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<p>
Next: <a href="Linear-Algebra-References-and-Further-Reading.html#Linear-Algebra-References-and-Further-Reading" accesskey="n" rel="next">Linear Algebra References and Further Reading</a>, Previous: <a href="Balancing.html#Balancing" accesskey="p" rel="previous">Balancing</a>, Up: <a href="Linear-Algebra.html#Linear-Algebra" accesskey="u" rel="up">Linear Algebra</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="Examples-8"></a>
<h3 class="section">14.20 Examples</h3>
<p>The following program solves the linear system <em>A x = b</em>. The
system to be solved is,
</p>
<div class="example">
<pre class="example">[ 0.18 0.60 0.57 0.96 ] [x0] [1.0]
[ 0.41 0.24 0.99 0.58 ] [x1] = [2.0]
[ 0.14 0.30 0.97 0.66 ] [x2] [3.0]
[ 0.51 0.13 0.19 0.85 ] [x3] [4.0]
</pre></div>
<p>and the solution is found using LU decomposition of the matrix <em>A</em>.
</p>
<div class="example">
<pre class="verbatim">#include <stdio.h>
#include <gsl/gsl_linalg.h>
int
main (void)
{
double a_data[] = { 0.18, 0.60, 0.57, 0.96,
0.41, 0.24, 0.99, 0.58,
0.14, 0.30, 0.97, 0.66,
0.51, 0.13, 0.19, 0.85 };
double b_data[] = { 1.0, 2.0, 3.0, 4.0 };
gsl_matrix_view m
= gsl_matrix_view_array (a_data, 4, 4);
gsl_vector_view b
= gsl_vector_view_array (b_data, 4);
gsl_vector *x = gsl_vector_alloc (4);
int s;
gsl_permutation * p = gsl_permutation_alloc (4);
gsl_linalg_LU_decomp (&m.matrix, p, &s);
gsl_linalg_LU_solve (&m.matrix, p, &b.vector, x);
printf ("x = \n");
gsl_vector_fprintf (stdout, x, "%g");
gsl_permutation_free (p);
gsl_vector_free (x);
return 0;
}
</pre></div>
<p>Here is the output from the program,
</p>
<div class="example">
<pre class="verbatim">x =
-4.05205
-12.6056
1.66091
8.69377
</pre></div>
<p>This can be verified by multiplying the solution <em>x</em> by the
original matrix <em>A</em> using <small>GNU OCTAVE</small>,
</p>
<div class="example">
<pre class="example">octave> A = [ 0.18, 0.60, 0.57, 0.96;
0.41, 0.24, 0.99, 0.58;
0.14, 0.30, 0.97, 0.66;
0.51, 0.13, 0.19, 0.85 ];
octave> x = [ -4.05205; -12.6056; 1.66091; 8.69377];
octave> A * x
ans =
1.0000
2.0000
3.0000
4.0000
</pre></div>
<p>This reproduces the original right-hand side vector, <em>b</em>, in
accordance with the equation <em>A x = b</em>.
</p>
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