From f85e41460b7a855879e72795b6f407973ce1e9fd Mon Sep 17 00:00:00 2001 From: Janita Willumsen Date: Fri, 22 Sep 2023 08:38:30 +0200 Subject: [PATCH 1/9] Start implementing plot functionality --- src/plot.py | 45 +++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 45 insertions(+) create mode 100644 src/plot.py diff --git a/src/plot.py b/src/plot.py new file mode 100644 index 0000000..c217079 --- /dev/null +++ b/src/plot.py @@ -0,0 +1,45 @@ +import numpy as np +import matplotlib.pyplot as plt +import pandas as pd +import seaborn as sns + +sns.set_theme() +sns.dark_palette("seagreen") + +"""Write to file (for dense matrix): +Line give size of matrix (column give number of transformations until convergence) + N 1 (2 3 4 5) + 3 + 6 + 9 + 12 + 15 +""" + +def read_data(filename: str) -> tuple: + N = [] + T = [] + with open(filename, "r") as f: + lines = f.readlines() + for line in lines: + n_i, t_i = line.strip().split(",") + N.append(float(n_i)) + T.append(float(t_i)) + return (N, T) + + + +def plot_similarity_transformations(N: np.ndarray, T: np.ndarray) -> None: + fig, ax = plt.subplots() + ax.plot(N, T, label='Transformations') + ax.set_xlabel('N') + ax.set_ylabel('Similarity transformations') + ax.set_xlim(xmin=N[0], xmax=N[-1]) + fig.savefig("similarity_transformation.pdf") + +def plot_eigenvectors(): + pass + + +if __name__ == '__main__': + pass \ No newline at end of file From 24f9f88af51e75d1d934ea8bfa164bb4d6bf4f36 Mon Sep 17 00:00:00 2001 From: Janita Willumsen Date: Sat, 23 Sep 2023 15:13:24 +0200 Subject: [PATCH 2/9] Finish problem 5 and 6 --- src/main.cpp | 127 +++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 127 insertions(+) diff --git a/src/main.cpp b/src/main.cpp index e69de29..3a55c90 100644 --- a/src/main.cpp +++ b/src/main.cpp @@ -0,0 +1,127 @@ +/** @file main.cpp + * @brief Main program for Project 2 + * + * The program performs the Jacobi rotation method. + * The size of the matrix, and number of transformations + * performed are written to file. + * Eigenvector correstonding to the 3 smallest eigenvalues + * for matrices of size 6x6 and 100x100 are written to file. + * + * @author Cory Alexander Balaton (coryab) + * @author Janita Ovidie Sandtrøen Willumsen (janitaws) + * @bug No known bugs + */ +#include +#include +#include + +#include "utils.hpp" +#include "matrix.hpp" +#include "jacobi.hpp" + + +void write_transformation(int N, bool dense) +{ + std::ofstream ofile; + + ofile.open("../latex/output/transform_dense.csv"); + ofile << "N,T" << std::endl; + + // Increase size of matrix, start at 5 to avoid logic_error of N=4 + for (int i = 5; i <= N; i++) { + arma::mat A = arma::mat(i, i).randn(); + A = arma::symmatu(A); + arma::vec eigval; + arma::mat eigvec; + + int iters; + bool converged; + + jacobi_eigensolver(A, 10e-14, eigval, eigvec, 100000, iters, converged); + + // Write size, number of iterations, and converge status to file + ofile << i << "," << iters << std::endl; + } + ofile.close(); +} + + +void write_transformation(int N) +{ + std::ofstream ofile; + + double h; + double a, d; + + ofile.open("../latex/output/transform_tridiag.csv"); + ofile << "N,T" << std::endl; + + // Increase size of matrix, start at 5 to avoid logic_error of N=4 + for (int i = 5; i <= N; i++) { + h = 1. / (double) (i+1); + a = -1. / (h*h), d = 2. / (h*h); + + arma::mat A = create_symmetric_tridiagonal(i, a, d); + arma::vec