Update README

Janitaws/finish text document

README.md

@@ -4,6 +4,20 @@
 
 - [Project](https://anderkve.github.io/FYS3150/book/projects/project2.html)
 
+## Requirements
+
+To compile the C++ programs, you need to have these packages installed:
+
+- Armadillo
+- Openmp
+
+To run the Python scripts, you need to have these packages:
+
+- numpy
+- matplotlib
+- pandas
+- seaborn
+
 ## Compile and run C++ programs
 
 Compiling and linking is done using Make, make sure you are in the root directory. 

doc/html/main_8cpp.html

@@ -79,7 +79,10 @@ $(function() {
 <a href="#details">More...</a></p>
 <div class="textblock"><code>#include &lt;cassert&gt;</code><br />
 <code>#include &lt;cmath&gt;</code><br />
+<code>#include &lt;ctime&gt;</code><br />
 <code>#include &lt;iostream&gt;</code><br />
+<code>#include &lt;omp.h&gt;</code><br />
+<code>#include &lt;ostream&gt;</code><br />
 <code>#include &quot;<a class="el" href="utils_8hpp_source.html">utils.hpp</a>&quot;</code><br />
 <code>#include &quot;<a class="el" href="matrix_8hpp_source.html">matrix.hpp</a>&quot;</code><br />
 <code>#include &quot;<a class="el" href="jacobi_8hpp_source.html">jacobi.hpp</a>&quot;</code><br />
@@ -101,7 +104,7 @@ int&#160;</td><td class="memItemRight" valign="bottom"><b>main</b> ()</td></tr>
 </table>
 <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
 <div class="textblock"><p>Main program for Project 2. </p>
-<p>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.</p>
+<p>The program performs the Jacobi rotation method. The size of the matrix, and number of transformations performed are written to file. Eigenvector corresponding to the 3 smallest eigenvalues for matrices of size 6x6 and 100x100 are written to file.</p>
 <dl class="section author"><dt>Author</dt><dd>Cory Alexander Balaton (coryab) </dd>
 <dd>
 Janita Ovidie Sandtrøen Willumsen (janitaws) </dd></dl>

doc/html/matrix_8hpp.html

@@ -82,6 +82,7 @@ $(function() {
 <p>Function prototypes for creating tridiagonal matrices.  
 <a href="#details">More...</a></p>
 <div class="textblock"><code>#include &lt;armadillo&gt;</code><br />
+<code>#include &lt;omp.h&gt;</code><br />
 </div>
 <p><a href="matrix_8hpp_source.html">Go to the source code of this file.</a></p>
 <table class="memberdecls">

