56ebde57d7b8f9a57">write_simulation_to_dir</a>(<span class="stringliteral">&quot;output/N_steps/euler/&quot;</span> +</div>
+<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>                                         std::to_string(steps) + <span class="stringliteral">&quot;_steps&quot;</span>,</div>
+<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>                                     time, steps, <span class="stringliteral">&quot;euler&quot;</span>, <span class="keyword">false</span>);</div>
 <div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>    }</div>
 <div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>}</div>
 <div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span> </div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span><span class="keywordtype">int</span> main()</div>
+<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span><span class="keywordtype">void</span> simulate_100_particles()</div>
 <div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>{</div>
-<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    <span class="keywordtype">double</span> start = omp_get_wtime();</div>
-<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span> </div>
-<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>    simulate_100_particles();</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span> </div>
-<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>    <span class="keywordtype">double</span> end = omp_get_wtime();</div>
-<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span> </div>
-<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>    std::cout &lt;&lt; <span class="stringliteral">&quot;Time: &quot;</span> &lt;&lt; end - start &lt;&lt; <span class="stringliteral">&quot; seconds&quot;</span> &lt;&lt; std::endl;</div>
-<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span> </div>
-<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>}</div>
+<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    <a class="code hl_class" href="classPenningTrap.html">PenningTrap</a> trap((<span class="keywordtype">unsigned</span>)100, <a class="code hl_define" href="constants_8hpp.html#a0acb682b8260ab1c60b918599864e2e5">T</a>,</div>
+<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>                     [](<span class="keywordtype">double</span> t) {</div>
+<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>                         <span class="keywordflow">return</span> 25. * <a class="code hl_define" href="constants_8hpp.html#af40a326b23c68a27cebe60f16634a2cb">V</a> / 1000. *</div>
+<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>                                (1. + .4 * std::cos(1.5 * t));</div>
+<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>                     },</div>
+<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>                     500., 0);</div>
+<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span> </div>
+<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>    <span class="keywordtype">double</span> time = 500.; <span class="comment">// microseconds</span></div>
+<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span> </div>
+<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>    trap.<a class="code hl_function" href="classPenningTrap.html#abbb832a85139b1a56ebde57d7b8f9a57">write_simulation_to_dir</a>(<span class="stringliteral">&quot;output/simulate_100_particles&quot;</span>, time, N*5);</div>
+<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>}</div>
+<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span> </div>
+<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span><span class="keywordtype">void</span> simulate_100_particles_with_time_potential()</div>
+<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>{</div>
+<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>    <span class="keywordtype">double</span> amplitudes[]{.1, .4, .7};</div>
+<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span> </div>
+<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>    <span class="keywordtype">double</span> freq_start = .2;</div>
+<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>    <span class="keywordtype">double</span> freq_end = 2.5;</div>
+<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>    <span class="keywordtype">double</span> freq_increment = .02;</div>
+<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>    <span class="keywordtype">size_t</span> freq_iterations = (size_t) ((freq_end - freq_start) / freq_increment);</div>
+<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span> </div>
+<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>    std::string path = <span class="stringliteral">&quot;output/time_dependent_potential/&quot;</span>;</div>
+<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    <a class="code hl_function" href="utils_8hpp.html#a6fdd7217b750aff5b6295ece7cbdeffa">mkpath</a>(path);</div>
+<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span> </div>
+<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>    std::ofstream ofile;</div>
+<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span> </div>
+<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    <span class="keywordflow">for</span> (<span class="keywordtype">double</span> f : amplitudes) {</div>
+<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>        ofile.open(path + <span class="stringliteral">&quot;f_&quot;</span> + std::to_string(f) + <span class="stringliteral">&quot;.txt&quot;</span>);</div>
+<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span><span class="preprocessor">        #pragma omp parallel for ordered schedule(static, 1)</span></div>
+<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i=0; i &lt; freq_iterations; i++) {</div>
+<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>            <span class="keywordtype">double</span> freq = freq_start + i*freq_increment;</div>
+<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>            <a class="code hl_class" href="classPenningTrap.html">PenningTrap</a> trap((<span class="keywordtype">unsigned</span>)100, <a class="code hl_define" href="constants_8hpp.html#a0acb682b8260ab1c60b918599864e2e5">T</a>,</div>
+<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>                             [f, freq](<span class="keywordtype">double</span> t) {</div>
+<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>                                 <span class="keywordflow">return</span> (25. * <a class="code hl_define" href="constants_8hpp.html#af40a326b23c68a27cebe60f16634a2cb">V</a> / 1000.) *</div>
+<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>                                        (1. + f * std::cos(freq * t));</div>
+<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>                             },</div>
+<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>                             500., 0.);</div>
+<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>            <span class="keywordtype">double</span> res = trap.<a class="code hl_function" href="classPenningTrap.html#a0194be61c956a9259c747c23e4163c5b">fraction_of_particles_left</a>(500., 40000, <span class="stringliteral">&quot;rk4&quot;</span>, <span class="keyword">true</span>);</div>
+<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span><span class="preprocessor">            #pragma omp ordered</span></div>
+<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>            ofile &lt;&lt; freq &lt;&lt; <span class="stringliteral">&quot;,&quot;</span> &lt;&lt; res &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>        }</div>
+<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>        ofile.close();</div>
+<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    }</div>
+<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>}</div>
+<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span> </div>
+<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span><span class="keywordtype">int</span> main()</div>
+<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>{</div>
+<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span> </div>
+<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>    simulate_single_particle();</div>
+<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span> </div>
+<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>    simulate_two_particles();</div>
+<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span> </div>
+<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>    simulate_single_particle_with_different_steps();</div>
+<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span> </div>
+<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>    <span class="keywordtype">double</span> start = omp_get_wtime();</div>
+<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span> </div>
+<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>    <span class="comment">//simulate_100_particles();</span></div>
+<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span> </div>
+<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>    simulate_100_particles_with_time_potential();</div>
+<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span> </div>
+<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>    <span class="keywordtype">double</span> end = omp_get_wtime();</div>
+<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span> </div>
+<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>    std::cout &lt;&lt; <span class="stringliteral">&quot;Time: &quot;</span> &lt;&lt; end - start &lt;&lt; <span class="stringliteral">&quot; seconds&quot;</span> &lt;&lt; std::endl;</div>
+<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span> </div>
+<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>}</div>
 <div class="ttc" id="aPenningTrap_8hpp_html"><div class="ttname"><a href="PenningTrap_8hpp.html">PenningTrap.hpp</a></div><div class="ttdoc">A class for simulating a Penning trap.</div></div>
-<div class="ttc" id="aclassParticle_html"><div class="ttname"><a href="classParticle.html">Particle</a></div><div class="ttdoc">A class that holds attributes of a particle.</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00019">Particle.hpp:19</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html"><div class="ttname"><a href="classPenningTrap.html">PenningTrap</a></div><div class="ttdoc">A class that simulates a Penning trap.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00029">PenningTrap.hpp:29</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a6e9776ff5b149f01080800716455d7c8"><div class="ttname"><a href="classPenningTrap.html#a6e9776ff5b149f01080800716455d7c8">PenningTrap::add_particle</a></div><div class="ttdeci">void add_particle(Particle particle)</div><div class="ttdoc">Add a particle to the system.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00027">PenningTrap.cpp:27</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_ab891b839c40eeb38d8a2a636c70090a9"><div class="ttname"><a href="classPenningTrap.html#ab891b839c40eeb38d8a2a636c70090a9">PenningTrap::evolve_RK4</a></div><div class="ttdeci">void evolve_RK4(double dt)</div><div class="ttdoc">Go forward one timestep using the RK4 method.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00104">PenningTrap.cpp:104</a></div></div>
+<div class="ttc" id="aclassParticle_html"><div class="ttname"><a href="classParticle.html">Particle</a></div><div class="ttdoc">A class that holds attributes of a particle.</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00021">Particle.hpp:21</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html"><div class="ttname"><a href="classPenningTrap.html">PenningTrap</a></div><div class="ttdoc">A class that simulates a Penning trap.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00030">PenningTrap.hpp:30</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a0194be61c956a9259c747c23e4163c5b"><div class="ttname"><a href="classPenningTrap.html#a0194be61c956a9259c747c23e4163c5b">PenningTrap::fraction_of_particles_left</a></div><div class="ttdeci">double fraction_of_particles_left(double time, unsigned int steps, std::string method=&quot;rk4&quot;, bool particle_interaction=true)</div><div class="ttdoc">Simulate and calculate what fraction of particles are still left inside the Penning trap after the si...</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00266">PenningTrap.cpp:266</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_abbb832a85139b1a56ebde57d7b8f9a57"><div class="ttname"><a href="classPenningTrap.html#abbb832a85139b1a56ebde57d7b8f9a57">PenningTrap::write_simulation_to_dir</a></div><div class="ttdeci">void write_simulation_to_dir(std::string path, double time, unsigned int steps, std::string method=&quot;rk4&quot;, bool particle_interaction=true)</div><div class="ttdoc">Simulate and write the displacement of all particles to files.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00240">PenningTrap.cpp:240</a></div></div>
+<div class="ttc" id="aconstants_8hpp_html_a0acb682b8260ab1c60b918599864e2e5"><div class="ttname"><a href="constants_8hpp.html#a0acb682b8260ab1c60b918599864e2e5">T</a></div><div class="ttdeci">#define T</div><div class="ttdoc">1 Tesla. unit:</div><div class="ttdef"><b>Definition:</b> <a href="constants_8hpp_source.html#l00017">constants.hpp:17</a></div></div>
+<div class="ttc" id="aconstants_8hpp_html_af40a326b23c68a27cebe60f16634a2cb"><div class="ttname"><a href="constants_8hpp.html#af40a326b23c68a27cebe60f16634a2cb">V</a></div><div class="ttdeci">#define V</div><div class="ttdoc">1 Volt. unit:</div><div class="ttdef"><b>Definition:</b> <a href="constants_8hpp_source.html#l00019">constants.hpp:19</a></div></div>
+<div class="ttc" id="atypedefs_8hpp_html_a9f33f4962c8fb62cc5ccd0e4e039a8df"><div class="ttname"><a href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a></div><div class="ttdeci">arma::vec::fixed&lt; 3 &gt; vec_3d</div><div class="ttdoc">Typedef for a fixed 3d arma vector.</div><div class="ttdef"><b>Definition:</b> <a href="typedefs_8hpp_source.html#l00036">typedefs.hpp:36</a></div></div>
+<div class="ttc" id="autils_8hpp_html"><div class="ttname"><a href="utils_8hpp.html">utils.hpp</a></div><div class="ttdoc">Function prototypes and macros that are useful.</div></div>
+<div class="ttc" id="autils_8hpp_html_a6fdd7217b750aff5b6295ece7cbdeffa"><div class="ttname"><a href="utils_8hpp.html#a6fdd7217b750aff5b6295ece7cbdeffa">mkpath</a></div><div class="ttdeci">bool mkpath(std::string path, int mode=0777)</div><div class="ttdoc">Make path given.</div><div class="ttdef"><b>Definition:</b> <a href="utils_8cpp_source.html#l00076">utils.cpp:76</a></div></div>
+<div class="ttc" id="autils_8hpp_html_aecc1f7a8a2493b9e021e5bff76a00a5b"><div class="ttname"><a href="utils_8hpp.html#aecc1f7a8a2493b9e021e5bff76a00a5b">DEBUG</a></div><div class="ttdeci">#define DEBUG(msg)</div><div class="ttdoc">Writes a debug message.</div><div class="ttdef"><b>Definition:</b> <a href="utils_8hpp_source.html#l00036">utils.hpp:36</a></div></div>
 </div><!-- fragment --></div><!-- contents -->
 </div><!-- doc-content -->
 <!-- start footer part -->
diff --git a/docs/menudata.js b/docs/menudata.js
index 88ec31f..74c1d7b 100644
--- a/docs/menudata.js
+++ b/docs/menudata.js
@@ -38,4 +38,5 @@ var menudata={children:[
 {text:"File Members",url:"globals.html",children:[
 {text:"All",url:"globals.html"},
 {text:"Functions",url:"globals_func.html"},
+{text:"Typedefs",url:"globals_type.html"},
 {text:"Macros",url:"globals_defs.html"}]}]}]}
diff --git a/docs/navtreedata.js b/docs/navtreedata.js
index 10ee5ad..9640812 100644
--- a/docs/navtreedata.js
+++ b/docs/navtreedata.js
@@ -27,7 +27,6 @@ var NAVTREE =
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     [ "Credits", "index.html#autotoc_md1", null ],
     [ "Bug List", "bug.html", null ],
-    [ "Todo List", "todo.html", null ],
     [ "Classes", "annotated.html", [
       [ "Class List", "annotated.html", "annotated_dup" ],
       [ "Class Index", "classes.html", null ],
@@ -43,6 +42,7 @@ var NAVTREE =
       [ "File Members", "globals.html", [
         [ "All", "globals.html", null ],
         [ "Functions", "globals_func.html", null ],
+        [ "Typedefs", "globals_type.html", null ],
         [ "Macros", "globals_defs.html", null ]
       ] ]
     ] ]
diff --git a/docs/navtreeindex0.js b/docs/navtreeindex0.js
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--- a/docs/navtreeindex0.js
+++ b/docs/navtreeindex0.js
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diff --git a/docs/plot__particles__left_8py_source.html b/docs/plot__particles__left_8py_source.html
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+<meta name="viewport" content="width=device-width, initial-scale=1"/>
+<title>Penning Trap Simulation: src/plot_particles_left.py Source File</title>
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+   <div id="projectname">Penning Trap Simulation
+   </div>
+   <div id="projectbrief">Simulate particle behavior inside a Penning Trap</div>
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+  <div class="headertitle"><div class="title">plot_particles_left.py</div></div>
+</div><!--header-->
+<div class="contents">
+<div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span><span class="keyword">import</span> matplotlib.pyplot <span class="keyword">as</span> plt</div>
+<div class="line"><a id="l00002" name="l00002"></a><span class="lineno">    2</span> </div>
+<div class="line"><a id="l00003" name="l00003"></a><span class="lineno">    3</span><span class="keyword">def </span>main():</div>
+<div class="line"><a id="l00004" name="l00004"></a><span class="lineno">    4</span>    files = [</div>
+<div class="line"><a id="l00005" name="l00005"></a><span class="lineno">    5</span>        <span class="stringliteral">&quot;output/time_dependent_potential/f_0.100000.txt&quot;</span>,</div>
+<div class="line"><a id="l00006" name="l00006"></a><span class="lineno">    6</span>        <span class="stringliteral">&quot;output/time_dependent_potential/f_0.400000.txt&quot;</span>,</div>
+<div class="line"><a id="l00007" name="l00007"></a><span class="lineno">    7</span>        <span class="stringliteral">&quot;output/time_dependent_potential/f_0.700000.txt&quot;</span>,</div>
+<div class="line"><a id="l00008" name="l00008"></a><span class="lineno">    8</span>    ]</div>
+<div class="line"><a id="l00009" name="l00009"></a><span class="lineno">    9</span>    vals = [</div>
+<div class="line"><a id="l00010" name="l00010"></a><span class="lineno">   10</span>        .1,</div>
+<div class="line"><a id="l00011" name="l00011"></a><span class="lineno">   11</span>        .4,</div>
+<div class="line"><a id="l00012" name="l00012"></a><span class="lineno">   12</span>        .7</div>
+<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span>    ]</div>
+<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span>    <span class="keywordflow">for</span> i <span class="keywordflow">in</span> range(3):</div>
+<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span>        <span class="keyword">with</span> open(files[i]) <span class="keyword">as</span> f:</div>
+<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span>            lines = f.readlines()</div>
+<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span>            x = []</div>
+<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span>            y = []</div>
+<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span>            <span class="keywordflow">for</span> line <span class="keywordflow">in</span> lines:</div>
+<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span>                a,b = line.strip().split(<span class="stringliteral">&quot;,&quot;</span>)</div>
+<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span>                x.append(float(a))</div>
+<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span>                y.append(float(b))</div>
+<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span>            plt.plot(x,y,label=f<span class="stringliteral">&quot;amplitude: {vals[i]}&quot;</span>)</div>
+<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span> </div>
+<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span>    plt.xlabel(<span class="stringliteral">r&quot;$\omega_V$&quot;</span>)</div>
+<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span>    plt.ylabel(<span class="stringliteral">r&quot;Fraction of particles left&quot;</span>)</div>
+<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span>    plt.title(<span class="stringliteral">r&quot;The fraction of particles left in the Penning trap &quot;</span></div>
+<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span>              <span class="stringliteral">&quot;after 500 microseconds for different amplitudes and frequencies&quot;</span>)</div>
+<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>    plt.legend()</div>
+<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span>    plt.show()</div>
+<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span> </div>
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+<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>    main()</div>
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new file mode 100644
index 0000000..06f433f
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+++ b/docs/search/defines_5.js
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index 1ca9264..5e3fea9 100644
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@@ -1,4 +1,5 @@
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index c031fe4..c4c479f 100644
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index 30ce46b..ffb26d6 100644
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index 2dc79c5..852716e 100644
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diff --git a/docs/search/functions_5.js b/docs/search/functions_5.js
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new file mode 100644
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--- /dev/null
+++ b/docs/search/functions_7.js
@@ -0,0 +1,6 @@
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new file mode 100644
index 0000000..8d7b6ff
--- /dev/null
+++ b/docs/search/functions_8.js
@@ -0,0 +1,4 @@
+var searchData=
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new file mode 100644
index 0000000..1b9fc74
--- /dev/null
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+var searchData=
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+];
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index 906104d..4d47bbf 100644
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+  0: "_abcdefkmpqrstuvw",
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-  3: "aefmpst",
-  4: "bdmpqrv",
-  5: "p",
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-  7: "bpt"
+  3: "aefmprstvw",
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+  5: "sv",
+  6: "p",
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-  6: "defines",
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+  6: "Friends",
+  7: "Macros",
+  8: "Pages"
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new file mode 100644
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new file mode 100644
index 0000000..c7c5d99
--- /dev/null
+++ b/docs/search/variables_7.js
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+var searchData=
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new file mode 100644
index 0000000..601b41d
--- /dev/null
+++ b/docs/search/variables_8.js
@@ -0,0 +1,5 @@
+var searchData=
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diff --git a/docs/test__suite_8cpp.html b/docs/test__suite_8cpp.html
index 787939b..7c69921 100644
--- a/docs/test__suite_8cpp.html
+++ b/docs/test__suite_8cpp.html
@@ -131,7 +131,7 @@ Functions</h2></td></tr>
 <dd>
 Janita Ovidie Sandtrøen Willumsen (janitaws)</dd></dl>
 <dl class="section version"><dt>Version</dt><dd>0.1</dd></dl>
-<dl class="bug"><dt><b><a class="el" href="bug.html#_bug000008">Bug:</a></b></dt><dd>No known bugs </dd></dl>
+<dl class="bug"><dt><b><a class="el" href="bug.html#_bug000009">Bug:</a></b></dt><dd>No known bugs </dd></dl>
 
 <p class="definition">Definition in file <a class="el" href="test__suite_8cpp_source.html">test_suite.cpp</a>.</p>
 </div><h2 class="groupheader">Function Documentation</h2>
diff --git a/docs/test__suite_8cpp_source.html b/docs/test__suite_8cpp_source.html
index 3fab92c..b317c82 100644
--- a/docs/test__suite_8cpp_source.html
+++ b/docs/test__suite_8cpp_source.html
@@ -136,9 +136,9 @@ $(document).ready(function(){initNavTree('test__suite_8cpp_source.html',''); ini
 <div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>        arma::vec result;</div>
 <div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>        arma::vec v;</div>
 <div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>        std::stringstream msg;</div>
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+<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; tests.size(); i++) {</div>
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-<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>            result = trap.<a class="code hl_function" href="classPenningTrap.html#a978a2e2026a4b5308d5184712f81704b">external_E_field</a>(v);</div>
+<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>            result = trap.<a class="code hl_function" href="classPenningTrap.html#a1d58feaa2c9e34cbf26b1c5ed75ca9d9">external_E_field</a>(v);</div>
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 <div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>            msg &lt;&lt; <span class="stringliteral">&quot;Testing the external E field at (&quot;</span> &lt;&lt; std::setprecision(2)</div>
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 <div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>        <span class="comment">// on position.</span></div>
 <div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>        <a class="code hl_class" href="classPenningTrap.html">PenningTrap</a> trap;</div>
 <div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>        arma::vec expected{0., 0., <a class="code hl_define" href="constants_8hpp.html#a0acb682b8260ab1c60b918599864e2e5">T</a>};</div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>        arma::vec result = trap.<a class="code hl_function" href="classPenningTrap.html#a2a3e7f480ba52e9f24d4c50c3981a784">external_B_field</a>(arma::vec{0., 0., 0.});</div>
+<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>        arma::vec result = trap.<a class="code hl_function" href="classPenningTrap.html#acbf065c9c125682329ad82a8d166554c">external_B_field</a>(arma::vec{0., 0., 0.});</div>
 <div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        <a class="code hl_define" href="utils_8hpp.html#a73d4f21ad937dbc50a0c0538c78fd4f9">ASSERT</a>(<a class="code hl_function" href="utils_8hpp.html#a0c95c4791692b06f8811905a76dbd772">arma_vector_close_to</a>(expected, result),</div>
 <div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>               <span class="stringliteral">&quot;Testing the external B field at (0,0,0)&quot;</span>);</div>
 <div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    }</div>
@@ -171,14 +171,14 @@ $(document).ready(function(){initNavTree('test__suite_8cpp_source.html',''); ini
 <div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span> </div>
 <div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>        <span class="comment">// Test p0 and p1</span></div>
 <div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>        arma::vec expected{-1., 0., 0.};</div>
-<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>        arma::vec result = trap.<a class="code hl_function" href="classPenningTrap.html#a4790f41e4fbc6ede4991aa7bbda92182">force_on_particle</a>(0, 1);</div>
+<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>        arma::vec result = trap.<a class="code hl_function" href="classPenningTrap.html#a9ae34ad740a230e667e96bc6ee8730ce">force_on_particle</a>(0, 1);</div>
 <div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>        <a class="code hl_define" href="utils_8hpp.html#a73d4f21ad937dbc50a0c0538c78fd4f9">ASSERT</a>(<a class="code hl_function" href="utils_8hpp.html#a0c95c4791692b06f8811905a76dbd772">arma_vector_close_to</a>(expected, result),</div>
 <div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>               <span class="stringliteral">&quot;Testing the force on a particle at (0,0,0) from a &quot;</span></div>
 <div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>               <span class="stringliteral">&quot;particle at (1,0,0).&quot;</span>);</div>
 <div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span> </div>
 <div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>        <span class="comment">// Test p0 and p2</span></div>
 <div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>        expected = arma::vec{0, -.024, -.032};</div>
-<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>        result = trap.<a class="code hl_function" href="classPenningTrap.html#a4790f41e4fbc6ede4991aa7bbda92182">force_on_particle</a>(0, 2);</div>
+<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>        result = trap.<a class="code hl_function" href="classPenningTrap.html#a9ae34ad740a230e667e96bc6ee8730ce">force_on_particle</a>(0, 2);</div>
 <div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>        <a class="code hl_define" href="utils_8hpp.html#a73d4f21ad937dbc50a0c0538c78fd4f9">ASSERT</a>(<a class="code hl_function" href="utils_8hpp.html#a0c95c4791692b06f8811905a76dbd772">arma_vector_close_to</a>(expected, result),</div>
 <div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>               <span class="stringliteral">&quot;Testing the force on a particle at (0,0,0) from a &quot;</span></div>
 <div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>               <span class="stringliteral">&quot;particle at (0,3,4).&quot;</span>);</div>
@@ -191,7 +191,7 @@ $(document).ready(function(){initNavTree('test__suite_8cpp_source.html',''); ini
 <div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>            <a class="code hl_class" href="classParticle.html">Particle</a>(1., 40., arma::vec{1., 2., 3.}, arma::vec{3., 4., 5.}));</div>
 <div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span> </div>
 <div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>        arma::vec expected{395.58954878, -270.15871624, -57.89115348};</div>
-<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>        arma::vec result = trap.<a class="code hl_function" href="classPenningTrap.html#a045adb85e97a8e0c38fb36d2fd74eeee">total_force_external</a>(0);</div>
+<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>        arma::vec result = trap.<a class="code hl_function" href="classPenningTrap.html#ae72d203b0bfa1b9e72bea28cb2863c56">total_force_external</a>(0);</div>
 <div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>        <a class="code hl_define" href="utils_8hpp.html#a73d4f21ad937dbc50a0c0538c78fd4f9">ASSERT</a>(<a class="code hl_function" href="utils_8hpp.html#a0c95c4791692b06f8811905a76dbd772">arma_vector_close_to</a>(expected, result),</div>
 <div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>               <span class="stringliteral">&quot;Testing the total external force on a particle at &quot;</span></div>
 <div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>               <span class="stringliteral">&quot;(1,2,3) with velocity (3,4,5)&quot;</span>);</div>
@@ -204,7 +204,7 @@ $(document).ready(function(){initNavTree('test__suite_8cpp_source.html',''); ini
 <div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>            <a class="code hl_class" href="classParticle.html">Particle</a>(1., 40., arma::vec{0., 0., 0.}, arma::vec{0., 0., 0.}));</div>
 <div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span> </div>
 <div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>        arma::vec expected{0., 0., 0.};</div>
-<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>        arma::vec result = trap.<a class="code hl_function" href="classPenningTrap.html#a135db7d991d9b88b00fde4edee71f78d">total_force_particles</a>(0);</div>
+<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>        arma::vec result = trap.<a class="code hl_function" href="classPenningTrap.html#a46a954a0946def199e30fb300ba1c47b">total_force_particles</a>(0);</div>
 <div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>        <a class="code hl_define" href="utils_8hpp.html#a73d4f21ad937dbc50a0c0538c78fd4f9">ASSERT</a>(<a class="code hl_function" href="utils_8hpp.html#a0c95c4791692b06f8811905a76dbd772">arma_vector_close_to</a>(expected, result),</div>
 <div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>               <span class="stringliteral">&quot;Testing the total force of all particles on particle 0 &quot;</span></div>
 <div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>               <span class="stringliteral">&quot;with only a single particle&quot;</span>);</div>
@@ -217,7 +217,7 @@ $(document).ready(function(){initNavTree('test__suite_8cpp_source.html',''); ini
 <div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>            <a class="code hl_class" href="classParticle.html">Particle</a>(1., 40., arma::vec{0., 0., 1.}, arma::vec{0., 0., 0.}));</div>
 <div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span> </div>
 <div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>        expected = arma::vec(3, arma::fill::value(-3473.383325));</div>
-<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>        result = trap.<a class="code hl_function" href="classPenningTrap.html#a135db7d991d9b88b00fde4edee71f78d">total_force_particles</a>(0);</div>
+<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>        result = trap.<a class="code hl_function" href="classPenningTrap.html#a46a954a0946def199e30fb300ba1c47b">total_force_particles</a>(0);</div>
 <div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>        <a class="code hl_define" href="utils_8hpp.html#a73d4f21ad937dbc50a0c0538c78fd4f9">ASSERT</a>(<a class="code hl_function" href="utils_8hpp.html#a0c95c4791692b06f8811905a76dbd772">arma_vector_close_to</a>(expected, result),</div>
 <div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>               <span class="stringliteral">&quot;Testing the total force of all particles on particle 0 &quot;</span></div>
 <div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>               <span class="stringliteral">&quot;with 3 other particles.&quot;</span>);</div>
@@ -234,18 +234,18 @@ $(document).ready(function(){initNavTree('test__suite_8cpp_source.html',''); ini
 <div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>    <span class="keywordflow">return</span> 0;</div>
 <div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>}</div>
 <div class="ttc" id="aPenningTrap_8hpp_html"><div class="ttname"><a href="PenningTrap_8hpp.html">PenningTrap.hpp</a></div><div class="ttdoc">A class for simulating a Penning trap.</div></div>
-<div class="ttc" id="aclassParticle_html"><div class="ttname"><a href="classParticle.html">Particle</a></div><div class="ttdoc">A class that holds attributes of a particle.</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00019">Particle.hpp:19</a></div></div>
+<div class="ttc" id="aclassParticle_html"><div class="ttname"><a href="classParticle.html">Particle</a></div><div class="ttdoc">A class that holds attributes of a particle.</div><div class="ttdef"><b>Definition:</b> <a href="Particle_8hpp_source.html#l00021">Particle.hpp:21</a></div></div>
 <div class="ttc" id="aclassPenningTrapTest_html"><div class="ttname"><a href="classPenningTrapTest.html">PenningTrapTest</a></div><div class="ttdef"><b>Definition:</b> <a href="test__suite_8cpp_source.html#l00020">test_suite.cpp:20</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html"><div class="ttname"><a href="classPenningTrap.html">PenningTrap</a></div><div class="ttdoc">A class that simulates a Penning trap.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00029">PenningTrap.hpp:29</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a045adb85e97a8e0c38fb36d2fd74eeee"><div class="ttname"><a href="classPenningTrap.html#a045adb85e97a8e0c38fb36d2fd74eeee">PenningTrap::total_force_external</a></div><div class="ttdeci">arma::vec total_force_external(int i)</div><div class="ttdoc">Calculate the total external force on a particle.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00065">PenningTrap.cpp:65</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a135db7d991d9b88b00fde4edee71f78d"><div class="ttname"><a href="classPenningTrap.html#a135db7d991d9b88b00fde4edee71f78d">PenningTrap::total_force_particles</a></div><div class="ttdeci">arma::vec total_force_particles(int i)</div><div class="ttdoc">Calculate the total force on a particle from other particles.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00080">PenningTrap.cpp:80</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a2a3e7f480ba52e9f24d4c50c3981a784"><div class="ttname"><a href="classPenningTrap.html#a2a3e7f480ba52e9f24d4c50c3981a784">PenningTrap::external_B_field</a></div><div class="ttdeci">arma::vec external_B_field(arma::vec r)</div><div class="ttdoc">Calculate B at point r.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00043">PenningTrap.cpp:43</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a4790f41e4fbc6ede4991aa7bbda92182"><div class="ttname"><a href="classPenningTrap.html#a4790f41e4fbc6ede4991aa7bbda92182">PenningTrap::force_on_particle</a></div><div class="ttdeci">arma::vec force_on_particle(int i, int j)</div><div class="ttdoc">Calculate the force between 2 particles.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00050">PenningTrap.cpp:50</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a6e9776ff5b149f01080800716455d7c8"><div class="ttname"><a href="classPenningTrap.html#a6e9776ff5b149f01080800716455d7c8">PenningTrap::add_particle</a></div><div class="ttdeci">void add_particle(Particle particle)</div><div class="ttdoc">Add a particle to the system.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00027">PenningTrap.cpp:27</a></div></div>
-<div class="ttc" id="aclassPenningTrap_html_a978a2e2026a4b5308d5184712f81704b"><div class="ttname"><a href="classPenningTrap.html#a978a2e2026a4b5308d5184712f81704b">PenningTrap::external_E_field</a></div><div class="ttdeci">arma::vec external_E_field(arma::vec r)</div><div class="ttdoc">Calculate E at point r.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00032">PenningTrap.cpp:32</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html"><div class="ttname"><a href="classPenningTrap.html">PenningTrap</a></div><div class="ttdoc">A class that simulates a Penning trap.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8hpp_source.html#l00030">PenningTrap.hpp:30</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a1d58feaa2c9e34cbf26b1c5ed75ca9d9"><div class="ttname"><a href="classPenningTrap.html#a1d58feaa2c9e34cbf26b1c5ed75ca9d9">PenningTrap::external_E_field</a></div><div class="ttdeci">vec_3d external_E_field(vec_3d r)</div><div class="ttdoc">Calculate E at point r.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00087">PenningTrap.cpp:87</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a46a954a0946def199e30fb300ba1c47b"><div class="ttname"><a href="classPenningTrap.html#a46a954a0946def199e30fb300ba1c47b">PenningTrap::total_force_particles</a></div><div class="ttdeci">vec_3d total_force_particles(unsigned int i)</div><div class="ttdoc">Calculate the total force on a particle p_i from other particles.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00129">PenningTrap.cpp:129</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a6e9776ff5b149f01080800716455d7c8"><div class="ttname"><a href="classPenningTrap.html#a6e9776ff5b149f01080800716455d7c8">PenningTrap::add_particle</a></div><div class="ttdeci">void add_particle(Particle particle)</div><div class="ttdoc">Add a particle to the system.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00082">PenningTrap.cpp:82</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_a9ae34ad740a230e667e96bc6ee8730ce"><div class="ttname"><a href="classPenningTrap.html#a9ae34ad740a230e667e96bc6ee8730ce">PenningTrap::force_on_particle</a></div><div class="ttdeci">vec_3d force_on_particle(unsigned int i, unsigned int j)</div><div class="ttdoc">Calculate the force between 2 particles.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00100">PenningTrap.cpp:100</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_acbf065c9c125682329ad82a8d166554c"><div class="ttname"><a href="classPenningTrap.html#acbf065c9c125682329ad82a8d166554c">PenningTrap::external_B_field</a></div><div class="ttdeci">vec_3d external_B_field(vec_3d r)</div><div class="ttdoc">Calculate B at point r.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00095">PenningTrap.cpp:95</a></div></div>
+<div class="ttc" id="aclassPenningTrap_html_ae72d203b0bfa1b9e72bea28cb2863c56"><div class="ttname"><a href="classPenningTrap.html#ae72d203b0bfa1b9e72bea28cb2863c56">PenningTrap::total_force_external</a></div><div class="ttdeci">vec_3d total_force_external(unsigned int i)</div><div class="ttdoc">Calculate the total external force on a particle.</div><div class="ttdef"><b>Definition:</b> <a href="PenningTrap_8cpp_source.html#l00114">PenningTrap.cpp:114</a></div></div>
 <div class="ttc" id="aconstants_8hpp_html_a0acb682b8260ab1c60b918599864e2e5"><div class="ttname"><a href="constants_8hpp.html#a0acb682b8260ab1c60b918599864e2e5">T</a></div><div class="ttdeci">#define T</div><div class="ttdoc">1 Tesla. unit:</div><div class="ttdef"><b>Definition:</b> <a href="constants_8hpp_source.html#l00017">constants.hpp:17</a></div></div>
 <div class="ttc" id="autils_8hpp_html"><div class="ttname"><a href="utils_8hpp.html">utils.hpp</a></div><div class="ttdoc">Function prototypes and macros that are useful.</div></div>
-<div class="ttc" id="autils_8hpp_html_a0c95c4791692b06f8811905a76dbd772"><div class="ttname"><a href="utils_8hpp.html#a0c95c4791692b06f8811905a76dbd772">arma_vector_close_to</a></div><div class="ttdeci">bool arma_vector_close_to(arma::vec &amp;a, arma::vec &amp;b, double tol=1e-8)</div><div class="ttdoc">Test if two armadillo vectors are close to each other.</div><div class="ttdef"><b>Definition:</b> <a href="utils_8cpp_source.html#l00059">utils.cpp:59</a></div></div>
+<div class="ttc" id="autils_8hpp_html_a0c95c4791692b06f8811905a76dbd772"><div class="ttname"><a href="utils_8hpp.html#a0c95c4791692b06f8811905a76dbd772">arma_vector_close_to</a></div><div class="ttdeci">bool arma_vector_close_to(arma::vec &amp;a, arma::vec &amp;b, double tol=1e-8)</div><div class="ttdoc">Test if two armadillo vectors are close to each other.</div><div class="ttdef"><b>Definition:</b> <a href="utils_8cpp_source.html#l00062">utils.cpp:62</a></div></div>
 <div class="ttc" id="autils_8hpp_html_a73d4f21ad937dbc50a0c0538c78fd4f9"><div class="ttname"><a href="utils_8hpp.html#a73d4f21ad937dbc50a0c0538c78fd4f9">ASSERT</a></div><div class="ttdeci">#define ASSERT(expr, msg)</div><div class="ttdoc">A prettier assertion function.</div><div class="ttdef"><b>Definition:</b> <a href="utils_8hpp_source.html#l00045">utils.hpp:45</a></div></div>
 </div><!-- fragment --></div><!-- contents -->
 </div><!-- doc-content -->
diff --git a/docs/typedefs_8hpp.html b/docs/typedefs_8hpp.html
new file mode 100644
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--- /dev/null
+++ b/docs/typedefs_8hpp.html
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+   <div id="projectname">Penning Trap Simulation
+   </div>
+   <div id="projectbrief">Simulate particle behavior inside a Penning Trap</div>
+  </td>
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+ </tbody>
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+<div class="header">
+  <div class="summary">
+<a href="#typedef-members">Typedefs</a>  </div>
+  <div class="headertitle"><div class="title">typedefs.hpp File Reference</div></div>
+</div><!--header-->
+<div class="contents">
+
+<p>Useful typedefs for cleaner code.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;vector&gt;</code><br />
+<code>#include &lt;armadillo&gt;</code><br />
+</div>
+<p><a href="typedefs_8hpp_source.html">Go to the source code of this file.</a></p>
+<table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="typedef-members" name="typedef-members"></a>
+Typedefs</h2></td></tr>
+<tr class="memitem:a7c2dfa854274262c4e00e4ef0ab2ce23"><td class="memItemLeft" align="right" valign="top">typedef std::vector&lt; arma::vec::fixed&lt; 3 &gt; &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="typedefs_8hpp.html#a7c2dfa854274262c4e00e4ef0ab2ce23">sim_cols</a></td></tr>
+<tr class="memdesc:a7c2dfa854274262c4e00e4ef0ab2ce23"><td class="mdescLeft">&#160;</td><td class="mdescRight">Typedef for the column of the result vector from simulating particles.  <br /></td></tr>
+<tr class="separator:a7c2dfa854274262c4e00e4ef0ab2ce23"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a8502989b1b361725834fc185bd575f66"><td class="memItemLeft" align="right" valign="top">typedef std::vector&lt; arma::vec::fixed&lt; 3 &gt; &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="typedefs_8hpp.html#a8502989b1b361725834fc185bd575f66">sim_rows</a></td></tr>
+<tr class="memdesc:a8502989b1b361725834fc185bd575f66"><td class="mdescLeft">&#160;</td><td class="mdescRight">Typedef for the row of the result vector from simulating particles.  <br /></td></tr>
+<tr class="separator:a8502989b1b361725834fc185bd575f66"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:aec69d34220fff45de238b9e01f2686af"><td class="memItemLeft" align="right" valign="top">typedef std::vector&lt; <a class="el" href="typedefs_8hpp.html#a7c2dfa854274262c4e00e4ef0ab2ce23">sim_cols</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="typedefs_8hpp.html#aec69d34220fff45de238b9e01f2686af">sim_arr</a></td></tr>
+<tr class="memdesc:aec69d34220fff45de238b9e01f2686af"><td class="mdescLeft">&#160;</td><td class="mdescRight">Typedef for the result of the simulate method.  <br /></td></tr>
+<tr class="separator:aec69d34220fff45de238b9e01f2686af"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a9f33f4962c8fb62cc5ccd0e4e039a8df"><td class="memItemLeft" align="right" valign="top">typedef arma::vec::fixed&lt; 3 &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="typedefs_8hpp.html#a9f33f4962c8fb62cc5ccd0e4e039a8df">vec_3d</a></td></tr>
+<tr class="memdesc:a9f33f4962c8fb62cc5ccd0e4e039a8df"><td class="mdescLeft">&#160;</td><td class="mdescRight">Typedef for a fixed 3d arma vector.  <br /></td></tr>
+<tr class="separator:a9f33f4962c8fb62cc5ccd0e4e039a8df"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Useful typedefs for cleaner code. </p>
+<dl class="section author"><dt>Author</dt><dd>Cory Alexander Balaton (coryab) </dd>
+<dd>
+Janita Ovidie Sandtrøen Willumsen (janitaws)</dd></dl>
+<dl class="section version"><dt>Version</dt><dd>1.0</dd></dl>
+<p>These typedefs make the code more readable and easy to follow along.</p>
+<dl class="bug"><dt><b><a class="el" href="bug.html#_bug000004">Bug:</a></b></dt><dd>No known bugs </dd></dl>
+
+<p class="definition">Definition in file <a class="el" href="typedefs_8hpp_source.html">typedefs.hpp</a>.</p>
+</div><h2 class="groupheader">Typedef Documentation</h2>
+<a id="aec69d34220fff45de238b9e01f2686af" name="aec69d34220fff45de238b9e01f2686af"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aec69d34220fff45de238b9e01f2686af">&#9670;&#160;</a></span>sim_arr</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">typedef std::vector&lt;<a class="el" href="typedefs_8hpp.html#a7c2dfa854274262c4e00e4ef0ab2ce23">sim_cols</a>&gt; <a class="el" href="typedefs_8hpp.html#aec69d34220fff45de238b9e01f2686af">sim_arr</a></td>
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+      </table>
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+<p>Typedef for the result of the simulate method. </p>
+
+<p class="definition">Definition at line <a class="el" href="typedefs_8hpp_source.html#l00032">32</a> of file <a class="el" href="typedefs_8hpp_source.html">typedefs.hpp</a>.</p>
+
+</div>
+</div>
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+<h2 class="memtitle"><span class="permalink"><a href="#a7c2dfa854274262c4e00e4ef0ab2ce23">&#9670;&#160;</a></span>sim_cols</h2>
+
+<div class="memitem">
+<div class="memproto">
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+          <td class="memname">typedef std::vector&lt;arma::vec::fixed&lt;3&gt; &gt; <a class="el" href="typedefs_8hpp.html#a7c2dfa854274262c4e00e4ef0ab2ce23">sim_cols</a></td>
+        </tr>
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+<p>Typedef for the column of the result vector from simulating particles. </p>
+
+<p class="definition">Definition at line <a class="el" href="typedefs_8hpp_source.html#l00024">24</a> of file <a class="el" href="typedefs_8hpp_source.html">typedefs.hpp</a>.</p>
+
+</div>
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+<p>Typedef for the row of the result vector from simulating particles. </p>
+
+<p class="definition">Definition at line <a class="el" href="typedefs_8hpp_source.html#l00028">28</a> of file <a class="el" href="typedefs_8hpp_source.html">typedefs.hpp</a>.</p>
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+<h2 class="memtitle"><span class="permalink"><a href="#a9f33f4962c8fb62cc5ccd0e4e039a8df">&#9670;&#160;</a></span>vec_3d</h2>
+
+<div class="memitem">
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+  <div class="headertitle"><div class="title">typedefs.hpp</div></div>
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+<div class="contents">
+<a href="typedefs_8hpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span> </div>
+<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span><span class="preprocessor">#ifndef __TYPEDEFS__</span></div>
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+<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span><span class="preprocessor">#include &lt;armadillo&gt;</span></div>
+<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span> </div>
+<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"><a class="line" href="typedefs_8hpp.html#a7c2dfa854274262c4e00e4ef0ab2ce23">   24</a></span><span class="keyword">typedef</span> std::vector&lt;arma::vec::fixed&lt;3&gt;&gt; <a class="code hl_typedef" href="typedefs_8hpp.html#a7c2dfa854274262c4e00e4ef0ab2ce23">sim_cols</a>;</div>
+<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span> </div>
+<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"><a class="line" href="typedefs_8hpp.html#a8502989b1b361725834fc185bd575f66">   28</a></span><span class="keyword">typedef</span> std::vector&lt;arma::vec::fixed&lt;3&gt;&gt; <a class="code hl_typedef" href="typedefs_8hpp.html#a8502989b1b361725834fc185bd575f66">sim_rows</a>;</div>
+<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span> </div>
+<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"><a class="line" href="typedefs_8hpp.html#aec69d34220fff45de238b9e01f2686af">   32</a></span><span class="keyword">typedef</span> std::vector&lt;sim_cols&gt; <a class="code hl_typedef" href="typedefs_8hpp.html#aec69d34220fff45de238b9e01f2686af">sim_arr</a>;</div>
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+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="navelem"><a class="el" href="dir_d44c64559bbebec7f509842c48db8b23.html">include</a></li><li class="navelem"><a class="el" href="typedefs_8hpp.html">typedefs.hpp</a></li>
+    <li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.6 </li>
+  </ul>
+</div>
+</body>
+</html>
diff --git a/docs/utils_8cpp.html b/docs/utils_8cpp.html
index c2ffd2e..9401b51 100644
--- a/docs/utils_8cpp.html
+++ b/docs/utils_8cpp.html
@@ -106,7 +106,8 @@ $(document).ready(function(){initNavTree('utils_8cpp.html',''); initResizable();
 