eigval; + arma::mat eigvec; + + int iters; + bool converged; + + jacobi_eigensolver(A, 10e-14, eigval, eigvec, 100000, iters, converged); + + // Write size, number of iterations, and converge status to file + ofile << i << "," << iters << std::endl; + } + ofile.close(); +} + + +void write_eigenvec(int N) +{ + double h = 1. / (double) (N+1); + double a = -1. / (h*h); + double d = 2. / (h*h); + double x = 0.; + + arma::mat A = create_symmetric_tridiagonal(N, a, d); + arma::vec eigval; + arma::mat eigvec; + + int iters; + bool converged; + + jacobi_eigensolver(A, 10e-14, eigval, eigvec, 100000, iters, converged); + + std::ofstream ofile; + ofile.open("../latex/output/eigenvector_" + std::to_string(N) + ".csv"); + ofile << "x,Vector 1,Vector 2,Vector 3" << std::endl; + + ofile << scientific_format(0., 16) << "," + << scientific_format(0., 16) << "," + << scientific_format(0., 16) << "," + << scientific_format(0., 16) << std::endl; + + for (int i = 0; i < N; i++) { + x += h; + ofile << scientific_format(x, 16)<< "," + << scientific_format(eigvec(i,0), 16) << "," + << scientific_format(eigvec(i,1), 16) << "," + << scientific_format(eigvec(i,2), 16) << std::endl; + } + ofile << scientific_format(1., 16) << "," + << scientific_format(0., 16) << "," + << scientific_format(0., 16) << "," + << scientific_format(0., 16) << std::endl; + ofile.close(); +} + + +int main() +{ + write_transformation(100); + write_transformation(100, true); + write_eigenvec(6); + write_eigenvec(100); + return 0; +} From 2b103b9e3a564f2462aaf055703e8489314861eb Mon Sep 17 00:00:00 2001 From: Janita Willumsen Date: Sat, 23 Sep 2023 15:14:15 +0200 Subject: [PATCH 3/9] Add program for plotting problem 5 and 6 --- src/plot.py | 66 ++++++++++++++++++++++++++++++----------------------- 1 file changed, 37 insertions(+), 29 deletions(-) diff --git a/src/plot.py b/src/plot.py index c217079..511ba8c 100644 --- a/src/plot.py +++ b/src/plot.py @@ -4,42 +4,50 @@ import pandas as pd import seaborn as sns sns.set_theme() -sns.dark_palette("seagreen") - -"""Write to file (for dense matrix): -Line give size of matrix (column give number of transformations until convergence) - N 1 (2 3 4 5) - 3 - 6 - 9 - 12 - 15 -""" - -def read_data(filename: str) -> tuple: - N = [] - T = [] - with open(filename, "r") as f: - lines = f.readlines() - for line in lines: - n_i, t_i = line.strip().split(",") - N.append(float(n_i)) - T.append(float(t_i)) - return (N, T) +plt.rcParams['text.usetex'] = True +def plot_transformations(save: bool=False) -> None: + # Load data + tridiag = pd.read_csv("../latex/output/transform_tridiag.csv", header=0) + dense = pd.read_csv("../latex/output/transform_dense.csv", header=0) -def plot_similarity_transformations(N: np.ndarray, T: np.ndarray) -> None: fig, ax = plt.subplots() - ax.plot(N, T, label='Transformations') + ax.loglog(dense['N'], dense['T'], '--', label='Dense') + ax.loglog(tridiag['N'], tridiag['T'], label='Tridiagonal') ax.set_xlabel('N') ax.set_ylabel('Similarity transformations') - ax.set_xlim(xmin=N[0], xmax=N[-1]) - fig.savefig("similarity_transformation.pdf") + ax.legend() -def plot_eigenvectors(): - pass + # Save to file + if save is True: + fig.savefig("../latex/images/transform.pdf") + + + +def plot_eigenvectors(N: int, save: bool=False) -> None: + # Load data based on matrix size + name = "eigenvector_" + str(N) + path = "../latex/output/" + name + ".csv" + eigvec = pd.read_csv(path, header=0) + + fig, ax = plt.subplots() + ax.plot(eigvec['x'], eigvec['Vector 1'], label='Vector 1') + ax.plot(eigvec['x'], eigvec['Vector 2'], label='Vector 2') + ax.plot(eigvec['x'], eigvec['Vector 3'], label='Vector 3') + ax.set_xlabel(r'Element $\hat{x}_{i}$') + ax.set_ylabel(r'Value of element $v_{i}$') + ax.legend() + + # Save to file + if save is True: + fig.savefig("../latex/images/" + name + ".pdf") + + if __name__ == '__main__': - pass \ No newline at end of file + plot_transformations(True) + plot_eigenvectors(6, True) + plot_eigenvectors(100, True) + # plt.show() \ No newline at end of file From e979c3955ea80b7a1b62c14794e8de27fd12d983 Mon Sep 17 00:00:00 2001 From: Janita Willumsen Date: Sat, 23 Sep 2023 15:14:57 +0200 Subject: [PATCH 4/9] Add comment on how main is linked --- src/Makefile | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/src/Makefile b/src/Makefile index 443b225..b5e052f 100644 --- a/src/Makefile +++ b/src/Makefile @@ -8,6 +8,9 @@ DEBUG=-DDBG .PHONY: clean +# main: main.o utils.o matrix.o jacobi.o +# $(CC) $^ -o $@ $(CCFLAGS) + test_suite: test_suite.o matrix.o jacobi.o 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used for plotting --- latex/output/eigenvector_100.csv | 103 +++++++++++++++++++++++++++++ latex/output/eigenvector_6.csv | 9 +++ latex/output/transform_dense.csv | 97 +++++++++++++++++++++++++++ latex/output/transform_tridiag.csv | 97 +++++++++++++++++++++++++++ 4 files changed, 306 insertions(+) create mode 100644 latex/output/eigenvector_100.csv create mode 100644 latex/output/eigenvector_6.csv create mode 100644 latex/output/transform_dense.csv create mode 100644 latex/output/transform_tridiag.csv diff --git a/latex/output/eigenvector_100.csv b/latex/output/eigenvector_100.csv new file mode 100644 index 0000000..91bd971 --- /dev/null +++ b/latex/output/eigenvector_100.csv @@ -0,0 +1,103 @@ +x,Vector 1,Vector 2,Vector 3 +0.0000000000e+00,0.0000000000e+00,0.0000000000e+00,0.0000000000e+00 +9.9009900990e-03,4.3763580486e-03,-8.7484808732e-03,-1.3112140868e-02 +1.9801980198e-02,8.7484805374e-03,-1.7463118426e-02,-2.6110190173e-02 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+1.0000000000e+00,0.0000000000e+00,0.0000000000e+00,0.0000000000e+00 diff --git a/latex/output/eigenvector_6.csv b/latex/output/eigenvector_6.csv new file mode 100644 index 0000000..17c5bc3 --- /dev/null +++ b/latex/output/eigenvector_6.csv @@ -0,0 +1,9 @@ +x,Vector 1,Vector 2,Vector 3 +0.0000000000e+00,0.0000000000e+00,0.0000000000e+00,0.0000000000e+00 +1.4285714286e-01,2.3192061397e-01,-4.1790650593e-01,-5.2112088916e-01 +2.8571428571e-01,4.1790650598e-01,-5.2112088916e-01,-2.3192061388e-01 +4.2857142857e-01,5.2112088920e-01,-2.3192061385e-01,4.1790650595e-01 +5.7142857143e-01,5.2112088915e-01,2.3192061400e-01,4.1790650592e-01 +7.1428571429e-01,4.1790650588e-01,5.2112088921e-01,-2.3192061394e-01 +8.5714285714e-01,2.3192061389e-01,4.1790650591e-01,-5.2112088921e-01 +1.0000000000e+00,0.0000000000e+00,0.0000000000e+00,0.0000000000e+00 diff --git a/latex/output/transform_dense.csv b/latex/output/transform_dense.csv new file mode 100644 index 0000000..6258a6c --- /dev/null +++ b/latex/output/transform_dense.csv @@ -0,0 +1,97 @@ +N,T +5,32 +6,53 +7,73 +8,98 +9,130 +10,157 +11,201 +12,254 +13,293 +14,349 +15,394 +16,458 +17,518 +18,587 +19,649 +20,740 +21,827 +22,911 +23,999 +24,1073 +25,1187 +26,1299 +27,1410 +28,1502 +29,1604 +30,1725 +31,1856 +32,1979 +33,2089 +34,2227 +35,2383 +36,2536 +37,2644 +38,2810 +39,3000 +40,3138 +41,3299 +42,3445 +43,3638 +44,3828 +45,4015 +46,4143 +47,4348 +48,4611 +49,4773 +50,4994 +51,5163 +52,5363 +53,5586 +54,5784 +55,6075 +56,6275 +57,6550 +58,6711 +59,6957 +60,7225 +61,7483 +62,7782 +63,7952 +64,8265 +65,8531 +66,8764 +67,9060 +68,9331 +69,9686 +70,9913 +71,10098 +72,10417 +73,10795 +74,11108 +75,11342 +76,11703 +77,12104 +78,12356 +79,12623 +80,13066 +81,13513 +82,13706 +83,13998 +84,14333 +85,14694 +86,15160 +87,15470 +88,15845 +89,16211 +90,16551 +91,17047 +92,17237 +93,17669 +94,18055 +95,18614 +96,18838 +97,19253 +98,19868 +99,20092 +100,20517 diff --git a/latex/output/transform_tridiag.csv b/latex/output/transform_tridiag.csv new file mode 100644 index 0000000..a3530ec --- /dev/null +++ b/latex/output/transform_tridiag.csv @@ -0,0 +1,97 @@ +N,T +5,35 +6,41 +7,78 +8,104 +9,135 +10,177 +11,222 +12,238 +13,305 +14,335 +15,417 +16,460 +17,537 +18,606 +19,688 +20,756 +21,840 +22,917 +23,1017 +24,1095 +25,1207 +26,1298 +27,1420 +28,1492 +29,1629 +30,1766 +31,1869 +32,1965 +33,2132 +34,2275 +35,2403 +36,2570 +37,2670 +38,2794 +39,2962 +40,3169 +41,3284 +42,3469 +43,3619 +44,3840 +45,3977 +46,4161 +47,4406 +48,4523 +49,4710 +50,4919 +51,5207 +52,5336 +53,5582 +54,5801 +55,5997 +56,6248 +57,6465 +58,6694 +59,6911 +60,7078 +61,7355 +62,7618 +63,7880 +64,8170 +65,8407 +66,8651 +67,8899 +68,9139 +69,9478 +70,9786 +71,10059 +72,10325 +73,10608 +74,10887 +75,11223 +76,11514 +77,11794 +78,12120 +79,12420 +80,12738 +81,13111 +82,13402 +83,13772 +84,14018 +85,14393 +86,14820 +87,15096 +88,15451 +89,15866 +90,16243 +91,16688 +92,16864 +93,17359 +94,17701 +95,18027 +96,18473 +97,18810 +98,19231 +99,19573 +100,19992 From 97e6b3511218b571b69212261d1a41221446a189 Mon Sep 17 00:00:00 2001 From: Janita Willumsen Date: Sat, 23 Sep 2023 16:21:51 +0200 Subject: [PATCH 7/9] Added comments and renamed functions --- src/main.cpp | 19 +++++++++++++------ 1 file changed, 13 insertions(+), 6 deletions(-) diff --git a/src/main.cpp b/src/main.cpp index 3a55c90..1a1b1d8 100644 --- a/src/main.cpp +++ b/src/main.cpp @@ -20,7 +20,7 @@ #include "jacobi.hpp" -void write_transformation(int N, bool dense) +void write_transformation_dense(int N) { std::ofstream ofile; @@ -39,14 +39,14 @@ void write_transformation(int N, bool dense) jacobi_eigensolver(A, 10e-14, eigval, eigvec, 100000, iters, converged); - // Write size, number of iterations, and converge status to file + // Write size, and number of iterations to file ofile << i << "," << iters << std::endl; } ofile.close(); } -void write_transformation(int N) +void write_transformation_tridiag(int N) { std::ofstream ofile; @@ -54,6 +54,7 @@ void write_transformation(int N) double a, d; ofile.open("../latex/output/transform_tridiag.csv"); + // Write header line to file ofile << "N,T" << std::endl; // Increase size of matrix, start at 5 to avoid logic_error of N=4 @@ -70,7 +71,7 @@ void write_transformation(int N) jacobi_eigensolver(A, 10e-14, eigval, eigvec, 100000, iters, converged); - // Write size, number of iterations, and converge status to file + // Write size, and number of iterations to file ofile << i << "," << iters << std::endl; } ofile.close(); @@ -84,6 +85,7 @@ void write_eigenvec(int N) double d = 2. / (h*h); double x = 0.; + // Create tridiagonal matrix