--------------------------------------------------------------
GSL version number: 1.9
hardware and operating system, OS details:
Linux phit1 2.6.25.20-0.5-default #1 SMP 2009-08-14 01:48:11 +0200 x86_64
x86_64 x86_64 GNU/Linux
gcc version:
gcc version 4.3.1 20080507 (prerelease) [gcc-4_3-branch revision 135036]
(SUSE Linux)
genre: linalg, SVD, gsl_linalg_SV_decomp
description of the bug behavior: NaN results in gsl_linalg_SV_decomp
short program which exercises the bug: attached
--------------------------------------------------------------
Dear GSL devolopers,
your library is a great help for me and I use it very much. Thank you very
much for your great work!
Recently, I encountered a problem in the SVD routine of GSL version 1.9:
Certain matrices A with very many zeros lead to an SVD with NaN ("not a
number") results in the vector of singular values S as well as in the left and
right singular vectors.
I tracked the error down to the function trailing_eigenvalue in svdstep.c:
If tb, tab and dt are all zero, the calculated eigenvalue is undefined:
mu = tb - (tab * tab) / (dt + hypot (dt, tab)) = 0 - 0 / 0;
This NaN result is then propagated in the function qrstep via create_givens to
all the other results.
I attach a test program reproducing the problem when applied to a certain
matrix of 462 rows and 421 columns i.e. 194502 elements of which 189694 are
zeros and 4808 are ones, saved in a file of 389 kbyte. The distribution of
ones in the matrix is not random. I can send this matrix file to whoever is
interested (This mailing list refuses attachments of this size).
Here's the output of this program on my machine with the following architecture:
Linux phit1 2.6.25.20-0.5-default #1 SMP 2009-08-14 01:48:11 +0200 x86_64 x86_64
x86_64 GNU/Linux
--------------------------------------------------------------
(phit1 ~/pj) gcc `gsl-config --cflags` svdbug.c `gsl-config --libs` -o svdbug
&&
./svdbug
000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000
0000000000000000
000000000000000000000000000000000000000000000000000000000100010001000000000000000
010000000000000000000000000000000000000000000000000000000000000000000000000000000
000000001000000111000000000000000000000100000000000000100000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000
0000000000000000
000000000000000000000000000000000000000000000000000000000000001000000000000000000
000000000000000000000000000000000000000000000000100000000000000001000000000000000
000000000000011000000000000000000000000000000000000000000000000000000000000000000
000000100000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000
0000000000000000
000000100000000000000000000000000000000000000000000000000000001000100000000000000
000000000000100000000000000000000000000000000000000000000000000001000000000000000
000000000000011000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000
0000000000000000
000000000000000000000000000000000000000000000000000001000000001000000000000000000
000000000000000000000000000000000000000000000000000000000000000001000000000000000
000000000000011000000000000000000000000000000000000000000000000000000000000000000
001000010000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000
0000000000000000
000000000000000100000000000000000000000000000000000000000000100000000000000000000
000000000000000000000000000000000000000000000000100000000000000000000000000000000
000000000011100000000000000000000000000000000000000010000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000
0000000000000000
000000000000000100000000000000000000000000000001000000000000100000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000
010000000011100000100000000000000000000000000000000100000000000000000000000000000
000000000000010000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000
0000000000000000
000000000000000100000000000000000000000000000001000000000000100000000000000000100
000000000000000000000000000000000000000000000000000000000000000000000000000000000
010000000011100000100000000000000000000000000000000100000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000
0000000000000000
000000000000000000000000000000000000000000000000000000011000010001000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000
001000001000000000100000000000000000110100000000000101000100010000000000000000100
000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000
0000000000000000
000000000000000000000000000000000000010000000001000000000000100000000000000000000
001000000000000000000000000001000000000000000000000000000000000000000000000000000
010000000111100000001000000001000000000000000000001000010000000000000000000000000
000000000000010000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000010000000000000000000000000000000000000000000000010
0000000000000000
m = 462, n = 421, 189694 zeros, 4808 ones, 194502 elements
first 10 singular values:
0, 0, nan, nan, nan, nan, nan, nan, nan, nan
(phit1 ~/pj)
--------------------------------------------------------------
Kind regards,
Bruno Daniel
/*
GSL version: 1.9
Compile and run:
gcc `gsl-config --cflags` svdbug.c `gsl-config --libs` -o svdbug && ./svdbug
*/
#include <stdio.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_vector.h>
int main(int argc, char** argv) {
int m = 462, n = 421;
gsl_matrix* A = gsl_matrix_alloc(m, n);
// Read the matrix A from the file svdbug.c, show the first 10 lines and
report
// the number of zeros and ones.
FILE* fp = fopen("svdbug.csv", "r");
int i, j, n_ones = 0, n_zeros = 0;
for (i = 0; i < m; i++) {
for (j = 0; j < n; j++) {
double a;
fscanf(fp, "%lf", &a);
gsl_matrix_set(A, i, j, a);
if (i < 10) { printf("%g", a); }
if (a == 0) { n_zeros++; }
else if (a == 1) { n_ones++; }
}
if (i < 10) { printf("\n"); }
}
fclose(fp);
printf("m = %d, n = %d, %d zeros, %d ones, %d elements\n", m, n, n_zeros,
n_ones, m * n);
gsl_matrix* V = gsl_matrix_alloc(n, n);
gsl_vector* S = gsl_vector_alloc(n);
gsl_vector* work = gsl_vector_alloc(n);
gsl_linalg_SV_decomp(A, V, S, work);
printf("first 10 singular values:\n");
for (i = 0; i < 10; i++) {
if (i > 0) { printf(", "); }
printf("%g", gsl_vector_get(S, i));
}
return 0;
}
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