Change front ticks to back ticks.

Janitaws/plot and latex

README.md

@@ -10,29 +10,29 @@ Make sure that you are inside the **src** directory before compiling the code.
 
 Now you can execute the command shown under to compile:
 
-´´´
+```
     make
-´´´
+```
 
 This will create object files and link them together into 2 executable files.
 These files are called **main** and **analyticPlot**. 
 To run them, you can simply use the commands below:
 
-´´´
+```
     ./main
-´´´
+```
 
-´´´
+```
     ./analyticPlot
-´´´
+```
 
 ## How to generate plots
 
 For generating the plots, there are 4 Python scripts. 
 You can run each one of them by using this command:
 
-´´´
+```
     python <PythonFile>
-´´´
+```
 
 The plots will be saved inside **latex/images**.

latex/problems/problem10.tex

@@ -1,3 +1,8 @@
 \section*{Problem 10}
 
 % Time and show result, and link to relevant files
+\begin{figure}[H]
+    \centering 
+    \includegraphics[width=0.7\linewidth]{images/problem10.pdf}
+    \caption{Timing of general algorithm vs. special for step sizes $n_{steps}$}
+\end{figure}

latex/problems/problem2.tex

@@ -6,6 +6,8 @@ Point generator code: https://github.uio.no/FYS3150-G2-203/Project-1/blob/main/s
 
 Plotting code: https://github.uio.no/FYS3150-G2-2023/Project-1/blob/main/src/analyticPlot.py
 
-Here is the plot of the analytical solution for $u(x)$.
+\begin{figure}[H]
-
+    \centering
-\includegraphics[scale=.5]{analytical_solution.pdf}
+    \includegraphics[width=0.8\linewidth]{images/analytical_solution.pdf}
+    \caption{Plot of the analytical solution $u(x)$.}
+\end{figure}

latex/problems/problem7.tex

@@ -2,8 +2,13 @@
 
 \subsection*{a)}
 % Link to relevant files on gh and possibly add some comments
-The code can be found at https://github.uio.no/FYS3150-G2-2023/Project-1/blob/coryab/final-run/src/generalAlgorithm.cpp
+The code can be found at https://github.uio.no/FYS3150-G2-2023/Project-1/blob/main/src/generalAlgorithm.cpp
 
 \subsection*{b)}
+Increasing the number of steps results in an approximation close to the exact solution.
+\begin{figure}[H]
+    \centering 
+    \includegraphics[width=0.8\linewidth]{images/problem7.pdf}
+    \caption{Plot showing the numeric solution of $u_{approx}$ for $n_{steps}$ and the exact solution $u_{exact}$.}
+\end{figure}
 
-\includegraphics{problem7}

latex/problems/problem8.tex

@@ -1,3 +1,27 @@
 \section*{Problem 8}
 
 %link to relvant files and show plots
+\subsection*{a)}
+Increasing number of steps result in a decrease of absolute error.
+\begin{figure}[H]
+    \centering 
+    \includegraphics[width=0.8\linewidth]{images/problem8_a.pdf}
+    \caption{Absolute error for different step sizes $n_{steps}$.}
+\end{figure}
+
+\subsection*{b)}
+Increasing number of steps also result in a decrease of absolute error.
+\begin{figure}[H]
+    \centering 
+    \includegraphics[width=0.8\linewidth]{images/problem8_b.pdf}
+    \caption{Relative error for different step sizes $n_{steps}$.}
+\end{figure}
+
+\subsection*{c)}
+Increasing number of steps result in a decrease of maximum relative error, up to a certain number of steps. At $n_{steps} \approx 10^{5}$ the maximumrelative error increase. 
+This can be related to loss of numerical precicion when step size is small.
+\begin{figure}[H]
+    \centering 
+    \includegraphics[width=0.7\linewidth]{images/problem8_c.pdf}
+    \caption{Maximum relative error for each step sizes $n_{steps}$.}
+\end{figure}

src/analyticPlot.cpp

@@ -7,7 +7,7 @@
 #include <iomanip>
 
 #define RANGE 1000
-#define FILENAME "analytical_solution.txt"
+#define FILENAME "output/analytical_solution.txt"
 
 double u(double x);
 void generate_range(std::vector<double> &vec, double start, double stop, int n);

src/funcs.hpp

@@ -4,7 +4,9 @@
 #include <armadillo>
 #include <cmath>
 
-#define PRECISION 20
+#define PRECISION 8
+
+#define N_STEPS_EXP 7
 
 double f(double x);
 

src/generalAlgorithm.cpp

@@ -33,7 +33,7 @@ void general_algorithm_main()
     int steps;
     double step_size;
 
-    for (int i = 0; i < 6; i++) {
+    for (int i = 0; i < N_STEPS_EXP; i++) {
         steps = std::pow(10, i+1);
         step_size = 1./(double) steps;
 