doc/html/matrix_8hpp_source.html

@@ -81,22 +81,23 @@ $(function() {
 <div class="line"><a id="l00011" name="l00011"></a><span class="lineno">   11</span><span class="preprocessor">#define __MATRIX__</span></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="preprocessor">#include &lt;armadillo&gt;</span></div>
-<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</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="l00028" name="l00028"></a><span class="lineno">   28</span>arma::mat <a class="code hl_function" href="matrix_8hpp.html#aa524feaf9f44790470df4cb99bb714af">create_tridiagonal</a>(</div>
+<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span> </div>
-<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>    <span class="keyword">const</span> arma::vec&amp; a, </div>
+<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>arma::mat <a class="code hl_function" href="matrix_8hpp.html#aa524feaf9f44790470df4cb99bb714af">create_tridiagonal</a>(</div>
-<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span>    <span class="keyword">const</span> arma::vec&amp; d, </div>
+<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span>    <span class="keyword">const</span> arma::vec&amp; a, </div>
-<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span>    <span class="keyword">const</span> arma::vec&amp; e);</div>
+<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span>    <span class="keyword">const</span> arma::vec&amp; d, </div>
-<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span> </div>
+<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>    <span class="keyword">const</span> arma::vec&amp; e);</div>
-<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>arma::mat <a class="code hl_function" href="matrix_8hpp.html#aa524feaf9f44790470df4cb99bb714af">create_tridiagonal</a>(<span class="keywordtype">int</span> n, <span class="keywordtype">double</span> a, <span class="keywordtype">double</span> d, <span class="keywordtype">double</span> e);</div>
+<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span> </div>
-<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span> </div>
+<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>arma::mat <a class="code hl_function" href="matrix_8hpp.html#aa524feaf9f44790470df4cb99bb714af">create_tridiagonal</a>(<span class="keywordtype">int</span> n, <span class="keywordtype">double</span> a, <span class="keywordtype">double</span> d, <span class="keywordtype">double</span> e);</div>
-<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>arma::mat <a class="code hl_function" href="matrix_8hpp.html#a564688c96a8e4282e995a0663545d627">create_symmetric_tridiagonal</a>(<span class="keywordtype">int</span> n, <span class="keywordtype">double</span> a, <span class="keywordtype">double</span> d);</div>
+<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span> </div>
-<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span> </div>
+<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>arma::mat <a class="code hl_function" href="matrix_8hpp.html#a564688c96a8e4282e995a0663545d627">create_symmetric_tridiagonal</a>(<span class="keywordtype">int</span> n, <span class="keywordtype">double</span> a, <span class="keywordtype">double</span> d);</div>
-<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span><span class="keywordtype">double</span> <a class="code hl_function" href="matrix_8hpp.html#af42e501cbf71bec9c77ececc22723df9">max_offdiag_symmetric</a>(arma::mat&amp; A, <span class="keywordtype">int</span>&amp; k, <span class="keywordtype">int</span>&amp; l);</div>
+<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span> </div>
-<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span> </div>
+<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span><span class="keywordtype">double</span> <a class="code hl_function" href="matrix_8hpp.html#af42e501cbf71bec9c77ececc22723df9">max_offdiag_symmetric</a>(arma::mat&amp; A, <span class="keywordtype">int</span>&amp; k, <span class="keywordtype">int</span>&amp; l);</div>
-<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span><span class="preprocessor">#endif</span></div>
+<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span> </div>
-<div class="ttc" id="amatrix_8hpp_html_a564688c96a8e4282e995a0663545d627"><div class="ttname"><a href="matrix_8hpp.html#a564688c96a8e4282e995a0663545d627">create_symmetric_tridiagonal</a></div><div class="ttdeci">arma::mat create_symmetric_tridiagonal(int n, double a, double d)</div><div class="ttdoc">Create a symmetric tridiagonal matrix.</div><div class="ttdef"><b>Definition:</b> matrix.cpp:44</div></div>
+<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span><span class="preprocessor">#endif</span></div>
+<div class="ttc" id="amatrix_8hpp_html_a564688c96a8e4282e995a0663545d627"><div class="ttname"><a href="matrix_8hpp.html#a564688c96a8e4282e995a0663545d627">create_symmetric_tridiagonal</a></div><div class="ttdeci">arma::mat create_symmetric_tridiagonal(int n, double a, double d)</div><div class="ttdoc">Create a symmetric tridiagonal matrix.</div><div class="ttdef"><b>Definition:</b> matrix.cpp:45</div></div>
 <div class="ttc" id="amatrix_8hpp_html_aa524feaf9f44790470df4cb99bb714af"><div class="ttname"><a href="matrix_8hpp.html#aa524feaf9f44790470df4cb99bb714af">create_tridiagonal</a></div><div class="ttdeci">arma::mat create_tridiagonal(const arma::vec &amp;a, const arma::vec &amp;d, const arma::vec &amp;e)</div><div class="ttdoc">Create a tridiagonal matrix.</div><div class="ttdef"><b>Definition:</b> matrix.cpp:12</div></div>
-<div class="ttc" id="amatrix_8hpp_html_af42e501cbf71bec9c77ececc22723df9"><div class="ttname"><a href="matrix_8hpp.html#af42e501cbf71bec9c77ececc22723df9">max_offdiag_symmetric</a></div><div class="ttdeci">double max_offdiag_symmetric(arma::mat &amp;A, int &amp;k, int &amp;l)</div><div class="ttdoc">Find the off-diagonal element with the largest absolute value.</div><div class="ttdef"><b>Definition:</b> matrix.cpp:49</div></div>
+<div class="ttc" id="amatrix_8hpp_html_af42e501cbf71bec9c77ececc22723df9"><div class="ttname"><a href="matrix_8hpp.html#af42e501cbf71bec9c77ececc22723df9">max_offdiag_symmetric</a></div><div class="ttdeci">double max_offdiag_symmetric(arma::mat &amp;A, int &amp;k, int &amp;l)</div><div class="ttdoc">Find the off-diagonal element with the largest absolute value.</div><div class="ttdef"><b>Definition:</b> matrix.cpp:50</div></div>
 </div><!-- fragment --></div><!-- contents -->
 <!-- start footer part -->
 <hr class="footer"/><address class="footer"><small>