arma::mat A = create_symmetric_tridiagonal(N, a, d); arma::vec eigval; arma::mat eigvec; @@ -91,17 +93,21 @@ void write_eigenvec(int N) int iters; bool converged; + // Solve using Jacobi rotation method jacobi_eigensolver(A, 10e-14, eigval, eigvec, 100000, iters, converged); std::ofstream ofile; + // Create file based on matrix size, and write header line to file ofile.open("../latex/output/eigenvector_" + std::to_string(N) + ".csv"); ofile << "x,Vector 1,Vector 2,Vector 3" << std::endl; + // Add boundary value for x=0 ofile << scientific_format(0., 16) << "," << scientific_format(0., 16) << "," << scientific_format(0., 16) << "," << scientific_format(0., 16) << std::endl; + // Add x-value and element i of each eigenvector to same line for (int i = 0; i < N; i++) { x += h; ofile << scientific_format(x, 16)<< "," @@ -109,6 +115,7 @@ void write_eigenvec(int N) << scientific_format(eigvec(i,1), 16) << "," << scientific_format(eigvec(i,2), 16) << std::endl; } + // Add boundary value for x=1 ofile << scientific_format(1., 16) << "," << scientific_format(0., 16) << "," << scientific_format(0., 16) << "," @@ -119,8 +126,8 @@ void write_eigenvec(int N) int main() { - write_transformation(100); - write_transformation(100, true); + write_transformation_tridiag(100); + write_transformation_dense(100); write_eigenvec(6); write_eigenvec(100); return 0; From 3c9a84598d477f4612f0d8cfb289d885e4d892bf Mon Sep 17 00:00:00 2001 From: Janita Willumsen Date: Sat, 23 Sep 2023 16:22:56 +0200 Subject: [PATCH 8/9] Use f-strings --- src/plot.py | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) diff --git a/src/plot.py b/src/plot.py index 511ba8c..adacd80 100644 --- a/src/plot.py +++ b/src/plot.py @@ -27,8 +27,7 @@ def plot_transformations(save: bool=False) -> None: def plot_eigenvectors(N: int, save: bool=False) -> None: # Load data based on matrix size - name = "eigenvector_" + str(N) - path = "../latex/output/" + name + ".csv" + path = f"../latex/output/eigenvector_{N}.csv" eigvec = pd.read_csv(path, header=0) fig, ax = plt.subplots() @@ -41,7 +40,7 @@ def plot_eigenvectors(N: int, save: bool=False) -> None: # Save to file if save is True: - fig.savefig("../latex/images/" + name + ".pdf") + fig.savefig(f"../latex/images/eigenvector_{N}.pdf") From 97997b9f1d610dbd49eb408d8cbcf09bc9592333 Mon Sep 17 00:00:00 2001 From: Janita Willumsen Date: Sat, 23 Sep 2023 16:23:28 +0200 Subject: [PATCH 9/9] Update plots --- latex/images/eigenvector_100.pdf | Bin 249600 -> 249600 bytes latex/images/eigenvector_6.pdf | Bin 247374 -> 247374 bytes latex/images/transform.pdf | Bin 114866 -> 114866 bytes 3 files changed, 0 insertions(+), 0 deletions(-) diff --git a/latex/images/eigenvector_100.pdf b/latex/images/eigenvector_100.pdf index 2e10a06831ed9474879634f283e7664ba079eab9..23be24aef70847ff0a188b8b2c497b208bcd231a 100644 GIT binary patch delta 27 hcmZpe$KL=%EsQNpTbTc!Vl^`|Ff`iEa+>)MGXRe+3GM&@ delta 27 hcmZpe$KL=%EsQNpTbTc!Vl_1|Gd9`Ia+>)MGXRfc3H1N~ diff --git a/latex/images/eigenvector_6.pdf b/latex/images/eigenvector_6.pdf index 8c8f54c85fd6caf8ccfb71327c9e8f944660be92..912d3004c713189c1a3d7fefbae8455b879f12c2 100644 GIT binary patch delta 27 jcmX@t!+)-azoCV(g=q`3?;%z*BLhRD?Lmi_|1bjpl7tEI delta 27 jcmX@t!+)-azoCV(g=q`3?;%!G12bcj?Lmi_|1bjplDP@^ diff --git a/latex/images/transform.pdf b/latex/images/transform.pdf index 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