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<title>GNU Scientific Library &ndash; Reference Manual: Sparse Matrices Examples</title>

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<a name="Sparse-Matrices-Examples"></a>
<div class="header">
<p>
Next: <a href="Sparse-Matrices-References-and-Further-Reading.html#Sparse-Matrices-References-and-Further-Reading" accesskey="n" rel="next">Sparse Matrices References and Further Reading</a>, Previous: <a href="Sparse-Matrices-Conversion-Between-Sparse-and-Dense.html#Sparse-Matrices-Conversion-Between-Sparse-and-Dense" accesskey="p" rel="previous">Sparse Matrices Conversion Between Sparse and Dense</a>, Up: <a href="Sparse-Matrices.html#Sparse-Matrices" accesskey="u" rel="up">Sparse Matrices</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="Examples-31"></a>
<h3 class="section">41.13 Examples</h3>
<a name="index-sparse-matrices_002c-examples"></a>

<p>The following example program builds a 5-by-4 sparse matrix
and prints it in triplet, compressed column, and compressed
row format. The matrix which is constructed is
The output of the program is
</p>
<div class="example">
<pre class="example">printing all matrix elements:
A(0,0) = 0
A(0,1) = 0
A(0,2) = 3.1
A(0,3) = 4.6
A(1,0) = 1
.
.
.
A(4,0) = 4.1
A(4,1) = 0
A(4,2) = 0
A(4,3) = 0
matrix in triplet format (i,j,Aij):
(0, 2, 3.1)
(0, 3, 4.6)
(1, 0, 1.0)
(1, 2, 7.2)
(3, 0, 2.1)
(3, 1, 2.9)
(3, 3, 8.5)
(4, 0, 4.1)
matrix in compressed column format:
i = [ 1, 3, 4, 3, 0, 1, 0, 3, ]
p = [ 0, 3, 4, 6, 8, ]
d = [ 1, 2.1, 4.1, 2.9, 3.1, 7.2, 4.6, 8.5, ]
matrix in compressed row format:
i = [ 2, 3, 0, 2, 0, 1, 3, 0, ]
p = [ 0, 2, 4, 4, 7, 8, ]
d = [ 3.1, 4.6, 1, 7.2, 2.1, 2.9, 8.5, 4.1, ]
</pre></div>
<p>We see in the compressed column output, the data array stores
each column contiguously, the array <em>i</em> stores
the row index of the corresponding data element, and the
array <em>p</em> stores the index of the start of each column in the
data array. Similarly, for the compressed row output, the
data array stores each row contiguously, the array <em>i</em>
stores the column index of the corresponding data element, and
the <em>p</em> array stores the index of the start of each row
in the data array.
</p>
<div class="example">
<pre class="verbatim">#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;

#include &lt;gsl/gsl_spmatrix.h&gt;

int
main()
{
  gsl_spmatrix *A = gsl_spmatrix_alloc(5, 4); /* triplet format */
  gsl_spmatrix *B, *C;
  size_t i, j;

  /* build the sparse matrix */
  gsl_spmatrix_set(A, 0, 2, 3.1);
  gsl_spmatrix_set(A, 0, 3, 4.6);
  gsl_spmatrix_set(A, 1, 0, 1.0);
  gsl_spmatrix_set(A, 1, 2, 7.2);
  gsl_spmatrix_set(A, 3, 0, 2.1);
  gsl_spmatrix_set(A, 3, 1, 2.9);
  gsl_spmatrix_set(A, 3, 3, 8.5);
  gsl_spmatrix_set(A, 4, 0, 4.1);

  printf(&quot;printing all matrix elements:\n&quot;);
  for (i = 0; i &lt; 5; ++i)
    for (j = 0; j &lt; 4; ++j)
      printf(&quot;A(%zu,%zu) = %g\n&quot;, i, j,
             gsl_spmatrix_get(A, i, j));

  /* print out elements in triplet format */
  printf(&quot;matrix in triplet format (i,j,Aij):\n&quot;);
  gsl_spmatrix_fprintf(stdout, A, &quot;%.1f&quot;);

  /* convert to compressed column format */
  B = gsl_spmatrix_ccs(A);

  printf(&quot;matrix in compressed column format:\n&quot;);
  printf(&quot;i = [ &quot;);
  for (i = 0; i &lt; B-&gt;nz; ++i)
    printf(&quot;%zu, &quot;, B-&gt;i[i]);
  printf(&quot;]\n&quot;);

  printf(&quot;p = [ &quot;);
  for (i = 0; i &lt; B-&gt;size2 + 1; ++i)
    printf(&quot;%zu, &quot;, B-&gt;p[i]);
  printf(&quot;]\n&quot;);

  printf(&quot;d = [ &quot;);
  for (i = 0; i &lt; B-&gt;nz; ++i)
    printf(&quot;%g, &quot;, B-&gt;data[i]);
  printf(&quot;]\n&quot;);

  /* convert to compressed row format */
  C = gsl_spmatrix_crs(A);

  printf(&quot;matrix in compressed row format:\n&quot;);
  printf(&quot;i = [ &quot;);
  for (i = 0; i &lt; C-&gt;nz; ++i)
    printf(&quot;%zu, &quot;, C-&gt;i[i]);
  printf(&quot;]\n&quot;);

  printf(&quot;p = [ &quot;);
  for (i = 0; i &lt; C-&gt;size1 + 1; ++i)
    printf(&quot;%zu, &quot;, C-&gt;p[i]);
  printf(&quot;]\n&quot;);

  printf(&quot;d = [ &quot;);
  for (i = 0; i &lt; C-&gt;nz; ++i)
    printf(&quot;%g, &quot;, C-&gt;data[i]);
  printf(&quot;]\n&quot;);

  gsl_spmatrix_free(A);
  gsl_spmatrix_free(B);
  gsl_spmatrix_free(C);

  return 0;
}
</pre></div>

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<p>
Next: <a href="Sparse-Matrices-References-and-Further-Reading.html#Sparse-Matrices-References-and-Further-Reading" accesskey="n" rel="next">Sparse Matrices References and Further Reading</a>, Previous: <a href="Sparse-Matrices-Conversion-Between-Sparse-and-Dense.html#Sparse-Matrices-Conversion-Between-Sparse-and-Dense" accesskey="p" rel="previous">Sparse Matrices Conversion Between Sparse and Dense</a>, Up: <a href="Sparse-Matrices.html#Sparse-Matrices" accesskey="u" rel="up">Sparse Matrices</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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