include/matrix.hpp

@@ -11,6 +11,7 @@
 #define __MATRIX__
 
 #include <armadillo>
+#include <omp.h>
 
 /** @brief Create a tridiagonal matrix.
  *  

latex/output/eigenvector_6.csv

@@ -1,9 +0,0 @@
-x,Vector 1,Vector 2,Vector 3,Analytic 1,Analytic 2,Analytic 3
-0.0000000000e+00,0.0000000000e+00,0.0000000000e+00,0.0000000000e+00,0.0000000000e+00,0.0000000000e+00,0.0000000000e+00
-1.4285714286e-01,2.3192061397e-01,-4.1790650593e-01,-5.2112088916e-01,2.3192061392e-01,-4.1790650594e-01,-5.2112088917e-01
-2.8571428571e-01,4.1790650598e-01,-5.2112088916e-01,-2.3192061388e-01,4.1790650594e-01,-5.2112088917e-01,-2.3192061392e-01
-4.2857142857e-01,5.2112088920e-01,-2.3192061385e-01,4.1790650595e-01,5.2112088917e-01,-2.3192061392e-01,4.1790650594e-01
-5.7142857143e-01,5.2112088915e-01,2.3192061400e-01,4.1790650592e-01,5.2112088917e-01,2.3192061392e-01,4.1790650594e-01
-7.1428571429e-01,4.1790650588e-01,5.2112088921e-01,-2.3192061394e-01,4.1790650594e-01,5.2112088917e-01,-2.3192061392e-01
-8.5714285714e-01,2.3192061389e-01,4.1790650591e-01,-5.2112088921e-01,2.3192061392e-01,4.1790650594e-01,-5.2112088917e-01
-1.0000000000e+00,0.0000000000e+00,0.0000000000e+00,0.0000000000e+00,0.0000000000e+00,0.0000000000e+00,0.0000000000e+00

latex/output/transform_dense.csv

@@ -1,97 +1,97 @@
 N,T
 5,32
-6,53
+6,51
-7,73
+7,68
-8,98
+8,103
-9,130
+9,127
-10,157
+10,160
-11,201
+11,199
-12,254
+12,248
-13,293
+13,281
-14,349
+14,346
-15,394
+15,406
-16,458
+16,459
-17,518
+17,530
-18,587
+18,593
-19,649
+19,659
-20,740
+20,742
-21,827
+21,839
-22,911
+22,892
-23,999
+23,982
-24,1073
+24,1087
-25,1187
+25,1168
-26,1299
+26,1264
-27,1410
+27,1385
-28,1502
+28,1463
-29,1604
+29,1615
-30,1725
+30,1715
-31,1856
+31,1850
-32,1979
+32,1971
-33,2089
+33,2106
-34,2227
+34,2211
-35,2383
+35,2384
-36,2536
+36,2501
-37,2644
+37,2674
-38,2810
+38,2836
-39,3000
+39,3007
-40,3138
+40,3118
-41,3299
+41,3262
-42,3445
+42,3476
-43,3638
+43,3616
-44,3828
+44,3836
-45,4015
+45,3987
-46,4143
+46,4219
-47,4348
+47,4360
-48,4611
+48,4593
-49,4773
+49,4747
-50,4994
+50,4957
-51,5163
+51,5185
-52,5363
+52,5344
-53,5586
+53,5602
-54,5784
+54,5790
-55,6075
+55,6069
-56,6275
+56,6271
-57,6550
+57,6473
-58,6711
+58,6764
 59,6957
-60,7225
+60,7235
-61,7483
+61,7514
-62,7782
+62,7675
-63,7952
+63,7985
-64,8265
+64,8242
-65,8531
+65,8534
-66,8764
+66,8718
-67,9060
+67,8997
-68,9331
+68,9330
-69,9686
+69,9602
-70,9913
+70,9930
-71,10098
+71,10181
-72,10417
+72,10451
-73,10795
+73,10812
-74,11108
+74,11076
-75,11342
+75,11364
-76,11703
+76,11719
-77,12104
+77,12054
-78,12356
+78,12368
-79,12623
+79,12654
-80,13066
+80,13032
-81,13513
+81,13392
-82,13706
+82,13736
-83,13998
+83,14043
-84,14333
+84,14408
-85,14694
+85,14682
-86,15160
+86,15134
-87,15470
+87,15503
-88,15845
+88,15850
-89,16211
+89,16246
-90,16551
+90,16565
-91,17047
+91,16993
-92,17237
+92,17336
-93,17669
+93,17636
-94,18055
+94,18073
-95,18614
+95,18461
-96,18838
+96,18968
-97,19253
+97,19335
-98,19868
+98,19709
-99,20092
+99,20207
-100,20517
+100,20593