 <p>Implementation of the utils.  
 <a href="#details">More...</a></p>
-<div class="textblock"><code>#include &quot;<a class="el" href="utils_8hpp_source.html">utils.hpp</a>&quot;</code><br />
+<div class="textblock"><code>#include &lt;sys/stat.h&gt;</code><br />
+<code>#include &quot;<a class="el" href="utils_8hpp_source.html">utils.hpp</a>&quot;</code><br />
 </div>
 <p><a href="utils_8cpp_source.html">Go to the source code of this file.</a></p>
 <table class="memberdecls">
@@ -124,6 +125,9 @@ Functions</h2></td></tr>
 <tr class="memitem:a5d2e1e032fd19614f2fbb58149a7b02a"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="utils_8cpp.html#a5d2e1e032fd19614f2fbb58149a7b02a">arma_vector_close_to</a> (arma::vec &amp;a, arma::vec &amp;b, double tol)</td></tr>
 <tr class="memdesc:a5d2e1e032fd19614f2fbb58149a7b02a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Test if two armadillo vectors are close to each other.  <br /></td></tr>
 <tr class="separator:a5d2e1e032fd19614f2fbb58149a7b02a"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:acf13f4e492199cb7231bfa646dbd08de"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="utils_8cpp.html#acf13f4e492199cb7231bfa646dbd08de">mkpath</a> (std::string path, int mode)</td></tr>
+<tr class="memdesc:acf13f4e492199cb7231bfa646dbd08de"><td class="mdescLeft">&#160;</td><td class="mdescRight">Make path given.  <br /></td></tr>
+<tr class="separator:acf13f4e492199cb7231bfa646dbd08de"><td class="memSeparator" colspan="2">&#160;</td></tr>
 </table>
 <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
 <div class="textblock"><p>Implementation of the utils. </p>
@@ -131,7 +135,7 @@ Functions</h2></td></tr>
 <dd>
 Janita Ovidie Sandtrøen Willumsen (janitaws)</dd></dl>
 <dl class="section version"><dt>Version</dt><dd>1.0</dd></dl>
-<dl class="bug"><dt><b><a class="el" href="bug.html#_bug000009">Bug:</a></b></dt><dd>No known bugs </dd></dl>
+<dl class="bug"><dt><b><a class="el" href="bug.html#_bug000010">Bug:</a></b></dt><dd>No known bugs </dd></dl>
 
 <p class="definition">Definition in file <a class="el" href="utils_8cpp_source.html">utils.cpp</a>.</p>
 </div><h2 class="groupheader">Function Documentation</h2>
@@ -177,9 +181,9 @@ Janita Ovidie Sandtrøen Willumsen (janitaws)</dd></dl>
   </table>
   </dd>
 </dl>
-<dl class="section return"><dt>Returns</dt><dd>Boolean </dd></dl>
+<dl class="section return"><dt>Returns</dt><dd>bool </dd></dl>
 
-<p class="definition">Definition at line <a class="el" href="utils_8cpp_source.html#l00059">59</a> of file <a class="el" href="utils_8cpp_source.html">utils.cpp</a>.</p>
+<p class="definition">Definition at line <a class="el" href="utils_8cpp_source.html#l00062">62</a> of file <a class="el" href="utils_8cpp_source.html">utils.cpp</a>.</p>
 
 </div>
 </div>
@@ -247,7 +251,48 @@ Janita Ovidie Sandtrøen Willumsen (janitaws)</dd></dl>
   </dd>
 </dl>
 
-<p class="definition">Definition at line <a class="el" href="utils_8cpp_source.html#l00040">40</a> of file <a class="el" href="utils_8cpp_source.html">utils.cpp</a>.</p>
+<p class="definition">Definition at line <a class="el" href="utils_8cpp_source.html#l00043">43</a> of file <a class="el" href="utils_8cpp_source.html">utils.cpp</a>.</p>
+
+</div>
+</div>
+<a id="acf13f4e492199cb7231bfa646dbd08de" name="acf13f4e492199cb7231bfa646dbd08de"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#acf13f4e492199cb7231bfa646dbd08de">&#9670;&#160;</a></span>mkpath()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">bool mkpath </td>
+          <td>(</td>
+          <td class="paramtype">std::string&#160;</td>
+          <td class="paramname"><em>path</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>mode</em> = <code>0777</code>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p>Make path given. </p>
+<p>This tries to be the equivalent to "mkdir -p" and creates a new directory whenever it needs to.</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">path</td><td>The path to be created </td></tr>
+    <tr><td class="paramname">mode</td><td>The mode/permissions for all the new directories</td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>bool </dd></dl>
+
+<p class="definition">Definition at line <a class="el" href="utils_8cpp_source.html#l00076">76</a> of file <a class="el" href="utils_8cpp_source.html">utils.cpp</a>.</p>
 
 </div>
 </div>
@@ -284,6 +329,7 @@ Janita Ovidie Sandtrøen Willumsen (janitaws)</dd></dl>
 </div><div class="memdoc">
 
 <p>Turns a vector of doubles into a string written in scientific format. </p>
+<p>The code is stolen from <a href="https://github.com/anderkve/FYS3150">https://github.com/anderkve/FYS3150</a>.</p>
 <dl class="params"><dt>Parameters</dt><dd>
   <table class="params">
     <tr><td class="paramname">v</td><td>The vector to stringify </td></tr>
@@ -292,9 +338,9 @@ Janita Ovidie Sandtrøen Willumsen (janitaws)</dd></dl>
   </table>
   </dd>
 </dl>
-<dl class="section return"><dt>Returns</dt><dd>String </dd></dl>
+<dl class="section return"><dt>Returns</dt><dd>std::string </dd></dl>
 
-<p class="definition">Definition at line <a class="el" href="utils_8cpp_source.html#l00021">21</a> of file <a class="el" href="utils_8cpp_source.html">utils.cpp</a>.</p>
+<p class="definition">Definition at line <a class="el" href="utils_8cpp_source.html#l00024">24</a> of file <a class="el" href="utils_8cpp_source.html">utils.cpp</a>.</p>
 
 </div>
 </div>
@@ -331,7 +377,7 @@ Janita Ovidie Sandtrøen Willumsen (janitaws)</dd></dl>
 </div><div class="memdoc">
 
 <p>Turns a double into a string written in scientific format. </p>
-<p>Code stolen from <a href="https://github.com/anderkve/FYS3150">https://github.com/anderkve/FYS3150</a> Header: <a href="https://github.com/anderkve/FYS3150/blob/master/code_examples/compilation_linking/example_1/include/utils.hpp">https://github.com/anderkve/FYS3150/blob/master/code_examples/compilation_linking/example_1/include/utils.hpp</a> Source: <a href="https://github.com/anderkve/FYS3150/blob/master/code_examples/compilation_linking/example_1/src/utils.cpp">https://github.com/anderkve/FYS3150/blob/master/code_examples/compilation_linking/example_1/src/utils.cpp</a> </p>
+<p>The code is stolen from <a href="https://github.com/anderkve/FYS3150">https://github.com/anderkve/FYS3150</a>.</p>
 <dl class="params"><dt>Parameters</dt><dd>
   <table class="params">
     <tr><td class="paramname">d</td><td>The number to stringify </td></tr>
@@ -340,9 +386,9 @@ Janita Ovidie Sandtrøen Willumsen (janitaws)</dd></dl>
   </table>
   </dd>
 </dl>
-<dl class="section return"><dt>Returns</dt><dd>String </dd></dl>
+<dl class="section return"><dt>Returns</dt><dd>std::string </dd></dl>
 
-<p class="definition">Definition at line <a class="el" href="utils_8cpp_source.html#l00014">14</a> of file <a class="el" href="utils_8cpp_source.html">utils.cpp</a>.</p>
+<p class="definition">Definition at line <a class="el" href="utils_8cpp_source.html#l00017">17</a> of file <a class="el" href="utils_8cpp_source.html">utils.cpp</a>.</p>
 
 </div>
 </div>
diff --git a/docs/utils_8cpp.js b/docs/utils_8cpp.js
index 36c50fa..362b36a 100644
--- a/docs/utils_8cpp.js
+++ b/docs/utils_8cpp.js
@@ -2,6 +2,7 @@ var utils_8cpp =
 [
     [ "arma_vector_close_to", "utils_8cpp.html#a5d2e1e032fd19614f2fbb58149a7b02a", null ],
     [ "m_assert", "utils_8cpp.html#aff5e07c3c1d321709b0cc38e999f427b", null ],
+    [ "mkpath", "utils_8cpp.html#acf13f4e492199cb7231bfa646dbd08de", null ],
     [ "scientific_format", "utils_8cpp.html#a58565270b643b24e3132f38c653e0199", null ],
     [ "scientific_format", "utils_8cpp.html#acd2a9c7a7d5a7fe9163be8c4cc110746", null ]
 ];
\ No newline at end of file
diff --git a/docs/utils_8cpp_source.html b/docs/utils_8cpp_source.html
index 069cd7c..5ed9571 100644
--- a/docs/utils_8cpp_source.html
+++ b/docs/utils_8cpp_source.html
@@ -102,69 +102,97 @@ $(document).ready(function(){initNavTree('utils_8cpp_source.html',''); initResiz
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 <div class="contents">
 <a href="utils_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span> </div>
-<div class="line"><a id="l00012" name="l00012"></a><span class="lineno">   12</span><span class="preprocessor">#include &quot;<a class="code" href="utils_8hpp.html">utils.hpp</a>&quot;</span></div>
-<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span> </div>
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-<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span>{</div>
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-<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span>    ss &lt;&lt; std::setw(width) &lt;&lt; std::setprecision(prec) &lt;&lt; std::scientific &lt;&lt; d;</div>
-<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span>    <span class="keywordflow">return</span> ss.str();</div>
-<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span>}</div>
-<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span> </div>
-<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"><a class="line" href="utils_8hpp.html#ad54b96a1074f9df4dc892a41d115b72d">   21</a></span>std::string <a class="code hl_function" href="utils_8cpp.html#acd2a9c7a7d5a7fe9163be8c4cc110746">scientific_format</a>(<span class="keyword">const</span> std::vector&lt;double&gt; &amp;v, <span class="keywordtype">int</span> width, <span class="keywordtype">int</span> prec)</div>
-<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span>{</div>
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-<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>        std::cout &lt;&lt; <span class="stringliteral">&quot;message: &quot;</span> &lt;&lt; msg &lt;&lt; <span class="stringliteral">&quot;\n\n&quot;</span>;</div>
-<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>    }</div>
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-<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>        std::cout &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span><span class="preprocessor">#include &lt;sys/stat.h&gt;</span></div>
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+<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span><span class="preprocessor">#include &quot;<a class="code" href="utils_8hpp.html">utils.hpp</a>&quot;</span></div>
+<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span> </div>
+<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"><a class="line" href="utils_8hpp.html#adfb618b2fdff47ef30a4a2b62c04f384">   17</a></span>std::string <a class="code hl_function" href="utils_8cpp.html#acd2a9c7a7d5a7fe9163be8c4cc110746">scientific_format</a>(<span class="keywordtype">double</span> d, <span class="keywordtype">int</span> width, <span class="keywordtype">int</span> prec)</div>
+<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span>{</div>
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+<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span>    <span class="keywordflow">return</span> ss.str();</div>
+<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span>}</div>
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+<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span>{</div>
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+<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>{</div>
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-<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>    std::cout &lt;&lt; f &lt;&lt; <span class="stringliteral">&quot;: &quot;</span>;</div>
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-<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>                  &lt;&lt; <span class="stringliteral">&quot;\&quot; Failed\n\n&quot;</span>;</div>
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-<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span> </div>
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-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>{</div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>    <span class="keywordflow">if</span> (a.n_elem != b.n_elem) {</div>
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-<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span> </div>
-<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; a.n_elem; i++) {</div>
-<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        <span class="keywordflow">if</span> (std::abs(a(i) - b(i)) &gt;= tol) {</div>
-<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
-<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>        }</div>
-<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>    }</div>
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-<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>}</div>
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-<div class="ttc" id="autils_8cpp_html_acd2a9c7a7d5a7fe9163be8c4cc110746"><div class="ttname"><a href="utils_8cpp.html#acd2a9c7a7d5a7fe9163be8c4cc110746">scientific_format</a></div><div class="ttdeci">std::string scientific_format(double d, int width, int prec)</div><div class="ttdoc">Turns a double into a string written in scientific format.</div><div class="ttdef"><b>Definition:</b> <a href="utils_8cpp_source.html#l00014">utils.cpp:14</a></div></div>
-<div class="ttc" id="autils_8cpp_html_aff5e07c3c1d321709b0cc38e999f427b"><div class="ttname"><a href="utils_8cpp.html#aff5e07c3c1d321709b0cc38e999f427b">m_assert</a></div><div class="ttdeci">void m_assert(bool expr, std::string expr_str, std::string f, std::string file, int line, std::string msg)</div><div class="ttdoc">Test an expression, confirm that test is ok, or abort execution.</div><div class="ttdef"><b>Definition:</b> <a href="utils_8cpp_source.html#l00040">utils.cpp:40</a></div></div>
+<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>    <span class="keywordflow">else</span> {</div>
+<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>        std::cout &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>    }</div>
+<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>}</div>
+<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span> </div>
+<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"><a class="line" href="utils_8hpp.html#a2cc3a2cdb635bac3c8b02e89d4d6af38">   43</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="utils_8cpp.html#aff5e07c3c1d321709b0cc38e999f427b">m_assert</a>(<span class="keywordtype">bool</span> expr, std::string expr_str, std::string f, std::string file,</div>
+<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>              <span class="keywordtype">int</span> line, std::string msg)</div>
+<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>{</div>
+<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>    std::string new_assert(f.size() + (expr ? 4 : 6), <span class="charliteral">&#39;-&#39;</span>);</div>
+<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>    std::cout &lt;&lt; <span class="stringliteral">&quot;\x1B[36m&quot;</span> &lt;&lt; new_assert &lt;&lt; <span class="stringliteral">&quot;\033[0m\n&quot;</span>;</div>
+<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>    std::cout &lt;&lt; f &lt;&lt; <span class="stringliteral">&quot;: &quot;</span>;</div>
+<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>    <span class="keywordflow">if</span> (expr) {</div>
+<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>        std::cout &lt;&lt; <span class="stringliteral">&quot;\x1B[32mOK\033[0m\n&quot;</span>;</div>
+<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>        print_message(msg);</div>
+<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>    }</div>
+<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>    <span class="keywordflow">else</span> {</div>
+<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>        std::cout &lt;&lt; <span class="stringliteral">&quot;\x1B[31mFAIL\033[0m\n&quot;</span>;</div>
+<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>        print_message(msg);</div>
+<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>        std::cout &lt;&lt; file &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; line &lt;&lt; <span class="stringliteral">&quot;: Assertion \&quot;&quot;</span> &lt;&lt; expr_str</div>
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+<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>        abort();</div>
+<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    }</div>
+<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>}</div>
+<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span> </div>
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+<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>{</div>
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+<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    }</div>
+<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span> </div>
+<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; a.n_elem; i++) {</div>
+<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>        <span class="keywordflow">if</span> (std::abs(a(i) - b(i)) &gt;= tol) {</div>
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+<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>        }</div>
+<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>    }</div>
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+<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span> </div>
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+<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>    <span class="keywordflow">if</span> (path.back() != <span class="charliteral">&#39;/&#39;</span>) {</div>
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+<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    }</div>
+<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>    <span class="keywordflow">while</span> (<span class="keyword">true</span>) {</div>
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+<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>        pos = path.find(<span class="charliteral">&#39;/&#39;</span>, pos);</div>
+<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>        <span class="keywordflow">if</span> (pos != std::string::npos) {</div>
+<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>            cur_dir = path.substr(0, pos);</div>
+<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>            <span class="keywordflow">if</span> (mkdir(cur_dir.c_str(), mode) != 0 &amp;&amp; stat(cur_dir.c_str(), &amp;buf) != 0) {</div>
+<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>                <span class="keywordflow">return</span> -1;</div>
+<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>            }</div>
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+<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>        <span class="keywordflow">else</span> {</div>
+<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>            <span class="keywordflow">break</span>;</div>
+<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>        }</div>
+<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>    }</div>
+<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>}</div>
+<div class="ttc" id="autils_8cpp_html_a5d2e1e032fd19614f2fbb58149a7b02a"><div class="ttname"><a href="utils_8cpp.html#a5d2e1e032fd19614f2fbb58149a7b02a">arma_vector_close_to</a></div><div class="ttdeci">bool arma_vector_close_to(arma::vec &amp;a, arma::vec &amp;b, double tol)</div><div class="ttdoc">Test if two armadillo vectors are close to each other.</div><div class="ttdef"><b>Definition:</b> <a href="utils_8cpp_source.html#l00062">utils.cpp:62</a></div></div>
+<div class="ttc" id="autils_8cpp_html_acd2a9c7a7d5a7fe9163be8c4cc110746"><div class="ttname"><a href="utils_8cpp.html#acd2a9c7a7d5a7fe9163be8c4cc110746">scientific_format</a></div><div class="ttdeci">std::string scientific_format(double d, int width, int prec)</div><div class="ttdoc">Turns a double into a string written in scientific format.</div><div class="ttdef"><b>Definition:</b> <a href="utils_8cpp_source.html#l00017">utils.cpp:17</a></div></div>
+<div class="ttc" id="autils_8cpp_html_acf13f4e492199cb7231bfa646dbd08de"><div class="ttname"><a href="utils_8cpp.html#acf13f4e492199cb7231bfa646dbd08de">mkpath</a></div><div class="ttdeci">bool mkpath(std::string path, int mode)</div><div class="ttdoc">Make path given.</div><div class="ttdef"><b>Definition:</b> <a href="utils_8cpp_source.html#l00076">utils.cpp:76</a></div></div>
+<div class="ttc" id="autils_8cpp_html_aff5e07c3c1d321709b0cc38e999f427b"><div class="ttname"><a href="utils_8cpp.html#aff5e07c3c1d321709b0cc38e999f427b">m_assert</a></div><div class="ttdeci">void m_assert(bool expr, std::string expr_str, std::string f, std::string file, int line, std::string msg)</div><div class="ttdoc">Test an expression, confirm that test is ok, or abort execution.</div><div class="ttdef"><b>Definition:</b> <a href="utils_8cpp_source.html#l00043">utils.cpp:43</a></div></div>
 <div class="ttc" id="autils_8hpp_html"><div class="ttname"><a href="utils_8hpp.html">utils.hpp</a></div><div class="ttdoc">Function prototypes and macros that are useful.</div></div>
 </div><!-- fragment --></div><!-- contents -->
 </div><!-- doc-content -->
diff --git a/docs/utils_8hpp.html b/docs/utils_8hpp.html
index dea4601..2866ae0 100644
--- a/docs/utils_8hpp.html
+++ b/docs/utils_8hpp.html
@@ -124,6 +124,7 @@ Macros</h2></td></tr>
 <tr class="memdesc:a73d4f21ad937dbc50a0c0538c78fd4f9"><td class="mdescLeft">&#160;</td><td class="mdescRight">A prettier assertion function.  <br /></td></tr>
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 <tr class="memitem:a60dca3177fb9cb5256609adc7af55168"><td class="memItemLeft" align="right" valign="top">#define&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="utils_8hpp.html#a60dca3177fb9cb5256609adc7af55168">__METHOD_NAME__</a>&#160;&#160;&#160;methodName(__PRETTY_FUNCTION__)</td></tr>
+<tr class="memdesc:a60dca3177fb9cb5256609adc7af55168"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get the name of the current method/function.  <br /></td></tr>
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@@ -140,6 +141,9 @@ Functions</h2></td></tr>
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 <tr class="memdesc:a0c95c4791692b06f8811905a76dbd772"><td class="mdescLeft">&#160;</td><td class="mdescRight">Test if two armadillo vectors are close to each other.  <br /></td></tr>
 <tr class="separator:a0c95c4791692b06f8811905a76dbd772"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a6fdd7217b750aff5b6295ece7cbdeffa"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="utils_8hpp.html#a6fdd7217b750aff5b6295ece7cbdeffa">mkpath</a> (std::string path, int mode=0777)</td></tr>
+<tr class="memdesc:a6fdd7217b750aff5b6295ece7cbdeffa"><td class="mdescLeft">&#160;</td><td class="mdescRight">Make path given.  <br /></td></tr>
+<tr class="separator:a6fdd7217b750aff5b6295ece7cbdeffa"><td class="memSeparator" colspan="2">&#160;</td></tr>
 </table>
 <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
 <div class="textblock"><p>Function prototypes and macros that are useful. </p>
@@ -148,7 +152,7 @@ Functions</h2></td></tr>
 Janita Ovidie Sandtrøen Willumsen (janitaws)</dd></dl>
 <dl class="section version"><dt>Version</dt><dd>1.0</dd></dl>
 <p>These utility function are mainly for convenience and aren't directly related to the project.</p>
-<dl class="bug"><dt><b><a class="el" href="bug.html#_bug000004">Bug:</a></b></dt><dd>No known bugs </dd></dl>
+<dl class="bug"><dt><b><a class="el" href="bug.html#_bug000005">Bug:</a></b></dt><dd>No known bugs </dd></dl>
 
 <p class="definition">Definition in file <a class="el" href="utils_8hpp_source.html">utils.hpp</a>.</p>
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@@ -164,7 +168,9 @@ Janita Ovidie Sandtrøen Willumsen (janitaws)</dd></dl>
       </table>
 </div><div class="memdoc">
 
-<p class="definition">Definition at line <a class="el" href="utils_8hpp_source.html#l00048">48</a> of file <a class="el" href="utils_8hpp_source.html">utils.hpp</a>.</p>
+<p>Get the name of the current method/function. </p>
+
+<p class="definition">Definition at line <a class="el" href="utils_8hpp_source.html#l00051">51</a> of file <a class="el" href="utils_8hpp_source.html">utils.hpp</a>.</p>
 
 </div>
 </div>
@@ -193,9 +199,10 @@ Janita Ovidie Sandtrøen Willumsen (janitaws)</dd></dl>
         </tr>
       </table>
 </div><div class="memdoc">
-<b>Value:</b><div class="fragment"><div class="line">                                   <a class="code hl_function" href="utils_8hpp.html#a2cc3a2cdb635bac3c8b02e89d4d6af38">m_assert</a>(expr, #expr, __METHOD_NAME__, __FILE__, \</div>
+<b>Value:</b><div class="fragment"><div class="line">                                   <a class="code hl_function" href="utils_8hpp.html#a2cc3a2cdb635bac3c8b02e89d4d6af38">m_assert</a>(expr, #expr, <a class="code hl_define" href="utils_8hpp.html#a60dca3177fb9cb5256609adc7af55168">__METHOD_NAME__</a>, __FILE__, \</div>
 <div class="line">                                   __LINE__, msg)</div>
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+<div class="ttc" id="autils_8hpp_html_a2cc3a2cdb635bac3c8b02e89d4d6af38"><div class="ttname"><a href="utils_8hpp.html#a2cc3a2cdb635bac3c8b02e89d4d6af38">m_assert</a></div><div class="ttdeci">void m_assert(bool expr, std::string expr_str, std::string func, std::string file, int line, std::string msg)</div><div class="ttdoc">Test an expression, confirm that test is ok, or abort execution.</div><div class="ttdef"><b>Definition:</b> <a href="utils_8cpp_source.html#l00043">utils.cpp:43</a></div></div>
+<div class="ttc" id="autils_8hpp_html_a60dca3177fb9cb5256609adc7af55168"><div class="ttname"><a href="utils_8hpp.html#a60dca3177fb9cb5256609adc7af55168">__METHOD_NAME__</a></div><div class="ttdeci">#define __METHOD_NAME__</div><div class="ttdoc">Get the name of the current method/function.</div><div class="ttdef"><b>Definition:</b> <a href="utils_8hpp_source.html#l00051">utils.hpp:51</a></div></div>
 </div><!-- fragment -->
 <p>A prettier assertion function. </p>
 <p>This macro calls the m_assert function which is a more informative assertion function than the regular assert function from cassert. </p>
@@ -270,9 +277,9 @@ Janita Ovidie Sandtrøen Willumsen (janitaws)</dd></dl>
   </table>
   </dd>
 </dl>
-<dl class="section return"><dt>Returns</dt><dd>Boolean </dd></dl>
+<dl class="section return"><dt>Returns</dt><dd>bool </dd></dl>
 
-<p class="definition">Definition at line <a class="el" href="utils_8cpp_source.html#l00059">59</a> of file <a class="el" href="utils_8cpp_source.html">utils.cpp</a>.</p>
+<p class="definition">Definition at line <a class="el" href="utils_8cpp_source.html#l00062">62</a> of file <a class="el" href="utils_8cpp_source.html">utils.cpp</a>.</p>
 
 </div>
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@@ -340,7 +347,48 @@ Janita Ovidie Sandtrøen Willumsen (janitaws)</dd></dl>
   </dd>
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-<p class="definition">Definition at line <a class="el" href="utils_8cpp_source.html#l00040">40</a> of file <a class="el" href="utils_8cpp_source.html">utils.cpp</a>.</p>
+<p class="definition">Definition at line <a class="el" href="utils_8cpp_source.html#l00043">43</a> of file <a class="el" href="utils_8cpp_source.html">utils.cpp</a>.</p>
+
+</div>
+</div>
+<a id="a6fdd7217b750aff5b6295ece7cbdeffa" name="a6fdd7217b750aff5b6295ece7cbdeffa"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a6fdd7217b750aff5b6295ece7cbdeffa">&#9670;&#160;</a></span>mkpath()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">bool mkpath </td>
+          <td>(</td>
+          <td class="paramtype">std::string&#160;</td>
+          <td class="paramname"><em>path</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>mode</em> = <code>0777</code>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p>Make path given. </p>
+<p>This tries to be the equivalent to "mkdir -p" and creates a new directory whenever it needs to.</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">path</td><td>The path to be created </td></tr>
+    <tr><td class="paramname">mode</td><td>The mode/permissions for all the new directories</td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>bool </dd></dl>
+
+<p class="definition">Definition at line <a class="el" href="utils_8cpp_source.html#l00076">76</a> of file <a class="el" href="utils_8cpp_source.html">utils.cpp</a>.</p>
 
 </div>
 </div>
@@ -377,6 +425,7 @@ Janita Ovidie Sandtrøen Willumsen (janitaws)</dd></dl>
 </div><div class="memdoc">
 
 <p>Turns a vector of doubles into a string written in scientific format. </p>
+<p>The code is stolen from <a href="https://github.com/anderkve/FYS3150">https://github.com/anderkve/FYS3150</a>.</p>
 <dl class="params"><dt>Parameters</dt><dd>
   <table class="params">
     <tr><td class="paramname">v</td><td>The vector to stringify </td></tr>
@@ -385,9 +434,9 @@ Janita Ovidie Sandtrøen Willumsen (janitaws)</dd></dl>
   </table>
   </dd>
 </dl>
-<dl class="section return"><dt>Returns</dt><dd>String </dd></dl>
+<dl class="section return"><dt>Returns</dt><dd>std::string </dd></dl>
 
-<p class="definition">Definition at line <a class="el" href="utils_8cpp_source.html#l00021">21</a> of file <a class="el" href="utils_8cpp_source.html">utils.cpp</a>.</p>
+<p class="definition">Definition at line <a class="el" href="utils_8cpp_source.html#l00024">24</a> of file <a class="el" href="utils_8cpp_source.html">utils.cpp</a>.</p>
 
 </div>
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 <p>Turns a double into a string written in scientific format. </p>
-<p>Code stolen from <a href="https://github.com/anderkve/FYS3150">https://github.com/anderkve/FYS3150</a> Header: <a href="https://github.com/anderkve/FYS3150/blob/master/code_examples/compilation_linking/example_1/include/utils.hpp">https://github.com/anderkve/FYS3150/blob/master/code_examples/compilation_linking/example_1/include/utils.hpp</a> Source: <a href="https://github.com/anderkve/FYS3150/blob/master/code_examples/compilation_linking/example_1/src/utils.cpp">https://github.com/anderkve/FYS3150/blob/master/code_examples/compilation_linking/example_1/src/utils.cpp</a> </p>
+<p>The code is stolen from <a href="https://github.com/anderkve/FYS3150">https://github.com/anderkve/FYS3150</a>.</p>
 <dl class="params"><dt>Parameters</dt><dd>
   <table class="params">
     <tr><td class="paramname">d</td><td>The number to stringify </td></tr>
@@ -433,9 +482,9 @@ Janita Ovidie Sandtrøen Willumsen (janitaws)</dd></dl>
   </table>
   </dd>
 </dl>
-<dl class="section return"><dt>Returns</dt><dd>String </dd></dl>
+<dl class="section return"><dt>Returns</dt><dd>std::string </dd></dl>
 
-<p class="definition">Definition at line <a class="el" href="utils_8cpp_source.html#l00014">14</a> of file <a class="el" href="utils_8cpp_source.html">utils.cpp</a>.</p>
+<p class="definition">Definition at line <a class="el" href="utils_8cpp_source.html#l00017">17</a> of file <a class="el" href="utils_8cpp_source.html">utils.cpp</a>.</p>
 
 </div>
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diff --git a/docs/utils_8hpp.js b/docs/utils_8hpp.js
index 34c7b36..68951df 100644
--- a/docs/utils_8hpp.js
+++ b/docs/utils_8hpp.js
@@ -1,9 +1,11 @@
 var utils_8hpp =
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+    [ "__METHOD_NAME__", "utils_8hpp.html#a60dca3177fb9cb5256609adc7af55168", null ],
     [ "ASSERT", "utils_8hpp.html#a73d4f21ad937dbc50a0c0538c78fd4f9", null ],
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     [ "arma_vector_close_to", "utils_8hpp.html#a0c95c4791692b06f8811905a76dbd772", null ],
     [ "m_assert", "utils_8hpp.html#a2cc3a2cdb635bac3c8b02e89d4d6af38", null ],
+    [ "mkpath", "utils_8hpp.html#a6fdd7217b750aff5b6295ece7cbdeffa", null ],
     [ "scientific_format", "utils_8hpp.html#ad54b96a1074f9df4dc892a41d115b72d", null ],
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+<div class="ttc" id="autils_8hpp_html_a0c95c4791692b06f8811905a76dbd772"><div class="ttname"><a href="utils_8hpp.html#a0c95c4791692b06f8811905a76dbd772">arma_vector_close_to</a></div><div class="ttdeci">bool arma_vector_close_to(arma::vec &amp;a, arma::vec &amp;b, double tol=1e-8)</div><div class="ttdoc">Test if two armadillo vectors are close to each other.</div><div class="ttdef"><b>Definition:</b> <a href="utils_8cpp_source.html#l00062">utils.cpp:62</a></div></div>
+<div class="ttc" id="autils_8hpp_html_a2cc3a2cdb635bac3c8b02e89d4d6af38"><div class="ttname"><a href="utils_8hpp.html#a2cc3a2cdb635bac3c8b02e89d4d6af38">m_assert</a></div><div class="ttdeci">void m_assert(bool expr, std::string expr_str, std::string func, std::string file, int line, std::string msg)</div><div class="ttdoc">Test an expression, confirm that test is ok, or abort execution.</div><div class="ttdef"><b>Definition:</b> <a href="utils_8cpp_source.html#l00043">utils.cpp:43</a></div></div>
+<div class="ttc" id="autils_8hpp_html_a6fdd7217b750aff5b6295ece7cbdeffa"><div class="ttname"><a href="utils_8hpp.html#a6fdd7217b750aff5b6295ece7cbdeffa">mkpath</a></div><div class="ttdeci">bool mkpath(std::string path, int mode=0777)</div><div class="ttdoc">Make path given.</div><div class="ttdef"><b>Definition:</b> <a href="utils_8cpp_source.html#l00076">utils.cpp:76</a></div></div>
+<div class="ttc" id="autils_8hpp_html_adfb618b2fdff47ef30a4a2b62c04f384"><div class="ttname"><a href="utils_8hpp.html#adfb618b2fdff47ef30a4a2b62c04f384">scientific_format</a></div><div class="ttdeci">std::string scientific_format(double d, int width=20, int prec=10)</div><div class="ttdoc">Turns a double into a string written in scientific format.</div><div class="ttdef"><b>Definition:</b> <a href="utils_8cpp_source.html#l00017">utils.cpp:17</a></div></div>
 </div><!-- fragment --></div><!-- contents -->
 </div><!-- doc-content -->
 <!-- start footer part -->
diff --git a/man_pages/man3/Particle.3 b/man_pages/man3/Particle.3
index f37639d..ebff781 100644
--- a/man_pages/man3/Particle.3
+++ b/man_pages/man3/Particle.3
@@ -1,4 +1,4 @@
-.TH "Particle" 3 "Sun Oct 8 2023" "Penning Trap Simulation" \" -*- nroff -*-
+.TH "Particle" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
 .ad l
 .nh
 .SH NAME
@@ -13,7 +13,7 @@ Particle \- A class that holds attributes of a particle\&.
 
