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/* -*- mode: C -*- */
/*
IGraph library.
Copyright (C) 2010-2012 Gabor Csardi <csardi.gabor@gmail.com>
334 Harvard st, Cambridge MA, 02139 USA
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 2 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, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301 USA
*/
#include <igraph.h>
#include <time.h>
#include <stdio.h>
#define DIM 10
int real_cplx_mult(const igraph_matrix_t *A,
const igraph_vector_t *v_real,
const igraph_vector_t *v_imag,
igraph_vector_t *res_real,
igraph_vector_t *res_imag) {
int n=igraph_vector_size(v_real);
int r, c;
if (igraph_matrix_nrow(A) != n ||
igraph_matrix_ncol(A) != n ||
igraph_vector_size(v_imag) != n) {
printf("Wrong matrix or vector size");
return 1;
}
igraph_vector_resize(res_real, n);
igraph_vector_resize(res_imag, n);
for (r=0; r<n; r++) {
igraph_real_t s_real=0.0;
igraph_real_t s_imag=0.0;
for (c=0; c<n; c++) {
s_real += MATRIX(*A, r, c) * VECTOR(*v_real)[c];
s_imag += MATRIX(*A, r, c) * VECTOR(*v_imag)[c];
}
VECTOR(*res_real)[r]=s_real;
VECTOR(*res_imag)[r]=s_imag;
}
return 0;
}
int sc_cplx_cplx_mult(igraph_real_t lambda_real,
igraph_real_t lambda_imag,
const igraph_vector_t *v_real,
const igraph_vector_t *v_imag,
igraph_vector_t *res_real,
igraph_vector_t *res_imag) {
int r;
int n=igraph_vector_size(v_real);
if (igraph_vector_size(v_imag) != n) {
printf("Wrong vector sizes");
return 1;
}
igraph_vector_resize(res_real, n);
igraph_vector_resize(res_imag, n);
for (r=0; r<n; r++) {
VECTOR(*res_real)[r] = (lambda_real * VECTOR(*v_real)[r] -
lambda_imag * VECTOR(*v_imag)[r]);
VECTOR(*res_imag)[r] = (lambda_imag * VECTOR(*v_real)[r] +
lambda_real * VECTOR(*v_imag)[r]);
}
return 0;
}
igraph_bool_t check_ev(const igraph_matrix_t *A,
const igraph_vector_t *values_real,
const igraph_vector_t *values_imag,
const igraph_matrix_t *vectors_left,
const igraph_matrix_t *vectors_right,
igraph_real_t tol) {
int i, n=igraph_matrix_nrow(A);
igraph_vector_t v_real, v_imag;
igraph_vector_t AV_real, AV_imag, lv_real, lv_imag;
igraph_vector_t null;
if (igraph_matrix_ncol(A) != n) { return 1; }
if (igraph_vector_size(values_real) != n) { return 1; }
if (igraph_vector_size(values_imag) != n) { return 1; }
if (igraph_matrix_nrow(vectors_left) != n) { return 1; }
if (igraph_matrix_ncol(vectors_left) != n) { return 1; }
if (igraph_matrix_nrow(vectors_right) != n) { return 1; }
if (igraph_matrix_ncol(vectors_right) != n) { return 1; }
igraph_vector_init(&AV_real, n);
igraph_vector_init(&AV_imag, n);
igraph_vector_init(&lv_real, n);
igraph_vector_init(&lv_imag, n);
igraph_vector_init(&null, n);
igraph_vector_null(&null);
for (i=0; i<n; i++) {
if (VECTOR(*values_imag)[i]==0.0) {
igraph_vector_view(&v_real, &MATRIX(*vectors_right, 0, i), n);
igraph_vector_view(&v_imag, VECTOR(null), n);
} else if (VECTOR(*values_imag)[i] > 0.0) {
igraph_vector_view(&v_real, &MATRIX(*vectors_right, 0, i), n);
igraph_vector_view(&v_imag, &MATRIX(*vectors_right, 0, i+1), n);
