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8.4.13 Example programs for matrices

The program below shows how to allocate, initialize and read from a matrix using the functions gsl_matrix_alloc, gsl_matrix_set and gsl_matrix_get.

#include <stdio.h>
#include <gsl/gsl_matrix.h>

int
main (void)
{
  int i, j; 
  gsl_matrix * m = gsl_matrix_alloc (10, 3);
  
  for (i = 0; i < 10; i++)
    for (j = 0; j < 3; j++)
      gsl_matrix_set (m, i, j, 0.23 + 100*i + j);
  
  for (i = 0; i < 100; i++)  /* OUT OF RANGE ERROR */
    for (j = 0; j < 3; j++)
      printf ("m(%d,%d) = %g\n", i, j, 
              gsl_matrix_get (m, i, j));

  gsl_matrix_free (m);

  return 0;
}

Here is the output from the program. The final loop attempts to read outside the range of the matrix m, and the error is trapped by the range-checking code in gsl_matrix_get.

$ ./a.out
m(0,0) = 0.23
m(0,1) = 1.23
m(0,2) = 2.23
m(1,0) = 100.23
m(1,1) = 101.23
m(1,2) = 102.23
...
m(9,2) = 902.23
gsl: matrix_source.c:13: ERROR: first index out of range
Default GSL error handler invoked.
Aborted (core dumped)

The next program shows how to write a matrix to a file.

#include <stdio.h>
#include <gsl/gsl_matrix.h>

int
main (void)
{
  int i, j, k = 0; 
  gsl_matrix * m = gsl_matrix_alloc (100, 100);
  gsl_matrix * a = gsl_matrix_alloc (100, 100);
  
  for (i = 0; i < 100; i++)
    for (j = 0; j < 100; j++)
      gsl_matrix_set (m, i, j, 0.23 + i + j);

  {  
     FILE * f = fopen ("test.dat", "wb");
     gsl_matrix_fwrite (f, m);
     fclose (f);
  }

  {  
     FILE * f = fopen ("test.dat", "rb");
     gsl_matrix_fread (f, a);
     fclose (f);
  }

  for (i = 0; i < 100; i++)
    for (j = 0; j < 100; j++)
      {
        double mij = gsl_matrix_get (m, i, j);
        double aij = gsl_matrix_get (a, i, j);
        if (mij != aij) k++;
      }

  gsl_matrix_free (m);
  gsl_matrix_free (a);

  printf ("differences = %d (should be zero)\n", k);
  return (k > 0);
}

After running this program the file test.dat should contain the elements of m, written in binary format. The matrix which is read back in using the function gsl_matrix_fread should be exactly equal to the original matrix.

The following program demonstrates the use of vector views. The program computes the column norms of a matrix.

#include <math.h>
#include <stdio.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_blas.h>

int
main (void)
{
  size_t i,j;

  gsl_matrix *m = gsl_matrix_alloc (10, 10);

  for (i = 0; i < 10; i++)
    for (j = 0; j < 10; j++)
      gsl_matrix_set (m, i, j, sin (i) + cos (j));

  for (j = 0; j < 10; j++)
    {
      gsl_vector_view column = gsl_matrix_column (m, j);
      double d;

      d = gsl_blas_dnrm2 (&column.vector);

      printf ("matrix column %d, norm = %g\n", j, d);
    }

  gsl_matrix_free (m);

  return 0;
}

Here is the output of the program,

$ ./a.out
matrix column 0, norm = 4.31461
matrix column 1, norm = 3.1205
matrix column 2, norm = 2.19316
matrix column 3, norm = 3.26114
matrix column 4, norm = 2.53416
matrix column 5, norm = 2.57281
matrix column 6, norm = 4.20469
matrix column 7, norm = 3.65202
matrix column 8, norm = 2.08524
matrix column 9, norm = 3.07313

The results can be confirmed using GNU OCTAVE,

$ octave
GNU Octave, version 2.0.16.92
octave> m = sin(0:9)' * ones(1,10) 
               + ones(10,1) * cos(0:9); 
octave> sqrt(sum(m.^2))
ans =
  4.3146  3.1205  2.1932  3.2611  2.5342  2.5728
  4.2047  3.6520  2.0852  3.0731

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