From 3aee2fd43e3059a699af2b63c6f2395e5a55e515 Mon Sep 17 00:00:00 2001
From: KatolaZ <katolaz@freaknet.org>
Date: Wed, 27 Sep 2017 15:06:31 +0100
Subject: First commit on github -- NetBunch 1.0

---
 src/pm/pm.c | 231 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 231 insertions(+)
 create mode 100644 src/pm/pm.c

(limited to 'src/pm/pm.c')

diff --git a/src/pm/pm.c b/src/pm/pm.c
new file mode 100644
index 0000000..99e680b
--- /dev/null
+++ b/src/pm/pm.c
@@ -0,0 +1,231 @@
+/**
+ *  This program is free software: you can redistribute it and/or
+ *  modify it under the terms of the GNU General Public License as
+ *  published by the Free Software Foundation, either version 3 of the
+ *  License, or (at your option) any later version.
+ *
+ *  This program is distributed in the hope that it will be useful,
+ *  but WITHOUT ANY WARRANTY; without even the implied warranty of
+ *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ *  General Public License for more details.
+ *
+ *  You should have received a copy of the GNU General Public License
+ *  along with this program.  If not, see
+ *  <http://www.gnu.org/licenses/>.
+ *
+ *  (c) Vincenzo Nicosia 2009-2017 -- <v.nicosia@qmul.ac.uk>
+ * 
+ *  This file is part of NetBunch, a package for complex network
+ *  analysis and modelling. For more information please visit:
+ *
+ *             http://www.complex-networks.net/
+ *
+ *  If you use this software, please add a reference to 
+ *
+ *               V. Latora, V. Nicosia, G. Russo             
+ *   "Complex Networks: Principles, Methods and Applications"
+ *              Cambridge University Press (2017) 
+ *                ISBN: 9781107103184
+ *
+ ***********************************************************************
+ *
+ *  This program computes the leading eigenvector and the leading
+ *  eigenvalue of a given graph, using the power method. The value of
+ *  the leading eigenvalue is printed on the standard output, while
+ *  the associated eigenvector is reported.
+ *
+ *
+ */
+
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <math.h>
+
+#include "utils.h"
+
+#define MAX(x,y) ((x)>(y)? (x) : (y))
+
+
+void usage(char *argv[]){
+  printf("********************************************************************\n"
+         "**                                                                **\n"
+         "**                        -*-     pm     -*-                      **\n"
+         "**                                                                **\n"
+         "**   Compute the leading eigenvalue and the leading eigenvector   **\n"
+         "**   of a graph, with a relative error smaller than 'eps' using   **\n"
+         "**   the power method (Rayleigh iteration).                       **\n"
+         "**                                                                **\n"
+         "**   The input file 'graph_in' is an edge-list:                   **\n"
+         "**                                                                **\n"
+         "**                            I_1 J_1                             **\n"
+         "**                            I_2 J_2                             **\n"
+         "**                            I_3 J_3                             **\n"
+         "**                            ... ...                             **\n"
+         "**                            I_K J_K                             **\n"
+         "**                                                                **\n"
+         "**    If 'graph_in' is equal to '-' (dash), read the file from    **\n" 
+         "**    the standard input (STDIN).                                 **\n"
+         "**                                                                **\n"
+         "**   'is_dir' should be set either to 0 (zero) if the graph is    **\n"
+         "**   undirected, or to 1 (one) if the graph is directed.          **\n"
