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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");
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 %zu, 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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