} else if (VECTOR(*values_imag)[i] < 0.0) {
igraph_vector_view(&v_real, &MATRIX(*vectors_right, 0, i-1), n);
igraph_vector_view(&v_imag, &MATRIX(*vectors_right, 0, i), n);
igraph_vector_scale(&v_imag, -1.0);
}
real_cplx_mult(A, &v_real, &v_imag, &AV_real, &AV_imag);
sc_cplx_cplx_mult(VECTOR(*values_real)[i], VECTOR(*values_imag)[i],
&v_real, &v_imag, &lv_real, &lv_imag);
if (igraph_vector_maxdifference(&AV_real, &lv_real) > tol ||
igraph_vector_maxdifference(&AV_imag, &lv_imag) > tol) {
printf("ERROR:\n");
igraph_vector_print(&AV_real); igraph_vector_print(&AV_imag);
igraph_vector_print(&lv_real); igraph_vector_print(&lv_imag);
return 1;
}
}
igraph_vector_destroy(&null);
igraph_vector_destroy(&AV_imag);
igraph_vector_destroy(&AV_real);
igraph_vector_destroy(&lv_imag);
igraph_vector_destroy(&lv_real);
return 0;
}
int main() {
igraph_matrix_t A;
igraph_matrix_t vectors_left, vectors_right;
igraph_vector_t values_real, values_imag;
int i, j;
int info=1;
igraph_rng_seed(igraph_rng_default(), 42);
igraph_matrix_init(&A, DIM, DIM);
igraph_matrix_init(&vectors_left, 0, 0);
igraph_matrix_init(&vectors_right, 0, 0);
igraph_vector_init(&values_real, 0);
igraph_vector_init(&values_imag, 0);
for (i=0; i<DIM; i++) {
for (j=0; j<DIM; j++) {
MATRIX(A, i, j) = igraph_rng_get_integer(igraph_rng_default(), 1, 10);
}
}
igraph_lapack_dgeev(&A, &values_real, &values_imag,
&vectors_left, &vectors_right, &info);
if (check_ev(&A, &values_real, &values_imag,
&vectors_left, &vectors_right, /*tol=*/ 1e-8)) {
return 1;
}
/* ------------------------------------------------------- */
/* igraph_matrix_resize(&A, 10, 10); */
/* igraph_matrix_null(&A); */
/* for (i=0; i<10; i++) { MATRIX(A, i, i) = 1.0; } */
/* MATRIX(A,0,1) = 1.0; */
/* igraph_lapack_dgeev(&A, &values_real, &values_imag, */
/* &vectors_left, &vectors_right, &info); */
/* if (check_ev(&A, &values_real, &values_imag, */
/* &vectors_left, &vectors_right, /\*tol=*\/ 1e-8)) { */
/* return 2; */
/* } */
/* ------------------------------------------------------- */
igraph_matrix_resize(&A, 10, 10);
igraph_matrix_null(&A);
MATRIX(A,0,1) = MATRIX(A,0,2) = MATRIX(A,0,3) = 1/3.0;
MATRIX(A,1,0) = MATRIX(A,1,4) = MATRIX(A,1,5) = MATRIX(A,1,6) = 1/4.0;
MATRIX(A,2,0) = MATRIX(A,2,7) = MATRIX(A,2,8) = MATRIX(A,2,9) = 1/4.0;
MATRIX(A,3,0) = 1.0;
MATRIX(A,4,1) = 1.0;
MATRIX(A,5,1) = 1.0;
MATRIX(A,6,1) = 1.0;
MATRIX(A,7,2) = 1.0;
MATRIX(A,8,2) = 1.0;
MATRIX(A,9,2) = 1.0;
info=0;
igraph_lapack_dgeev(&A, &values_real, &values_imag,
&vectors_left, &vectors_right, &info);
/* igraph_matrix_print(&A); */
/* printf("---\n"); */
/* igraph_vector_print(&values_real); */
/* igraph_vector_print(&values_imag); */
/* igraph_matrix_print(&vectors_left); */
if (check_ev(&A, &values_real, &values_imag,
&vectors_left, &vectors_right, /*tol=*/ 1e-8)) {
return 3;
}
igraph_vector_destroy(&values_imag);
igraph_vector_destroy(&values_real);
igraph_matrix_destroy(&vectors_right);
igraph_matrix_destroy(&vectors_left);
igraph_matrix_destroy(&A);
return 0;
}
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