 .in +1c
 .ti -1c
-.RI "\fBParticle\fP (double \fBq\fP, double \fBm\fP, arma::vec::fixed< 3 > \fBr_vec\fP, arma::vec::fixed< 3 > \fBv_vec\fP)"
+.RI "\fBParticle\fP (double \fBq\fP, double \fBm\fP, \fBvec_3d\fP \fBr_vec\fP, \fBvec_3d\fP \fBv_vec\fP)"
 .br
 .RI "Initialize the particle\&. "
 .in -1c
@@ -29,11 +29,11 @@ Particle \- A class that holds attributes of a particle\&.
 .br
 .RI "Mass\&. "
 .ti -1c
-.RI "arma::vec::fixed< 3 > \fBr_vec\fP"
+.RI "\fBvec_3d\fP \fBr_vec\fP"
 .br
 .RI "position "
 .ti -1c
-.RI "arma::vec::fixed< 3 > \fBv_vec\fP"
+.RI "\fBvec_3d\fP \fBv_vec\fP"
 .br
 .RI "velocity "
 .in -1c
@@ -49,15 +49,28 @@ Particle \- A class that holds attributes of a particle\&.
 .PP 
 A class that holds attributes of a particle\&. 
 .PP
-Definition at line \fB19\fP of file \fBParticle\&.hpp\fP\&.
+Definition at line \fB21\fP of file \fBParticle\&.hpp\fP\&.
 .SH "Constructor & Destructor Documentation"
 .PP 
-.SS "Particle::Particle (double q, double m, arma::vec::fixed< 3 > r_vec, arma::vec::fixed< 3 > v_vec)"
+.SS "Particle::Particle (double q, double m, \fBvec_3d\fP r_vec, \fBvec_3d\fP v_vec)"
 
 .PP
-Initialize the particle\&. Initialize the particle with a charge, mass, position and velocity\&. 
+Initialize the particle\&. Initialize the particle with a charge, mass, position and velocity\&.
 .PP
-Definition at line \fB16\fP of file \fBParticle\&.cpp\fP\&.
+\fBParameters\fP
+.RS 4
+\fIq\fP The charge of the particle 
+.br
+\fIm\fP The mass of the particle 
+.br
+\fIr_vec\fP The initial position of the particle 
+.br
+\fIv_vec\fP The initial velocity of the particle 
+.RE
+.PP
+
+.PP
+Definition at line \fB15\fP of file \fBParticle\&.cpp\fP\&.
 .SH "Friends And Related Function Documentation"
 .PP 
 .SS "friend class \fBPenningTrap\fP\fC [friend]\fP"
@@ -65,7 +78,7 @@ Definition at line \fB16\fP of file \fBParticle\&.cpp\fP\&.
 .PP
 Make private attributes available for \fBPenningTrap\fP\&. 
 .PP
-Definition at line \fB38\fP of file \fBParticle\&.hpp\fP\&.
+Definition at line \fB43\fP of file \fBParticle\&.hpp\fP\&.
 .SH "Member Data Documentation"
 .PP 
 .SS "double Particle::m\fC [private]\fP"
@@ -73,25 +86,25 @@ Definition at line \fB38\fP of file \fBParticle\&.hpp\fP\&.
 .PP
 Mass\&. 
 .PP
-Definition at line \fB22\fP of file \fBParticle\&.hpp\fP\&.
+Definition at line \fB24\fP of file \fBParticle\&.hpp\fP\&.
 .SS "double Particle::q\fC [private]\fP"
 
 .PP
 Charge\&. 
 .PP
-Definition at line \fB21\fP of file \fBParticle\&.hpp\fP\&.
-.SS "arma::vec::fixed<3> Particle::r_vec\fC [private]\fP"
+Definition at line \fB23\fP of file \fBParticle\&.hpp\fP\&.
+.SS "\fBvec_3d\fP Particle::r_vec\fC [private]\fP"
 
 .PP
 position 
 .PP
-Definition at line \fB23\fP of file \fBParticle\&.hpp\fP\&.
-.SS "arma::vec::fixed<3> Particle::v_vec\fC [private]\fP"
+Definition at line \fB25\fP of file \fBParticle\&.hpp\fP\&.
+.SS "\fBvec_3d\fP Particle::v_vec\fC [private]\fP"
 
 .PP
 velocity 
 .PP
-Definition at line \fB24\fP of file \fBParticle\&.hpp\fP\&.
+Definition at line \fB26\fP of file \fBParticle\&.hpp\fP\&.
 
 .SH "Author"
 .PP 
diff --git a/man_pages/man3/Particle.cpp.3 b/man_pages/man3/Particle.cpp.3
index 7a93b45..904c7a4 100644
--- a/man_pages/man3/Particle.cpp.3
+++ b/man_pages/man3/Particle.cpp.3
@@ -1,4 +1,4 @@
-.TH "src/Particle.cpp" 3 "Sun Oct 8 2023" "Penning Trap Simulation" \" -*- nroff -*-
+.TH "src/Particle.cpp" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
 .ad l
 .nh
 .SH NAME
@@ -31,7 +31,7 @@ Janita Ovidie Sandtrøen Willumsen (janitaws)
 .PP
 \fBBug\fP
 .RS 4
-No known bugs
+No known bugs 
 .RE
 .PP
 
diff --git a/man_pages/man3/Particle.hpp.3 b/man_pages/man3/Particle.hpp.3
index abb26a7..2033d14 100644
--- a/man_pages/man3/Particle.hpp.3
+++ b/man_pages/man3/Particle.hpp.3
@@ -1,4 +1,4 @@
-.TH "include/Particle.hpp" 3 "Sun Oct 8 2023" "Penning Trap Simulation" \" -*- nroff -*-
+.TH "include/Particle.hpp" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
 .ad l
 .nh
 .SH NAME
@@ -9,6 +9,8 @@ include/Particle.hpp \- A class that holds the properties of a particle\&.
 .PP
 \fC#include <armadillo>\fP
 .br
+\fC#include 'typedefs\&.hpp'\fP
+.br
 
 .SS "Classes"
 
diff --git a/man_pages/man3/PenningTrap.3 b/man_pages/man3/PenningTrap.3
index 2087bb5..51cca93 100644
--- a/man_pages/man3/PenningTrap.3
+++ b/man_pages/man3/PenningTrap.3
@@ -1,4 +1,4 @@
-.TH "PenningTrap" 3 "Sun Oct 8 2023" "Penning Trap Simulation" \" -*- nroff -*-
+.TH "PenningTrap" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
 .ad l
 .nh
 .SH NAME
@@ -13,51 +13,77 @@ PenningTrap \- A class that simulates a Penning trap\&.
 
 .in +1c
 .ti -1c
-.RI "\fBPenningTrap\fP (double \fBB_0\fP=\fBT\fP, double \fBV_0\fP=25\&.*\fBV\fP/1000\&., double \fBd\fP=500\&.)"
+.RI "\fBPenningTrap\fP (double \fBB_0\fP=\fBT\fP, std::function< double(double)> \fBV_0\fP=[](double \fBt\fP) { return 25\&. *\fBV\fP/1000\&.;}, double \fBd\fP=500\&., double \fBt\fP=0\&.)"
 .br
-.RI "Set B_0, V_0 and d\&. "
+.RI "Constructor for the \fBPenningTrap\fP class\&. "
+.ti -1c
+.RI "\fBPenningTrap\fP (unsigned int i, double \fBB_0\fP=\fBT\fP, std::function< double(double)> \fBV_0\fP=[](double \fBt\fP) { return 25\&. *\fBV\fP/1000\&.;}, double \fBd\fP=500\&., double \fBt\fP=0\&.)"
+.br
+.RI "Constructor for the \fBPenningTrap\fP class\&. "
+.ti -1c
+.RI "\fBPenningTrap\fP (std::vector< \fBParticle\fP > \fBparticles\fP, double \fBB_0\fP=\fBT\fP, std::function< double(double)> \fBV_0\fP=[](double \fBt\fP) { return 25\&. *\fBV\fP/1000\&.;}, double \fBd\fP=500\&., double \fBt\fP=0\&.)"
+.br
+.RI "Constructor for the \fBPenningTrap\fP class\&. "
 .ti -1c
 .RI "void \fBadd_particle\fP (\fBParticle\fP particle)"
 .br
 .RI "Add a particle to the system\&. "
 .ti -1c
-.RI "arma::vec \fBexternal_E_field\fP (arma::vec r)"
+.RI "\fBvec_3d\fP \fBexternal_E_field\fP (\fBvec_3d\fP r)"
 .br
 .RI "Calculate E at point r\&. "
 .ti -1c
-.RI "arma::vec \fBexternal_B_field\fP (arma::vec r)"
+.RI "\fBvec_3d\fP \fBexternal_B_field\fP (\fBvec_3d\fP r)"
 .br
 .RI "Calculate B at point r\&. "
 .ti -1c
-.RI "arma::vec \fBforce_on_particle\fP (int i, int j)"
+.RI "\fBvec_3d\fP \fBforce_on_particle\fP (unsigned int i, unsigned int j)"
 .br
 .RI "Calculate the force between 2 particles\&. "
 .ti -1c
-.RI "arma::vec \fBtotal_force_external\fP (int i)"
+.RI "\fBvec_3d\fP \fBtotal_force_external\fP (unsigned int i)"
 .br
 .RI "Calculate the total external force on a particle\&. "
 .ti -1c
-.RI "arma::vec \fBtotal_force_particles\fP (int i)"
+.RI "\fBvec_3d\fP \fBtotal_force_particles\fP (unsigned int i)"
 .br
-.RI "Calculate the total force on a particle from other particles\&. "
+.RI "Calculate the total force on a particle p_i from other particles\&. "
 .ti -1c
-.RI "arma::vec \fBtotal_force\fP (int i)"
+.RI "\fBvec_3d\fP \fBtotal_force\fP (unsigned int i)"
 .br
-.RI "calculate the total force on a particle\&. "
+.RI "calculate the total force on a particle p_i\&. "
 .ti -1c
-.RI "void \fBevolve_RK4\fP (double dt)"
+.RI "void \fBevolve_RK4\fP (double dt, bool particle_interaction=true)"
 .br
 .RI "Go forward one timestep using the RK4 method\&. "
 .ti -1c
-.RI "void \fBevolve_forward_euler\fP (double dt)"
+.RI "void \fBevolve_forward_euler\fP (double dt, bool particle_interaction=true)"
 .br
 .RI "Go forward one timestep using the forward Euler method\&. "
 .ti -1c
-.RI "arma::vec \fBget_particle\fP (int i)"
+.RI "\fBsim_arr\fP \fBsimulate\fP (double time, unsigned int steps, std::string method='rk4', bool particle_interaction=true)"
 .br
+.RI "Simulate the particle system inside the Penning trap over a certain amount of time\&. "
 .ti -1c
-.RI "double \fBget_d\fP ()"
+.RI "void \fBwrite_simulation_to_dir\fP (std::string path, double time, unsigned int steps, std::string method='rk4', bool particle_interaction=true)"
 .br
+.RI "Simulate and write the displacement of all particles to files\&. "
+.ti -1c
+.RI "double \fBfraction_of_particles_left\fP (double time, unsigned int steps, std::string method='rk4', bool particle_interaction=true)"
+.br
+.RI "Simulate and calculate what fraction of particles are still left inside the Penning trap after the simulation\&. "
+.in -1c
+.SS "Private Member Functions"
+
+.in +1c
+.ti -1c
+.RI "\fBvec_3d\fP \fBv_func\fP (unsigned int i, unsigned int j, double dt)"
+.br
+.RI "Helper for evolve_RK4 when calculating $k_{v,i,j}$ values\&. "
+.ti -1c
+.RI "\fBvec_3d\fP \fBr_func\fP (unsigned int i, unsigned int j, double dt)"
+.br
+.RI "Helper for evolve_RK4 when calculating $k_{r,i,j}$ values\&. "
 .in -1c
 .SS "Private Attributes"
 
@@ -67,7 +93,7 @@ PenningTrap \- A class that simulates a Penning trap\&.
 .br
 .RI "Magnetic field strength\&. "
 .ti -1c
-.RI "double \fBV_0\fP"
+.RI "std::function< double(double)> \fBV_0\fP"
 .br
 .RI "Applied potential\&. "
 .ti -1c
@@ -75,9 +101,19 @@ PenningTrap \- A class that simulates a Penning trap\&.
 .br
 .RI "Characteristic dimension\&. "
 .ti -1c
+.RI "double \fBt\fP"
+.br
+.RI "Current time\&. "
+.ti -1c
 .RI "std::vector< \fBParticle\fP > \fBparticles\fP"
 .br
 .RI "The particles in the Penning trap\&. "
+.ti -1c
+.RI "\fBsim_arr\fP \fBk_v\fP"
+.br
+.ti -1c
+.RI "\fBsim_arr\fP \fBk_r\fP"
+.br
 .in -1c
 .SH "Detailed Description"
 .PP 
@@ -85,15 +121,70 @@ A class that simulates a Penning trap\&.
 
 This class simulates a Penning trap\&. It can take in a number of particles and simulate how they would behave inside a Penning trap\&. 
 .PP
-Definition at line \fB29\fP of file \fBPenningTrap\&.hpp\fP\&.
+Definition at line \fB30\fP of file \fBPenningTrap\&.hpp\fP\&.
 .SH "Constructor & Destructor Documentation"
 .PP 
-.SS "PenningTrap::PenningTrap (double B_0 = \fC\fBT\fP\fP, double V_0 = \fC25\&.*\fBV\fP/1000\&.\fP, double d = \fC500\&.\fP)"
+.SS "PenningTrap::PenningTrap (double B_0 = \fC\fBT\fP\fP, std::function< double(double)> V_0 = \fC[](double \fBt\fP) { return 25\&. * \fBV\fP / 1000\&.; }\fP, double d = \fC500\&.\fP, double t = \fC0\&.\fP)"
 
 .PP
-Set B_0, V_0 and d\&. 
+Constructor for the \fBPenningTrap\fP class\&. 
 .PP
-Definition at line \fB20\fP of file \fBPenningTrap\&.cpp\fP\&.
+\fBParameters\fP
+.RS 4
+\fIB_0\fP The magnetic field strength 
+.br
+\fIV_0\fP The time dependent applied potential 
+.br
+\fId\fP The characteristic dimension 
+.br
+\fIt\fP The starting time 
+.RE
+.PP
+
+.PP
+Definition at line \fB18\fP of file \fBPenningTrap\&.cpp\fP\&.
+.SS "PenningTrap::PenningTrap (unsigned int i, double B_0 = \fC\fBT\fP\fP, std::function< double(double)> V_0 = \fC[](double \fBt\fP) { return 25\&. * \fBV\fP / 1000\&.; }\fP, double d = \fC500\&.\fP, double t = \fC0\&.\fP)"
+
+.PP
+Constructor for the \fBPenningTrap\fP class\&. 
+.PP
+\fBParameters\fP
+.RS 4
+\fIi\fP The number of particles to generate 
+.br
+\fIB_0\fP The magnetic field strength 
+.br
+\fIV_0\fP The time dependent applied potential 
+.br
+\fId\fP The characteristic dimension 
+.br
+\fIt\fP The starting time 
+.RE
+.PP
+
+.PP
+Definition at line \fB27\fP of file \fBPenningTrap\&.cpp\fP\&.
+.SS "PenningTrap::PenningTrap (std::vector< \fBParticle\fP > particles, double B_0 = \fC\fBT\fP\fP, std::function< double(double)> V_0 = \fC[](double \fBt\fP) { return 25\&. * \fBV\fP / 1000\&.; }\fP, double d = \fC500\&.\fP, double t = \fC0\&.\fP)"
+
+.PP
+Constructor for the \fBPenningTrap\fP class\&. 
+.PP
+\fBParameters\fP
+.RS 4
+\fIparticles\fP The starting particles 
+.br
+\fIB_0\fP The magnetic field strength 
+.br
+\fIV_0\fP The time dependent applied potential 
+.br
+\fId\fP The characteristic dimension 
+.br
+\fIt\fP The starting time 
+.RE
+.PP
+
+.PP
+Definition at line \fB39\fP of file \fBPenningTrap\&.cpp\fP\&.
 .SH "Member Function Documentation"
 .PP 
 .SS "void PenningTrap::add_particle (\fBParticle\fP particle)"
@@ -101,63 +192,262 @@ Definition at line \fB20\fP of file \fBPenningTrap\&.cpp\fP\&.
 .PP
 Add a particle to the system\&. 
 .PP
-Definition at line \fB27\fP of file \fBPenningTrap\&.cpp\fP\&.
-.SS "void PenningTrap::evolve_forward_euler (double dt)"
+\fBParameters\fP
+.RS 4
+\fIparticle\fP The particle to add to the Penning trap 
+.RE
+.PP
+
+.PP
+Definition at line \fB82\fP of file \fBPenningTrap\&.cpp\fP\&.
+.SS "void PenningTrap::evolve_forward_euler (double dt, bool particle_interaction = \fCtrue\fP)"
 
 .PP
 Go forward one timestep using the forward Euler method\&. 
 .PP
-Definition at line \fB167\fP of file \fBPenningTrap\&.cpp\fP\&.
-.SS "void PenningTrap::evolve_RK4 (double dt)"
+\fBParameters\fP
+.RS 4
+\fIdt\fP The step length 
+.br
+\fIparticle_interaction\fP Turn particle interactions on/off 
+.RE
+.PP
+
+.PP
+Definition at line \fB186\fP of file \fBPenningTrap\&.cpp\fP\&.
+.SS "void PenningTrap::evolve_RK4 (double dt, bool particle_interaction = \fCtrue\fP)"
 
 .PP
 Go forward one timestep using the RK4 method\&. 
 .PP
-Definition at line \fB104\fP of file \fBPenningTrap\&.cpp\fP\&.
-.SS "arma::vec PenningTrap::external_B_field (arma::vec r)"
+\fBParameters\fP
+.RS 4
+\fIdt\fP The step length 
+.br
+\fIparticle_interaction\fP Turn particle interactions on/off 
+.RE
+.PP
+
+.PP
+Definition at line \fB151\fP of file \fBPenningTrap\&.cpp\fP\&.
+.SS "\fBvec_3d\fP PenningTrap::external_B_field (\fBvec_3d\fP r)"
 
 .PP
 Calculate B at point r\&. 
 .PP
-Definition at line \fB43\fP of file \fBPenningTrap\&.cpp\fP\&.
-.SS "arma::vec PenningTrap::external_E_field (arma::vec r)"
+\fBParameters\fP
+.RS 4
+\fIr\fP The position where we want to calculate the B field
+.RE
+.PP
+\fBReturns\fP
+.RS 4
+vec_3d 
+.RE
+.PP
+
+.PP
+Definition at line \fB95\fP of file \fBPenningTrap\&.cpp\fP\&.
+.SS "\fBvec_3d\fP PenningTrap::external_E_field (\fBvec_3d\fP r)"
 
 .PP
 Calculate E at point r\&. 
 .PP
-Definition at line \fB32\fP of file \fBPenningTrap\&.cpp\fP\&.
-.SS "arma::vec PenningTrap::force_on_particle (int i, int j)"
+\fBParameters\fP
+.RS 4
+\fIr\fP The position where we want to calculate the E field
+.RE
+.PP
+\fBReturns\fP
+.RS 4
+vec_3d 
+.RE
+.PP
 
 .PP
-Calculate the force between 2 particles\&. Calculate the force exhibited on particle p_i from particle p_j\&. 
-.PP
-Definition at line \fB50\fP of file \fBPenningTrap\&.cpp\fP\&.
-.SS "double PenningTrap::get_d ()"
+Definition at line \fB87\fP of file \fBPenningTrap\&.cpp\fP\&.
+.SS "\fBvec_3d\fP PenningTrap::force_on_particle (unsigned int i, unsigned int j)"
 
 .PP
-Definition at line \fB188\fP of file \fBPenningTrap\&.cpp\fP\&.
-.SS "arma::vec PenningTrap::get_particle (int i)"
+Calculate the force between 2 particles\&. Calculate the force exhibited on particle p_i from particle p_j\&.
+.PP
+\fBParameters\fP
+.RS 4
+\fIi\fP The index of particle p_i 
+.br
+\fIj\fP The index of particle p_j
+.RE
+.PP
+\fBReturns\fP
+.RS 4
+vec_3d 
+.RE
+.PP
 
 .PP
-Definition at line \fB183\fP of file \fBPenningTrap\&.cpp\fP\&.
-.SS "arma::vec PenningTrap::total_force (int i)"
+Definition at line \fB100\fP of file \fBPenningTrap\&.cpp\fP\&.
+.SS "double PenningTrap::fraction_of_particles_left (double time, unsigned int steps, std::string method = \fC'rk4'\fP, bool particle_interaction = \fCtrue\fP)"
 
 .PP
-calculate the total force on a particle\&. 
+Simulate and calculate what fraction of particles are still left inside the Penning trap after the simulation\&. 
+.PP
+\fBParameters\fP
+.RS 4
+\fItime\fP The time to simulate in microseconds 
+.br
+\fIsteps\fP The amount of steps for the whole simulation 
+.br
+\fImethod\fP The method to use when moving forward a timestep 
+.br
+\fIparticle_interaction\fP Turn particle interactions on/off
+.RE
+.PP
+\fBReturns\fP
+.RS 4
+double 
+.RE
 .PP
-Definition at line \fB99\fP of file \fBPenningTrap\&.cpp\fP\&.
-.SS "arma::vec PenningTrap::total_force_external (int i)"
 
 .PP
-Calculate the total external force on a particle\&. Calculate the total amount of force that E and B exhibits on particle p_i\&. 
-.PP
-Definition at line \fB65\fP of file \fBPenningTrap\&.cpp\fP\&.
-.SS "arma::vec PenningTrap::total_force_particles (int i)"
+Definition at line \fB266\fP of file \fBPenningTrap\&.cpp\fP\&.
+.SS "\fBvec_3d\fP PenningTrap::r_func (unsigned int i, unsigned int j, double dt)\fC [private]\fP"
 
 .PP
-Calculate the total force on a particle from other particles\&. 
+Helper for evolve_RK4 when calculating $k_{r,i,j}$ values\&. Something
 .PP
-Definition at line \fB80\fP of file \fBPenningTrap\&.cpp\fP\&.
+\fBParameters\fP
+.RS 4
+\fIi\fP Index i for $k_{r,i,j}$ 
+.br
+\fIj\fP Index j for $k_{r,i,j}$ 
+.br
+\fIdt\fP the step length (delta time)
+.RE
+.PP
+\fBReturns\fP
+.RS 4
+vec_3d 
+.RE
+.PP
+
+.PP
+Definition at line \fB64\fP of file \fBPenningTrap\&.cpp\fP\&.
+.SS "\fBsim_arr\fP PenningTrap::simulate (double time, unsigned int steps, std::string method = \fC'rk4'\fP, bool particle_interaction = \fCtrue\fP)"
+
+.PP
+Simulate the particle system inside the Penning trap over a certain amount of time\&. 
+.PP
+\fBParameters\fP
+.RS 4
+\fItime\fP The time to simulate in microseconds 
+.br
+\fIsteps\fP The amount of steps for the whole simulation 
+.br
+\fImethod\fP The method to use when moving forward a timestep 
+.br
+\fIparticle_interaction\fP Turn particle interactions on/off 
+.RE
+.PP
+
+.PP
+Definition at line \fB211\fP of file \fBPenningTrap\&.cpp\fP\&.
+.SS "\fBvec_3d\fP PenningTrap::total_force (unsigned int i)"
+
+.PP
+calculate the total force on a particle p_i\&. 
+.PP
+\fBParameters\fP
+.RS 4
+\fIi\fP The index of particle p_i
+.RE
+.PP
+\fBReturns\fP
+.RS 4
+vec_3d 
+.RE
+.PP
+
+.PP
+Definition at line \fB146\fP of file \fBPenningTrap\&.cpp\fP\&.
+.SS "\fBvec_3d\fP PenningTrap::total_force_external (unsigned int i)"
+
+.PP
+Calculate the total external force on a particle\&. Calculate the total amount of force that E and B exhibits on particle p_i\&.
+.PP
+\fBParameters\fP
+.RS 4
+\fIi\fP The index of particle p_i
+.RE
+.PP
+\fBReturns\fP
+.RS 4
+vec_3d 
+.RE
+.PP
+
+.PP
+Definition at line \fB114\fP of file \fBPenningTrap\&.cpp\fP\&.
+.SS "\fBvec_3d\fP PenningTrap::total_force_particles (unsigned int i)"
+
+.PP
+Calculate the total force on a particle p_i from other particles\&. 
+.PP
+\fBParameters\fP
+.RS 4
+\fIi\fP The index of particle p_i
+.RE
+.PP
+\fBReturns\fP
+.RS 4
+vec_3d 
+.RE
+.PP
+
+.PP
+Definition at line \fB129\fP of file \fBPenningTrap\&.cpp\fP\&.
+.SS "\fBvec_3d\fP PenningTrap::v_func (unsigned int i, unsigned int j, double dt)\fC [private]\fP"
+
+.PP
+Helper for evolve_RK4 when calculating $k_{v,i,j}$ values\&. Something
+.PP
+\fBParameters\fP
+.RS 4
+\fIi\fP Index i for $k_{v,i,j}$ 
+.br
+\fIj\fP Index j for $k_{v,i,j}$ 
+.br
+\fIdt\fP the step length (delta time)
+.RE
+.PP
+\fBReturns\fP
+.RS 4
+vec_3d 
+.RE
+.PP
+
+.PP
+Definition at line \fB46\fP of file \fBPenningTrap\&.cpp\fP\&.
+.SS "void PenningTrap::write_simulation_to_dir (std::string path, double time, unsigned int steps, std::string method = \fC'rk4'\fP, bool particle_interaction = \fCtrue\fP)"
+
+.PP
+Simulate and write the displacement of all particles to files\&. 
+.PP
+\fBParameters\fP
+.RS 4
+\fIpath\fP The directory to save the data 
+.br
+\fItime\fP The time to simulate in microseconds 
+.br
+\fIsteps\fP The amount of steps for the whole simulation 
+.br
+\fImethod\fP The method to use when moving forward a timestep 
+.br
+\fIparticle_interaction\fP Turn particle interactions on/off 
+.RE
+.PP
+
+.PP
+Definition at line \fB240\fP of file \fBPenningTrap\&.cpp\fP\&.
 .SH "Member Data Documentation"
 .PP 
 .SS "double PenningTrap::B_0\fC [private]\fP"
@@ -165,25 +455,39 @@ Definition at line \fB80\fP of file \fBPenningTrap\&.cpp\fP\&.
 .PP
 Magnetic field strength\&. 
 .PP
-Definition at line \fB31\fP of file \fBPenningTrap\&.hpp\fP\&.
+Definition at line \fB32\fP of file \fBPenningTrap\&.hpp\fP\&.
 .SS "double PenningTrap::d\fC [private]\fP"
 
 .PP
 Characteristic dimension\&. 
 .PP
-Definition at line \fB33\fP of file \fBPenningTrap\&.hpp\fP\&.
+Definition at line \fB34\fP of file \fBPenningTrap\&.hpp\fP\&.
+.SS "\fBsim_arr\fP PenningTrap::k_r\fC [private]\fP"
+A 2D vector containing all $k_{i,j}$ where $j$ is the index of a particle 
+.PP
+Definition at line \fB39\fP of file \fBPenningTrap\&.hpp\fP\&.
+.SS "\fBsim_arr\fP PenningTrap::k_v\fC [private]\fP"
+A 2D vector containing all $k_{i,j}$ where $j$ is the index of a particle 
+.PP
+Definition at line \fB37\fP of file \fBPenningTrap\&.hpp\fP\&.
 .SS "std::vector<\fBParticle\fP> PenningTrap::particles\fC [private]\fP"
 
 .PP
 The particles in the Penning trap\&. 
 .PP
-Definition at line \fB34\fP of file \fBPenningTrap\&.hpp\fP\&.
-.SS "double PenningTrap::V_0\fC [private]\fP"
+Definition at line \fB36\fP of file \fBPenningTrap\&.hpp\fP\&.
+.SS "double PenningTrap::t\fC [private]\fP"
+
+.PP
+Current time\&. 
+.PP
+Definition at line \fB35\fP of file \fBPenningTrap\&.hpp\fP\&.
+.SS "std::function<double(double)> PenningTrap::V_0\fC [private]\fP"
 
 .PP
 Applied potential\&. 
 .PP
-Definition at line \fB32\fP of file \fBPenningTrap\&.hpp\fP\&.
+Definition at line \fB33\fP of file \fBPenningTrap\&.hpp\fP\&.
 
 .SH "Author"
 .PP 
diff --git a/man_pages/man3/PenningTrap.cpp.3 b/man_pages/man3/PenningTrap.cpp.3
index f850299..d080d97 100644
--- a/man_pages/man3/PenningTrap.cpp.3
+++ b/man_pages/man3/PenningTrap.cpp.3
@@ -1,4 +1,4 @@
-.TH "src/PenningTrap.cpp" 3 "Sun Oct 8 2023" "Penning Trap Simulation" \" -*- nroff -*-
+.TH "src/PenningTrap.cpp" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
 .ad l
 .nh
 .SH NAME
@@ -11,6 +11,8 @@ src/PenningTrap.cpp \- The implementation of the \fBPenningTrap\fP class\&.
 .br
 \fC#include 'constants\&.hpp'\fP
 .br
+\fC#include 'typedefs\&.hpp'\fP
+.br
 \fC#include 'utils\&.hpp'\fP
 .br
 
@@ -35,15 +37,7 @@ Janita Ovidie Sandtrøen Willumsen (janitaws)
 .PP
 \fBBug\fP
 .RS 4
-No known bugs
-.RE
-.PP
-.PP
-\fBTodo\fP
-.RS 4
-Implement evolve_RK4 
-.PP
-Implement evolve_forward_euler 
+No known bugs 
 .RE
 .PP
 
diff --git a/man_pages/man3/PenningTrap.hpp.3 b/man_pages/man3/PenningTrap.hpp.3
index c16a94b..15d155f 100644
--- a/man_pages/man3/PenningTrap.hpp.3
+++ b/man_pages/man3/PenningTrap.hpp.3
@@ -1,4 +1,4 @@
-.TH "include/PenningTrap.hpp" 3 "Sun Oct 8 2023" "Penning Trap Simulation" \" -*- nroff -*-
+.TH "include/PenningTrap.hpp" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
 .ad l
 .nh
 .SH NAME
@@ -15,6 +15,8 @@ include/PenningTrap.hpp \- A class for simulating a Penning trap\&.
 .br
 \fC#include 'constants\&.hpp'\fP
 .br
+\fC#include 'typedefs\&.hpp'\fP
+.br
 
 .SS "Classes"
 
diff --git a/man_pages/man3/PenningTrapTest.3 b/man_pages/man3/PenningTrapTest.3
index 07c0b75..3bbe27c 100644
--- a/man_pages/man3/PenningTrapTest.3
+++ b/man_pages/man3/PenningTrapTest.3
@@ -1,4 +1,4 @@
-.TH "PenningTrapTest" 3 "Sun Oct 8 2023" "Penning Trap Simulation" \" -*- nroff -*-
+.TH "PenningTrapTest" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
 .ad l
 .nh
 .SH NAME
diff --git a/man_pages/man3/bug.3 b/man_pages/man3/bug.3
index f93d6e3..d21bde1 100644
--- a/man_pages/man3/bug.3
+++ b/man_pages/man3/bug.3
@@ -1,4 +1,4 @@
-.TH "bug" 3 "Sun Oct 8 2023" "Penning Trap Simulation" \" -*- nroff -*-
+.TH "bug" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
 .ad l
 .nh
 .SH NAME
@@ -10,15 +10,17 @@ No known bugs
 .IP "\fBFile \fBmain\&.cpp\fP \fP" 1c
 No known bugs  
 .IP "\fBFile \fBParticle\&.cpp\fP \fP" 1c
-No known bugs 
+No known bugs  
 .IP "\fBFile \fBParticle\&.hpp\fP \fP" 1c
 No known bugs  
 .IP "\fBFile \fBPenningTrap\&.cpp\fP \fP" 1c
-No known bugs 
+No known bugs  
 .IP "\fBFile \fBPenningTrap\&.hpp\fP \fP" 1c
 No known bugs  
 .IP "\fBFile \fBtest_suite\&.cpp\fP \fP" 1c
 No known bugs  
+.IP "\fBFile \fBtypedefs\&.hpp\fP \fP" 1c
+No known bugs  
 .IP "\fBFile \fButils\&.cpp\fP \fP" 1c
 No known bugs  
 .IP "\fBFile \fButils\&.hpp\fP \fP" 1c
diff --git a/man_pages/man3/constants.hpp.3 b/man_pages/man3/constants.hpp.3
index ed6ff65..b1d978f 100644
--- a/man_pages/man3/constants.hpp.3
+++ b/man_pages/man3/constants.hpp.3
@@ -1,4 +1,4 @@
-.TH "include/constants.hpp" 3 "Sun Oct 8 2023" "Penning Trap Simulation" \" -*- nroff -*-
+.TH "include/constants.hpp" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
 .ad l
 .nh
 .SH NAME
diff --git a/man_pages/man3/main.cpp.3 b/man_pages/man3/main.cpp.3
index e02bbe4..23983a7 100644
--- a/man_pages/man3/main.cpp.3
+++ b/man_pages/man3/main.cpp.3
@@ -1,4 +1,4 @@
-.TH "src/main.cpp" 3 "Sun Oct 8 2023" "Penning Trap Simulation" \" -*- nroff -*-
+.TH "src/main.cpp" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
 .ad l
 .nh
 .SH NAME
@@ -7,14 +7,22 @@ src/main.cpp \- The main program for this project\&.
 .SH SYNOPSIS
 .br
 .PP
+\fC#include <cmath>\fP
+.br
 \fC#include <fstream>\fP
 .br
 \fC#include <omp\&.h>\fP
 .br
+\fC#include <string>\fP
+.br
 \fC#include <sys/stat\&.h>\fP
 .br
+\fC#include <vector>\fP
+.br
 \fC#include 'PenningTrap\&.hpp'\fP
 .br
+\fC#include 'utils\&.hpp'\fP
+.br
 
 .SS "Macros"
 
@@ -36,12 +44,34 @@ src/main.cpp \- The main program for this project\&.
 
 .in +1c
 .ti -1c
+.RI "void \fBsimulate_single_particle\fP ()"
+.br
+.ti -1c
+.RI "void \fBsimulate_two_particles\fP ()"
+.br
+.ti -1c
+.RI "void \fBsimulate_single_particle_with_different_steps\fP ()"
+.br
+.ti -1c
 .RI "void \fBsimulate_100_particles\fP ()"
 .br
 .ti -1c
+.RI "void \fBsimulate_100_particles_with_time_potential\fP ()"
+.br
+.ti -1c
 .RI "int \fBmain\fP ()"
 .br
 .in -1c
+.SS "Variables"
+
+.in +1c
+.ti -1c
+.RI "\fBParticle\fP \fBp1\fP (CHARGE, MASS, \fBvec_3d\fP{20\&., 0\&., 20\&.}, \fBvec_3d\fP{0\&., 25\&., 0\&.})"
+.br
+.ti -1c
+.RI "\fBParticle\fP \fBp2\fP (CHARGE, MASS, \fBvec_3d\fP{25\&., 25\&., 0\&.}, \fBvec_3d\fP{0\&., 40\&., 5\&.})"
+.br
+.in -1c
 .SH "Detailed Description"
 .PP 
 The main program for this project\&. 
@@ -74,29 +104,45 @@ Definition in file \fBmain\&.cpp\fP\&.
 .SS "#define CHARGE   1\&."
 
 .PP
-Definition at line \fB21\fP of file \fBmain\&.cpp\fP\&.
+Definition at line \fB25\fP of file \fBmain\&.cpp\fP\&.
 .SS "#define MASS   40\&."
 