+         "**                                                                **\n"
+         "**   The value of the leading eigenvalue is printed on the        **\n"
+         "**   standard output (STDOUT) while the associated eigenvector    **\n"
+         "**   is printed on the standard error (STDERR).                   **\n"
+         "**                                                                **\n"
+         "**                                                                **\n"
+         "********************************************************************\n"
+         " This is Free Software - You can use and distribute it under \n"
+         " the terms of the GNU General Public License, version 3 or later\n\n"
+         " Please visit http://www.complex-networks.net for more information\n\n"
+         " (c) Vincenzo Nicosia 2010-2017 (v.nicosia@qmul.ac.uk)\n"
+         "********************************************************************\n\n"
+         );
+  
+  printf("Usage: %s <graph_in> <is_dir> <eps>\n", argv[0]);
+}
+
+
+/* Product of a matrix by a vector */
+
+void matrix_vector_product(unsigned int *I, unsigned int *J, unsigned int K,
+                           double *src, double *dst, unsigned int N){
+  
+  int i;
+
+  for(i=0; i<N; i ++){
+    dst[i] = 0;
+  }
+  
+  for (i=0; i<K; i++){
+    dst[I[i]] += src[J[i]];
+  }
+  return;
+}
+
+/* product between two row vectors (v1 * v2') */
+
+double vector_vector_product(double *v1, double *v2, unsigned int N){
+  
+  int i;
+  double sum = 0;
+
+  for(i=0; i<N; i ++){
+    sum += v1[i] * v2[i];
+  }
+  return sum;
+}
+
+/* compute the 2-norm of a vector */
+
+double vector_norm(double *v,unsigned int N){
+
+  double norm = 0.0;
+  int i;
+
+  for(i=0; i<N; i++){
+    norm += v[i] * v[i];
+  }
+  norm = sqrt(norm);
+  return norm;
+}
+
+
+double compute_relative_error(double *x_new, double *x_old, double lambda, unsigned int N){
+  
+  double val, num, den;
+  int i;
+  
+  num = den = 0.0;
+  for (i=0; i<N; i++){
+    val = x_new[i] - lambda * x_old [i];
+    num += val * val;
+    den += x_new[i] * x_new[i];
+  }
+  return sqrt(num / den);
+}
+
+
+int main(int argc, char *argv[]){
+  
+  unsigned int *I, *J;
+  unsigned int N, K;
+  double *x1, *x2, *tmp;
+  double norm, lambda, err, eps;
+  int i, is_dir;
+
+  FILE *filein, *fileout;
+  
+  if(argc < 4){
+    usage(argv);
+    exit(1);
+  }
+
+
+  if (!strcmp(argv[1], "-")){
+    /* take the input from STDIN */
+    filein = stdin;
+  }
+  else {
+    filein = openfile_or_exit(argv[1], "r", 2);
+  }
+  is_dir = atoi(argv[2]);
+  eps = fabs(atof(argv[3]));
+  lambda = 0.0;
+
+  
+  K = read_ij(filein, &I, &J);
+  if (! is_dir){
+    K = 2*K;
+    I = realloc(I, K * sizeof(unsigned int));
+    J = realloc(J, K * sizeof(unsigned int));
+    for (i=K/2; i<K; i++){
+      I[i] = J[i-K/2];
+      J[i] = I[i-K/2];
+    }
+
+  }
+  N = 1 + MAX(find_max(I, K), find_max(J, K));
+
+  fclose(filein);
+  
+  x1 = malloc(N * sizeof(double));
+  x2 = malloc(N * sizeof(double));
+  
+  for(i=0; i<N; i++){
+    x1[i] = 1;
+    x2[i] = 0;
+  }
+  
+  /* The following cycle is the actual implementation of the power
+     method (Rayleigh iteration) */ 
+  err = 100*eps;
+  
+  while (err > eps) {
+    norm = vector_norm(x1, N);
+    for(i=0; i<N; i ++){
+      x1[i] /= norm;
+    }
+    matrix_vector_product(I, J, K, x1, x2, N);
+    lambda = vector_vector_product(x2, x1, N);
+    /* compute the relative error */
+    err = compute_relative_error(x2, x1, lambda, N);
+    tmp = x1;
+    x1 = x2;
+    x2 = tmp;
+  }
+  
+  fileout = stderr;
+  norm = vector_norm(x1, N);
+
+  for(i=0; i<N; i++){
+    fprintf(fileout, "%d %g\n", i, x1[i]/norm);
+  }
+  printf("%2.15g\n", lambda);
+  free(I);
+  free(J);
+  free(x1);
+  free(x2);
+}
-- 
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