latex/output/transform_tridiag.csv

@@ -6,7 +6,7 @@ N,T
 9,135
 10,177
 11,222
-12,238
+12,264
 13,305
 14,335
 15,417

src/Makefile

@@ -6,6 +6,7 @@ LIBOBJS=$(LIBSRCS:.cpp=.o)
 INCLUDE=../include
 
 CFLAGS=-larmadillo -llapack -std=c++11
+OPENMP=-fopenmp
 
 # Add a debug flag when compiling (For the DEBUG macro in utils.hpp)
 DEBUG ?= 0
@@ -22,14 +23,14 @@ all: test_suite main
 
 # Rules for executables
 main: main.o $(LIBOBJS)
-	$(CC) $^ -o $@ $(CFLAGS) $(DBGFLAG) -I$(INCLUDE)
+	$(CC) $^ -o $@ $(CFLAGS) $(DBGFLAG) -I$(INCLUDE) $(OPENMP)
 
 test_suite: test_suite.o $(LIBOBJS)
-	$(CC) $^ -o $@ $(CFLAGS) $(DBGFLAG) -I$(INCLUDE)
+	$(CC) $^ -o $@ $(CFLAGS) $(DBGFLAG) -I$(INCLUDE) $(OPENMP)
 
 # Rule for object files
 %.o: %.cpp
-	$(CC) -c $^ -o $@ $(DBGFLAG) -I$(INCLUDE)
+	$(CC) -c $^ -o $@ $(DBGFLAG) -I$(INCLUDE) $(OPENMP)
 
 # Make documentation
 doxygen:

src/main.cpp

@@ -4,8 +4,8 @@
  *  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 
+ *  Eigenvector corresponding to the 3 smallest eigenvalues 
- *  for matrices of size 6x6 and 100x100 are written to file.
+ *  for matrices of size 10x10 and 100x100 are written to file.
  *
  *  @author Cory Alexander Balaton (coryab)
  *  @author Janita Ovidie Sandtrøen Willumsen (janitaws)
@@ -13,7 +13,10 @@
  */
 #include <cassert>
 #include <cmath>
+#include <ctime>
 #include <iostream>
+#include <omp.h>
+#include <ostream>
 
 #include "utils.hpp"
 #include "matrix.hpp"
@@ -28,6 +31,7 @@ void write_transformation_dense(int N)
     ofile << "N,T" << std::endl;
 
     // Increase size of matrix, start at 5 to avoid logic_error of N=4
+    #pragma omp parallel for ordered schedule(static, 1)
     for (int i = 5; i <= N; i++) {
         arma::mat A = arma::mat(i, i).randn();
         A = arma::symmatu(A);
@@ -40,8 +44,11 @@ void write_transformation_dense(int N)
         jacobi_eigensolver(A, 10e-14, eigval, eigvec, 100000, iters, converged);
 
         // Write size, and number of iterations to file
+        #pragma omp ordered
+        {
             ofile << i << "," << iters << std::endl;
         }
+    }
     ofile.close();
 }
 
@@ -58,6 +65,7 @@ void write_transformation_tridiag(int N)
     ofile << "N,T" << std::endl;
 
     // Increase size of matrix, start at 5 to avoid logic_error of N=4
+    #pragma omp parallel for ordered schedule(static, 1)
     for (int i = 5; i <= N; i++) {
         h = 1. / (double) (i+1);
         a = -1. / (h*h), d = 2. / (h*h);
@@ -72,8 +80,11 @@ void write_transformation_tridiag(int N)
         jacobi_eigensolver(A, 10e-14, eigval, eigvec, 100000, iters, converged);
 
         // Write size, and number of iterations to file
+        #pragma omp ordered
+        {
             ofile << i << "," << iters << std::endl;
         }
+    }
     ofile.close();
 }
 

src/matrix.cpp

@@ -20,6 +20,7 @@ arma::mat create_tridiagonal(
     A(0, 0) = d(0);
     A(0, 1) = e(0);
 
+    #pragma omp parallel for if(n > 50)
     for (int i = 1; i < n-1; i++) {
         A(i, i-1) = a(i-1);
         A(i, i) = d(i);