 .PP
-Definition at line \fB22\fP of file \fBmain\&.cpp\fP\&.
+Definition at line \fB26\fP of file \fBmain\&.cpp\fP\&.
 .SS "#define N   10000"
 
 .PP
-Definition at line \fB20\fP of file \fBmain\&.cpp\fP\&.
+Definition at line \fB24\fP of file \fBmain\&.cpp\fP\&.
 .SS "#define PARTICLES   100"
 
 .PP
-Definition at line \fB19\fP of file \fBmain\&.cpp\fP\&.
+Definition at line \fB23\fP of file \fBmain\&.cpp\fP\&.
 .SH "Function Documentation"
 .PP 
 .SS "int main ()"
 
 .PP
-Definition at line \fB77\fP of file \fBmain\&.cpp\fP\&.
+Definition at line \fB124\fP of file \fBmain\&.cpp\fP\&.
 .SS "void simulate_100_particles ()"
 
 .PP
-Definition at line \fB24\fP of file \fBmain\&.cpp\fP\&.
+Definition at line \fB77\fP of file \fBmain\&.cpp\fP\&.
+.SS "void simulate_100_particles_with_time_potential ()"
+
+.PP
+Definition at line \fB91\fP of file \fBmain\&.cpp\fP\&.
+.SS "void simulate_single_particle ()"
+
+.PP
+Definition at line \fB31\fP of file \fBmain\&.cpp\fP\&.
+.SS "void simulate_single_particle_with_different_steps ()"
+
+.PP
+Definition at line \fB55\fP of file \fBmain\&.cpp\fP\&.
+.SS "void simulate_two_particles ()"
+
+.PP
+Definition at line \fB42\fP of file \fBmain\&.cpp\fP\&.
 .SH "Author"
 .PP 
 Generated automatically by Doxygen for Penning Trap Simulation from the source code\&.
diff --git a/man_pages/man3/test_suite.cpp.3 b/man_pages/man3/test_suite.cpp.3
index fa522ef..c185469 100644
--- a/man_pages/man3/test_suite.cpp.3
+++ b/man_pages/man3/test_suite.cpp.3
@@ -1,4 +1,4 @@
-.TH "src/test_suite.cpp" 3 "Sun Oct 8 2023" "Penning Trap Simulation" \" -*- nroff -*-
+.TH "src/test_suite.cpp" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
 .ad l
 .nh
 .SH NAME
diff --git a/man_pages/man3/todo.3 b/man_pages/man3/todo.3
index a66e064..ef888e2 100644
--- a/man_pages/man3/todo.3
+++ b/man_pages/man3/todo.3
@@ -1,4 +1,4 @@
-.TH "todo" 3 "Sun Oct 8 2023" "Penning Trap Simulation" \" -*- nroff -*-
+.TH "todo" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
 .ad l
 .nh
 .SH NAME
diff --git a/man_pages/man3/typedefs.hpp.3 b/man_pages/man3/typedefs.hpp.3
new file mode 100644
index 0000000..1933ad3
--- /dev/null
+++ b/man_pages/man3/typedefs.hpp.3
@@ -0,0 +1,92 @@
+.TH "include/typedefs.hpp" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
+.ad l
+.nh
+.SH NAME
+include/typedefs.hpp \- Useful typedefs for cleaner code\&.  
+
+.SH SYNOPSIS
+.br
+.PP
+\fC#include <vector>\fP
+.br
+\fC#include <armadillo>\fP
+.br
+
+.SS "Typedefs"
+
+.in +1c
+.ti -1c
+.RI "typedef std::vector< arma::vec::fixed< 3 > > \fBsim_cols\fP"
+.br
+.RI "Typedef for the column of the result vector from simulating particles\&. "
+.ti -1c
+.RI "typedef std::vector< arma::vec::fixed< 3 > > \fBsim_rows\fP"
+.br
+.RI "Typedef for the row of the result vector from simulating particles\&. "
+.ti -1c
+.RI "typedef std::vector< \fBsim_cols\fP > \fBsim_arr\fP"
+.br
+.RI "Typedef for the result of the simulate method\&. "
+.ti -1c
+.RI "typedef arma::vec::fixed< 3 > \fBvec_3d\fP"
+.br
+.RI "Typedef for a fixed 3d arma vector\&. "
+.in -1c
+.SH "Detailed Description"
+.PP 
+Useful typedefs for cleaner code\&. 
+
+
+.PP
+\fBAuthor\fP
+.RS 4
+Cory Alexander Balaton (coryab) 
+.PP
+Janita Ovidie Sandtrøen Willumsen (janitaws)
+.RE
+.PP
+\fBVersion\fP
+.RS 4
+1\&.0
+.RE
+.PP
+.PP
+These typedefs make the code more readable and easy to follow along\&.
+.PP
+\fBBug\fP
+.RS 4
+No known bugs 
+.RE
+.PP
+
+.PP
+Definition in file \fBtypedefs\&.hpp\fP\&.
+.SH "Typedef Documentation"
+.PP 
+.SS "typedef std::vector<\fBsim_cols\fP> \fBsim_arr\fP"
+
+.PP
+Typedef for the result of the simulate method\&. 
+.PP
+Definition at line \fB32\fP of file \fBtypedefs\&.hpp\fP\&.
+.SS "typedef std::vector<arma::vec::fixed<3> > \fBsim_cols\fP"
+
+.PP
+Typedef for the column of the result vector from simulating particles\&. 
+.PP
+Definition at line \fB24\fP of file \fBtypedefs\&.hpp\fP\&.
+.SS "typedef std::vector<arma::vec::fixed<3> > \fBsim_rows\fP"
+
+.PP
+Typedef for the row of the result vector from simulating particles\&. 
+.PP
+Definition at line \fB28\fP of file \fBtypedefs\&.hpp\fP\&.
+.SS "typedef arma::vec::fixed<3> \fBvec_3d\fP"
+
+.PP
+Typedef for a fixed 3d arma vector\&. 
+.PP
+Definition at line \fB36\fP of file \fBtypedefs\&.hpp\fP\&.
+.SH "Author"
+.PP 
+Generated automatically by Doxygen for Penning Trap Simulation from the source code\&.
diff --git a/man_pages/man3/utils.cpp.3 b/man_pages/man3/utils.cpp.3
index 3d60a86..335b5f5 100644
--- a/man_pages/man3/utils.cpp.3
+++ b/man_pages/man3/utils.cpp.3
@@ -1,4 +1,4 @@
-.TH "src/utils.cpp" 3 "Sun Oct 8 2023" "Penning Trap Simulation" \" -*- nroff -*-
+.TH "src/utils.cpp" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
 .ad l
 .nh
 .SH NAME
@@ -7,6 +7,8 @@ src/utils.cpp \- Implementation of the utils\&.
 .SH SYNOPSIS
 .br
 .PP
+\fC#include <sys/stat\&.h>\fP
+.br
 \fC#include 'utils\&.hpp'\fP
 .br
 
@@ -29,6 +31,10 @@ src/utils.cpp \- Implementation of the utils\&.
 .RI "bool \fBarma_vector_close_to\fP (arma::vec &a, arma::vec &b, double tol)"
 .br
 .RI "Test if two armadillo vectors are close to each other\&. "
+.ti -1c
+.RI "bool \fBmkpath\fP (std::string path, int mode)"
+.br
+.RI "Make path given\&. "
 .in -1c
 .SH "Detailed Description"
 .PP 
@@ -75,12 +81,12 @@ Test if two armadillo vectors are close to each other\&. This function takes in
 .PP
 \fBReturns\fP
 .RS 4
-Boolean 
+bool 
 .RE
 .PP
 
 .PP
-Definition at line \fB59\fP of file \fButils\&.cpp\fP\&.
+Definition at line \fB62\fP of file \fButils\&.cpp\fP\&.
 .SS "void m_assert (bool expr, std::string expr_str, std::string func, std::string file, int line, std::string msg)"
 
 .PP
@@ -103,11 +109,31 @@ Test an expression, confirm that test is ok, or abort execution\&. This function
 .PP
 
 .PP
-Definition at line \fB40\fP of file \fButils\&.cpp\fP\&.
+Definition at line \fB43\fP of file \fButils\&.cpp\fP\&.
+.SS "bool mkpath (std::string path, int mode = \fC0777\fP)"
+
+.PP
+Make path given\&. This tries to be the equivalent to 'mkdir -p' and creates a new directory whenever it needs to\&.
+.PP
+\fBParameters\fP
+.RS 4
+\fIpath\fP The path to be created 
+.br
+\fImode\fP The mode/permissions for all the new directories
+.RE
+.PP
+\fBReturns\fP
+.RS 4
+bool 
+.RE
+.PP
+
+.PP
+Definition at line \fB76\fP of file \fButils\&.cpp\fP\&.
 .SS "std::string scientific_format (const std::vector< double > & v, int width = \fC20\fP, int prec = \fC10\fP)"
 
 .PP
-Turns a vector of doubles into a string written in scientific format\&. 
+Turns a vector of doubles into a string written in scientific format\&. The code is stolen from https://github.com/anderkve/FYS3150\&.
 .PP
 \fBParameters\fP
 .RS 4
@@ -120,16 +146,16 @@ Turns a vector of doubles into a string written in scientific format\&.
 .PP
 \fBReturns\fP
 .RS 4
-String 
+std::string 
 .RE
 .PP
 
 .PP
-Definition at line \fB21\fP of file \fButils\&.cpp\fP\&.
+Definition at line \fB24\fP of file \fButils\&.cpp\fP\&.
 .SS "std::string scientific_format (double d, int width = \fC20\fP, int prec = \fC10\fP)"
 
 .PP
-Turns a double into a string written in scientific format\&. Code stolen from https://github.com/anderkve/FYS3150 Header: https://github.com/anderkve/FYS3150/blob/master/code_examples/compilation_linking/example_1/include/utils.hpp Source: https://github.com/anderkve/FYS3150/blob/master/code_examples/compilation_linking/example_1/src/utils.cpp 
+Turns a double into a string written in scientific format\&. The code is stolen from https://github.com/anderkve/FYS3150\&.
 .PP
 \fBParameters\fP
 .RS 4
@@ -142,12 +168,12 @@ Turns a double into a string written in scientific format\&. Code stolen from ht
 .PP
 \fBReturns\fP
 .RS 4
-String 
+std::string 
 .RE
 .PP
 
 .PP
-Definition at line \fB14\fP of file \fButils\&.cpp\fP\&.
+Definition at line \fB17\fP of file \fButils\&.cpp\fP\&.
 .SH "Author"
 .PP 
 Generated automatically by Doxygen for Penning Trap Simulation from the source code\&.
diff --git a/man_pages/man3/utils.hpp.3 b/man_pages/man3/utils.hpp.3
index a67beb7..3f934d0 100644
--- a/man_pages/man3/utils.hpp.3
+++ b/man_pages/man3/utils.hpp.3
@@ -1,4 +1,4 @@
-.TH "include/utils.hpp" 3 "Sun Oct 8 2023" "Penning Trap Simulation" \" -*- nroff -*-
+.TH "include/utils.hpp" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
 .ad l
 .nh
 .SH NAME
@@ -32,6 +32,7 @@ include/utils.hpp \- Function prototypes and macros that are useful\&.
 .ti -1c
 .RI "#define \fB__METHOD_NAME__\fP   methodName(__PRETTY_FUNCTION__)"
 .br
+.RI "Get the name of the current method/function\&. "
 .in -1c
 .SS "Functions"
 
@@ -52,6 +53,10 @@ include/utils.hpp \- Function prototypes and macros that are useful\&.
 .RI "bool \fBarma_vector_close_to\fP (arma::vec &a, arma::vec &b, double tol=1e\-8)"
 .br
 .RI "Test if two armadillo vectors are close to each other\&. "
+.ti -1c
+.RI "bool \fBmkpath\fP (std::string path, int mode=0777)"
+.br
+.RI "Make path given\&. "
 .in -1c
 .SH "Detailed Description"
 .PP 
@@ -87,7 +92,9 @@ Definition in file \fButils\&.hpp\fP\&.
 .SS "#define __METHOD_NAME__   methodName(__PRETTY_FUNCTION__)"
 
 .PP
-Definition at line \fB48\fP of file \fButils\&.hpp\fP\&.
+Get the name of the current method/function\&. 
+.PP
+Definition at line \fB51\fP of file \fButils\&.hpp\fP\&.
 .SS "#define ASSERT(expr, msg)"
 \fBValue:\fP.PP
 .nf
@@ -123,12 +130,12 @@ Test if two armadillo vectors are close to each other\&. This function takes in
 .PP
 \fBReturns\fP
 .RS 4
-Boolean 
+bool 
 .RE
 .PP
 
 .PP
-Definition at line \fB59\fP of file \fButils\&.cpp\fP\&.
+Definition at line \fB62\fP of file \fButils\&.cpp\fP\&.
 .SS "void m_assert (bool expr, std::string expr_str, std::string func, std::string file, int line, std::string msg)"
 
 .PP
@@ -151,11 +158,31 @@ Test an expression, confirm that test is ok, or abort execution\&. This function
 .PP
 
 .PP
-Definition at line \fB40\fP of file \fButils\&.cpp\fP\&.
+Definition at line \fB43\fP of file \fButils\&.cpp\fP\&.
+.SS "bool mkpath (std::string path, int mode = \fC0777\fP)"
+
+.PP
+Make path given\&. This tries to be the equivalent to 'mkdir -p' and creates a new directory whenever it needs to\&.
+.PP
+\fBParameters\fP
+.RS 4
+\fIpath\fP The path to be created 
+.br
+\fImode\fP The mode/permissions for all the new directories
+.RE
+.PP
+\fBReturns\fP
+.RS 4
+bool 
+.RE
+.PP
+
+.PP
+Definition at line \fB76\fP of file \fButils\&.cpp\fP\&.
 .SS "std::string scientific_format (const std::vector< double > & v, int width = \fC20\fP, int prec = \fC10\fP)"
 
 .PP
-Turns a vector of doubles into a string written in scientific format\&. 
+Turns a vector of doubles into a string written in scientific format\&. The code is stolen from https://github.com/anderkve/FYS3150\&.
 .PP
 \fBParameters\fP
 .RS 4
@@ -168,16 +195,16 @@ Turns a vector of doubles into a string written in scientific format\&.
 .PP
 \fBReturns\fP
 .RS 4
-String 
+std::string 
 .RE
 .PP
 
 .PP
-Definition at line \fB21\fP of file \fButils\&.cpp\fP\&.
+Definition at line \fB24\fP of file \fButils\&.cpp\fP\&.
 .SS "std::string scientific_format (double d, int width = \fC20\fP, int prec = \fC10\fP)"
 
 .PP
-Turns a double into a string written in scientific format\&. Code stolen from https://github.com/anderkve/FYS3150 Header: https://github.com/anderkve/FYS3150/blob/master/code_examples/compilation_linking/example_1/include/utils.hpp Source: https://github.com/anderkve/FYS3150/blob/master/code_examples/compilation_linking/example_1/src/utils.cpp 
+Turns a double into a string written in scientific format\&. The code is stolen from https://github.com/anderkve/FYS3150\&.
 .PP
 \fBParameters\fP
 .RS 4
@@ -190,12 +217,12 @@ Turns a double into a string written in scientific format\&. Code stolen from ht
 .PP
 \fBReturns\fP
 .RS 4
-String 
+std::string 
 .RE
 .PP
 
 .PP
-Definition at line \fB14\fP of file \fButils\&.cpp\fP\&.
+Definition at line \fB17\fP of file \fButils\&.cpp\fP\&.
 .SH "Author"
 .PP 
 Generated automatically by Doxygen for Penning Trap Simulation from the source code\&.

From 58c9212e5c8a48310d5f7419c59873f201a51bae Mon Sep 17 00:00:00 2001
From: Cory <cory@balaton.dev>
Date: Sat, 14 Oct 2023 03:12:23 +0200
Subject: [PATCH 15/26] Update documentation

---
 include/Particle.hpp    |   5 ++
 include/PenningTrap.hpp | 167 ++++++++++++++++++++++++++++++++++------
 include/typedefs.hpp    |  26 +++++++
 include/utils.hpp       |  59 ++++++++++----
 src/Makefile            |   2 +-
 src/Particle.cpp        |   1 -
 src/PenningTrap.cpp     | 125 +++++++++++++-----------------
 src/main.cpp            |  65 ++++++++++++----
 8 files changed, 322 insertions(+), 128 deletions(-)

diff --git a/include/Particle.hpp b/include/Particle.hpp
index cf3232c..4b5e716 100644
--- a/include/Particle.hpp
+++ b/include/Particle.hpp
@@ -30,6 +30,11 @@ public:
      *
      *  @details Initialize the particle with a charge, mass, position and
      *  velocity.
+     *
+     *  @param q The charge of the particle
+     *  @param m The mass of the particle
+     *  @param r_vec The initial position of the particle
+     *  @param v_vec The initial velocity of the particle
      * */
     Particle(double q, double m, vec_3d r_vec, vec_3d v_vec);
 
diff --git a/include/PenningTrap.hpp b/include/PenningTrap.hpp
index eb7bff7..f6cf2c0 100644
--- a/include/PenningTrap.hpp
+++ b/include/PenningTrap.hpp
@@ -19,8 +19,7 @@
 #include "constants.hpp"
 #include "typedefs.hpp"
 
-
-#pragma omp declare reduction(+ : vec_3d : omp_out += omp_in)               \
+#pragma omp declare reduction(+ : vec_3d : omp_out += omp_in)                  \
     initializer(omp_priv = omp_orig)
 
 /** @brief A class that simulates a Penning trap.
@@ -30,36 +29,101 @@
  * */
 class PenningTrap {
 private:
-    double B_0;                      ///< Magnetic field strength
-    double V_0;                      ///< Applied potential
-    double d;                        ///< Characteristic dimension
-    std::vector<Particle> particles; ///< The particles in the Penning trap
-    sim_arr k_v;
-    sim_arr k_r;
+    double B_0;                        ///< Magnetic field strength
+    std::function<double(double)> V_0; ///< Applied potential
+    double d;                          ///< Characteristic dimension
+    double t;                          ///< Current time
+    std::vector<Particle> particles;   ///< The particles in the Penning trap
+    sim_arr k_v; ///< A 2D vector containing all \f$k_{i,j}\f$ where \f$j\f$ is
+                 ///< the index of a particle
+    sim_arr k_r; ///< A 2D vector containing all \f$k_{i,j}\f$ where \f$j\f$ is
+                 ///< the index of a particle
 
-    vec_3d v_func(int, int, double);
-    vec_3d r_func(int, int, double);
+    /** @brief Helper for evolve_RK4 when calculating \f$k_{v,i,j}\f$ values
+     *
+     *  @details Something
+     *
+     *  @param i Index i for \f$k_{v,i,j}\f$
+     *  @param j Index j for \f$k_{v,i,j}\f$
+     *  @param dt the step length (delta time)
+     *
+     *  @return vec_3d
+     * */
+    vec_3d v_func(unsigned int i, unsigned int j, double dt);
+
+    /** @brief Helper for evolve_RK4 when calculating \f$k_{r,i,j}\f$ values
+     *
+     *  @details Something
+     *
+     *  @param i Index i for \f$k_{r,i,j}\f$
+     *  @param j Index j for \f$k_{r,i,j}\f$
+     *  @param dt the step length (delta time)
+     *
+     *  @return vec_3d
+     * */
+    vec_3d r_func(unsigned int i, unsigned int j, double dt);
 
 public:
-    /** @brief Set B_0, V_0 and d.
+    /** @brief Constructor for the PenningTrap class
+     *
+     *  @param B_0 The magnetic field strength
+     *  @param V_0 The time dependent applied potential
+     *  @param d The characteristic dimension
+     *  @param t The starting time
      * */
-    PenningTrap(double B_0 = T, double V_0 = 25. * V / 1000., double d = 500.);
+    PenningTrap(
+        double B_0 = T,
+        std::function<double(double)> V_0 =
+            [](double t) { return 25. * V / 1000.; },
+        double d = 500., double t = 0.);
 
-    PenningTrap(int i, double B_0 = T, double V_0 = 25. * V / 1000.,
-                double d = 500.);
+    /** @brief Constructor for the PenningTrap class
+     *
+     *  @param i The number of particles to generate
+     *  @param B_0 The magnetic field strength
+     *  @param V_0 The time dependent applied potential
+     *  @param d The characteristic dimension
+     *  @param t The starting time
+     * */
+    PenningTrap(
+        unsigned int i, double B_0 = T,
+        std::function<double(double)> V_0 =
+            [](double t) { return 25. * V / 1000.; },
+        double d = 500., double t = 0.);
 
-    PenningTrap(std::vector<Particle> particles, double B_0 = T,
-                double V_0 = 25. * V / 1000., double d = 500.);
+    /** @brief Constructor for the PenningTrap class
+     *
+     *  @param particles The starting particles
+     *  @param B_0 The magnetic field strength
+     *  @param V_0 The time dependent applied potential
+     *  @param d The characteristic dimension
+     *  @param t The starting time
+     * */
+    PenningTrap(
+        std::vector<Particle> particles, double B_0 = T,
+        std::function<double(double)> V_0 =
+            [](double t) { return 25. * V / 1000.; },
+        double d = 500., double t = 0.);
 
     /** @brief Add a particle to the system
+     *
+     *  @param particle The particle to add to the Penning trap
      * */
     void add_particle(Particle particle);
 
     /** @brief Calculate E at point r
+     *
+     *  @param r The position where we want to calculate the E field
+     *
+     *  @return vec_3d
      * */
     vec_3d external_E_field(vec_3d r);
 
     /** @brief Calculate B at point r
+     *
+     *  @param r The position where we want to calculate the B field
+     *
+     *  @return vec_3d
      * */
     vec_3d external_B_field(vec_3d r);
 
@@ -67,39 +131,92 @@ public:
      *
      *  @details Calculate the force exhibited on particle p_i from
      *  particle p_j.
+     *
+     *  @param i The index of particle p_i
+     *  @param j The index of particle p_j
+     *
+     *  @return vec_3d
      * */
-    vec_3d force_on_particle(int i, int j);
+    vec_3d force_on_particle(unsigned int i, unsigned int j);
 
     /** @brief Calculate the total external force on a particle.
      *
      *  @details Calculate the total amount of force that E and B exhibits
      *  on particle p_i.
+     *
+     *  @param i The index of particle p_i
+     *
+     *  @return vec_3d
      * */
-    vec_3d total_force_external(int i);
+    vec_3d total_force_external(unsigned int i);
 
-    /** @brief Calculate the total force on a particle from other particles.
+    /** @brief Calculate the total force on a particle p_i from other particles.
+     *
+     *  @param i The index of particle p_i
+     *
+     *  @return vec_3d
      * */
     vec_3d total_force_particles(unsigned int i);
 
-    /** @brief calculate the total force on a particle.
+    /** @brief calculate the total force on a particle p_i.
+     *
+     *  @param i The index of particle p_i
+     *
+     *  @return vec_3d
      * */
-    vec_3d total_force(int i);
+    vec_3d total_force(unsigned int i);
 
     /** @brief Go forward one timestep using the RK4 method
+     *
+     *  @param dt The step length
+     *  @param particle_interaction Turn particle interactions on/off
      * */
     void evolve_RK4(double dt, bool particle_interaction = true);
 
     /** @brief Go forward one timestep using the forward Euler method
+     *
+     *  @param dt The step length
+     *  @param particle_interaction Turn particle interactions on/off
      * */
     void evolve_forward_euler(double dt, bool particle_interaction = true);
 
+    /** @brief Simulate the particle system inside the Penning trap over
+     *  a certain amount of time.
+     *
+     *  @param time The time to simulate in microseconds
+     *  @param steps The amount of steps for the whole simulation
+     *  @param method The method to use when moving forward a timestep
+     *  @param particle_interaction Turn particle interactions on/off
+     * */
     sim_arr simulate(double time, unsigned int steps,
-                                              std::string method = "rk4",
-                                              bool particle_interaction = true);
+                     std::string method = "rk4",
+                     bool particle_interaction = true);
 
-    void write_simulation_to_dir(std::string path, double time, int steps,
-                                 std::string method = "rk4",
+    /** @brief Simulate and write the displacement of all particles to files.
+     *
+     *  @param path The directory to save the data
+     *  @param time The time to simulate in microseconds
+     *  @param steps The amount of steps for the whole simulation
+     *  @param method The method to use when moving forward a timestep
+     *  @param particle_interaction Turn particle interactions on/off
+     * */
+    void write_simulation_to_dir(std::string path, double time,
+                                 unsigned int steps, std::string method = "rk4",
                                  bool particle_interaction = true);
+
+    /** @brief Simulate and calculate what fraction of particles are still
+     *  left inside the Penning trap after the simulation.
+     *
+     *  @param time The time to simulate in microseconds
+     *  @param steps The amount of steps for the whole simulation
+     *  @param method The method to use when moving forward a timestep
+     *  @param particle_interaction Turn particle interactions on/off
+     *
+     *  @return double
+     * */
+    double fraction_of_particles_left(double time, unsigned int steps,
+                                      std::string method = "rk4",
+                                      bool particle_interaction = true);
 };
 
 #endif
diff --git a/include/typedefs.hpp b/include/typedefs.hpp
index 42c00bb..f0ceca2 100644
--- a/include/typedefs.hpp
+++ b/include/typedefs.hpp
@@ -1,12 +1,38 @@
+/** @file typedefs.hpp
+ *
+ *  @author Cory Alexander Balaton (coryab)
+ *  @author Janita Ovidie Sandtrøen Willumsen (janitaws)
+ *
+ *  @version 1.0
+ *
+ *  @brief Useful typedefs for cleaner code.
+ *
+ *  @details These typedefs make the code more readable and easy to follow 
+ *  along.
+ *
+ *  @bug No known bugs
+ * */
 #ifndef __TYPEDEFS__
 #define __TYPEDEFS__
 
 #include <vector>
 #include <armadillo>
 
+/** @brief Typedef for the column of the result vector from simulating 
+ *  particles.
+ * */
 typedef std::vector<arma::vec::fixed<3>> sim_cols;
+
+/** @brief Typedef for the row of the result vector from simulating particles.
+ * */
 typedef std::vector<arma::vec::fixed<3>> sim_rows;
+
+/** @brief Typedef for the result of the simulate method.
+ * */
 typedef std::vector<sim_cols> sim_arr;
+
+/** @brief Typedef for a fixed 3d arma vector.
+ * */
 typedef arma::vec::fixed<3> vec_3d;
 
 #endif
diff --git a/include/utils.hpp b/include/utils.hpp
index 2210880..c9c9485 100644
--- a/include/utils.hpp
+++ b/include/utils.hpp
@@ -45,40 +45,44 @@
 #define ASSERT(expr, msg) m_assert(expr, #expr, __METHOD_NAME__, __FILE__, \
                                    __LINE__, msg)
 
+/** @def __METHOD_NAME__
+ *  @brief Get the name of the current method/function.
+ * */
 #define __METHOD_NAME__ methodName(__PRETTY_FUNCTION__)
 
 
-/** Code stolen from https://github.com/anderkve/FYS3150
- *  Header: https://github.com/anderkve/FYS3150/blob/master/code_examples/compilation_linking/example_1/include/utils.hpp
- *  Source: https://github.com/anderkve/FYS3150/blob/master/code_examples/compilation_linking/example_1/src/utils.cpp
- * */
-
 /** @brief Turns a double into a string written in scientific format.
+ *
+ *  @details The code is stolen from https://github.com/anderkve/FYS3150.
  *
  *  @param d The number to stringify
  *  @param width The reserved width of the string
  *  @param prec The precision of the stringified number
  *
- *  @return String
+ *  @return std::string
  * */
 std::string scientific_format(double d, int width=20, int prec=10);
 
+
 /** @brief Turns a vector of doubles into a string written in scientific format.
+ *  
+ *  @details The code is stolen from https://github.com/anderkve/FYS3150.
  *
  *  @param v The vector to stringify
  *  @param width The reserved width of the string
  *  @param prec The precision of the stringified number
  *
- *  @return String
+ *  @return std::string
  * */
 std::string scientific_format(const std::vector<double>& v, 
                               int width=20, 
                               int prec=10);
 
+
 /** @brief Test an expression, confirm that test is ok, or abort execution.
  *
- *  This function takes in an expression and prints an OK message if it's
- *  true, or it prints a fail message and aborts execution if it fails.
+ *  @details This function takes in an expression and prints an OK message if 
+ *  it's true, or it prints a fail message and aborts execution if it fails.
  *
  *  @param expr The expression to be evaluated
  *  @param expr_str The stringified version of the expression
@@ -97,27 +101,48 @@ void m_assert(bool expr,
 
 /** @brief Test if two armadillo vectors are close to each other.
  *
- *  This function takes in 2 vectors and checks if they are approximately
- *  equal to each other given a tolerance.
+ *  @details This function takes in 2 vectors and checks if they are 
+ *  approximately equal to each other given a tolerance.
  *
  *  @param a Vector a
  *  @param b Vector b
  *  @param tol The tolerance
  *
- *  @return Boolean
+ *  @return bool
  * */
 bool arma_vector_close_to(arma::vec &a, arma::vec &b, double tol=1e-8);
 
 
-static inline std::string methodName(const std::string& prettyFunction)
+/** @brief Takes in the __PRETTY_FUNCTION__ string and removes the return type.
+ *
+ *  @details This function should only be used for the __METHOD_NAME__ macro,
+ *  since it takes the output from __PRETTY_FUNCTION__ and strips the return
+ *  type.
+ *
+ *  @param pretty_function The string from __PRETTY_FUNCTION__
+ *
+ *  @return std::string
+ * */
+static inline std::string methodName(const std::string& pretty_function)
 {
-    size_t colons = prettyFunction.find("::");
-    size_t begin = prettyFunction.substr(0,colons).rfind(" ") + 1;
-    size_t end = prettyFunction.rfind("(") - begin;
+    size_t colons = pretty_function.find("::");
+    size_t begin = pretty_function.substr(0,colons).rfind(" ") + 1;
+    size_t end = pretty_function.rfind("(") - begin;
 
-    return prettyFunction.substr(begin,end) + "()";
+    return pretty_function.substr(begin,end) + "()";
 }
 
+
+/** @brief Make path given.
+ *
+ *  @details This tries to be the equivalent to "mkdir -p" and creates a new
+ *  directory whenever it needs to.
+ *
+ *  @param path The path to be created
+ *  @param mode The mode/permissions for all the new directories
+ *
+ *  @return bool
+ * */
 bool mkpath(std::string path, int mode = 0777);
 
 #endif
diff --git a/src/Makefile b/src/Makefile
index 69f309e..f678e43 100644
--- a/src/Makefile
+++ b/src/Makefile
@@ -8,7 +8,7 @@ CLASSOBJS=$(CLASSSRCS:.cpp=.o)
 
 INCLUDE=../include
 
-CFLAGS=-Wall -larmadillo -llapack -std=c++11 -O3
+CFLAGS=-Wall -larmadillo -lblas -llapack -std=c++11 -O3
 OPENMP=-fopenmp
 
 # Add a debug flag when compiling (For the DEBUG macro in utils.hpp)
diff --git a/src/Particle.cpp b/src/Particle.cpp
index 0ff18e8..2caad68 100644
--- a/src/Particle.cpp
+++ b/src/Particle.cpp
@@ -8,7 +8,6 @@
  *  @brief The implementation of the Particle class.
  *
  *  @bug No known bugs
- *
  * */
 
 #include "Particle.hpp"
diff --git a/src/PenningTrap.cpp b/src/PenningTrap.cpp
index 0c50836..d0478ec 100644
--- a/src/PenningTrap.cpp
+++ b/src/PenningTrap.cpp
@@ -8,33 +8,28 @@
  *  @brief The implementation of the PenningTrap class.
  *
  *  @bug No known bugs
- *
- *  @todo Implement evolve_RK4
- *  @todo Implement evolve_forward_euler
  * */
 
 #include "PenningTrap.hpp"
 #include "constants.hpp"
 #include "typedefs.hpp"
 #include "utils.hpp"
-#include <cstdlib>
-#include <functional>
-#include <string>
-#include <vector>
 
-PenningTrap::PenningTrap(double B_0, double V_0, double d)
+PenningTrap::PenningTrap(double B_0, std::function<double(double)> V_0,
+                         double d, double t)
 {
     this->B_0 = B_0;
     this->V_0 = V_0;
     this->d = d;
-
+    this->t = t;
 }
 
-PenningTrap::PenningTrap(int i, double B_0, double V_0, double d)
+PenningTrap::PenningTrap(unsigned int i, double B_0,
+                         std::function<double(double)> V_0, double d, double t)
     : PenningTrap::PenningTrap(B_0, V_0, d)
 {
     vec_3d r, v;
-    for (int j = 0; j < i; j++) {
+    for (size_t j = 0; j < i; j++) {
         r = vec_3d().randn() * .1 * this->d;
         v = vec_3d().randn() * .1 * this->d;
         this->add_particle(Particle(1., 40., r, v));
@@ -42,13 +37,13 @@ PenningTrap::PenningTrap(int i, double B_0, double V_0, double d)
 }
 
 PenningTrap::PenningTrap(std::vector<Particle> particles, double B_0,
-                         double V_0, double d)
+                         std::function<double(double)> V_0, double d, double t)
     : PenningTrap::PenningTrap(B_0, V_0, d)
 {
     this->particles = particles;
 }
 
-vec_3d PenningTrap::v_func(int i, int j, double dt)
+vec_3d PenningTrap::v_func(unsigned int i, unsigned int j, double dt)
 {
     switch (i) {
     case 0:
@@ -66,7 +61,7 @@ vec_3d PenningTrap::v_func(int i, int j, double dt)
     }
 }
 
-vec_3d PenningTrap::r_func(int i, int j, double dt)
+vec_3d PenningTrap::r_func(unsigned int i, unsigned int j, double dt)
 {
     switch (i) {
     case 0:
@@ -92,7 +87,7 @@ void PenningTrap::add_particle(Particle particle)
 vec_3d PenningTrap::external_E_field(vec_3d r)
 {
     r(2) *= -2.;
-    double f = this->V_0 / (this->d * this->d);
+    double f = this->V_0(this->t) / (this->d * this->d);
 
     return f * r;
 }
@@ -102,21 +97,21 @@ vec_3d PenningTrap::external_B_field(vec_3d r)
     return vec_3d{0., 0., this->B_0};
 }
 
-vec_3d PenningTrap::force_on_particle(int i, int j)
+vec_3d PenningTrap::force_on_particle(unsigned int i, unsigned int j)
 {
+    Particle p_j = this->particles[j];
     // Calculate the difference between the particles' position
-    vec_3d res = this->particles[i].r_vec - this->particles[j].r_vec;
+    vec_3d res = this->particles[i].r_vec - p_j.r_vec;
 
     // Get the distance between the particles
-    double norm = arma::norm(res);
+    double norm = arma::norm(res, 2);
 
     // Multiply res with p_j's charge divided by the norm cubed
-    res *= this->particles[j].q / (norm * norm * norm);
 
-    return res;
+    return vec_3d(res * p_j.q / (norm * norm * norm));
 }
 
-vec_3d PenningTrap::total_force_external(int i)
+vec_3d PenningTrap::total_force_external(unsigned int i)
 {
     Particle p = this->particles[i];
 
@@ -124,13 +119,9 @@ vec_3d PenningTrap::total_force_external(int i)
         return vec_3d{0., 0., 0.};
     }
 
-    vec_3d B = this->external_B_field(p.r_vec);
-
-    vec_3d v_cross_B{p.v_vec(1) * B(2) - p.v_vec(2) * B(1),
-                     p.v_vec(2) * B(0) - p.v_vec(0) * B(2),
-                     p.v_vec(0) * B(1) - p.v_vec(1) * B(0)};
-
-    vec_3d force = p.q * (this->external_E_field(p.r_vec) + v_cross_B);
+    vec_3d force =
+        p.q * (this->external_E_field(p.r_vec) +
+               arma::cross(p.v_vec, this->external_B_field(p.r_vec)));
 
     return force;
 }
@@ -140,9 +131,8 @@ vec_3d PenningTrap::total_force_particles(unsigned int i)
     Particle p = this->particles[i];
 
     vec_3d res;
-    size_t size = this->particles.size();
 
-    for (size_t j = 0; j < size; j++) {
+    for (size_t j = 0; j < this->particles.size(); j++) {
         if (i == j) {
             continue;
         }
@@ -150,12 +140,10 @@ vec_3d PenningTrap::total_force_particles(unsigned int i)
         res += this->force_on_particle(i, j);
     }
 
-    res *= K_E * (p.q / p.m);
-
-    return res;
+    return vec_3d(res * K_E * (p.q / p.m));
 }
 
-vec_3d PenningTrap::total_force(int i)
+vec_3d PenningTrap::total_force(unsigned int i)
 {
     return this->total_force_external(i) - this->total_force_particles(i);
 }
@@ -163,43 +151,36 @@ vec_3d PenningTrap::total_force(int i)
 void PenningTrap::evolve_RK4(double dt, bool particle_interaction)
 {
 
-    DEBUG("Inside RK4");
     std::vector<Particle> original_particles = this->particles;
     std::vector<Particle> tmp_particles = this->particles;
 
-    DEBUG("Choose force func");
-    std::function<vec_3d(int)> force;
+    vec_3d (PenningTrap::*force)(unsigned int);
     if (particle_interaction) {
-        force = [this](int i) { return this->total_force(i); };
+        force = &PenningTrap::total_force;
     }
     else {
-        force = [this](int i) { return this->total_force_external(i); };
+        force = &PenningTrap::total_force_external;
     }
 
-    DEBUG("Create k_v and k_r");
-    int size = this->particles.size();
+    size_t size = this->particles.size();
 
     this->k_v = sim_arr(4, sim_cols(size));
     this->k_r = sim_arr(4, sim_cols(size));
 
-    DEBUG("Loop");
-    for (int i = 0; i < 4; i++) {
-        DEBUG("Inside outer loop");
+    for (size_t i = 0; i < 4; i++) {
 #pragma omp parallel for
-        for (int j = 0; j < size; j++) {
-            DEBUG("Set k_v and k_r");
-            this->k_v[i][j] = this->total_force(j) / this->particles[j].m;
+        for (size_t j = 0; j < this->particles.size(); j++) {
+            this->k_v[i][j] = (this->*force)(j) / this->particles[j].m;
             this->k_r[i][j] = this->particles[j].v_vec;
 
             Particle *p = &tmp_particles[j];
 
-            DEBUG("Update v and r");
             p->v_vec = original_particles[j].v_vec + this->v_func(i, j, dt);
             p->r_vec = original_particles[j].r_vec + this->r_func(i, j, dt);
         }
-        DEBUG("After inner loop");
         this->particles = tmp_particles;
     }
+    this->t += dt;
 }
 
 void PenningTrap::evolve_forward_euler(double dt, bool particle_interaction)
@@ -208,58 +189,49 @@ void PenningTrap::evolve_forward_euler(double dt, bool particle_interaction)
 
     Particle *p;
 
-    std::function<vec_3d(int)> force;
+    vec_3d (PenningTrap::*force)(unsigned int);
     if (particle_interaction) {
-        force = [this](int i) { return this->total_force(i); };
+        force = &PenningTrap::total_force;
     }
     else {
-        force = [this](int i) { return this->total_force_external(i); };
+        force = &PenningTrap::total_force_external;
     }
 
 #pragma omp parallel for private(p)
     for (size_t i = 0; i < this->particles.size(); i++) {
         p = &new_state[i];
-        p->v_vec += dt * force(i) / p->m;
+        p->v_vec += dt * (this->*force)(i) / p->m;
         p->r_vec += dt * this->particles[i].v_vec;
     }
 
     this->particles = new_state;
+    this->t += dt;
 }
 
 sim_arr PenningTrap::simulate(double time, unsigned int steps,
                               std::string method, bool particle_interaction)
 {
-    DEBUG("Inside simulate");
     double dt = time / (double)steps;
 
     sim_arr res(this->particles.size(), sim_cols(steps));
 
