Example programs for matrices - GNU Scientific Library -- Reference Manual
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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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