@@ -58,7 +58,7 @@ void general_algorithm_error()
     int steps;
     double step_size, abs_err, rel_err, u_i, v_i;
 
-    for (int i=0; i < 7; i++) {
+    for (int i=0; i < N_STEPS_EXP; i++) {
         steps = std::pow(10, i+1);
         step_size = 1./(double) steps;
 

src/main.cpp

@@ -20,7 +20,7 @@ void timing() {
     ofile.open("output/timing.txt");
 
     // Timing
-    for (int i=1; i <= 6; i++) {
+    for (int i=1; i < N_STEPS_EXP; i++) {
         n_steps = std::pow(10, i);
         clock_t g_1, g_2, s_1, s_2;
         double g_res = 0, s_res = 0;

src/plot_analytic_solution.py

@@ -6,7 +6,7 @@ def main():
     x = []
     v = []
 
-    with open('analytical_solution.txt') as f:
+    with open('output/analytical_solution.txt') as f:
         for line in f:
             a, b = line.strip().split()
             x.append(float(a))

src/plot_general_alg.py

@@ -4,7 +4,7 @@ import numpy as np
 analytical_func = lambda x: 1 - (1 - np.exp(-10))*x - np.exp(-10*x)
 
 def main():
-    for i in range(6):
+    for i in range(7):
         x = []
         y = []
         x.append(0.)
@@ -19,10 +19,10 @@ def main():
         x.append(1.)
         y.append(0.)
 
-        plt.plot(x, y, label=f"n_steps={10**(i+1)}")
+        plt.plot(x, y, label=f"n$_{{steps}} = 10^{i+1}$")
 
     x = np.linspace(0, 1, 1001)
-    plt.plot(x, analytical_func(x), label="analytical plot")
+    plt.plot(x, analytical_func(x), label=f"u$_{{exact}}$")
     plt.legend()
     plt.savefig("../latex/images/problem7.pdf")
 

src/plot_general_alg_error.py

@@ -1,8 +1,10 @@
 import matplotlib.pyplot as plt
 
+# plt.rc('text', usetex=True)
+# plt.rc('font', family='serif')
+
 def main():
-    fig, axs = plt.subplots(1)
+    for i in range(7):
-    for i in range(6):
         x = []
         abs_err = []
         rel_err = []
@@ -14,16 +16,25 @@ def main():
                 abs_err.append(float(abs_err_i))
                 rel_err.append(float(rel_err_i))
 
-        axs[0].plot(x, abs_err, label=f"abs_err {10**(i+1)} steps")
+        plt.figure(1)
-        axs[1].plot(x, rel_err, label=f"rel_err {10**(i+1)} steps")
+        plt.plot(x, abs_err, label=f"n$_{{steps}} = 10^{i+1}$")
-        print(max(rel_err))
+        plt.figure(2)
-        axs[2].plot(i+1, max(rel_err), marker="o", markersize=10)
+        plt.plot(x, rel_err, label=f"n$_{{steps}} = 10^{i+1}$")
 
-    axs[0].legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)
+        plt.figure(3)
-    axs[1].legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)
+        plt.plot(i+1, max(rel_err), marker="o", markersize=10)
-    plt.savefig("../latex/images/problem8.pdf", bbox_inches="tight")
-    fig.2
     
+    plt.figure(1)
+    plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)
+    plt.figure(2)
+    plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)
+    
+    plt.figure(1)
+    plt.savefig("../latex/images/problem8_a.pdf", bbox_inches="tight")
+    plt.figure(2)
+    plt.savefig("../latex/images/problem8_b.pdf", bbox_inches="tight")
+    plt.figure(3)
+    plt.savefig("../latex/images/problem8_c.pdf", bbox_inches="tight")
 
 if __name__ == "__main__":
     main()

src/specialAlgorithm.cpp

@@ -33,7 +33,7 @@ void special_algorithm_main()
     int steps;
     double sub_sig, main_sig, sup_sig, step_size;
 
-    for (int i = 0; i < 6; i++) {
+    for (int i = 0; i < N_STEPS_EXP; i++) {
         steps = std::pow(10, i+1);
         step_size = 1./(double) steps;
         build_g_vec(steps, g_vec);

src/timing.py

@@ -1,5 +1,4 @@
 import matplotlib.pyplot as plt
-import numpy as np
 
 def main():
     x = []
@@ -13,8 +12,8 @@ def main():
             gen_alg.append(float(gen_i))
             spec_alg.append(float(spec_i))
 
-        plt.plot(x, gen_alg, label=f"general algorithm")
+        plt.plot(x, gen_alg, label=f"General algorithm")
-        plt.plot(x, spec_alg, label=f"general algorithm")
+        plt.plot(x, spec_alg, label=f"Special algorithm")
 
     plt.legend()
     plt.savefig("../latex/images/problem10.pdf")