-    DEBUG("Choose function to use");
-    std::function<void(double, bool)> func;
+    void (PenningTrap::*func)(double, bool);
     if (method == "rk4") {
-        func = [this](double dt, bool particle_interaction) {
-            DEBUG("Inside RK4 lambda");
-            this->evolve_RK4(dt, particle_interaction);
-        };
+        func = &PenningTrap::evolve_RK4;
     }
     else if (method == "euler") {
-        func = [this](double dt, bool particle_interaction) {
-            this->evolve_forward_euler(dt, particle_interaction);
-        };
+        func = &PenningTrap::evolve_forward_euler;
     }
     else {
         std::cout << "Not a valid method!" << std::endl;
         abort();
     }
 
-    DEBUG("Loop");
     for (size_t j = 0; j < steps; j++) {
-        DEBUG("Inside outer loop");
         for (size_t i = 0; i < this->particles.size(); i++) {
             res[i][j] = this->particles[i].r_vec;
         }
-        DEBUG("After inner loop");
-        func(dt, particle_interaction);
+        (this->*func)(dt, particle_interaction);
     }
 
     return res;
@@ -269,7 +241,6 @@ void PenningTrap::write_simulation_to_dir(std::string path, double time,
                                           int steps, std::string method,
                                           bool particle_interaction)
 {
-    DEBUG("Inside write to dir");
     if (path.back() != '/') {
         path += '/';
     }
@@ -278,12 +249,10 @@ void PenningTrap::write_simulation_to_dir(std::string path, double time,
         return;
     }
 
-    DEBUG("Create sim_arr");
     sim_arr res = this->simulate(time, steps, method, particle_interaction);
 
     std::ofstream ofile;
 
-    DEBUG("Loop");
 #pragma omp parallel for private(ofile)
     for (size_t i = 0; i < this->particles.size(); i++) {
         ofile.open(path + "particle_" + std::to_string(i) + ".txt");
@@ -293,3 +262,19 @@ void PenningTrap::write_simulation_to_dir(std::string path, double time,
         ofile.close();
     }
 }
+
+double PenningTrap::fraction_of_particles_left(double time, unsigned int steps, std::string method, bool particle_interaction)
+{
+    sim_arr res = this->simulate(time, steps, method, particle_interaction);
+
+    int particles_left = 0;
+
+    for (Particle p : this->particles) {
+        if (arma::norm(p.r_vec) < this->d) {
+            particles_left++;
+        }
+    }
+
+    return (double) particles_left / (double) this->particles.size();
+}
+
diff --git a/src/main.cpp b/src/main.cpp
index 35ec896..b07ed93 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -10,6 +10,7 @@
  *  @bug No known bugs
  * */
 
+#include <cmath>
 #include <fstream>
 #include <omp.h>
 #include <string>
@@ -59,45 +60,81 @@ void simulate_single_particle_with_different_steps()
     for (int i = 0; i < 4; i++) {
         int steps = 4000 * (i + 1);
         PenningTrap trap(std::vector<Particle>{p1});
-        trap.write_simulation_to_dir("output/N_steps/RK4/" + std::to_string(steps) +
-                                         "_steps",
+        trap.write_simulation_to_dir("output/N_steps/RK4/" +
+                                         std::to_string(steps) + "_steps",
                                      time, steps, "rk4", false);
     }
 
     for (int i = 0; i < 4; i++) {
         int steps = 4000 * (i + 1);
         PenningTrap trap(std::vector<Particle>{p1});
-        trap.write_simulation_to_dir("output/N_steps/euler/" + std::to_string(steps) +
-                                         "_steps",
+        trap.write_simulation_to_dir("output/N_steps/euler/" +
+                                         std::to_string(steps) + "_steps",
                                      time, steps, "euler", false);
     }
 }
 
 void simulate_100_particles()
 {
-    PenningTrap trap(100);
+    PenningTrap trap((unsigned)100, T,
+                     [](double t) {
+                         return 25. * V / 1000. *
+                                (1. + .4 * std::cos(1.5 * t));
+                     },
+                     500., 0);
 
-    double time = 50.; // microseconds
+    double time = 500.; // microseconds
 
-    trap.write_simulation_to_dir("output/simulate_100_particles", time, N);
+    trap.write_simulation_to_dir("output/simulate_100_particles", time, N*5);
+}
+
+void simulate_100_particles_with_time_potential()
+{
+    double amplitudes[]{.1, .4, .7};
+
+    double freq_start = .2;
+    double freq_end = 2.5;
+    double freq_increment = .02;
+    size_t freq_iterations = (size_t) ((freq_end - freq_start) / freq_increment);
+
+    std::string path = "output/time_dependent_potential/";
+    mkpath(path);
+
+    std::ofstream ofile;
+
+    for (double f : amplitudes) {
+        ofile.open(path + "f_" + std::to_string(f) + ".txt");
+        #pragma omp parallel for ordered schedule(static, 1)
+        for (size_t i=0; i < freq_iterations; i++) {
+            double freq = freq_start + i*freq_increment;
+            PenningTrap trap((unsigned)100, T,
+                             [f, freq](double t) {
+                                 return (25. * V / 1000.) *
+                                        (1. + f * std::cos(freq * t));
+                             },
+                             500., 0.);
+            double res = trap.fraction_of_particles_left(500., 40000, "rk4", true);
+            #pragma omp ordered
+            ofile << freq << "," << res << "\n";
+        }
+        ofile.close();
+    }
 }
 
 int main()
 {
-    DEBUG("Start");
-    double start = omp_get_wtime();
 
-    DEBUG("Single particle");
     simulate_single_particle();
 
-    DEBUG("Two particles");
     simulate_two_particles();
 
-    DEBUG("Single particle with different steps");
     simulate_single_particle_with_different_steps();
 
-    DEBUG("100 particles");
-    simulate_100_particles();
+    double start = omp_get_wtime();
+
+    //simulate_100_particles();
+
+    simulate_100_particles_with_time_potential();
 
     double end = omp_get_wtime();
 

From 3431e09aeba2ee5731ac0b85f8357b129c131148 Mon Sep 17 00:00:00 2001
From: Cory <cory@balaton.dev>
Date: Sat, 14 Oct 2023 03:12:38 +0200
Subject: [PATCH 16/26] Plot the amount of particles left in Penning trap

---
 src/plot_particles_left.py | 33 +++++++++++++++++++++++++++++++++
 1 file changed, 33 insertions(+)
 create mode 100644 src/plot_particles_left.py

diff --git a/src/plot_particles_left.py b/src/plot_particles_left.py
new file mode 100644
index 0000000..1d9a45c
--- /dev/null
+++ b/src/plot_particles_left.py
@@ -0,0 +1,33 @@
+import matplotlib.pyplot as plt
+
+def main():
+    files = [
+        "output/time_dependent_potential/f_0.100000.txt",
+        "output/time_dependent_potential/f_0.400000.txt",
+        "output/time_dependent_potential/f_0.700000.txt",
+    ]
+    vals = [
+        .1,
+        .4,
+        .7
+    ]
+    for i in range(3):
+        with open(files[i]) as f:
+            lines = f.readlines()
+            x = []
+            y = []
+            for line in lines:
+                a,b = line.strip().split(",")
+                x.append(float(a))
+                y.append(float(b))
+            plt.plot(x,y,label=f"amplitude: {vals[i]}")
+
+    plt.xlabel(r"$\omega_V$")
+    plt.ylabel(r"Fraction of particles left")
+    plt.title(r"The fraction of particles left in the Penning trap "
+              "after 500 microseconds for different amplitudes and frequencies")
+    plt.legend()
+    plt.show()
+
+if __name__ == "__main__":
+    main()

From 56080de56184e4bf5e62d91805f1eb420aad7eac Mon Sep 17 00:00:00 2001
From: Cory <cory@balaton.dev>
Date: Sun, 15 Oct 2023 23:01:03 +0200
Subject: [PATCH 17/26] Implemented pseudocode for forward Euler and RK4

---
 latex/main.pdf             | Bin 73209 -> 249290 bytes
 latex/sections/methods.tex | 149 ++++++++++++++++++++++++++++++++++++-
 2 files changed, 148 insertions(+), 1 deletion(-)

diff --git a/latex/main.pdf b/latex/main.pdf
index ed5a52cc460302f0453e07df750681a66ab12161..6e3a09369a9ae07bb88d6b583cfa2badd1227889 100644
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diff --git a/latex/sections/methods.tex b/latex/sections/methods.tex
index e2f6d07..fb2b32c 100644
--- a/latex/sections/methods.tex
+++ b/latex/sections/methods.tex
@@ -6,8 +6,155 @@
 
 \section{Methods}
 
+Newton's second law of motion is defined as
+\begin{equation}
+    \frac{d^2\vb{r}}{dt^2} = \frac{\vb{F}\left(t, \frac{d\vb{r}}{dt}, \vb{r}\right)}{m}.
+    \label{eq:newtonlaw2}
+\end{equation}
+We can then rewrite the second order ODE from equation~\ref{eq:newtonlaw2} 
+into a set of coupled first order ODEs. 
+We now redefine Newton's second law of motion as
+\begin{equation}
+    \begin{split}
+        \frac{d\vb{r}}{dt} &= \vb{v} \\
+        \frac{d\vb{v}}{dt} &= \frac{\vb{F}(t, \vb{v}, \vb{r})}{m}.
+    \end{split}
+    \label{eq:coupled}
+\end{equation}
 
+\subsection{Forward Euler}
+
+For a single particle, the forward Euler method for a coupled system is 
+expressed as
+
+\begin{equation}
+    \begin{split}
+        \vb{r}_{i+1} &= \vb{r}_i + h \cdot \frac{d\vb{r}_i}{dt} = \vb{r}_i + h \cdot \vb{v}_i \\
+        \vb{v}_{i+1} &= \vb{v}_i + h \cdot \frac{\vb{v}_i}{dt} = \vb{v}_i + h \cdot \frac{\vb{F}\left( t_i, \vb{v}_i, \vb{r}_i \right)}{m},
+    \end{split}
+\end{equation}
+where $\vb{v}_i$ is the current velocity of the particle, $\vb{r}_i$ is the
+current position of the particle, $m$ is the mass of the particle, and $h$
+is a predetermined timestep.
+
+When dealing with a multi-particle system, we need to ensure that we do not
+update the position of any particles until every particle has calculated their
+next step. An easy way of doing this is to create a copy of all the particles,
+then update the copy, and when all the particles have calculated their next 
+step, simply replace the particles with the copies. 
+Algorithm~\ref{algo:forwardeuler} provides an overview on how that can be achieved. % Make this better
+
+\begin{figure}[H]
+    \begin{algorithm}[H]
+    \caption{Forward Euler method}
+    \label{algo:forwardeuler}
+        \begin{algorithmic}
+            \Procedure{Evolve forward Euler}{$particles, dt$}
+            \State $new\_state \leftarrow particles$ \Comment{Create a copy of the particles}
+            \For{ $i = 1, 2, \ldots , \left| particles \right|$ }
+            \State $new\_state_i.\vb{v} \leftarrow particles_i.\vb{v} + dt \cdot \frac{\vb{F}}{m}$
+            \State $new\_state_i.\vb{r} \leftarrow particles_i.\vb{r} + dt \cdot particles_i.\vb{v}$
+            \EndFor
+            \State $particles \leftarrow new\_state$
+            \EndProcedure
+        \end{algorithmic}
+    \end{algorithm}
+\end{figure}
+
+\subsection{4th order Runge-Kutta}
+
+For a single particle, we can express the 4th order Runge-Kutta (RK4) method as
+\begin{equation}
+    \begin{split}
+        \vb{v}_{i+1} &= \vb{v}_i + \frac{h}{6} \left( \vb{k}_{\vb{v},1} 
+            + 2\vb{k}_{\vb{v},2} + 2\vb{k}_{\vb{v},3} + \vb{k}_{\vb{v},4} 
+            \right) \\
+        \vb{r}_{i+1} &= \vb{r}_i + \frac{h}{6} \left( \vb{k}_{\vb{r},1} 
+            + 2\vb{k}_{\vb{r},2} + 2\vb{k}_{\vb{r},3} + \vb{k}_{\vb{r},4} 
+            \right),
+    \end{split}
+\end{equation}
+where
+\begin{equation}
+    \begin{split}
+    \vb{k}_{\vb{v},1} &= \frac{\vb{F}(t_i, \vb{v}_i, \vb{r}_i)}{m} \\
+    \vb{k}_{\vb{r},1} &= \vb{v}_i \\
+    \vb{k}_{\vb{v},2} &= \frac{\vb{F}(t_i+\frac{h}{2}, \vb{v}_i + h \cdot \frac{\vb{k}_{\vb{v},1}}{2}, \vb{r}_i + h \cdot \frac{\vb{k}_{\vb{r},1}}{2})}{m} \\
+    \vb{k}_{\vb{r},2} &= \vb{v}_i + h \cdot \frac{\vb{k}_{\vb{v},1}}{2} \\
+    \vb{k}_{\vb{v},3} &= \frac{\vb{F}(t_i+\frac{h}{2}, \vb{v}_i + h \cdot \frac{\vb{k}_{\vb{v},2}}{2}, \vb{r}_i + h \frac{\cdot \vb{k}_{\vb{r},2}}{2})}{m} \\
+    \vb{k}_{\vb{r},3} &= \vb{v}_i + h \cdot \frac{\vb{k}_{\vb{v},2}}{2} \\
+    \vb{k}_{\vb{v},4} &= \frac{\vb{F}(t_i+h, \vb{v}_i + h \cdot \vb{k}_{\vb{v},3}, \vb{r}_i + h \cdot \vb{k}_{\vb{r},3})}{m} \\
+    \vb{k}_{\vb{r},4} &= \vb{v}_i + h \cdot \frac{\vb{k}_{\vb{v},1}}{2}.
+    \end{split}
+\end{equation}
+
+\newpage
+
+\begin{figure}
+    \begin{algorithm}[H]
+    \caption{RK4 method}
+    \label{algo:rk4}
+        \begin{algorithmic}
+            \Procedure{Evolve RK4}{$dt$}
+            \State $N \leftarrow \text{Number of particles inside the Penning trap}$
+            \State $orig\_p \leftarrow \text{Copy of particles}$ \Comment{Keep the original particles}
+            \State $tmp\_p \leftarrow \text{Array of particles of size }N$
+            \State $\vb{k}_{\vb{r}} \leftarrow \text{2D array of vectors of size } 4 \cross N$
+            \State $\vb{k}_{\vb{v}} \leftarrow \text{2D array of vectors of size } 4 \cross N$
+
+            \For{ $i = 1, 2, \ldots, N$ }
+            \State $\vb{k}_{\vb{r},1,i} \leftarrow \vb{v}$
+            \State $\vb{k}_{\vb{v},1,i} \leftarrow \frac{\vb{F}}{m}$
+
+            \State $tmp\_p_i.\vb{r} \leftarrow orig\_p_i.\vb{r} + \frac{dt}{2} \cdot \vb{k}_{\vb{r},1,i}$
+            \State $tmp\_p_i.\vb{v} \leftarrow orig\_p_i.\vb{v} + \frac{dt}{2} \cdot \vb{k}_{\vb{v},1,i}$
+            \EndFor
+
+            \State $particles \leftarrow tmp\_p$ \Comment{Update particles}
+
+            \For{ $i = 1, 2, \ldots, N$ }
+            \State $\vb{k}_{\vb{r},2,i} \leftarrow \vb{v}$
+            \State $\vb{k}_{\vb{v},2,i} \leftarrow \frac{\vb{F}}{m}$
+
+            \State $tmp\_p_i.\vb{r} \leftarrow orig\_p_i.\vb{r} + \frac{dt}{2} \cdot \vb{k}_{\vb{r},2,i}$
+            \State $tmp\_p_i.\vb{v} \leftarrow orig\_p_i.\vb{v} + \frac{dt}{2} \cdot \vb{k}_{\vb{v},2,i}$
+            \EndFor
+
+            \State $particles \leftarrow tmp\_p$ \Comment{Update particles}
+
+            \For{ $i = 1, 2, \ldots, N$ }
+            \State $\vb{k}_{\vb{r},3,i} \leftarrow \vb{v}$
+            \State $\vb{k}_{\vb{v},3,i} \leftarrow \frac{\vb{F}}{m}$
+
+            \State $tmp\_p_i.\vb{r} \leftarrow orig\_p_i.\vb{r} + dt \cdot \vb{k}_{\vb{r},3,i}$
+            \State $tmp\_p_i.\vb{v} \leftarrow orig\_p_i.\vb{v} + dt \cdot \vb{k}_{\vb{v},3,i}$
+            \EndFor
+
+            \State $particles \leftarrow tmp\_p$ \Comment{Update particles}
+
+            \For{ $i = 1, 2, \ldots, N$ }
+            \State $\vb{k}_{\vb{r},4,i} \leftarrow \vb{v}$
+            \State $\vb{k}_{\vb{v},4,i} \leftarrow \frac{\vb{F}}{m}$
+
+            \State $tmp\_p_i.\vb{r} \leftarrow orig\_p_i.\vb{r} + \frac{dt}{6} 
+            \cdot \left( \vb{k}_{\vb{r},1,i} + \vb{k}_{\vb{r},2,i} 
+            + \vb{k}_{\vb{r},3,i} + \vb{k}_{\vb{r},4,i} \right)$
+
+            \State $tmp\_p_i.\vb{v} \leftarrow orig\_p_i.\vb{v} + \frac{dt}{6} 
+            \cdot \left( \vb{k}_{\vb{v},1,i} + \vb{k}_{\vb{v},2,i} 
+            + \vb{k}_{\vb{v},3,i} + \vb{k}_{\vb{v},4,i} \right)$
+            
+            \EndFor
+
+            \State $particles \leftarrow tmp\_p$ \Comment{Final update}
+            \EndProcedure
+        \end{algorithmic}
+    \end{algorithm}
+    $\vb{F}$ in the algorithm does not take any arguments as it uses the 
+    velocities and positions of the particles inside the array $particles$ to
+    calculate the total force acting on particle $i$.
+\end{figure}
 
 
 \biblio
-\end{document}
\ No newline at end of file
+\end{document}

From 03344c3298af2ac652a9697abf66470253d75c3b Mon Sep 17 00:00:00 2001
From: Cory <cory@balaton.dev>
Date: Mon, 16 Oct 2023 12:58:34 +0200
Subject: [PATCH 18/26] Update methods

---
 latex/main.pdf                  | Bin 249290 -> 261496 bytes
 latex/references/references.bib |   9 ++++++
 latex/sections/methods.tex      |  51 ++++++++++++++++++++++++--------
 3 files changed, 47 insertions(+), 13 deletions(-)

diff --git a/latex/main.pdf b/latex/main.pdf
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diff --git a/latex/references/references.bib b/latex/references/references.bib
index 236bbd0..38b1079 100644
--- a/latex/references/references.bib
+++ b/latex/references/references.bib
@@ -7,3 +7,12 @@
 	publisher= "CRC Press",
 	year	= "2016",
 }
+
+@article{rk4_method,
+    author = "Morten Hjorth-Jensen",
+    title = "Computational Physics, Lecture Notes Fall 2015",
+    journal = "Department of Physics, University of Oslo",
+    year = "2015",
+    chapter = "8.4",
+    pages = "250--252",
+}
diff --git a/latex/sections/methods.tex b/latex/sections/methods.tex
index fb2b32c..80ca419 100644
--- a/latex/sections/methods.tex
+++ b/latex/sections/methods.tex
@@ -6,18 +6,31 @@
 
 \section{Methods}
 
-Newton's second law of motion is defined as
+For a multi-particles system, we need to modify $\vb{F}$ to account for the 
+force of other particles in the system acting upon each other. To do that, we
+add another term to $\vb{F}$
 \begin{equation}
-    \frac{d^2\vb{r}}{dt^2} = \frac{\vb{F}\left(t, \frac{d\vb{r}}{dt}, \vb{r}\right)}{m}.
+    \vb{F}_i(t, \vb{v}_i, \vb{r}_i) = q_i \vb{E}(t, \vb{r}_i) + q_i \vb{v}_i \cross \vb{B} - \vb{E}_p(t, \vb{r}_i),
+\end{equation}
+where $i$ and $j$ are particle indices and
+\begin{equation}
+    \vb{E}_p(t, \vb{r}_i) = q_i k_e \sum_{j \neq i} 
+    q_j \frac{\vb{r_i} - \vb{r_j}}{\left| \vb{r_i} - \vb{r_j} \right|^3}.
+    \label{eq:}
+\end{equation}
+
+Newton's second law for a particle $i$ is then
+\begin{equation}
+    \frac{d^2\vb{r}_i}{dt^2} = \frac{\vb{F}\left(t, \frac{d\vb{r}_i}{dt}, \vb{r_i}\right)}{m_i},
     \label{eq:newtonlaw2}
 \end{equation}
 We can then rewrite the second order ODE from equation~\ref{eq:newtonlaw2} 
 into a set of coupled first order ODEs. 
-We now redefine Newton's second law of motion as
+We now rewrite Newton's second law of motion as
 \begin{equation}
     \begin{split}
-        \frac{d\vb{r}}{dt} &= \vb{v} \\
-        \frac{d\vb{v}}{dt} &= \frac{\vb{F}(t, \vb{v}, \vb{r})}{m}.
+        \frac{d\vb{r}_i}{dt} &= \vb{v}_i \\
+        \frac{d\vb{v}_i}{dt} &= \frac{\vb{F}(t, \vb{v}_i, \vb{r}_i)}{m_i}.
     \end{split}
     \label{eq:coupled}
 \end{equation}
@@ -33,9 +46,8 @@ expressed as
         \vb{v}_{i+1} &= \vb{v}_i + h \cdot \frac{\vb{v}_i}{dt} = \vb{v}_i + h \cdot \frac{\vb{F}\left( t_i, \vb{v}_i, \vb{r}_i \right)}{m},
     \end{split}
 \end{equation}
-where $\vb{v}_i$ is the current velocity of the particle, $\vb{r}_i$ is the
-current position of the particle, $m$ is the mass of the particle, and $h$
-is a predetermined timestep.
+where $i$ is the current time step of the particle $m$ is the mass of the particle, and $h$
+is the time step length.
 
 When dealing with a multi-particle system, we need to ensure that we do not
 update the position of any particles until every particle has calculated their
@@ -50,12 +62,12 @@ Algorithm~\ref{algo:forwardeuler} provides an overview on how that can be achiev
     \label{algo:forwardeuler}
         \begin{algorithmic}
             \Procedure{Evolve forward Euler}{$particles, dt$}
-            \State $new\_state \leftarrow particles$ \Comment{Create a copy of the particles}
-            \For{ $i = 1, 2, \ldots , \left| particles \right|$ }
-            \State $new\_state_i.\vb{v} \leftarrow particles_i.\vb{v} + dt \cdot \frac{\vb{F}}{m}$
-            \State $new\_state_i.\vb{r} \leftarrow particles_i.\vb{r} + dt \cdot particles_i.\vb{v}$
+            \State $N \leftarrow \text{Number of particles in } particles$
+            \State $a \leftarrow \text{Calculate } \frac{\vb{F_i}}{m_i} \text{ for each particle in } particles$
+            \For{ $i = 1, 2, \ldots , N$ }
+            \State $particles_i.\vb{r} \leftarrow particles_i.\vb{r} + dt \cdot particles_i.\vb{v}$
+            \State $particles_i.\vb{v} \leftarrow particles_i.\vb{v} + dt \cdot a_i$
             \EndFor
-            \State $particles \leftarrow new\_state$
             \EndProcedure
         \end{algorithmic}
     \end{algorithm}
@@ -88,6 +100,19 @@ where
     \end{split}
 \end{equation}
 
+In order to find each $\vb{k}_{\vb{r},i}$ and $\vb{k}_{\vb{v},i}$, 
+we need to first compute all $\vb{k}_{\vb{r},i}$ and $\vb{k}_{\vb{v},i}$ 
+for all particles, then we can update the particles in order to compute 
+$\vb{k}_{\vb{r},i+1}$ and $\vb{k}_{\vb{v},i+1}$. In order for the algorithm
+to work, we need to save a copy of each particle before starting so that we
+can update the particles correctly for each step.
+
+This approach would require 8 loops to be able to complete the calculation since
+we cannot update the particles until after all $\vb{k}$ values have been 
+computed, however if we create a temporary array that holds particles, we can
+put the updated particles in there, and then use that array in the next loop.
+around 8 separate loops to calculate all $\vb{k}$ values
+
 \newpage
 
 \begin{figure}

From 0fc1ec1e3390c8be782a3a1fb461f96af06c4525 Mon Sep 17 00:00:00 2001
From: Cory <cory@balaton.dev>
Date: Mon, 16 Oct 2023 13:01:21 +0200
Subject: [PATCH 19/26] Fix signature

---
 src/PenningTrap.cpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/PenningTrap.cpp b/src/PenningTrap.cpp
index d0478ec..20e2db1 100644
--- a/src/PenningTrap.cpp
+++ b/src/PenningTrap.cpp
@@ -238,7 +238,7 @@ sim_arr PenningTrap::simulate(double time, unsigned int steps,
 }
 
 void PenningTrap::write_simulation_to_dir(std::string path, double time,
-                                          int steps, std::string method,
+                                          unsigned int steps, std::string method,
                                           bool particle_interaction)
 {
     if (path.back() != '/') {

From 95432102ea978b81a302cbd1f51ba2b651916d13 Mon Sep 17 00:00:00 2001
From: Cory <cory@balaton.dev>
Date: Mon, 16 Oct 2023 13:33:00 +0200
Subject: [PATCH 20/26] Small fix

---
 src/PenningTrap.cpp | 22 +++++++++++++---------
 src/main.cpp        | 10 ++++++----
 2 files changed, 19 insertions(+), 13 deletions(-)

diff --git a/src/PenningTrap.cpp b/src/PenningTrap.cpp
index 20e2db1..49f6d94 100644
--- a/src/PenningTrap.cpp
+++ b/src/PenningTrap.cpp
@@ -178,15 +178,15 @@ void PenningTrap::evolve_RK4(double dt, bool particle_interaction)
             p->v_vec = original_particles[j].v_vec + this->v_func(i, j, dt);
             p->r_vec = original_particles[j].r_vec + this->r_func(i, j, dt);
         }
-        this->particles = tmp_particles;
+        this->particles.swap(tmp_particles);
     }
     this->t += dt;
 }
 
 void PenningTrap::evolve_forward_euler(double dt, bool particle_interaction)
 {
-    std::vector<Particle> new_state = this->particles;
-
+    size_t size = this->particles.size();
+    vec_3d force_res[size];
     Particle *p;
 
     vec_3d (PenningTrap::*force)(unsigned int);
@@ -197,14 +197,18 @@ void PenningTrap::evolve_forward_euler(double dt, bool particle_interaction)
         force = &PenningTrap::total_force_external;
     }
 
-#pragma omp parallel for private(p)
-    for (size_t i = 0; i < this->particles.size(); i++) {
-        p = &new_state[i];
-        p->v_vec += dt * (this->*force)(i) / p->m;
-        p->r_vec += dt * this->particles[i].v_vec;
+#pragma omp parallel for
+    for (size_t i = 0; i < size; i++) {
+        force_res[i] = (this->*force)(i);
+    }
+
+#pragma omp parallel for private(p)
+    for (size_t i = 0; i < size; i++) {
+        p = &this->particles[i];
+        p->r_vec += dt * p->v_vec;
+        p->v_vec += dt * force_res[i] / p->m;
     }
 
-    this->particles = new_state;
     this->t += dt;
 }
 
diff --git a/src/main.cpp b/src/main.cpp
index b07ed93..96465cc 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -85,7 +85,7 @@ void simulate_100_particles()
 
     double time = 500.; // microseconds
 
-    trap.write_simulation_to_dir("output/simulate_100_particles", time, N*5);
+    trap.write_simulation_to_dir("output/simulate_100_particles", time, N*4);
 }
 
 void simulate_100_particles_with_time_potential()
@@ -132,13 +132,15 @@ int main()
 
     double start = omp_get_wtime();
 
-    //simulate_100_particles();
+    for (int i=0; i<5; i++) {
+        simulate_100_particles();
+    }
 
-    simulate_100_particles_with_time_potential();
+    //simulate_100_particles_with_time_potential();
 
     double end = omp_get_wtime();
 
-    std::cout << "Time: " << end - start << " seconds" << std::endl;
+    std::cout << "Average time: " << (end - start) / 5. << " seconds" << std::endl;
 
     return 0;
 }

From f29424f96ea80947719c3527f98f910b6c89b9e2 Mon Sep 17 00:00:00 2001
From: Cory <cory@balaton.dev>
Date: Mon, 16 Oct 2023 20:58:50 +0200
Subject: [PATCH 21/26] Fix some small things

---
 latex/main.pdf             | Bin 261496 -> 270632 bytes
 latex/sections/methods.tex | 134 +++++++++++++++++++++++++------------
 2 files changed, 92 insertions(+), 42 deletions(-)

diff --git a/latex/main.pdf b/latex/main.pdf
index 979dd80ca03c83d5b9e297b1dc809c8435539015..70446f4241cf1022d4696bc1441a4602eb7afba1 100644
GIT binary patch
delta 100627
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diff --git a/latex/sections/methods.tex b/latex/sections/methods.tex
index 80ca419..4c02530 100644
--- a/latex/sections/methods.tex
+++ b/latex/sections/methods.tex
@@ -6,6 +6,41 @@
 
 \section{Methods}
 
+\subsection{Units and constants}
+
+Before continuing, we need to define the units we'll be working with.
+Since we are working with particles, we need small units to work with so the
+numbers we are working with aren't so small that they could potentially lead
+to large round-off errors in our simulation. The units that we will use are listed in Table~\ref{tab:units}.
+\begin{table}[H]
+    \begin{center}
+        \begin{tabular}[c]{lll}
+            Dimension & Unit & Symbol \\
+            \hline
+            Length & micrometer & $\mu m$ \\
+            Time & microseconds & $\mu s$ \\
+            Mass & atomic mass unit & $u$ \\
+            Charge & the elementary charge & $e$ \\
+            \hline
+        \end{tabular}
+    \end{center}
+    \caption{The set of units we'll be working with.}\label{tab:units}
+\end{table}
+With these base units, we get
+\begin{equation}
+    k_e = 1.3893533 \cdot 10^5 \frac{u(\mu m)^3}{(\mu s)^2 e},
+\end{equation}
+and we get that the unit for magnetic field strength (Tesla, $T$) and electric potential (Volt, $V$) are
+\begin{equation}
+    \begin{split}
+        T &= 9.64852558 \cdot 10^1 \frac{u}{(\mu s) e} \\
+        V &= 9.64852558 \cdot 10^7 \frac{u (\mu m)^2}{(\mu s)^2 e}. \\
+    \end{split}
+    \label{eq:}
+\end{equation}
+
+\subsection{Dealing with a multi--particle system}
+
 For a multi-particles system, we need to modify $\vb{F}$ to account for the 
 force of other particles in the system acting upon each other. To do that, we
 add another term to $\vb{F}$
@@ -21,7 +56,7 @@ where $i$ and $j$ are particle indices and
 
 Newton's second law for a particle $i$ is then
 \begin{equation}
-    \frac{d^2\vb{r}_i}{dt^2} = \frac{\vb{F}\left(t, \frac{d\vb{r}_i}{dt}, \vb{r_i}\right)}{m_i},
+    \frac{d^2\vb{r}_i}{dt^2} = \frac{\vb{F}_i\left(t, \frac{d\vb{r}_i}{dt}, \vb{r_i}\right)}{m_i},
     \label{eq:newtonlaw2}
 \end{equation}
 We can then rewrite the second order ODE from equation~\ref{eq:newtonlaw2} 
@@ -30,24 +65,23 @@ We now rewrite Newton's second law of motion as
 \begin{equation}
     \begin{split}
         \frac{d\vb{r}_i}{dt} &= \vb{v}_i \\
-        \frac{d\vb{v}_i}{dt} &= \frac{\vb{F}(t, \vb{v}_i, \vb{r}_i)}{m_i}.
+        \frac{d\vb{v}_i}{dt} &= \frac{\vb{F}_i(t, \vb{v}_i, \vb{r}_i)}{m_i}.
     \end{split}
     \label{eq:coupled}
 \end{equation}
 
 \subsection{Forward Euler}
 
-For a single particle, the forward Euler method for a coupled system is 
+For a particle $i$, the forward Euler method for a coupled system is 
 expressed as
-
 \begin{equation}
     \begin{split}
-        \vb{r}_{i+1} &= \vb{r}_i + h \cdot \frac{d\vb{r}_i}{dt} = \vb{r}_i + h \cdot \vb{v}_i \\
-        \vb{v}_{i+1} &= \vb{v}_i + h \cdot \frac{\vb{v}_i}{dt} = \vb{v}_i + h \cdot \frac{\vb{F}\left( t_i, \vb{v}_i, \vb{r}_i \right)}{m},
+        \vb{r}_{i,j+1} &= \vb{r}_{i,j} + h \cdot \frac{d\vb{r}_{i,j}}{dt} = \vb{r}_{i,j} + h \cdot \vb{v}_{i,j} \\
+        \vb{v}_{i,j+1} &= \vb{v}_{i,j} + h \cdot \frac{\vb{v}_{i,j}}{dt} = \vb{v}_{i,j} + h \cdot \frac{\vb{F}\left( t_{j}, \vb{v}_{i,j}, \vb{r}_{i,j} \right)}{m},
     \end{split}
 \end{equation}
-where $i$ is the current time step of the particle $m$ is the mass of the particle, and $h$
-is the time step length.
+for particle $i$ where $j$ is the current time step of the particle, 
+$m$ is the mass of the particle, and $h$ is the step length.
 
