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/**
* 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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