 When dealing with a multi-particle system, we need to ensure that we do not
 update the position of any particles until every particle has calculated their
@@ -75,28 +109,38 @@ Algorithm~\ref{algo:forwardeuler} provides an overview on how that can be achiev
 
 \subsection{4th order Runge-Kutta}
 
-For a single particle, we can express the 4th order Runge-Kutta (RK4) method as
+For a particle $i$, we can express the 4th order Runge-Kutta (RK4) method as
 \begin{equation}
     \begin{split}
-        \vb{v}_{i+1} &= \vb{v}_i + \frac{h}{6} \left( \vb{k}_{\vb{v},1} 
-            + 2\vb{k}_{\vb{v},2} + 2\vb{k}_{\vb{v},3} + \vb{k}_{\vb{v},4} 
+        \vb{v}_{i,j+1} &= \vb{v}_{i,j} + \frac{h}{6} \left( \vb{k}_{\vb{v},1,i} 
+            + 2\vb{k}_{\vb{v},2,i} + 2\vb{k}_{\vb{v},3,i} + \vb{k}_{\vb{v},4,i} 
             \right) \\
-        \vb{r}_{i+1} &= \vb{r}_i + \frac{h}{6} \left( \vb{k}_{\vb{r},1} 
-            + 2\vb{k}_{\vb{r},2} + 2\vb{k}_{\vb{r},3} + \vb{k}_{\vb{r},4} 
+        \vb{r}_{i,j+1} &= \vb{r}_{i,j} + \frac{h}{6} \left( \vb{k}_{\vb{r},1,i} 
+            + 2\vb{k}_{\vb{r},2,i} + 2\vb{k}_{\vb{r},3,i} + \vb{k}_{\vb{r},4,i} 
             \right),
     \end{split}
 \end{equation}
 where
 \begin{equation}
     \begin{split}
-    \vb{k}_{\vb{v},1} &= \frac{\vb{F}(t_i, \vb{v}_i, \vb{r}_i)}{m} \\
-    \vb{k}_{\vb{r},1} &= \vb{v}_i \\
-    \vb{k}_{\vb{v},2} &= \frac{\vb{F}(t_i+\frac{h}{2}, \vb{v}_i + h \cdot \frac{\vb{k}_{\vb{v},1}}{2}, \vb{r}_i + h \cdot \frac{\vb{k}_{\vb{r},1}}{2})}{m} \\
-    \vb{k}_{\vb{r},2} &= \vb{v}_i + h \cdot \frac{\vb{k}_{\vb{v},1}}{2} \\
-    \vb{k}_{\vb{v},3} &= \frac{\vb{F}(t_i+\frac{h}{2}, \vb{v}_i + h \cdot \frac{\vb{k}_{\vb{v},2}}{2}, \vb{r}_i + h \frac{\cdot \vb{k}_{\vb{r},2}}{2})}{m} \\
-    \vb{k}_{\vb{r},3} &= \vb{v}_i + h \cdot \frac{\vb{k}_{\vb{v},2}}{2} \\
-    \vb{k}_{\vb{v},4} &= \frac{\vb{F}(t_i+h, \vb{v}_i + h \cdot \vb{k}_{\vb{v},3}, \vb{r}_i + h \cdot \vb{k}_{\vb{r},3})}{m} \\
-    \vb{k}_{\vb{r},4} &= \vb{v}_i + h \cdot \frac{\vb{k}_{\vb{v},1}}{2}.
+        \vb{k}_{\vb{v},1,i} &= \frac{\vb{F}_i(t_j, \vb{v}_{i,j}, 
+            \vb{r}_{i,j})}{m} \\
+        \vb{k}_{\vb{r},1,i} &= \vb{v}_{i,j} \\
+        \vb{k}_{\vb{v},2,i} &= \frac{\vb{F}_i(t_j+\frac{h}{2}, \vb{v}_{i,j} 
+            + h \cdot \frac{\vb{k}_{\vb{v},1,i}}{2}, \vb{r}_{i,j} 
+            + h \cdot \frac{\vb{k}_{\vb{r},1,i}}{2})}{m} \\
+        \vb{k}_{\vb{r},2,i} &= \vb{v}_{i,j} 
+            + h \cdot \frac{\vb{k}_{\vb{v},1,i}}{2} \\
+        \vb{k}_{\vb{v},3,i} &= \frac{\vb{F}_i(t_j+\frac{h}{2}, \vb{v}_{i,j} 
+            + h \cdot \frac{\vb{k}_{\vb{v},2,i}}{2}, \vb{r}_{i,j} 
+            + h \frac{\cdot \vb{k}_{\vb{r},2,i}}{2})}{m} \\
+        \vb{k}_{\vb{r},3,i} &= \vb{v}_{i,j} 
+            + h \cdot \frac{\vb{k}_{\vb{v},2,i}}{2} \\
+        \vb{k}_{\vb{v},4,i} &= \frac{\vb{F}_i(t_j+h, \vb{v}_{i,j} 
+            + h \cdot \vb{k}_{\vb{v},3,i}, \vb{r}_{i,j} 
+            + h \cdot \vb{k}_{\vb{r},3,i})}{m} \\
+        \vb{k}_{\vb{r},4,i} &= \vb{v}_{i,j} 
+            + h \cdot \frac{\vb{k}_{\vb{v},1,i}}{2}.
     \end{split}
 \end{equation}
 
@@ -110,46 +154,48 @@ can update the particles correctly for each step.
 This approach would require 8 loops to be able to complete the calculation since
 we cannot update the particles until after all $\vb{k}$ values have been 
 computed, however if we create a temporary array that holds particles, we can
-put the updated particles in there, and then use that array in the next loop.
-around 8 separate loops to calculate all $\vb{k}$ values
-
-\newpage
+put the updated particles in there, and then use that array in the next loop,
+and would reduce the required amount of loops down to 4.
 
 \begin{figure}
     \begin{algorithm}[H]
     \caption{RK4 method}
     \label{algo:rk4}
         \begin{algorithmic}
-            \Procedure{Evolve RK4}{$dt$}
+            \Procedure{Evolve RK4}{$particles, dt$}
             \State $N \leftarrow \text{Number of particles inside the Penning trap}$
-            \State $orig\_p \leftarrow \text{Copy of particles}$ \Comment{Keep the original particles}
+            \State $orig\_p \leftarrow \text{Copy of particles}$ 
             \State $tmp\_p \leftarrow \text{Array of particles of size }N$
             \State $\vb{k}_{\vb{r}} \leftarrow \text{2D array of vectors of size } 4 \cross N$
             \State $\vb{k}_{\vb{v}} \leftarrow \text{2D array of vectors of size } 4 \cross N$
 
             \For{ $i = 1, 2, \ldots, N$ }
-            \State $\vb{k}_{\vb{r},1,i} \leftarrow \vb{v}$
-            \State $\vb{k}_{\vb{v},1,i} \leftarrow \frac{\vb{F}}{m}$
+            \State $\vb{k}_{\vb{r},1,i} \leftarrow particles_i.\vb{v}$
+            \State $\vb{k}_{\vb{v},1,i} \leftarrow \frac{\vb{F}_i}{m_i}$
 
-            \State $tmp\_p_i.\vb{r} \leftarrow orig\_p_i.\vb{r} + \frac{dt}{2} \cdot \vb{k}_{\vb{r},1,i}$
-            \State $tmp\_p_i.\vb{v} \leftarrow orig\_p_i.\vb{v} + \frac{dt}{2} \cdot \vb{k}_{\vb{v},1,i}$
+            \State $tmp\_p_i.\vb{r} \leftarrow orig\_p_i.\vb{r} 
+                + \frac{dt}{2} \cdot \vb{k}_{\vb{r},1,i}$
+            \State $tmp\_p_i.\vb{v} \leftarrow orig\_p_i.\vb{v} 
+                + \frac{dt}{2} \cdot \vb{k}_{\vb{v},1,i}$
             \EndFor
 
             \State $particles \leftarrow tmp\_p$ \Comment{Update particles}
 
             \For{ $i = 1, 2, \ldots, N$ }
-            \State $\vb{k}_{\vb{r},2,i} \leftarrow \vb{v}$
-            \State $\vb{k}_{\vb{v},2,i} \leftarrow \frac{\vb{F}}{m}$
+            \State $\vb{k}_{\vb{r},2,i} \leftarrow particles_i.\vb{v}$
+            \State $\vb{k}_{\vb{v},2,i} \leftarrow \frac{\vb{F}_i}{m_i}$
 
-            \State $tmp\_p_i.\vb{r} \leftarrow orig\_p_i.\vb{r} + \frac{dt}{2} \cdot \vb{k}_{\vb{r},2,i}$
-            \State $tmp\_p_i.\vb{v} \leftarrow orig\_p_i.\vb{v} + \frac{dt}{2} \cdot \vb{k}_{\vb{v},2,i}$
+            \State $tmp\_p_i.\vb{r} \leftarrow orig\_p_i.\vb{r} 
+                + \frac{dt}{2} \cdot \vb{k}_{\vb{r},2,i}$
+            \State $tmp\_p_i.\vb{v} \leftarrow orig\_p_i.\vb{v} 
+                + \frac{dt}{2} \cdot \vb{k}_{\vb{v},2,i}$
             \EndFor
 
             \State $particles \leftarrow tmp\_p$ \Comment{Update particles}
 
             \For{ $i = 1, 2, \ldots, N$ }
-            \State $\vb{k}_{\vb{r},3,i} \leftarrow \vb{v}$
-            \State $\vb{k}_{\vb{v},3,i} \leftarrow \frac{\vb{F}}{m}$
+            \State $\vb{k}_{\vb{r},3,i} \leftarrow particles_i.\vb{v}$
+            \State $\vb{k}_{\vb{v},3,i} \leftarrow \frac{\vb{F}_i}{m}$
 
             \State $tmp\_p_i.\vb{r} \leftarrow orig\_p_i.\vb{r} + dt \cdot \vb{k}_{\vb{r},3,i}$
             \State $tmp\_p_i.\vb{v} \leftarrow orig\_p_i.\vb{v} + dt \cdot \vb{k}_{\vb{v},3,i}$
@@ -158,16 +204,16 @@ around 8 separate loops to calculate all $\vb{k}$ values
             \State $particles \leftarrow tmp\_p$ \Comment{Update particles}
 
             \For{ $i = 1, 2, \ldots, N$ }
-            \State $\vb{k}_{\vb{r},4,i} \leftarrow \vb{v}$
+            \State $\vb{k}_{\vb{r},4,i} \leftarrow particles_i.\vb{v}$
             \State $\vb{k}_{\vb{v},4,i} \leftarrow \frac{\vb{F}}{m}$
 
             \State $tmp\_p_i.\vb{r} \leftarrow orig\_p_i.\vb{r} + \frac{dt}{6} 
-            \cdot \left( \vb{k}_{\vb{r},1,i} + \vb{k}_{\vb{r},2,i} 
-            + \vb{k}_{\vb{r},3,i} + \vb{k}_{\vb{r},4,i} \right)$
+                \cdot \left( \vb{k}_{\vb{r},1,i} + \vb{k}_{\vb{r},2,i} 
+                + \vb{k}_{\vb{r},3,i} + \vb{k}_{\vb{r},4,i} \right)$
 
             \State $tmp\_p_i.\vb{v} \leftarrow orig\_p_i.\vb{v} + \frac{dt}{6} 
-            \cdot \left( \vb{k}_{\vb{v},1,i} + \vb{k}_{\vb{v},2,i} 
-            + \vb{k}_{\vb{v},3,i} + \vb{k}_{\vb{v},4,i} \right)$
+                \cdot \left( \vb{k}_{\vb{v},1,i} + \vb{k}_{\vb{v},2,i} 
+                + \vb{k}_{\vb{v},3,i} + \vb{k}_{\vb{v},4,i} \right)$
             
             \EndFor
 
@@ -181,5 +227,9 @@ around 8 separate loops to calculate all $\vb{k}$ values
 \end{figure}
 
 
+\subsection{Testing the simulation}
+
+\subsection{Relative error and error convergance rate}
+
 \biblio
 \end{document}

From 5ed7cedfae89549a0064bbbe94a58bc57abc7cf8 Mon Sep 17 00:00:00 2001
From: Cory <cory@balaton.dev>
Date: Tue, 17 Oct 2023 17:01:50 +0200
Subject: [PATCH 22/26] Stuff

---
 .gitignore                                 |   1 +
 Doxyfile                                   |   2 +-
 include/PenningTrap.hpp                    |  11 +-
 latex/images/particles_left.pdf            | Bin 0 -> 17840 bytes
 latex/images/single_particle.pdf           | Bin 0 -> 21430 bytes
 man_pages/man3/Particle.3                  | 111 -----
 man_pages/man3/Particle.cpp.3              |  42 --
 man_pages/man3/Particle.hpp.3              |  52 ---
 man_pages/man3/PenningTrap.3               | 494 ---------------------
 man_pages/man3/PenningTrap.cpp.3           |  48 --
 man_pages/man3/PenningTrap.hpp.3           |  58 ---
 man_pages/man3/PenningTrapTest.3           |  56 ---
 man_pages/man3/bug.3                       |  29 --
 man_pages/man3/constants.hpp.3             |  75 ----
 man_pages/man3/main.cpp.3                  | 148 ------
 man_pages/man3/test_suite.cpp.3            |  70 ---
 man_pages/man3/todo.3                      |  14 -
 man_pages/man3/typedefs.hpp.3              |  92 ----
 man_pages/man3/utils.cpp.3                 | 179 --------
 man_pages/man3/utils.hpp.3                 | 228 ----------
 src/PenningTrap.cpp                        |  50 ++-
 src/main.cpp                               |  69 +--
 src/plot_particles_left.py                 |  33 --
 src/{ => scripts}/animate_100_particles.py |   0
 src/scripts/plot_particles_left.py         |  30 ++
 src/scripts/plot_single_particle.py        |  29 ++
 26 files changed, 142 insertions(+), 1779 deletions(-)
 create mode 100644 latex/images/particles_left.pdf
 create mode 100644 latex/images/single_particle.pdf
 delete mode 100644 man_pages/man3/Particle.3
 delete mode 100644 man_pages/man3/Particle.cpp.3
 delete mode 100644 man_pages/man3/Particle.hpp.3
 delete mode 100644 man_pages/man3/PenningTrap.3
 delete mode 100644 man_pages/man3/PenningTrap.cpp.3
 delete mode 100644 man_pages/man3/PenningTrap.hpp.3
 delete mode 100644 man_pages/man3/PenningTrapTest.3
 delete mode 100644 man_pages/man3/bug.3
 delete mode 100644 man_pages/man3/constants.hpp.3
 delete mode 100644 man_pages/man3/main.cpp.3
 delete mode 100644 man_pages/man3/test_suite.cpp.3
 delete mode 100644 man_pages/man3/todo.3
 delete mode 100644 man_pages/man3/typedefs.hpp.3
 delete mode 100644 man_pages/man3/utils.cpp.3
 delete mode 100644 man_pages/man3/utils.hpp.3
 delete mode 100644 src/plot_particles_left.py
 rename src/{ => scripts}/animate_100_particles.py (100%)
 create mode 100644 src/scripts/plot_particles_left.py
 create mode 100644 src/scripts/plot_single_particle.py

diff --git a/.gitignore b/.gitignore
index 5f54c8c..17c5519 100644
--- a/.gitignore
+++ b/.gitignore
@@ -47,3 +47,4 @@ src/*
 !src/*.hpp
 !src/*.py
 !src/Doxyfile
+!src/scripts
diff --git a/Doxyfile b/Doxyfile
index eeba27f..7b951c6 100644
--- a/Doxyfile
+++ b/Doxyfile
@@ -2174,7 +2174,7 @@ RTF_EXTENSIONS_FILE    =
 # classes and files.
 # The default value is: NO.
 
-GENERATE_MAN           = YES
+GENERATE_MAN           = NO
 
 # The MAN_OUTPUT tag is used to specify where the man pages will be put. If a
 # relative path is entered the value of OUTPUT_DIRECTORY will be put in front of
diff --git a/include/PenningTrap.hpp b/include/PenningTrap.hpp
index f6cf2c0..eaf89be 100644
--- a/include/PenningTrap.hpp
+++ b/include/PenningTrap.hpp
@@ -22,6 +22,11 @@
 #pragma omp declare reduction(+ : vec_3d : omp_out += omp_in)                  \
     initializer(omp_priv = omp_orig)
 
+typedef struct simulation {
+    sim_arr r_vecs;
+    sim_arr v_vecs;
+} simulation_t;
+
 /** @brief A class that simulates a Penning trap.
  *
  *  This class simulates a Penning trap. It can take in a number of particles
@@ -188,9 +193,9 @@ public:
      *  @param method The method to use when moving forward a timestep
      *  @param particle_interaction Turn particle interactions on/off
      * */
-    sim_arr simulate(double time, unsigned int steps,
-                     std::string method = "rk4",
-                     bool particle_interaction = true);
+    simulation_t simulate(double time, unsigned int steps,
+                          std::string method = "rk4",
+                          bool particle_interaction = true);
 
     /** @brief Simulate and write the displacement of all particles to files.
      *
diff --git a/latex/images/particles_left.pdf b/latex/images/particles_left.pdf
new file mode 100644
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diff --git a/man_pages/man3/Particle.3 b/man_pages/man3/Particle.3
deleted file mode 100644
index ebff781..0000000
--- a/man_pages/man3/Particle.3
+++ /dev/null
@@ -1,111 +0,0 @@
-.TH "Particle" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
-.ad l
-.nh
-.SH NAME
-Particle \- A class that holds attributes of a particle\&.  
-
-.SH SYNOPSIS
-.br
-.PP
-.PP
-\fC#include <Particle\&.hpp>\fP
-.SS "Public Member Functions"
-
-.in +1c
-.ti -1c
-.RI "\fBParticle\fP (double \fBq\fP, double \fBm\fP, \fBvec_3d\fP \fBr_vec\fP, \fBvec_3d\fP \fBv_vec\fP)"
-.br
-.RI "Initialize the particle\&. "
-.in -1c
-.SS "Private Attributes"
-
-.in +1c
-.ti -1c
-.RI "double \fBq\fP"
-.br
-.RI "Charge\&. "
-.ti -1c
-.RI "double \fBm\fP"
-.br
-.RI "Mass\&. "
-.ti -1c
-.RI "\fBvec_3d\fP \fBr_vec\fP"
-.br
-.RI "position "
-.ti -1c
-.RI "\fBvec_3d\fP \fBv_vec\fP"
-.br
-.RI "velocity "
-.in -1c
-.SS "Friends"
-
-.in +1c
-.ti -1c
-.RI "class \fBPenningTrap\fP"
-.br
-.RI "Make private attributes available for \fBPenningTrap\fP\&. "
-.in -1c
-.SH "Detailed Description"
-.PP 
-A class that holds attributes of a particle\&. 
-.PP
-Definition at line \fB21\fP of file \fBParticle\&.hpp\fP\&.
-.SH "Constructor & Destructor Documentation"
-.PP 
-.SS "Particle::Particle (double q, double m, \fBvec_3d\fP r_vec, \fBvec_3d\fP v_vec)"
-
-.PP
-Initialize the particle\&. Initialize the particle with a charge, mass, position and velocity\&.
-.PP
-\fBParameters\fP
-.RS 4
-\fIq\fP The charge of the particle 
-.br
-\fIm\fP The mass of the particle 
-.br
-\fIr_vec\fP The initial position of the particle 
-.br
-\fIv_vec\fP The initial velocity of the particle 
-.RE
-.PP
-
-.PP
-Definition at line \fB15\fP of file \fBParticle\&.cpp\fP\&.
-.SH "Friends And Related Function Documentation"
-.PP 
-.SS "friend class \fBPenningTrap\fP\fC [friend]\fP"
-
-.PP
-Make private attributes available for \fBPenningTrap\fP\&. 
-.PP
-Definition at line \fB43\fP of file \fBParticle\&.hpp\fP\&.
-.SH "Member Data Documentation"
-.PP 
-.SS "double Particle::m\fC [private]\fP"
-
-.PP
-Mass\&. 
-.PP
-Definition at line \fB24\fP of file \fBParticle\&.hpp\fP\&.
-.SS "double Particle::q\fC [private]\fP"
-
-.PP
-Charge\&. 
-.PP
-Definition at line \fB23\fP of file \fBParticle\&.hpp\fP\&.
-.SS "\fBvec_3d\fP Particle::r_vec\fC [private]\fP"
-
-.PP
-position 
-.PP
-Definition at line \fB25\fP of file \fBParticle\&.hpp\fP\&.
-.SS "\fBvec_3d\fP Particle::v_vec\fC [private]\fP"
-
-.PP
-velocity 
-.PP
-Definition at line \fB26\fP of file \fBParticle\&.hpp\fP\&.
-
-.SH "Author"
-.PP 
-Generated automatically by Doxygen for Penning Trap Simulation from the source code\&.
diff --git a/man_pages/man3/Particle.cpp.3 b/man_pages/man3/Particle.cpp.3
deleted file mode 100644
index 904c7a4..0000000
--- a/man_pages/man3/Particle.cpp.3
+++ /dev/null
@@ -1,42 +0,0 @@
-.TH "src/Particle.cpp" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
-.ad l
-.nh
-.SH NAME
-src/Particle.cpp \- The implementation of the \fBParticle\fP class\&.  
-
-.SH SYNOPSIS
-.br
-.PP
-\fC#include 'Particle\&.hpp'\fP
-.br
-
-.SH "Detailed Description"
-.PP 
-The implementation of the \fBParticle\fP class\&. 
-
-
-.PP
-\fBAuthor\fP
-.RS 4
-Cory Alexander Balaton (coryab) 
-.PP
-Janita Ovidie Sandtrøen Willumsen (janitaws)
-.RE
-.PP
-\fBVersion\fP
-.RS 4
-0\&.1
-.RE
-.PP
-.PP
-\fBBug\fP
-.RS 4
-No known bugs 
-.RE
-.PP
-
-.PP
-Definition in file \fBParticle\&.cpp\fP\&.
-.SH "Author"
-.PP 
-Generated automatically by Doxygen for Penning Trap Simulation from the source code\&.
diff --git a/man_pages/man3/Particle.hpp.3 b/man_pages/man3/Particle.hpp.3
deleted file mode 100644
index 2033d14..0000000
--- a/man_pages/man3/Particle.hpp.3
+++ /dev/null
@@ -1,52 +0,0 @@
-.TH "include/Particle.hpp" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
-.ad l
-.nh
-.SH NAME
-include/Particle.hpp \- A class that holds the properties of a particle\&.  
-
-.SH SYNOPSIS
-.br
-.PP
-\fC#include <armadillo>\fP
-.br
-\fC#include 'typedefs\&.hpp'\fP
-.br
-
-.SS "Classes"
-
-.in +1c
-.ti -1c
-.RI "class \fBParticle\fP"
-.br
-.RI "A class that holds attributes of a particle\&. "
-.in -1c
-.SH "Detailed Description"
-.PP 
-A class that holds the properties of a particle\&. 
-
-
-.PP
-\fBAuthor\fP
-.RS 4
-Cory Alexander Balaton (coryab) 
-.PP
-Janita Ovidie Sandtrøen Willumsen (janitaws)
-.RE
-.PP
-\fBVersion\fP
-.RS 4
-0\&.1
-.RE
-.PP
-.PP
-\fBBug\fP
-.RS 4
-No known bugs 
-.RE
-.PP
-
-.PP
-Definition in file \fBParticle\&.hpp\fP\&.
-.SH "Author"
-.PP 
-Generated automatically by Doxygen for Penning Trap Simulation from the source code\&.
diff --git a/man_pages/man3/PenningTrap.3 b/man_pages/man3/PenningTrap.3
deleted file mode 100644
index 51cca93..0000000
--- a/man_pages/man3/PenningTrap.3
+++ /dev/null
@@ -1,494 +0,0 @@
-.TH "PenningTrap" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
-.ad l
-.nh
-.SH NAME
-PenningTrap \- A class that simulates a Penning trap\&.  
-
-.SH SYNOPSIS
-.br
-.PP
-.PP
-\fC#include <PenningTrap\&.hpp>\fP
-.SS "Public Member Functions"
-
-.in +1c
-.ti -1c
-.RI "\fBPenningTrap\fP (double \fBB_0\fP=\fBT\fP, std::function< double(double)> \fBV_0\fP=[](double \fBt\fP) { return 25\&. *\fBV\fP/1000\&.;}, double \fBd\fP=500\&., double \fBt\fP=0\&.)"
-.br
-.RI "Constructor for the \fBPenningTrap\fP class\&. "
-.ti -1c
-.RI "\fBPenningTrap\fP (unsigned int i, double \fBB_0\fP=\fBT\fP, std::function< double(double)> \fBV_0\fP=[](double \fBt\fP) { return 25\&. *\fBV\fP/1000\&.;}, double \fBd\fP=500\&., double \fBt\fP=0\&.)"
-.br
-.RI "Constructor for the \fBPenningTrap\fP class\&. "
-.ti -1c
-.RI "\fBPenningTrap\fP (std::vector< \fBParticle\fP > \fBparticles\fP, double \fBB_0\fP=\fBT\fP, std::function< double(double)> \fBV_0\fP=[](double \fBt\fP) { return 25\&. *\fBV\fP/1000\&.;}, double \fBd\fP=500\&., double \fBt\fP=0\&.)"
-.br
-.RI "Constructor for the \fBPenningTrap\fP class\&. "
-.ti -1c
-.RI "void \fBadd_particle\fP (\fBParticle\fP particle)"
-.br
-.RI "Add a particle to the system\&. "
-.ti -1c
-.RI "\fBvec_3d\fP \fBexternal_E_field\fP (\fBvec_3d\fP r)"
-.br
-.RI "Calculate E at point r\&. "
-.ti -1c
-.RI "\fBvec_3d\fP \fBexternal_B_field\fP (\fBvec_3d\fP r)"
-.br
-.RI "Calculate B at point r\&. "
-.ti -1c
-.RI "\fBvec_3d\fP \fBforce_on_particle\fP (unsigned int i, unsigned int j)"
-.br
-.RI "Calculate the force between 2 particles\&. "
-.ti -1c
-.RI "\fBvec_3d\fP \fBtotal_force_external\fP (unsigned int i)"
-.br
-.RI "Calculate the total external force on a particle\&. "
-.ti -1c
-.RI "\fBvec_3d\fP \fBtotal_force_particles\fP (unsigned int i)"
-.br
-.RI "Calculate the total force on a particle p_i from other particles\&. "
-.ti -1c
-.RI "\fBvec_3d\fP \fBtotal_force\fP (unsigned int i)"
-.br
-.RI "calculate the total force on a particle p_i\&. "
-.ti -1c
-.RI "void \fBevolve_RK4\fP (double dt, bool particle_interaction=true)"
-.br
-.RI "Go forward one timestep using the RK4 method\&. "
-.ti -1c
-.RI "void \fBevolve_forward_euler\fP (double dt, bool particle_interaction=true)"
-.br
-.RI "Go forward one timestep using the forward Euler method\&. "
-.ti -1c
-.RI "\fBsim_arr\fP \fBsimulate\fP (double time, unsigned int steps, std::string method='rk4', bool particle_interaction=true)"
-.br
-.RI "Simulate the particle system inside the Penning trap over a certain amount of time\&. "
-.ti -1c
-.RI "void \fBwrite_simulation_to_dir\fP (std::string path, double time, unsigned int steps, std::string method='rk4', bool particle_interaction=true)"
-.br
-.RI "Simulate and write the displacement of all particles to files\&. "
-.ti -1c
-.RI "double \fBfraction_of_particles_left\fP (double time, unsigned int steps, std::string method='rk4', bool particle_interaction=true)"
-.br
-.RI "Simulate and calculate what fraction of particles are still left inside the Penning trap after the simulation\&. "
-.in -1c
-.SS "Private Member Functions"
-
-.in +1c
-.ti -1c
-.RI "\fBvec_3d\fP \fBv_func\fP (unsigned int i, unsigned int j, double dt)"
-.br
-.RI "Helper for evolve_RK4 when calculating $k_{v,i,j}$ values\&. "
-.ti -1c
-.RI "\fBvec_3d\fP \fBr_func\fP (unsigned int i, unsigned int j, double dt)"
-.br
-.RI "Helper for evolve_RK4 when calculating $k_{r,i,j}$ values\&. "
-.in -1c
-.SS "Private Attributes"
-
-.in +1c
-.ti -1c
-.RI "double \fBB_0\fP"
-.br
-.RI "Magnetic field strength\&. "
-.ti -1c
-.RI "std::function< double(double)> \fBV_0\fP"
-.br
-.RI "Applied potential\&. "
-.ti -1c
-.RI "double \fBd\fP"
-.br
-.RI "Characteristic dimension\&. "
-.ti -1c
-.RI "double \fBt\fP"
-.br
-.RI "Current time\&. "
-.ti -1c
-.RI "std::vector< \fBParticle\fP > \fBparticles\fP"
-.br
-.RI "The particles in the Penning trap\&. "
-.ti -1c
-.RI "\fBsim_arr\fP \fBk_v\fP"
-.br
-.ti -1c
-.RI "\fBsim_arr\fP \fBk_r\fP"
-.br
-.in -1c
-.SH "Detailed Description"
-.PP 
-A class that simulates a Penning trap\&. 
-
-This class simulates a Penning trap\&. It can take in a number of particles and simulate how they would behave inside a Penning trap\&. 
-.PP
-Definition at line \fB30\fP of file \fBPenningTrap\&.hpp\fP\&.
-.SH "Constructor & Destructor Documentation"
-.PP 
-.SS "PenningTrap::PenningTrap (double B_0 = \fC\fBT\fP\fP, std::function< double(double)> V_0 = \fC[](double \fBt\fP) { return 25\&. * \fBV\fP / 1000\&.; }\fP, double d = \fC500\&.\fP, double t = \fC0\&.\fP)"
-
-.PP
-Constructor for the \fBPenningTrap\fP class\&. 
-.PP
-\fBParameters\fP
-.RS 4
-\fIB_0\fP The magnetic field strength 
-.br
-\fIV_0\fP The time dependent applied potential 
-.br
-\fId\fP The characteristic dimension 
-.br
-\fIt\fP The starting time 
-.RE
-.PP
-
-.PP
-Definition at line \fB18\fP of file \fBPenningTrap\&.cpp\fP\&.
-.SS "PenningTrap::PenningTrap (unsigned int i, double B_0 = \fC\fBT\fP\fP, std::function< double(double)> V_0 = \fC[](double \fBt\fP) { return 25\&. * \fBV\fP / 1000\&.; }\fP, double d = \fC500\&.\fP, double t = \fC0\&.\fP)"
-
-.PP
-Constructor for the \fBPenningTrap\fP class\&. 
-.PP
-\fBParameters\fP
-.RS 4
-\fIi\fP The number of particles to generate 
-.br
-\fIB_0\fP The magnetic field strength 
-.br
-\fIV_0\fP The time dependent applied potential 
-.br
-\fId\fP The characteristic dimension 
-.br
-\fIt\fP The starting time 
-.RE
-.PP
-
-.PP
-Definition at line \fB27\fP of file \fBPenningTrap\&.cpp\fP\&.
-.SS "PenningTrap::PenningTrap (std::vector< \fBParticle\fP > particles, double B_0 = \fC\fBT\fP\fP, std::function< double(double)> V_0 = \fC[](double \fBt\fP) { return 25\&. * \fBV\fP / 1000\&.; }\fP, double d = \fC500\&.\fP, double t = \fC0\&.\fP)"
-
-.PP
-Constructor for the \fBPenningTrap\fP class\&. 
-.PP
-\fBParameters\fP
-.RS 4
-\fIparticles\fP The starting particles 
-.br
-\fIB_0\fP The magnetic field strength 
-.br
-\fIV_0\fP The time dependent applied potential 
-.br
-\fId\fP The characteristic dimension 
-.br
-\fIt\fP The starting time 
-.RE
-.PP
-
-.PP
-Definition at line \fB39\fP of file \fBPenningTrap\&.cpp\fP\&.
-.SH "Member Function Documentation"
-.PP 
-.SS "void PenningTrap::add_particle (\fBParticle\fP particle)"
-
-.PP
-Add a particle to the system\&. 
-.PP
-\fBParameters\fP
-.RS 4
-\fIparticle\fP The particle to add to the Penning trap 
-.RE
-.PP
-
-.PP
-Definition at line \fB82\fP of file \fBPenningTrap\&.cpp\fP\&.
-.SS "void PenningTrap::evolve_forward_euler (double dt, bool particle_interaction = \fCtrue\fP)"
-
-.PP
-Go forward one timestep using the forward Euler method\&. 
-.PP
-\fBParameters\fP
-.RS 4
-\fIdt\fP The step length 
-.br
-\fIparticle_interaction\fP Turn particle interactions on/off 
-.RE
-.PP
-
-.PP
-Definition at line \fB186\fP of file \fBPenningTrap\&.cpp\fP\&.
-.SS "void PenningTrap::evolve_RK4 (double dt, bool particle_interaction = \fCtrue\fP)"
-
-.PP
-Go forward one timestep using the RK4 method\&. 
-.PP
-\fBParameters\fP
-.RS 4
-\fIdt\fP The step length 
-.br
-\fIparticle_interaction\fP Turn particle interactions on/off 
-.RE
-.PP
-
-.PP
-Definition at line \fB151\fP of file \fBPenningTrap\&.cpp\fP\&.
-.SS "\fBvec_3d\fP PenningTrap::external_B_field (\fBvec_3d\fP r)"
-
-.PP
-Calculate B at point r\&. 
-.PP
-\fBParameters\fP
-.RS 4
-\fIr\fP The position where we want to calculate the B field
-.RE
-.PP
-\fBReturns\fP
-.RS 4
-vec_3d 
-.RE
-.PP
-
-.PP
-Definition at line \fB95\fP of file \fBPenningTrap\&.cpp\fP\&.
-.SS "\fBvec_3d\fP PenningTrap::external_E_field (\fBvec_3d\fP r)"
-
-.PP
-Calculate E at point r\&. 
-.PP
-\fBParameters\fP
-.RS 4
-\fIr\fP The position where we want to calculate the E field
-.RE
-.PP
-\fBReturns\fP
-.RS 4
-vec_3d 
-.RE
-.PP
-
-.PP
-Definition at line \fB87\fP of file \fBPenningTrap\&.cpp\fP\&.
-.SS "\fBvec_3d\fP PenningTrap::force_on_particle (unsigned int i, unsigned int j)"
-
-.PP
-Calculate the force between 2 particles\&. Calculate the force exhibited on particle p_i from particle p_j\&.
-.PP
-\fBParameters\fP
-.RS 4
-\fIi\fP The index of particle p_i 
-.br
-\fIj\fP The index of particle p_j
-.RE
-.PP
-\fBReturns\fP
-.RS 4
-vec_3d 
-.RE
-.PP
-
-.PP
-Definition at line \fB100\fP of file \fBPenningTrap\&.cpp\fP\&.
-.SS "double PenningTrap::fraction_of_particles_left (double time, unsigned int steps, std::string method = \fC'rk4'\fP, bool particle_interaction = \fCtrue\fP)"
-
-.PP
-Simulate and calculate what fraction of particles are still left inside the Penning trap after the simulation\&. 
-.PP
-\fBParameters\fP
-.RS 4
-\fItime\fP The time to simulate in microseconds 
-.br
-\fIsteps\fP The amount of steps for the whole simulation 
-.br
-\fImethod\fP The method to use when moving forward a timestep 
-.br
-\fIparticle_interaction\fP Turn particle interactions on/off
-.RE
-.PP
-\fBReturns\fP
-.RS 4
-double 
-.RE
-.PP
-
-.PP
-Definition at line \fB266\fP of file \fBPenningTrap\&.cpp\fP\&.
-.SS "\fBvec_3d\fP PenningTrap::r_func (unsigned int i, unsigned int j, double dt)\fC [private]\fP"
-
-.PP
-Helper for evolve_RK4 when calculating $k_{r,i,j}$ values\&. Something
-.PP
-\fBParameters\fP
-.RS 4
-\fIi\fP Index i for $k_{r,i,j}$ 
-.br
-\fIj\fP Index j for $k_{r,i,j}$ 
-.br
-\fIdt\fP the step length (delta time)
-.RE
-.PP
-\fBReturns\fP
-.RS 4
-vec_3d 
-.RE
-.PP
-
-.PP
-Definition at line \fB64\fP of file \fBPenningTrap\&.cpp\fP\&.
-.SS "\fBsim_arr\fP PenningTrap::simulate (double time, unsigned int steps, std::string method = \fC'rk4'\fP, bool particle_interaction = \fCtrue\fP)"
-
-.PP
-Simulate the particle system inside the Penning trap over a certain amount of time\&. 
-.PP
-\fBParameters\fP
-.RS 4
-\fItime\fP The time to simulate in microseconds 
-.br
-\fIsteps\fP The amount of steps for the whole simulation 
-.br
-\fImethod\fP The method to use when moving forward a timestep 
-.br
-\fIparticle_interaction\fP Turn particle interactions on/off 
-.RE
-.PP
-
-.PP
-Definition at line \fB211\fP of file \fBPenningTrap\&.cpp\fP\&.
-.SS "\fBvec_3d\fP PenningTrap::total_force (unsigned int i)"
-
-.PP
-calculate the total force on a particle p_i\&. 
-.PP
-\fBParameters\fP
-.RS 4
-\fIi\fP The index of particle p_i
-.RE
-.PP
-\fBReturns\fP
-.RS 4
-vec_3d 
-.RE
-.PP
-
-.PP
-Definition at line \fB146\fP of file \fBPenningTrap\&.cpp\fP\&.
-.SS "\fBvec_3d\fP PenningTrap::total_force_external (unsigned int i)"
-
-.PP
-Calculate the total external force on a particle\&. Calculate the total amount of force that E and B exhibits on particle p_i\&.
-.PP
-\fBParameters\fP
-.RS 4
-\fIi\fP The index of particle p_i
-.RE
-.PP
-\fBReturns\fP
-.RS 4
-vec_3d 
-.RE
-.PP
-
-.PP
-Definition at line \fB114\fP of file \fBPenningTrap\&.cpp\fP\&.
-.SS "\fBvec_3d\fP PenningTrap::total_force_particles (unsigned int i)"
-
-.PP
-Calculate the total force on a particle p_i from other particles\&. 
-.PP
-\fBParameters\fP
-.RS 4
-\fIi\fP The index of particle p_i
-.RE
-.PP
-\fBReturns\fP
-.RS 4
-vec_3d 
-.RE
-.PP
-
-.PP
-Definition at line \fB129\fP of file \fBPenningTrap\&.cpp\fP\&.
-.SS "\fBvec_3d\fP PenningTrap::v_func (unsigned int i, unsigned int j, double dt)\fC [private]\fP"
-
-.PP
-Helper for evolve_RK4 when calculating $k_{v,i,j}$ values\&. Something
-.PP
-\fBParameters\fP
-.RS 4
-\fIi\fP Index i for $k_{v,i,j}$ 
-.br
-\fIj\fP Index j for $k_{v,i,j}$ 
-.br
-\fIdt\fP the step length (delta time)
-.RE
-.PP
-\fBReturns\fP
-.RS 4
-vec_3d 
-.RE
-.PP
-
-.PP
-Definition at line \fB46\fP of file \fBPenningTrap\&.cpp\fP\&.
-.SS "void PenningTrap::write_simulation_to_dir (std::string path, double time, unsigned int steps, std::string method = \fC'rk4'\fP, bool particle_interaction = \fCtrue\fP)"
-
-.PP
-Simulate and write the displacement of all particles to files\&. 
-.PP
-\fBParameters\fP
-.RS 4
-\fIpath\fP The directory to save the data 
-.br
-\fItime\fP The time to simulate in microseconds 
-.br
-\fIsteps\fP The amount of steps for the whole simulation 
-.br
-\fImethod\fP The method to use when moving forward a timestep 
-.br
-\fIparticle_interaction\fP Turn particle interactions on/off 
-.RE
-.PP
-
-.PP
-Definition at line \fB240\fP of file \fBPenningTrap\&.cpp\fP\&.
-.SH "Member Data Documentation"
-.PP 
-.SS "double PenningTrap::B_0\fC [private]\fP"
-
-.PP
-Magnetic field strength\&. 
-.PP
-Definition at line \fB32\fP of file \fBPenningTrap\&.hpp\fP\&.
-.SS "double PenningTrap::d\fC [private]\fP"
-
-.PP
-Characteristic dimension\&. 
-.PP
-Definition at line \fB34\fP of file \fBPenningTrap\&.hpp\fP\&.
-.SS "\fBsim_arr\fP PenningTrap::k_r\fC [private]\fP"
-A 2D vector containing all $k_{i,j}$ where $j$ is the index of a particle 
-.PP
-Definition at line \fB39\fP of file \fBPenningTrap\&.hpp\fP\&.
-.SS "\fBsim_arr\fP PenningTrap::k_v\fC [private]\fP"
-A 2D vector containing all $k_{i,j}$ where $j$ is the index of a particle 
-.PP
-Definition at line \fB37\fP of file \fBPenningTrap\&.hpp\fP\&.
-.SS "std::vector<\fBParticle\fP> PenningTrap::particles\fC [private]\fP"
-
-.PP
-The particles in the Penning trap\&. 
-.PP
-Definition at line \fB36\fP of file \fBPenningTrap\&.hpp\fP\&.
-.SS "double PenningTrap::t\fC [private]\fP"
-
-.PP
-Current time\&. 
-.PP
-Definition at line \fB35\fP of file \fBPenningTrap\&.hpp\fP\&.
-.SS "std::function<double(double)> PenningTrap::V_0\fC [private]\fP"
-
-.PP
-Applied potential\&. 
-.PP
-Definition at line \fB33\fP of file \fBPenningTrap\&.hpp\fP\&.
-
-.SH "Author"
-.PP 
-Generated automatically by Doxygen for Penning Trap Simulation from the source code\&.
diff --git a/man_pages/man3/PenningTrap.cpp.3 b/man_pages/man3/PenningTrap.cpp.3
deleted file mode 100644
index d080d97..0000000
--- a/man_pages/man3/PenningTrap.cpp.3
+++ /dev/null
@@ -1,48 +0,0 @@
-.TH "src/PenningTrap.cpp" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
-.ad l
-.nh
-.SH NAME
-src/PenningTrap.cpp \- The implementation of the \fBPenningTrap\fP class\&.  
-
-.SH SYNOPSIS
-.br
-.PP
-\fC#include 'PenningTrap\&.hpp'\fP
-.br
-\fC#include 'constants\&.hpp'\fP
-.br
-\fC#include 'typedefs\&.hpp'\fP
-.br
-\fC#include 'utils\&.hpp'\fP
-.br
-
-.SH "Detailed Description"
-.PP 
-The implementation of the \fBPenningTrap\fP class\&. 
-
-
-.PP
-\fBAuthor\fP
-.RS 4
-Cory Alexander Balaton (coryab) 
-.PP
-Janita Ovidie Sandtrøen Willumsen (janitaws)
-.RE
-.PP
-\fBVersion\fP
-.RS 4
-0\&.1
-.RE
-.PP
-.PP
-\fBBug\fP
-.RS 4
-No known bugs 
-.RE
-.PP
-
-.PP
-Definition in file \fBPenningTrap\&.cpp\fP\&.
-.SH "Author"
-.PP 
-Generated automatically by Doxygen for Penning Trap Simulation from the source code\&.
diff --git a/man_pages/man3/PenningTrap.hpp.3 b/man_pages/man3/PenningTrap.hpp.3
deleted file mode 100644
index 15d155f..0000000
--- a/man_pages/man3/PenningTrap.hpp.3
+++ /dev/null
@@ -1,58 +0,0 @@
-.TH "include/PenningTrap.hpp" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
-.ad l
-.nh
-.SH NAME
-include/PenningTrap.hpp \- A class for simulating a Penning trap\&.  
-
-.SH SYNOPSIS
-.br
-.PP
-\fC#include <armadillo>\fP
-.br
-\fC#include <omp\&.h>\fP
-.br
-\fC#include 'Particle\&.hpp'\fP
-.br
-\fC#include 'constants\&.hpp'\fP
-.br
-\fC#include 'typedefs\&.hpp'\fP
-.br
-
-.SS "Classes"
-
-.in +1c
-.ti -1c
-.RI "class \fBPenningTrap\fP"
-.br
-.RI "A class that simulates a Penning trap\&. "
-.in -1c
-.SH "Detailed Description"
-.PP 
-A class for simulating a Penning trap\&. 
-
-
-.PP
-\fBAuthor\fP
-.RS 4
-Cory Alexander Balaton (coryab) 
-.PP
-Janita Ovidie Sandtrøen Willumsen (janitaws)
-.RE
-.PP
-\fBVersion\fP
-.RS 4
-0\&.1
-.RE
-.PP
-.PP
-\fBBug\fP
-.RS 4
-No known bugs 
-.RE
-.PP
-
-.PP
-Definition in file \fBPenningTrap\&.hpp\fP\&.
-.SH "Author"
-.PP 
-Generated automatically by Doxygen for Penning Trap Simulation from the source code\&.
diff --git a/man_pages/man3/PenningTrapTest.3 b/man_pages/man3/PenningTrapTest.3
deleted file mode 100644
index 3bbe27c..0000000
--- a/man_pages/man3/PenningTrapTest.3
+++ /dev/null
@@ -1,56 +0,0 @@
-.TH "PenningTrapTest" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
-.ad l
-.nh
-.SH NAME
-PenningTrapTest
-.SH SYNOPSIS
-.br
-.PP
-.SS "Static Public Member Functions"
-
-.in +1c
-.ti -1c
-.RI "static void \fBtest_external_E_field\fP ()"
-.br
-.ti -1c
-.RI "static void \fBtest_external_B_field\fP ()"
-.br
-.ti -1c
-.RI "static void \fBtest_force_on_particle\fP ()"
-.br
-.ti -1c
-.RI "static void \fBtest_total_force_external\fP ()"
-.br
-.ti -1c
-.RI "static void \fBtest_total_force_particles\fP ()"
-.br
-.in -1c
-.SH "Detailed Description"
-.PP 
-Definition at line \fB20\fP of file \fBtest_suite\&.cpp\fP\&.
-.SH "Member Function Documentation"
-.PP 
-.SS "static void PenningTrapTest::test_external_B_field ()\fC [inline]\fP, \fC [static]\fP"
-
-.PP
-Definition at line \fB59\fP of file \fBtest_suite\&.cpp\fP\&.
-.SS "static void PenningTrapTest::test_external_E_field ()\fC [inline]\fP, \fC [static]\fP"
-
-.PP
-Definition at line \fB22\fP of file \fBtest_suite\&.cpp\fP\&.
-.SS "static void PenningTrapTest::test_force_on_particle ()\fC [inline]\fP, \fC [static]\fP"
-
-.PP
-Definition at line \fB70\fP of file \fBtest_suite\&.cpp\fP\&.
-.SS "static void PenningTrapTest::test_total_force_external ()\fC [inline]\fP, \fC [static]\fP"
-
-.PP
-Definition at line \fB95\fP of file \fBtest_suite\&.cpp\fP\&.
-.SS "static void PenningTrapTest::test_total_force_particles ()\fC [inline]\fP, \fC [static]\fP"
-
-.PP
-Definition at line \fB108\fP of file \fBtest_suite\&.cpp\fP\&.
-
-.SH "Author"
-.PP 
-Generated automatically by Doxygen for Penning Trap Simulation from the source code\&.
diff --git a/man_pages/man3/bug.3 b/man_pages/man3/bug.3
deleted file mode 100644
index d21bde1..0000000
--- a/man_pages/man3/bug.3
+++ /dev/null
@@ -1,29 +0,0 @@
-.TH "bug" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
-.ad l
-.nh
-.SH NAME
-bug \- Bug List 
-.PP
-
-.IP "\fBFile \fBconstants\&.hpp\fP \fP" 1c
-No known bugs  
-.IP "\fBFile \fBmain\&.cpp\fP \fP" 1c
-No known bugs  
-.IP "\fBFile \fBParticle\&.cpp\fP \fP" 1c
-No known bugs  
-.IP "\fBFile \fBParticle\&.hpp\fP \fP" 1c
-No known bugs  
-.IP "\fBFile \fBPenningTrap\&.cpp\fP \fP" 1c
-No known bugs  
-.IP "\fBFile \fBPenningTrap\&.hpp\fP \fP" 1c
-No known bugs  
-.IP "\fBFile \fBtest_suite\&.cpp\fP \fP" 1c
-No known bugs  
-.IP "\fBFile \fBtypedefs\&.hpp\fP \fP" 1c
-No known bugs  
-.IP "\fBFile \fButils\&.cpp\fP \fP" 1c
-No known bugs  
-.IP "\fBFile \fButils\&.hpp\fP \fP" 1c
-No known bugs 
-.PP
-
diff --git a/man_pages/man3/constants.hpp.3 b/man_pages/man3/constants.hpp.3
deleted file mode 100644
index b1d978f..0000000
--- a/man_pages/man3/constants.hpp.3
+++ /dev/null
@@ -1,75 +0,0 @@
-.TH "include/constants.hpp" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
-.ad l
-.nh
-.SH NAME
-include/constants.hpp \- Library of constants\&.  
-
-.SH SYNOPSIS
-.br
-.PP
-.SS "Macros"
-
-.in +1c
-.ti -1c
-.RI "#define \fBK_E\fP   138935\&.333"
-.br
-.RI "Coulomb constant\&. unit: $\frac{u(\mu m)^3}{(\mu s)^2 e^2}$\&. "
-.ti -1c
-.RI "#define \fBT\fP   96\&.4852558"
-.br
-.RI "1 Tesla\&. unit: $ \frac{u}{(\mu s) e} $ "
-.ti -1c
-.RI "#define \fBV\fP   96485255\&.8"
-.br
-.RI "1 Volt\&. unit: $ \frac{u (\mu m)^2}{(\mu s)^2 e} $ "
-.in -1c
-.SH "Detailed Description"
-.PP 
-Library of constants\&. 
-
-
-.PP
-\fBAuthor\fP
-.RS 4
-Cory Alexander Balaton (coryab) 
-.PP
-Janita Ovidie Sandtrøen Willumsen (janitaws)
-.RE
-.PP
-\fBVersion\fP
-.RS 4
-0\&.1
-.RE
-.PP
-.PP
-\fBBug\fP
-.RS 4
-No known bugs 
-.RE
-.PP
-
-.PP
-Definition in file \fBconstants\&.hpp\fP\&.
-.SH "Macro Definition Documentation"
-.PP 
-.SS "#define K_E   138935\&.333"
-
-.PP
-Coulomb constant\&. unit: $\frac{u(\mu m)^3}{(\mu s)^2 e^2}$\&. 
-.PP
-Definition at line \fB15\fP of file \fBconstants\&.hpp\fP\&.
-.SS "#define T   96\&.4852558"
-
-.PP
-1 Tesla\&. unit: $ \frac{u}{(\mu s) e} $ 
-.PP
-Definition at line \fB17\fP of file \fBconstants\&.hpp\fP\&.
-.SS "#define V   96485255\&.8"
-
-.PP
-1 Volt\&. unit: $ \frac{u (\mu m)^2}{(\mu s)^2 e} $ 
-.PP
-Definition at line \fB19\fP of file \fBconstants\&.hpp\fP\&.
-.SH "Author"
-.PP 
-Generated automatically by Doxygen for Penning Trap Simulation from the source code\&.
diff --git a/man_pages/man3/main.cpp.3 b/man_pages/man3/main.cpp.3
deleted file mode 100644
index 23983a7..0000000
--- a/man_pages/man3/main.cpp.3
+++ /dev/null
@@ -1,148 +0,0 @@
-.TH "src/main.cpp" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
-.ad l
-.nh
-.SH NAME
-src/main.cpp \- The main program for this project\&.  
-
-.SH SYNOPSIS
-.br
-.PP
-\fC#include <cmath>\fP
-.br
-\fC#include <fstream>\fP
-.br
-\fC#include <omp\&.h>\fP
-.br
-\fC#include <string>\fP
-.br
-\fC#include <sys/stat\&.h>\fP
-.br
-\fC#include <vector>\fP
-.br
-\fC#include 'PenningTrap\&.hpp'\fP
-.br
-\fC#include 'utils\&.hpp'\fP
-.br
-
-.SS "Macros"
-
-.in +1c
-.ti -1c
-.RI "#define \fBPARTICLES\fP   100"
-.br
-.ti -1c
-.RI "#define \fBN\fP   10000"
-.br
-.ti -1c
-.RI "#define \fBCHARGE\fP   1\&."
-.br
-.ti -1c
-.RI "#define \fBMASS\fP   40\&."
-.br
-.in -1c
-.SS "Functions"
-
-.in +1c
-.ti -1c
-.RI "void \fBsimulate_single_particle\fP ()"
-.br
-.ti -1c
-.RI "void \fBsimulate_two_particles\fP ()"
-.br
-.ti -1c
-.RI "void \fBsimulate_single_particle_with_different_steps\fP ()"
-.br
-.ti -1c
-.RI "void \fBsimulate_100_particles\fP ()"
-.br
-.ti -1c
-.RI "void \fBsimulate_100_particles_with_time_potential\fP ()"
-.br
-.ti -1c
-.RI "int \fBmain\fP ()"
-.br
-.in -1c
-.SS "Variables"
-
-.in +1c
-.ti -1c
-.RI "\fBParticle\fP \fBp1\fP (CHARGE, MASS, \fBvec_3d\fP{20\&., 0\&., 20\&.}, \fBvec_3d\fP{0\&., 25\&., 0\&.})"
-.br
-.ti -1c
-.RI "\fBParticle\fP \fBp2\fP (CHARGE, MASS, \fBvec_3d\fP{25\&., 25\&., 0\&.}, \fBvec_3d\fP{0\&., 40\&., 5\&.})"
-.br
-.in -1c
-.SH "Detailed Description"
-.PP 
-The main program for this project\&. 
-
-
-.PP
-\fBAuthor\fP
-.RS 4
-Cory Alexander Balaton (coryab) 
-.PP
-Janita Ovidie Sandtrøen Willumsen (janitaws)
-.RE
-.PP
-\fBVersion\fP
-.RS 4
-0\&.1
-.RE
-.PP
-.PP
-\fBBug\fP
-.RS 4
-No known bugs 
-.RE
-.PP
-
-.PP
-Definition in file \fBmain\&.cpp\fP\&.
-.SH "Macro Definition Documentation"
-.PP 
-.SS "#define CHARGE   1\&."
-
-.PP
-Definition at line \fB25\fP of file \fBmain\&.cpp\fP\&.
-.SS "#define MASS   40\&."
-
-.PP
-Definition at line \fB26\fP of file \fBmain\&.cpp\fP\&.
-.SS "#define N   10000"
-
-.PP
-Definition at line \fB24\fP of file \fBmain\&.cpp\fP\&.
-.SS "#define PARTICLES   100"
-
-.PP
-Definition at line \fB23\fP of file \fBmain\&.cpp\fP\&.
-.SH "Function Documentation"
-.PP 
-.SS "int main ()"
-
-.PP
-Definition at line \fB124\fP of file \fBmain\&.cpp\fP\&.
-.SS "void simulate_100_particles ()"
-
-.PP
-Definition at line \fB77\fP of file \fBmain\&.cpp\fP\&.
-.SS "void simulate_100_particles_with_time_potential ()"
-
-.PP
-Definition at line \fB91\fP of file \fBmain\&.cpp\fP\&.
-.SS "void simulate_single_particle ()"
-
-.PP
-Definition at line \fB31\fP of file \fBmain\&.cpp\fP\&.
-.SS "void simulate_single_particle_with_different_steps ()"
-
-.PP
-Definition at line \fB55\fP of file \fBmain\&.cpp\fP\&.
-.SS "void simulate_two_particles ()"
-
-.PP
-Definition at line \fB42\fP of file \fBmain\&.cpp\fP\&.
-.SH "Author"
-.PP 
-Generated automatically by Doxygen for Penning Trap Simulation from the source code\&.
diff --git a/man_pages/man3/test_suite.cpp.3 b/man_pages/man3/test_suite.cpp.3
deleted file mode 100644
index c185469..0000000
--- a/man_pages/man3/test_suite.cpp.3
+++ /dev/null
@@ -1,70 +0,0 @@
-.TH "src/test_suite.cpp" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
-.ad l
-.nh
-.SH NAME
-src/test_suite.cpp \- The test suite for the project\&.  
-
-.SH SYNOPSIS
-.br
-.PP
-\fC#include 'PenningTrap\&.hpp'\fP
-.br
-\fC#include 'utils\&.hpp'\fP
-.br
-\fC#include <iomanip>\fP
-.br
-\fC#include <sstream>\fP
-.br
-\fC#include <string>\fP
-.br
-
-.SS "Classes"
-
-.in +1c
-.ti -1c
-.RI "class \fBPenningTrapTest\fP"
-.br
-.in -1c
-.SS "Functions"
-
-.in +1c
-.ti -1c
-.RI "int \fBmain\fP ()"
-.br
-.in -1c
-.SH "Detailed Description"
-.PP 
-The test suite for the project\&. 
-
-
-.PP
-\fBAuthor\fP
-.RS 4
-Cory Alexander Balaton (coryab) 
-.PP
-Janita Ovidie Sandtrøen Willumsen (janitaws)
-.RE
-.PP
-\fBVersion\fP
-.RS 4
-0\&.1
-.RE
-.PP
-.PP
-\fBBug\fP
-.RS 4
-No known bugs 
-.RE
-.PP
-
-.PP
-Definition in file \fBtest_suite\&.cpp\fP\&.
-.SH "Function Documentation"
-.PP 
-.SS "int main ()"
-
-.PP
-Definition at line \fB135\fP of file \fBtest_suite\&.cpp\fP\&.
-.SH "Author"
-.PP 
-Generated automatically by Doxygen for Penning Trap Simulation from the source code\&.
diff --git a/man_pages/man3/todo.3 b/man_pages/man3/todo.3
deleted file mode 100644
index ef888e2..0000000
--- a/man_pages/man3/todo.3
+++ /dev/null
@@ -1,14 +0,0 @@
-.TH "todo" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
-.ad l
-.nh
-.SH NAME
-todo \- Todo List 
-.PP
-
-.IP "\fBFile \fBPenningTrap\&.cpp\fP \fP" 1c
-Implement evolve_RK4 
-.PP
-.PP
-Implement evolve_forward_euler 
-.PP
-
diff --git a/man_pages/man3/typedefs.hpp.3 b/man_pages/man3/typedefs.hpp.3
deleted file mode 100644
index 1933ad3..0000000
--- a/man_pages/man3/typedefs.hpp.3
+++ /dev/null
@@ -1,92 +0,0 @@
-.TH "include/typedefs.hpp" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
-.ad l
-.nh
-.SH NAME
-include/typedefs.hpp \- Useful typedefs for cleaner code\&.  
-
-.SH SYNOPSIS
-.br
-.PP
-\fC#include <vector>\fP
-.br
-\fC#include <armadillo>\fP
-.br
-
-.SS "Typedefs"
-
-.in +1c
-.ti -1c
-.RI "typedef std::vector< arma::vec::fixed< 3 > > \fBsim_cols\fP"
-.br
-.RI "Typedef for the column of the result vector from simulating particles\&. "
-.ti -1c
-.RI "typedef std::vector< arma::vec::fixed< 3 > > \fBsim_rows\fP"
-.br
-.RI "Typedef for the row of the result vector from simulating particles\&. "
-.ti -1c
-.RI "typedef std::vector< \fBsim_cols\fP > \fBsim_arr\fP"
-.br
-.RI "Typedef for the result of the simulate method\&. "
-.ti -1c
-.RI "typedef arma::vec::fixed< 3 > \fBvec_3d\fP"
-.br
-.RI "Typedef for a fixed 3d arma vector\&. "
-.in -1c
-.SH "Detailed Description"
-.PP 
-Useful typedefs for cleaner code\&. 
-
-
-.PP
-\fBAuthor\fP
-.RS 4
-Cory Alexander Balaton (coryab) 
-.PP
-Janita Ovidie Sandtrøen Willumsen (janitaws)
-.RE
-.PP
-\fBVersion\fP
-.RS 4
-1\&.0
-.RE
-.PP
-.PP
-These typedefs make the code more readable and easy to follow along\&.
-.PP
-\fBBug\fP
-.RS 4
-No known bugs 
-.RE
-.PP
-
-.PP
-Definition in file \fBtypedefs\&.hpp\fP\&.
-.SH "Typedef Documentation"
-.PP 
-.SS "typedef std::vector<\fBsim_cols\fP> \fBsim_arr\fP"
-
-.PP
-Typedef for the result of the simulate method\&. 
-.PP
-Definition at line \fB32\fP of file \fBtypedefs\&.hpp\fP\&.
-.SS "typedef std::vector<arma::vec::fixed<3> > \fBsim_cols\fP"
-
-.PP
-Typedef for the column of the result vector from simulating particles\&. 
-.PP
-Definition at line \fB24\fP of file \fBtypedefs\&.hpp\fP\&.
-.SS "typedef std::vector<arma::vec::fixed<3> > \fBsim_rows\fP"
-
-.PP
-Typedef for the row of the result vector from simulating particles\&. 
-.PP
-Definition at line \fB28\fP of file \fBtypedefs\&.hpp\fP\&.
-.SS "typedef arma::vec::fixed<3> \fBvec_3d\fP"
-
-.PP
-Typedef for a fixed 3d arma vector\&. 
-.PP
-Definition at line \fB36\fP of file \fBtypedefs\&.hpp\fP\&.
-.SH "Author"
-.PP 
-Generated automatically by Doxygen for Penning Trap Simulation from the source code\&.
diff --git a/man_pages/man3/utils.cpp.3 b/man_pages/man3/utils.cpp.3
deleted file mode 100644
index 335b5f5..0000000
--- a/man_pages/man3/utils.cpp.3
+++ /dev/null
@@ -1,179 +0,0 @@
-.TH "src/utils.cpp" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
-.ad l
-.nh
-.SH NAME
-src/utils.cpp \- Implementation of the utils\&.  
-
-.SH SYNOPSIS
-.br
-.PP
-\fC#include <sys/stat\&.h>\fP
-.br
-\fC#include 'utils\&.hpp'\fP
-.br
-
-.SS "Functions"
-
-.in +1c
-.ti -1c
-.RI "std::string \fBscientific_format\fP (double d, int width, int prec)"
-.br
-.RI "Turns a double into a string written in scientific format\&. "
-.ti -1c
-.RI "std::string \fBscientific_format\fP (const std::vector< double > &v, int width, int prec)"
-.br
-.RI "Turns a vector of doubles into a string written in scientific format\&. "
-.ti -1c
-.RI "void \fBm_assert\fP (bool expr, std::string expr_str, std::string f, std::string file, int line, std::string msg)"
-.br
-.RI "Test an expression, confirm that test is ok, or abort execution\&. "
-.ti -1c
-.RI "bool \fBarma_vector_close_to\fP (arma::vec &a, arma::vec &b, double tol)"
-.br
-.RI "Test if two armadillo vectors are close to each other\&. "
-.ti -1c
-.RI "bool \fBmkpath\fP (std::string path, int mode)"
-.br
-.RI "Make path given\&. "
-.in -1c
-.SH "Detailed Description"
-.PP 
-Implementation of the utils\&. 
-
-
-.PP
-\fBAuthor\fP
-.RS 4
-Cory Alexander Balaton (coryab) 
-.PP
-Janita Ovidie Sandtrøen Willumsen (janitaws)
-.RE
-.PP
-\fBVersion\fP
-.RS 4
-1\&.0
-.RE
-.PP
-.PP
-\fBBug\fP
-.RS 4
-No known bugs 
-.RE
-.PP
-
-.PP
-Definition in file \fButils\&.cpp\fP\&.
-.SH "Function Documentation"
-.PP 
-.SS "bool arma_vector_close_to (arma::vec & a, arma::vec & b, double tol = \fC1e\-8\fP)"
-
-.PP
-Test if two armadillo vectors are close to each other\&. This function takes in 2 vectors and checks if they are approximately equal to each other given a tolerance\&.
-.PP
-\fBParameters\fP
-.RS 4
-\fIa\fP Vector a 
-.br
-\fIb\fP Vector b 
-.br
-\fItol\fP The tolerance
-.RE
-.PP
-\fBReturns\fP
-.RS 4
-bool 
-.RE
-.PP
-
-.PP
-Definition at line \fB62\fP of file \fButils\&.cpp\fP\&.
-.SS "void m_assert (bool expr, std::string expr_str, std::string func, std::string file, int line, std::string msg)"
-
-.PP
-Test an expression, confirm that test is ok, or abort execution\&. This function takes in an expression and prints an OK message if it's true, or it prints a fail message and aborts execution if it fails\&.
-.PP
-\fBParameters\fP
-.RS 4
-\fIexpr\fP The expression to be evaluated 
-.br
-\fIexpr_str\fP The stringified version of the expression 
-.br
-\fIfunc\fP The function name of the caller 
-.br
-\fIfile\fP The file of the caller 
-.br
-\fIline\fP The line number where this function is called from 
-.br
-\fImsg\fP The message to be displayed 
-.RE
-.PP
-
-.PP
-Definition at line \fB43\fP of file \fButils\&.cpp\fP\&.
-.SS "bool mkpath (std::string path, int mode = \fC0777\fP)"
-
-.PP
-Make path given\&. This tries to be the equivalent to 'mkdir -p' and creates a new directory whenever it needs to\&.
-.PP
-\fBParameters\fP
-.RS 4
-\fIpath\fP The path to be created 
-.br
-\fImode\fP The mode/permissions for all the new directories
-.RE
-.PP
-\fBReturns\fP
-.RS 4
-bool 
-.RE
-.PP
-
-.PP
-Definition at line \fB76\fP of file \fButils\&.cpp\fP\&.
-.SS "std::string scientific_format (const std::vector< double > & v, int width = \fC20\fP, int prec = \fC10\fP)"
-
-.PP
-Turns a vector of doubles into a string written in scientific format\&. The code is stolen from https://github.com/anderkve/FYS3150\&.
-.PP
-\fBParameters\fP
-.RS 4
-\fIv\fP The vector to stringify 
-.br
-\fIwidth\fP The reserved width of the string 
-.br
-\fIprec\fP The precision of the stringified number
-.RE
-.PP
-\fBReturns\fP
-.RS 4
-std::string 
-.RE
-.PP
-
-.PP
-Definition at line \fB24\fP of file \fButils\&.cpp\fP\&.
-.SS "std::string scientific_format (double d, int width = \fC20\fP, int prec = \fC10\fP)"
-
-.PP
-Turns a double into a string written in scientific format\&. The code is stolen from https://github.com/anderkve/FYS3150\&.
-.PP
-\fBParameters\fP
-.RS 4
-\fId\fP The number to stringify 
-.br
-\fIwidth\fP The reserved width of the string 
-.br
-\fIprec\fP The precision of the stringified number
-.RE
-.PP
-\fBReturns\fP
-.RS 4
-std::string 
-.RE
-.PP
-
-.PP
-Definition at line \fB17\fP of file \fButils\&.cpp\fP\&.
-.SH "Author"
-.PP 
-Generated automatically by Doxygen for Penning Trap Simulation from the source code\&.
diff --git a/man_pages/man3/utils.hpp.3 b/man_pages/man3/utils.hpp.3
deleted file mode 100644
index 3f934d0..0000000
--- a/man_pages/man3/utils.hpp.3
+++ /dev/null
@@ -1,228 +0,0 @@
-.TH "include/utils.hpp" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
-.ad l
-.nh
-.SH NAME
-include/utils.hpp \- Function prototypes and macros that are useful\&.  
-
-.SH SYNOPSIS
-.br
-.PP
-\fC#include <armadillo>\fP
-.br
-\fC#include <iomanip>\fP
-.br
-\fC#include <sstream>\fP
-.br
-\fC#include <string>\fP
-.br
-\fC#include <vector>\fP
-.br
-
-.SS "Macros"
-
-.in +1c
-.ti -1c
-.RI "#define \fBDEBUG\fP(msg)"
-.br
-.RI "Writes a debug message\&. "
-.ti -1c
-.RI "#define \fBASSERT\fP(expr,  msg)"
-.br
-.RI "A prettier assertion function\&. "
-.ti -1c
-.RI "#define \fB__METHOD_NAME__\fP   methodName(__PRETTY_FUNCTION__)"
-.br
-.RI "Get the name of the current method/function\&. "
-.in -1c
-.SS "Functions"
-
-.in +1c
-.ti -1c
-.RI "std::string \fBscientific_format\fP (double d, int width=20, int prec=10)"
-.br
-.RI "Turns a double into a string written in scientific format\&. "
-.ti -1c
-.RI "std::string \fBscientific_format\fP (const std::vector< double > &v, int width=20, int prec=10)"
-.br
-.RI "Turns a vector of doubles into a string written in scientific format\&. "
-.ti -1c
-.RI "void \fBm_assert\fP (bool expr, std::string expr_str, std::string func, std::string file, int line, std::string msg)"
-.br
-.RI "Test an expression, confirm that test is ok, or abort execution\&. "
-.ti -1c
-.RI "bool \fBarma_vector_close_to\fP (arma::vec &a, arma::vec &b, double tol=1e\-8)"
-.br
-.RI "Test if two armadillo vectors are close to each other\&. "
-.ti -1c
-.RI "bool \fBmkpath\fP (std::string path, int mode=0777)"
-.br
-.RI "Make path given\&. "
-.in -1c
-.SH "Detailed Description"
-.PP 
-Function prototypes and macros that are useful\&. 
-
-
-.PP
-\fBAuthor\fP
-.RS 4
-Cory Alexander Balaton (coryab) 
-.PP
-Janita Ovidie Sandtrøen Willumsen (janitaws)
-.RE
-.PP
-\fBVersion\fP
-.RS 4
-1\&.0
-.RE
-.PP
-.PP
-These utility function are mainly for convenience and aren't directly related to the project\&.
-.PP
-\fBBug\fP
-.RS 4
-No known bugs 
-.RE
-.PP
-
-.PP
-Definition in file \fButils\&.hpp\fP\&.
-.SH "Macro Definition Documentation"
-.PP 
-.SS "#define __METHOD_NAME__   methodName(__PRETTY_FUNCTION__)"
-
-.PP
-Get the name of the current method/function\&. 
-.PP
-Definition at line \fB51\fP of file \fButils\&.hpp\fP\&.
-.SS "#define ASSERT(expr, msg)"
-\fBValue:\fP.PP
-.nf
-                                   m_assert(expr, #expr, __METHOD_NAME__, __FILE__, \\
-                                   __LINE__, msg)
-.fi
-
-.PP
-A prettier assertion function\&. This macro calls the m_assert function which is a more informative assertion function than the regular assert function from cassert\&. 
-.PP
-Definition at line \fB45\fP of file \fButils\&.hpp\fP\&.
-.SS "#define DEBUG(msg)"
-
-.PP
-Writes a debug message\&. This macro writes a debug message that includes the filename, line number, and a custom message\&. The function is wrapped in an ifdef that checks if DBG is defined, so one can choose to display the debug messages by adding the -DDBG flag when compiling\&. 
-.PP
-Definition at line \fB36\fP of file \fButils\&.hpp\fP\&.
-.SH "Function Documentation"
-.PP 
-.SS "bool arma_vector_close_to (arma::vec & a, arma::vec & b, double tol = \fC1e\-8\fP)"
-
-.PP
-Test if two armadillo vectors are close to each other\&. This function takes in 2 vectors and checks if they are approximately equal to each other given a tolerance\&.
-.PP
-\fBParameters\fP
-.RS 4
-\fIa\fP Vector a 
-.br
-\fIb\fP Vector b 
-.br
-\fItol\fP The tolerance
-.RE
-.PP
-\fBReturns\fP
-.RS 4
-bool 
-.RE
-.PP
-
-.PP
-Definition at line \fB62\fP of file \fButils\&.cpp\fP\&.
-.SS "void m_assert (bool expr, std::string expr_str, std::string func, std::string file, int line, std::string msg)"
-
-.PP
-Test an expression, confirm that test is ok, or abort execution\&. This function takes in an expression and prints an OK message if it's true, or it prints a fail message and aborts execution if it fails\&.
-.PP
-\fBParameters\fP
-.RS 4
-\fIexpr\fP The expression to be evaluated 
-.br
-\fIexpr_str\fP The stringified version of the expression 
-.br
-\fIfunc\fP The function name of the caller 
-.br
-\fIfile\fP The file of the caller 
-.br
-\fIline\fP The line number where this function is called from 
-.br
-\fImsg\fP The message to be displayed 
-.RE
-.PP
-
-.PP
-Definition at line \fB43\fP of file \fButils\&.cpp\fP\&.
-.SS "bool mkpath (std::string path, int mode = \fC0777\fP)"
-
-.PP
-Make path given\&. This tries to be the equivalent to 'mkdir -p' and creates a new directory whenever it needs to\&.
-.PP
-\fBParameters\fP
-.RS 4
-\fIpath\fP The path to be created 
-.br
-\fImode\fP The mode/permissions for all the new directories
-.RE
-.PP
-\fBReturns\fP
-.RS 4
-bool 
-.RE
-.PP
-
-.PP
-Definition at line \fB76\fP of file \fButils\&.cpp\fP\&.
-.SS "std::string scientific_format (const std::vector< double > & v, int width = \fC20\fP, int prec = \fC10\fP)"
-
-.PP
-Turns a vector of doubles into a string written in scientific format\&. The code is stolen from https://github.com/anderkve/FYS3150\&.
-.PP
-\fBParameters\fP
-.RS 4
-\fIv\fP The vector to stringify 
-.br
-\fIwidth\fP The reserved width of the string 
-.br
-\fIprec\fP The precision of the stringified number
-.RE
-.PP
-\fBReturns\fP
-.RS 4
-std::string 
-.RE
-.PP
-
-.PP
-Definition at line \fB24\fP of file \fButils\&.cpp\fP\&.
-.SS "std::string scientific_format (double d, int width = \fC20\fP, int prec = \fC10\fP)"
-
-.PP
-Turns a double into a string written in scientific format\&. The code is stolen from https://github.com/anderkve/FYS3150\&.
-.PP
-\fBParameters\fP
-.RS 4
-\fId\fP The number to stringify 
-.br
-\fIwidth\fP The reserved width of the string 
-.br
-\fIprec\fP The precision of the stringified number
-.RE
-.PP
-\fBReturns\fP
-.RS 4
-std::string 
-.RE
-.PP
-
-.PP
-Definition at line \fB17\fP of file \fButils\&.cpp\fP\&.
-.SH "Author"
-.PP 
-Generated automatically by Doxygen for Penning Trap Simulation from the source code\&.
diff --git a/src/PenningTrap.cpp b/src/PenningTrap.cpp
index 49f6d94..ae8903b 100644
--- a/src/PenningTrap.cpp
+++ b/src/PenningTrap.cpp
@@ -53,8 +53,8 @@ vec_3d PenningTrap::v_func(unsigned int i, unsigned int j, double dt)
     case 2:
         return dt * this->k_v[2][j];
     case 3:
-        return (dt / 6.) * (this->k_v[0][j].eval() + this->k_v[1][j].eval() +
-                            this->k_v[2][j].eval() + this->k_v[3][j].eval());
+        return (dt / 6.) * (this->k_v[0][j] + this->k_v[1][j] +
+                            this->k_v[2][j] + this->k_v[3][j]);
     default:
         std::cout << "Not valid!" << std::endl;
         abort();
@@ -71,8 +71,8 @@ vec_3d PenningTrap::r_func(unsigned int i, unsigned int j, double dt)
     case 2:
         return dt * this->k_r[2][j];
     case 3:
-        return (dt / 6.) * (this->k_r[0][j].eval() + this->k_r[1][j].eval() +
-                            this->k_r[2][j].eval() + this->k_r[3][j].eval());
+        return (dt / 6.) * (this->k_r[0][j] + this->k_r[1][j] +
+                            this->k_r[2][j] + this->k_r[3][j]);
     default:
         std::cout << "Not valid!" << std::endl;
         abort();
@@ -212,12 +212,16 @@ void PenningTrap::evolve_forward_euler(double dt, bool particle_interaction)
     this->t += dt;
 }
 
-sim_arr PenningTrap::simulate(double time, unsigned int steps,
-                              std::string method, bool particle_interaction)
+simulation_t PenningTrap::simulate(double time, unsigned int steps,
+                                   std::string method,
+                                   bool particle_interaction)
 {
     double dt = time / (double)steps;
 
-    sim_arr res(this->particles.size(), sim_cols(steps));
+    unsigned int size = this->particles.size();
+    // sim_arr res(this->particles.size(), sim_cols(steps));
+    simulation_t res{sim_arr(size, sim_cols(steps)),
+                     sim_arr(size, sim_cols(steps))};
 
     void (PenningTrap::*func)(double, bool);
     if (method == "rk4") {
@@ -232,8 +236,9 @@ sim_arr PenningTrap::simulate(double time, unsigned int steps,
     }
 
     for (size_t j = 0; j < steps; j++) {
-        for (size_t i = 0; i < this->particles.size(); i++) {
-            res[i][j] = this->particles[i].r_vec;
+        for (size_t i = 0; i < size; i++) {
+            res.r_vecs[i][j] = this->particles[i].r_vec;
+            res.v_vecs[i][j] = this->particles[i].v_vec;
         }
         (this->*func)(dt, particle_interaction);
     }
@@ -242,7 +247,8 @@ sim_arr PenningTrap::simulate(double time, unsigned int steps,
 }
 
 void PenningTrap::write_simulation_to_dir(std::string path, double time,
-                                          unsigned int steps, std::string method,
+                                          unsigned int steps,
+                                          std::string method,
                                           bool particle_interaction)
 {
     if (path.back() != '/') {
@@ -253,23 +259,34 @@ void PenningTrap::write_simulation_to_dir(std::string path, double time,
         return;
     }
 
-    sim_arr res = this->simulate(time, steps, method, particle_interaction);
+    simulation_t res =
+        this->simulate(time, steps, method, particle_interaction);
 
     std::ofstream ofile;
 
 #pragma omp parallel for private(ofile)
     for (size_t i = 0; i < this->particles.size(); i++) {
-        ofile.open(path + "particle_" + std::to_string(i) + ".txt");
-        for (vec_3d &vec : res[i]) {
+        ofile.open(path + "particle_" + std::to_string(i) + "_r.txt");
+        for (vec_3d &vec : res.r_vecs[i]) {
             ofile << vec(0) << "," << vec(1) << "," << vec(2) << "\n";
         }
         ofile.close();
+        ofile.open(path + "particle_" + std::to_string(i) + "_v.txt");
+        for (vec_3d &vec : res.v_vecs[i]) {
+            ofile << scientific_format(vec(0), 10, 8) << ","
+                  << scientific_format(vec(1), 8, 10) << ","
+                  << scientific_format(vec(2), 8, 10) << "\n";
+        }
+        ofile.close();
     }
 }
 
-double PenningTrap::fraction_of_particles_left(double time, unsigned int steps, std::string method, bool particle_interaction)
+double PenningTrap::fraction_of_particles_left(double time, unsigned int steps,
+                                               std::string method,
+                                               bool particle_interaction)
 {
-    sim_arr res = this->simulate(time, steps, method, particle_interaction);
+    simulation_t res =
+        this->simulate(time, steps, method, particle_interaction);
 
     int particles_left = 0;
 
@@ -279,6 +296,5 @@ double PenningTrap::fraction_of_particles_left(double time, unsigned int steps,
         }
     }
 
-    return (double) particles_left / (double) this->particles.size();
+    return (double)particles_left / (double)this->particles.size();
 }
-
diff --git a/src/main.cpp b/src/main.cpp
index 96465cc..75a842d 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -12,6 +12,7 @@
 
 #include <cmath>
 #include <fstream>
+#include <functional>
 #include <omp.h>
 #include <string>
 #include <sys/stat.h>
@@ -21,7 +22,7 @@
 #include "utils.hpp"
 
 #define PARTICLES 100
-#define N 10000
+#define N 40000
 #define CHARGE 1.
 #define MASS 40. // unit: amu
 
@@ -36,7 +37,7 @@ void simulate_single_particle()
     double time = 50.; // microseconds
 
     DEBUG("Write to dir");
-    trap.write_simulation_to_dir("output/simulate_single_particle", time, N);
+    trap.write_simulation_to_dir("output/simulate_single_particle", time, N, "rk4", false);
 }
 
 void simulate_two_particles()
@@ -78,14 +79,13 @@ void simulate_100_particles()
 {
     PenningTrap trap((unsigned)100, T,
                      [](double t) {
-                         return 25. * V / 1000. *
-                                (1. + .4 * std::cos(1.5 * t));
+                         return 25. * V / 1000. * (1. + .4 * std::cos(1.5 * t));
                      },
                      500., 0);
 
     double time = 500.; // microseconds
 
-    trap.write_simulation_to_dir("output/simulate_100_particles", time, N*4);
+    trap.write_simulation_to_dir("output/simulate_100_particles", time, N * 4);
 }
 
 void simulate_100_particles_with_time_potential()
@@ -95,52 +95,63 @@ void simulate_100_particles_with_time_potential()
     double freq_start = .2;
     double freq_end = 2.5;
     double freq_increment = .02;
-    size_t freq_iterations = (size_t) ((freq_end - freq_start) / freq_increment);
+    size_t freq_iterations = (size_t)((freq_end - freq_start) / freq_increment);
+
+    double res[4][freq_iterations];
 
     std::string path = "output/time_dependent_potential/";
     mkpath(path);
 
     std::ofstream ofile;
 
-    for (double f : amplitudes) {
-        ofile.open(path + "f_" + std::to_string(f) + ".txt");
-        #pragma omp parallel for ordered schedule(static, 1)
-        for (size_t i=0; i < freq_iterations; i++) {
-            double freq = freq_start + i*freq_increment;
-            PenningTrap trap((unsigned)100, T,
-                             [f, freq](double t) {
-                                 return (25. * V / 1000.) *
-                                        (1. + f * std::cos(freq * t));
-                             },
-                             500., 0.);
-            double res = trap.fraction_of_particles_left(500., 40000, "rk4", true);
-            #pragma omp ordered
-            ofile << freq << "," << res << "\n";
-        }
-        ofile.close();
+    double freq = freq_start;
+    for (size_t i=0; i<freq_iterations; i++) {
+        res[0][i] = freq;
+        freq += freq_increment;
     }
+
+#pragma omp parallel for collapse(2) num_threads(4)
+    for (size_t i = 0; i < 3; i++) {
+        for (size_t j = 0; j < freq_iterations; j++) {
+            PenningTrap trap((unsigned)100, T,
+                             std::bind([](double f, double r, double t) {
+                                 return (25. * V / 1000.) *
+                                        (1. +
+                                         f * std::cos(r * t));
+                             }, amplitudes[i], res[0][j], std::placeholders::_1),
+                             500., 0.);
+            res[i + 1][j] =
+                trap.fraction_of_particles_left(500., 40000, "rk4", false);
+        }
+    }
+
+    ofile.open(path + "res.txt");
+    for (size_t i=0; i<freq_iterations; i++) {
+        ofile << res[0][i] << "," 
+            << res[1][i] << ","
+            << res[2][i] << ","
+            << res[3][i] << "\n";
+    }
+    ofile.close();
 }
 
 int main()
 {
+    double start = omp_get_wtime();
 
     simulate_single_particle();
 
     simulate_two_particles();
 
-    simulate_single_particle_with_different_steps();
+    //simulate_single_particle_with_different_steps();
 
-    double start = omp_get_wtime();
-
-    for (int i=0; i<5; i++) {
-        simulate_100_particles();
-    }
+    //simulate_100_particles();
 
     //simulate_100_particles_with_time_potential();
 
     double end = omp_get_wtime();
 
-    std::cout << "Average time: " << (end - start) / 5. << " seconds" << std::endl;
+    std::cout << "Time: " << (end - start) << " seconds" << std::endl;
 
     return 0;
 }
diff --git a/src/plot_particles_left.py b/src/plot_particles_left.py
deleted file mode 100644
index 1d9a45c..0000000
--- a/src/plot_particles_left.py
+++ /dev/null
@@ -1,33 +0,0 @@
-import matplotlib.pyplot as plt
-
-def main():
-    files = [
-        "output/time_dependent_potential/f_0.100000.txt",
-        "output/time_dependent_potential/f_0.400000.txt",
-        "output/time_dependent_potential/f_0.700000.txt",
-    ]
-    vals = [
-        .1,
-        .4,
-        .7
-    ]
-    for i in range(3):
-        with open(files[i]) as f:
-            lines = f.readlines()
-            x = []
-            y = []
-            for line in lines:
-                a,b = line.strip().split(",")
-                x.append(float(a))
-                y.append(float(b))
-            plt.plot(x,y,label=f"amplitude: {vals[i]}")
-
-    plt.xlabel(r"$\omega_V$")
-    plt.ylabel(r"Fraction of particles left")
-    plt.title(r"The fraction of particles left in the Penning trap "
-              "after 500 microseconds for different amplitudes and frequencies")
-    plt.legend()
-    plt.show()
-
-if __name__ == "__main__":
-    main()
diff --git a/src/animate_100_particles.py b/src/scripts/animate_100_particles.py
similarity index 100%
rename from src/animate_100_particles.py
rename to src/scripts/animate_100_particles.py
diff --git a/src/scripts/plot_particles_left.py b/src/scripts/plot_particles_left.py
new file mode 100644
index 0000000..85bfd78
--- /dev/null
+++ b/src/scripts/plot_particles_left.py
@@ -0,0 +1,30 @@
+import matplotlib.pyplot as plt
+
+def main():
+    with open("output/time_dependent_potential/res.txt") as f:
+        lines = f.readlines()
+        x = []
+        y1 = []
+        y2 = []
+        y3 = []
+        for line in lines:
+            l = line.strip().split(",")
+            x.append(float(l[0]))
+            y1.append(float(l[1]))
+            y2.append(float(l[2]))
+            y3.append(float(l[3]))
+
+        plt.plot(x,y1,label=f"amplitude: 0.1")
+        plt.plot(x,y2,label=f"amplitude: 0.4")
+        plt.plot(x,y3,label=f"amplitude: 0.7")
+
+    plt.xlabel(r"$\omega_V$ (MHz)")
+    plt.ylabel(r"Fraction of particles left")
+    plt.title(r"The fraction of particles left in the Penning trap "
+              "after 500 microseconds for different amplitudes and frequencies")
+    plt.legend()
+    # plt.show()
+    plt.savefig("../latex/images/particles_left.pdf")
+
+if __name__ == "__main__":
+    main()
diff --git a/src/scripts/plot_single_particle.py b/src/scripts/plot_single_particle.py
new file mode 100644
index 0000000..2874030
--- /dev/null
+++ b/src/scripts/plot_single_particle.py
@@ -0,0 +1,29 @@
+import matplotlib.pyplot as plt
+import numpy as np
+
+def z(t):
+    V_0 = 25.*9.64852558 * 10**4
+    m = 40.
+    d = 500.
+    w_z = np.sqrt((2.*V_0)/(m*d*d))
+    return 20.*np.cos(w_z*t)
+
+def main():
+    filename = "output/simulate_single_particle/particle_0_r.txt"
+    r = t = []
+    with open(filename) as f:
+        lines = f.readlines()
+        t = np.linspace(0, 50, len(lines))
+        r = np.array([list(map(float, line.strip().split(","))) for line in lines])
+
+    plt.plot(t, r[:, 2], label="approximation")
+    plt.plot(t, z(t), label="analytical")
+    plt.xlabel(r"time $(\mu s)$")
+    plt.ylabel(r"z $(\mu m)$")
+    plt.title(r"Movement of a single particle in the x direction")
+    plt.legend()
+    plt.savefig("../latex/images/single_particle.pdf")
+
+
+if __name__ == "__main__":
+    main()

From d7246b05b1f4d9c0e9c42741febe69d3a022b4c9 Mon Sep 17 00:00:00 2001
From: Cory <cory@balaton.dev>
Date: Tue, 17 Oct 2023 17:31:56 +0200
Subject: [PATCH 23/26] Fix last update of RK4

---
 src/PenningTrap.cpp | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/src/PenningTrap.cpp b/src/PenningTrap.cpp
index ae8903b..ab99599 100644
--- a/src/PenningTrap.cpp
+++ b/src/PenningTrap.cpp
@@ -53,8 +53,8 @@ vec_3d PenningTrap::v_func(unsigned int i, unsigned int j, double dt)
     case 2:
         return dt * this->k_v[2][j];
     case 3:
-        return (dt / 6.) * (this->k_v[0][j] + this->k_v[1][j] +
-                            this->k_v[2][j] + this->k_v[3][j]);
+        return (dt / 6.) * (this->k_v[0][j] + 2.*this->k_v[1][j] +
+                            2.*this->k_v[2][j] + this->k_v[3][j]);
     default:
         std::cout << "Not valid!" << std::endl;
         abort();
@@ -71,8 +71,8 @@ vec_3d PenningTrap::r_func(unsigned int i, unsigned int j, double dt)
     case 2:
         return dt * this->k_r[2][j];
     case 3:
-        return (dt / 6.) * (this->k_r[0][j] + this->k_r[1][j] +
-                            this->k_r[2][j] + this->k_r[3][j]);
+        return (dt / 6.) * (this->k_r[0][j] + 2.*this->k_r[1][j] +
+                            2.*this->k_r[2][j] + this->k_r[3][j]);
     default:
         std::cout << "Not valid!" << std::endl;
         abort();

From 4f38357db7e03ee989f50ded90f197b17c1ac0a0 Mon Sep 17 00:00:00 2001
From: Cory <cory@balaton.dev>
Date: Wed, 18 Oct 2023 13:34:23 +0200
Subject: [PATCH 24/26] Stuff

---
 include/PenningTrap.hpp                    |   3 +
 latex/images/3d_plot.pdf                   | Bin 0 -> 49072 bytes
 latex/images/phase_space_2_particles.pdf   | Bin 0 -> 53181 bytes
 latex/images/phase_space_2_particles_x.pdf | Bin 0 -> 53167 bytes
 latex/images/phase_space_2_particles_z.pdf | Bin 0 -> 24863 bytes
 latex/images/plot_2_particles_xy.pdf       | Bin 0 -> 71767 bytes
 latex/images/single_particle.pdf           | Bin 21430 -> 22021 bytes
 src/PenningTrap.cpp                        |  20 +++--
 src/main.cpp                               |  85 ++++++++++++++-------
 src/scripts/plot_2_particles.py            |  39 ++++++++++
 src/scripts/plot_3d.py                     |  40 ++++++++++
 src/scripts/plot_phase_space.py            |  53 +++++++++++++
 src/scripts/plot_relative_error.py         |  50 ++++++++++++
 src/scripts/plot_single_particle.py        |   3 +-
 14 files changed, 260 insertions(+), 33 deletions(-)
 create mode 100644 latex/images/3d_plot.pdf
 create mode 100644 latex/images/phase_space_2_particles.pdf
 create mode 100644 latex/images/phase_space_2_particles_x.pdf
 create mode 100644 latex/images/phase_space_2_particles_z.pdf
 create mode 100644 latex/images/plot_2_particles_xy.pdf
 create mode 100644 src/scripts/plot_2_particles.py
 create mode 100644 src/scripts/plot_3d.py
 create mode 100644 src/scripts/plot_phase_space.py
 create mode 100644 src/scripts/plot_relative_error.py

diff --git a/include/PenningTrap.hpp b/include/PenningTrap.hpp
index eaf89be..9a78784 100644
--- a/include/PenningTrap.hpp
+++ b/include/PenningTrap.hpp
@@ -222,6 +222,9 @@ public:
     double fraction_of_particles_left(double time, unsigned int steps,
                                       std::string method = "rk4",
                                       bool particle_interaction = true);
+
+    vec_3d get_r(int i);
+    double get_t();
 };
 
 #endif
diff --git a/latex/images/3d_plot.pdf b/latex/images/3d_plot.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..78b115e8aab59b5a61e6411a9dfc096d694c4478
GIT binary patch
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diff --git a/src/PenningTrap.cpp b/src/PenningTrap.cpp
index ab99599..d5a3b16 100644
--- a/src/PenningTrap.cpp
+++ b/src/PenningTrap.cpp
@@ -53,8 +53,8 @@ vec_3d PenningTrap::v_func(unsigned int i, unsigned int j, double dt)
     case 2:
         return dt * this->k_v[2][j];
     case 3:
-        return (dt / 6.) * (this->k_v[0][j] + 2.*this->k_v[1][j] +
-                            2.*this->k_v[2][j] + this->k_v[3][j]);
+        return (dt / 6.) * (this->k_v[0][j] + 2. * this->k_v[1][j] +
+                            2. * this->k_v[2][j] + this->k_v[3][j]);
     default:
         std::cout << "Not valid!" << std::endl;
         abort();
@@ -71,8 +71,8 @@ vec_3d PenningTrap::r_func(unsigned int i, unsigned int j, double dt)
     case 2:
         return dt * this->k_r[2][j];
     case 3:
-        return (dt / 6.) * (this->k_r[0][j] + 2.*this->k_r[1][j] +
-                            2.*this->k_r[2][j] + this->k_r[3][j]);
+        return (dt / 6.) * (this->k_r[0][j] + 2. * this->k_r[1][j] +
+                            2. * this->k_r[2][j] + this->k_r[3][j]);
     default:
         std::cout << "Not valid!" << std::endl;
         abort();
@@ -106,8 +106,6 @@ vec_3d PenningTrap::force_on_particle(unsigned int i, unsigned int j)
     // Get the distance between the particles
     double norm = arma::norm(res, 2);
 
-    // Multiply res with p_j's charge divided by the norm cubed
-
     return vec_3d(res * p_j.q / (norm * norm * norm));
 }
 
@@ -298,3 +296,13 @@ double PenningTrap::fraction_of_particles_left(double time, unsigned int steps,
 
     return (double)particles_left / (double)this->particles.size();
 }
+
+vec_3d PenningTrap::get_r(int i)
+{
+    return this->particles[i].r_vec;
+}
+
+double PenningTrap::get_t()
+{
+    return this->t;
+}
diff --git a/src/main.cpp b/src/main.cpp
index 75a842d..19ef8fd 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -11,6 +11,7 @@
  * */
 
 #include <cmath>
+#include <complex>
 #include <fstream>
 #include <functional>
 #include <omp.h>
@@ -29,6 +30,20 @@
 Particle p1(CHARGE, MASS, vec_3d{20., 0., 20.}, vec_3d{0., 25., 0.});
 Particle p2(CHARGE, MASS, vec_3d{25., 25., 0.}, vec_3d{0., 40., 5.});
 
+vec_3d analytical_solution_particle_1(double t)
+{
+    double w_0 = T / MASS;
+    double w_z2 = (50. * V / 1000.) / (MASS * 500. * 500.);
+    double w_p = (w_0 + std::sqrt(w_0 * w_0 - 2. * w_z2)) / 2.;
+    double w_n = (w_0 - std::sqrt(w_0 * w_0 - 2. * w_z2)) / 2.;
+    double A_p = (25. + w_n * 20.) / (w_n - w_p);
+    double A_n = -(25. + w_p * 20.) / (w_n - w_p);
+    std::complex<double> f = A_p * std::exp(std::complex<double>(0., -w_p * t)) +
+                             A_n * std::exp(std::complex<double>(0., -w_n * t));
+    vec_3d res{std::real(f), std::imag(f), 20. * std::cos(std::sqrt(w_z2) * t)};
+    return res;
+}
+
 void simulate_single_particle()
 {
     DEBUG("Inside single particle sim");
@@ -37,7 +52,8 @@ void simulate_single_particle()
     double time = 50.; // microseconds
 
     DEBUG("Write to dir");
-    trap.write_simulation_to_dir("output/simulate_single_particle", time, N, "rk4", false);
+    trap.write_simulation_to_dir("output/simulate_single_particle", time, N,
+                                 "rk4", false);
 }
 
 void simulate_two_particles()
@@ -56,22 +72,40 @@ void simulate_two_particles()
 void simulate_single_particle_with_different_steps()
 {
 
-    double time = 50; // microseconds
+    double time = 50.; // microseconds
+
+    std::ofstream ofile;
 
     for (int i = 0; i < 4; i++) {
-        int steps = 4000 * (i + 1);
+        int steps = 4000 * std::pow(2, i);
+        double dt = time / (double)steps;
+        std::string path = "output/relative_error/RK4/";
+        mkpath(path);
+        ofile.open(path + std::to_string(steps) + "_steps.txt");
         PenningTrap trap(std::vector<Particle>{p1});
-        trap.write_simulation_to_dir("output/N_steps/RK4/" +
-                                         std::to_string(steps) + "_steps",
-                                     time, steps, "rk4", false);
+        for (int i = 0; i < steps; i++) {
+            trap.evolve_RK4(dt);
+            ofile << arma::norm(trap.get_r(0) -
+                         analytical_solution_particle_1(trap.get_t()))
+                  << "\n";
+        }
+        ofile.close();
     }
 
     for (int i = 0; i < 4; i++) {
-        int steps = 4000 * (i + 1);
+        int steps = 4000 * std::pow(2, i);
+        double dt = time / (double)steps;
+        std::string path = "output/relative_error/euler/";
+        mkpath(path);
+        ofile.open(path + std::to_string(steps) + "_steps.txt");
         PenningTrap trap(std::vector<Particle>{p1});
-        trap.write_simulation_to_dir("output/N_steps/euler/" +
-                                         std::to_string(steps) + "_steps",
-                                     time, steps, "euler", false);
+        for (int i = 0; i < steps; i++) {
+            trap.evolve_forward_euler(dt);
+            ofile << arma::norm(trap.get_r(0) -
+                         analytical_solution_particle_1(trap.get_t()))
+                  << "\n";
+        }
+        ofile.close();
     }
 }
 
@@ -105,7 +139,7 @@ void simulate_100_particles_with_time_potential()
     std::ofstream ofile;
 
     double freq = freq_start;
-    for (size_t i=0; i<freq_iterations; i++) {
+    for (size_t i = 0; i < freq_iterations; i++) {
         res[0][i] = freq;
         freq += freq_increment;
     }
@@ -113,24 +147,23 @@ void simulate_100_particles_with_time_potential()
 #pragma omp parallel for collapse(2) num_threads(4)
     for (size_t i = 0; i < 3; i++) {
         for (size_t j = 0; j < freq_iterations; j++) {
-            PenningTrap trap((unsigned)100, T,
-                             std::bind([](double f, double r, double t) {
-                                 return (25. * V / 1000.) *
-                                        (1. +
-                                         f * std::cos(r * t));
-                             }, amplitudes[i], res[0][j], std::placeholders::_1),
-                             500., 0.);
+            PenningTrap trap(
+                (unsigned)100, T,
+                std::bind(
+                    [](double f, double r, double t) {
+                        return (25. * V / 1000.) * (1. + f * std::cos(r * t));
+                    },
+                    amplitudes[i], res[0][j], std::placeholders::_1),
+                500., 0.);
             res[i + 1][j] =
                 trap.fraction_of_particles_left(500., 40000, "rk4", false);
         }
     }
 
     ofile.open(path + "res.txt");
-    for (size_t i=0; i<freq_iterations; i++) {
-        ofile << res[0][i] << "," 
-            << res[1][i] << ","
-            << res[2][i] << ","
-            << res[3][i] << "\n";
+    for (size_t i = 0; i < freq_iterations; i++) {
+        ofile << res[0][i] << "," << res[1][i] << "," << res[2][i] << ","
+              << res[3][i] << "\n";
     }
     ofile.close();
 }
@@ -143,11 +176,11 @@ int main()
 
     simulate_two_particles();
 
-    //simulate_single_particle_with_different_steps();
+     simulate_single_particle_with_different_steps();
 
-    //simulate_100_particles();
+    // simulate_100_particles();
 
-    //simulate_100_particles_with_time_potential();
+    // simulate_100_particles_with_time_potential();
 
     double end = omp_get_wtime();
 
diff --git a/src/scripts/plot_2_particles.py b/src/scripts/plot_2_particles.py
new file mode 100644
index 0000000..17f327c
--- /dev/null
+++ b/src/scripts/plot_2_particles.py
@@ -0,0 +1,39 @@
+import matplotlib.pyplot as plt
+import numpy as np
+
+def main():
+    files = [
+        "output/simulate_2_particles/no_interaction/particle_0_r.txt",
+        "output/simulate_2_particles/no_interaction/particle_1_r.txt",
+        "output/simulate_2_particles/with_interaction/particle_0_r.txt",
+        "output/simulate_2_particles/with_interaction/particle_1_r.txt"
+    ]
+    labels = [
+        "particle 1 no interaction",
+        "particle 2 no interaction",
+        "particle 1 with interaction",
+        "particle 2 with interaction",
+    ]
+    colors = [
+        "lightskyblue",
+        "lightskyblue",
+        "salmon",
+        "salmon"
+    ]
+    for label, color, file in zip(labels, colors, files):
+        with open(file) as f:
+            lines = f.readlines()
+            t = np.linspace(0, 50, len(lines))
+            r = np.array([list(map(float, line.strip().split(","))) for line in lines])
+            plt.plot(r[:,0], r[:,1], label=label, color=color)
+    
+    plt.xlabel(r"x $(\mu m)$")
+    plt.ylabel(r"y $(\mu m)$")
+    plt.title(r"2 particles with and without interactions.")
+    # plt.legend()
+    # plt.show()
+    plt.savefig("../latex/images/plot_2_particles_xy.pdf")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/src/scripts/plot_3d.py b/src/scripts/plot_3d.py
new file mode 100644
index 0000000..811bf6a
--- /dev/null
+++ b/src/scripts/plot_3d.py
@@ -0,0 +1,40 @@
+import matplotlib.pyplot as plt
+import numpy as np
+
+def main():
+    files = [
+        "output/simulate_2_particles/no_interaction/particle_0_r.txt",
+        "output/simulate_2_particles/no_interaction/particle_1_r.txt",
+        "output/simulate_2_particles/with_interaction/particle_0_r.txt",
+        "output/simulate_2_particles/with_interaction/particle_1_r.txt"
+    ]
+    labels = [
+        "particle 1 no interaction",
+        "particle 2 no interaction",
+        "particle 1 with interaction",
+        "particle 2 with interaction",
+    ]
+    colors = [
+        "lightskyblue",
+        "deepskyblue",
+        "salmon",
+        "darkred"
+    ]
+    ax = plt.figure().add_subplot(projection="3d")
+    for label, color, file in zip(labels, colors, files):
+        with open(file) as f:
+            lines = f.readlines()
+            t = np.linspace(0, 50, len(lines))
+            r = np.array([list(map(float, line.strip().split(","))) for line in lines])
+            ax.plot(r[:,0], r[:,1], r[:,2], label=label, color=color)
+    
+    ax.set_xlabel(r"x $(\mu m)$")
+    ax.set_ylabel(r"y $(\mu m)$")
+    ax.set_zlabel(r"z $(\mu m)$")
+    plt.title(r"2 particles with and without interactions.")
+    plt.legend()
+    plt.savefig("../latex/images/3d_plot.pdf")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/src/scripts/plot_phase_space.py b/src/scripts/plot_phase_space.py
new file mode 100644
index 0000000..5a4c3ac
--- /dev/null
+++ b/src/scripts/plot_phase_space.py
@@ -0,0 +1,53 @@
+import matplotlib.pyplot as plt
+import numpy as np
+
+def main():
+    directories = {
+        "output/simulate_2_particles/no_interaction/",
+        "output/simulate_2_particles/with_interaction/",
+    }
+    titles = {
+        "particles without interaction",
+        "particles with interaction"
+    }
+    files = [
+        "particle_0_r.txt",
+        "particle_0_v.txt",
+        "particle_1_r.txt",
+        "particle_1_v.txt",
+    ]
+    labels = [
+        r"particle 1 r",
+        r"particle 1 v",
+        r"particle 2 r",
+        r"particle 2 v",
+    ]
+    colors = [
+        "lightskyblue",
+        "deepskyblue",
+        "salmon",
+        "tomato",
+    ]
+    fig1, axs1 = plt.subplots(2,1)
+    fig2, axs2 = plt.subplots(2,1)
+    for i, (dir, title) in enumerate(zip(directories, titles)):
+        for label, color, file in zip(labels, colors, files):
+            with open(dir+file) as f:
+                lines = f.readlines()
+                t = np.linspace(0, 50, len(lines))
+                r = np.array([list(map(float, line.strip().split(","))) for line in lines])
+                axs1[i].plot(t, r[:,0], label=label, color=color)
+                axs2[i].plot(t, r[:,2], label=label, color=color)
+        
+            axs1[i].set(xlabel=r"t $(\mu s)$", ylabel = r"z $(\mu m)$")
+        
+        axs1[i].legend()
+        axs1[i].set_title(title)
+
+    # plt.show()
+    fig1.savefig("../latex/images/phase_space_2_particles_x.pdf")
+    fig2.savefig("../latex/images/phase_space_2_particles_z.pdf")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/src/scripts/plot_relative_error.py b/src/scripts/plot_relative_error.py
new file mode 100644
index 0000000..54214c8
--- /dev/null
+++ b/src/scripts/plot_relative_error.py
@@ -0,0 +1,50 @@
+import matplotlib.pyplot as plt
+import numpy as np
+
+def main():
+    directories = {
+        "output/relative_error/RK4/",
+        "output/relative_error/euler/",
+    }
+    files = [
+        "4000_steps.txt",
+        "8000_steps.txt",
+        "16000_steps.txt",
+        "32000_steps.txt",
+    ]
+    labels = [
+        r"4000 steps",
+        r"8000 steps",
+        r"16000 steps",
+        r"32000 steps",
+    ]
+    titles = [
+        "Relative error for the RK4 method",
+        "Relative error for the forward Euler method"
+    ]
+    fig1, axs1 = plt.subplots(2,1)
+    for i, (dir, title) in enumerate(zip(directories, titles)):
+        max_err = []
+        for label, file in zip(labels, files):
+            with open(dir+file) as f:
+                lines = f.readlines()
+                t = np.linspace(0, 50, len(lines))
+                r = np.array([float(line.strip()) for line in lines])
+                max_err.append(max(r))
+                axs1[i].plot(t, r, label=label)
+        
+            axs1[i].set(xlabel=r"t $(\mu s)$", ylabel = r"relative_error $(\mu m)$")
+
+        
+        axs1[i].legend()
+        axs1[i].set_title(title)
+
+        conv_rate = 1/3 * sum([np.log10(max_err[i+1]/max_err[i])/np.log10(.5) for i in range(3)])
+        print(conv_rate)
+
+    plt.show()
+    # fig1.savefig("../latex/images/phase_space_2_particles_x.pdf")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/src/scripts/plot_single_particle.py b/src/scripts/plot_single_particle.py
index 2874030..f4bdc6a 100644
--- a/src/scripts/plot_single_particle.py
+++ b/src/scripts/plot_single_particle.py
@@ -22,7 +22,8 @@ def main():
     plt.ylabel(r"z $(\mu m)$")
     plt.title(r"Movement of a single particle in the x direction")
     plt.legend()
-    plt.savefig("../latex/images/single_particle.pdf")
+    # plt.savefig("../latex/images/single_particle.pdf")
+    plt.show()
 
 
 if __name__ == "__main__":

From d8059a92e1788c62dfe79fedffc50aaacf0e2f82 Mon Sep 17 00:00:00 2001
From: Cory <cory@balaton.dev>
Date: Wed, 18 Oct 2023 13:36:19 +0200
Subject: [PATCH 25/26] Delete file

---
 latex/main.pdf | Bin 73209 -> 0 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 latex/main.pdf

diff --git a/latex/main.pdf b/latex/main.pdf
deleted file mode 100644
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From e636bf17a21f29724abd0d4608bca244bb55f9bd Mon Sep 17 00:00:00 2001
From: Cory <cory@balaton.dev>
Date: Wed, 18 Oct 2023 14:51:01 +0200
Subject: [PATCH 26/26] Update latex

---
 latex/main.pdf             | Bin 293751 -> 294830 bytes
 latex/main.tex             |   3 ++
 latex/sections/methods.tex |  60 ++----------------------------------
 latex/sections/theory.tex  |  61 +++++++++++++++++++++++++++++++++++++
 4 files changed, 67 insertions(+), 57 deletions(-)
 create mode 100644 latex/sections/theory.tex

diff --git a/latex/main.pdf b/latex/main.pdf
index c6f27dbf76fc2dc1c6f6e9f87a5165967814ea6d..1ce8a25c2e5fb4cdc543a8d3b8c8816679d5d303 100644
GIT binary patch
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diff --git a/latex/main.tex b/latex/main.tex
index 4bd63f2..f9c63f7 100644
--- a/latex/main.tex
+++ b/latex/main.tex
@@ -63,6 +63,9 @@
 % Introduction
 \subfile{sections/introduction}
 
+% Theory
+\subfile{sections/theory}
+
 % Methods
 \subfile{sections/methods}
 
diff --git a/latex/sections/methods.tex b/latex/sections/methods.tex
index 42348f6..125bd37 100644
--- a/latex/sections/methods.tex
+++ b/latex/sections/methods.tex
@@ -3,63 +3,6 @@
 
 \begin{document}
 \section{Methods}
-% problem 1
-When we study the Penning traps effect on a particle with a charge $q$, we need to consider the forces acting on the particle. The sum of all forces acting on the particle, is given by the Lorentz force \eqref{eq:lorentz_force}.
-\begin{equation}\label{eq:lorentz_force}
-    \mathbf{F} = q \mathbf{E} + q \mathbf{v} \times \mathbf{B},
-\end{equation}
-We can use Newton's second law \eqref{eq:newton_second} to determine this sum by 
-\begin{align*}
-    \ddot{\mathbf{r}} &= \frac{1}{m} \sum_{i} \mathbf{F}_{i} \\
-    &= \frac{1}{m} (q \mathbf{E} + q \mathbf{v} \times \mathbf{B}) \\
-    &= \frac{q}{m} \big(\frac{V_{0}}{d^{2}} (x, y, -2z) + (B_{0}\dot{y}, -B_{0}\dot{x}, 0) \big),
-\end{align*}
-where the complete derivation can be found in \ref{sec:appendix_b}. We can now write the particle's position as
-\begin{align}
-    \label{eq:motion_x}
-    \ddot{x} - \omega_{0} \dot{y} - \frac{1}{2} \omega_{z}^{2} x &= 0, \\
-    \label{eq:motion_y}
-    \ddot{y} + \omega_{0} \dot{x} - \frac{1}{2} \omega_{z}^{2} y &= 0, \\
-    \label{eq:motion_z}
-    \ddot{z} + \omega_{z}^{2} z &= 0,
-\end{align}
-% define w_0 og w_z i appendix?
-In addition, we can find the general solution for eq. \eqref{eq:motion_z}, when we consider the characteristic equation of a second order differential equation \cite{lindstrom:2016:ch10:5}. 
-\begin{align*}
-    r^{2} + \omega_{z}^{2} &= 0 \\
-    r &= \pm \sqrt{- \omega_{z}^{2}} = \mp i \omega_{z},
-\end{align*}
-two complex roots which gives us solutions in the form of
-\begin{equation}\label{eq:all_diff_sol}
-    z = c_{1} e^{i \omega_{z} t} + c_{2} e^{-i \omega_{z} t},
-\end{equation}
-For a complex number $z = a + ib$, we can define $e^{z} \equiv e^{a} (\cos{b} + i \sin{b})$ \cite{lindstrom:2016:ch3}. We can rewrite \eqref{eq:all_diff_sol} as
-\begin{align*}
-    c_{1} e^{i \omega_{z} t} + c_{2} e^{-i \omega_{z} t} &= c_{1} (\cos{\omega_{z} t} + i \sin{\omega_{z} t}) + c_{2} (\cos{\omega_{z} t} - i \sin{\omega_{z} t} \\
-    &= E \cos{\omega_{z} t} + i F \sin{\omega_{z} t}
-\end{align*}
-%
-Since \eqref{eq:motion_x} and \eqref{eq:motion_y} are coupled, we want to rewrite it as a single differential equation. We can obtain this by introducing $f(t) = x(t) + iy(t)$,
-\begin{align*}
-    (\ddot{x} - \omega_{0} \dot{y} - \frac{1}{2} \omega_{z}^{2} x) + i (\ddot{y} + \omega_{0} \dot{x} - \frac{1}{2} \omega_{z}^{2} y) &= 0 \\
-    \ddot{x} - \omega_{0} \dot{y} - \frac{1}{2} \omega_{z}^{2} x + i\ddot{y} + i\omega_{0} \dot{x} - i \frac{1}{2} \omega_{z}^{2} y &= 0 \\
-    \ddot{x} + i\ddot{y} + i\omega_{0} \dot{x} - \omega_{0} \dot{y} - \frac{1}{2} \omega_{z}^{2} x - i \frac{1}{2} \omega_{z}^{2} y &= 0 \\ 
-    \ddot{x} + i\ddot{y} + i\omega_{0} (\dot{x} + i \dot{y}) - \frac{1}{2} \omega_{z}^{2} x - i \frac{1}{2} \omega_{z}^{2} y &= 0 \text{where $i \omega_{0} \dot{x} + (-1) \omega_{0} \dot{y} = i \omega_{0} \dot{x} + i^{2} \omega_{0} \dot{y}$} \\
-    \ddot{f} + i \omega_{0} \dot{f} - \frac{1}{2} \omega_{z}^{2} f &= 0
-\end{align*}
-
- 
-Physical properties given by newtons second law \eqref{eq:newton_second}
-\begin{equation}\label{eq:general_solution}
-    f(t) = A_{+}e^{-i(\omega_{+} t + \phi_{+})} + A_{-}e^{-i(\omega_{-} t + \phi_{-})}
-\end{equation}
-The particle moves and its position can be determined using newton. where the electric field
-
-\subsection*{Algorithm}
-
-
-\subsection*{Tools}
-We used matplotlib
 
 \subsection{Units and constants}
 
@@ -286,5 +229,8 @@ and would reduce the required amount of loops down to 4.
 
 \subsection{Relative error and error convergance rate}
 
+\subsection{Tools}
+We used matplotlib
+
 %\biblio
 \end{document}
diff --git a/latex/sections/theory.tex b/latex/sections/theory.tex
new file mode 100644
index 0000000..e8d43c8
--- /dev/null
+++ b/latex/sections/theory.tex
@@ -0,0 +1,61 @@
+\documentclass[../main.tex]{subfiles}
+\graphicspath{{\subfix{../images/}}}
+
+\begin{document}
+\section{Theory}
+% problem 1
+When we study the Penning traps effect on a particle with a charge $q$, we need to consider the forces acting on the particle. The sum of all forces acting on the particle, is given by the Lorentz force \eqref{eq:lorentz_force}.
+\begin{equation}\label{eq:lorentz_force}
+    \mathbf{F} = q \mathbf{E} + q \mathbf{v} \times \mathbf{B},
+\end{equation}
+We can use Newton's second law \eqref{eq:newton_second} to determine this sum by 
+\begin{align*}
+    \ddot{\mathbf{r}} &= \frac{1}{m} \sum_{i} \mathbf{F}_{i} \\
+    &= \frac{1}{m} (q \mathbf{E} + q \mathbf{v} \times \mathbf{B}) \\
+    &= \frac{q}{m} \big(\frac{V_{0}}{d^{2}} (x, y, -2z) + (B_{0}\dot{y}, -B_{0}\dot{x}, 0) \big),
+\end{align*}
+where the complete derivation can be found in \ref{sec:appendix_b}. We can now write the particle's position as
+\begin{align}
+    \label{eq:motion_x}
+    \ddot{x} - \omega_{0} \dot{y} - \frac{1}{2} \omega_{z}^{2} x &= 0, \\
+    \label{eq:motion_y}
+    \ddot{y} + \omega_{0} \dot{x} - \frac{1}{2} \omega_{z}^{2} y &= 0, \\
+    \label{eq:motion_z}
+    \ddot{z} + \omega_{z}^{2} z &= 0,
+\end{align}
+% define w_0 og w_z i appendix?
+In addition, we can find the general solution for eq. \eqref{eq:motion_z}, when we consider the characteristic equation of a second order differential equation \cite{lindstrom:2016:ch10:5}. 
+\begin{align*}
+    r^{2} + \omega_{z}^{2} &= 0 \\
+    r &= \pm \sqrt{- \omega_{z}^{2}} = \mp i \omega_{z},
+\end{align*}
+two complex roots which gives us solutions in the form of
+\begin{equation}\label{eq:all_diff_sol}
+    z = c_{1} e^{i \omega_{z} t} + c_{2} e^{-i \omega_{z} t},
+\end{equation}
+For a complex number $z = a + ib$, we can define $e^{z} \equiv e^{a} (\cos{b} + i \sin{b})$ \cite{lindstrom:2016:ch3}. We can rewrite \eqref{eq:all_diff_sol} as
+\begin{align*}
+    c_{1} e^{i \omega_{z} t} + c_{2} e^{-i \omega_{z} t} &= c_{1} (\cos{\omega_{z} t} + i \sin{\omega_{z} t}) + c_{2} (\cos{\omega_{z} t} - i \sin{\omega_{z} t} \\
+    &= E \cos{\omega_{z} t} + i F \sin{\omega_{z} t}
+\end{align*}
+%
+Since \eqref{eq:motion_x} and \eqref{eq:motion_y} are coupled, we want to rewrite it as a single differential equation. We can obtain this by introducing $f(t) = x(t) + iy(t)$,
+\begin{align*}
+    (\ddot{x} - \omega_{0} \dot{y} - \frac{1}{2} \omega_{z}^{2} x) + i (\ddot{y} + \omega_{0} \dot{x} - \frac{1}{2} \omega_{z}^{2} y) &= 0 \\
+    \ddot{x} - \omega_{0} \dot{y} - \frac{1}{2} \omega_{z}^{2} x + i\ddot{y} + i\omega_{0} \dot{x} - i \frac{1}{2} \omega_{z}^{2} y &= 0 \\
+    \ddot{x} + i\ddot{y} + i\omega_{0} \dot{x} - \omega_{0} \dot{y} - \frac{1}{2} \omega_{z}^{2} x - i \frac{1}{2} \omega_{z}^{2} y &= 0 \\ 
+    \ddot{x} + i\ddot{y} + i\omega_{0} (\dot{x} + i \dot{y}) - \frac{1}{2} \omega_{z}^{2} x - i \frac{1}{2} \omega_{z}^{2} y &= 0 \text{where $i \omega_{0} \dot{x} + (-1) \omega_{0} \dot{y} = i \omega_{0} \dot{x} + i^{2} \omega_{0} \dot{y}$} \\
+    \ddot{f} + i \omega_{0} \dot{f} - \frac{1}{2} \omega_{z}^{2} f &= 0
+\end{align*}
+
+ 
+Physical properties given by newtons second law \eqref{eq:newton_second}
+\begin{equation}\label{eq:general_solution}
+    f(t) = A_{+}e^{-i(\omega_{+} t + \phi_{+})} + A_{-}e^{-i(\omega_{-} t + \phi_{-})}
+\end{equation}
+The particle moves and its position can be determined using newton. where the electric field
+
+
+
+%\biblio
+\end{document}