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<title>GNU Scientific Library &ndash; Reference Manual: Triangular Systems</title>

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<a name="Triangular-Systems"></a>
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<p>
Next: <a href="Balancing.html#Balancing" accesskey="n" rel="next">Balancing</a>, Previous: <a href="Tridiagonal-Systems.html#Tridiagonal-Systems" accesskey="p" rel="previous">Tridiagonal Systems</a>, Up: <a href="Linear-Algebra.html#Linear-Algebra" accesskey="u" rel="up">Linear Algebra</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Triangular-Systems-1"></a>
<h3 class="section">14.18 Triangular Systems</h3>
<a name="index-triangular-systems"></a>

<dl>
<dt><a name="index-gsl_005flinalg_005ftri_005fupper_005finvert"></a>Function: <em>int</em> <strong>gsl_linalg_tri_upper_invert</strong> <em>(gsl_matrix * <var>T</var>)</em></dt>
<dt><a name="index-gsl_005flinalg_005ftri_005flower_005finvert"></a>Function: <em>int</em> <strong>gsl_linalg_tri_lower_invert</strong> <em>(gsl_matrix * <var>T</var>)</em></dt>
<dt><a name="index-gsl_005flinalg_005ftri_005fupper_005funit_005finvert"></a>Function: <em>int</em> <strong>gsl_linalg_tri_upper_unit_invert</strong> <em>(gsl_matrix * <var>T</var>)</em></dt>
<dt><a name="index-gsl_005flinalg_005ftri_005flower_005funit_005finvert"></a>Function: <em>int</em> <strong>gsl_linalg_tri_lower_unit_invert</strong> <em>(gsl_matrix * <var>T</var>)</em></dt>
<dd><p>These functions calculate the in-place inverse of the triangular matrix <var>T</var>. When
the <code>upper</code> prefix is specified, then the upper triangle of <var>T</var> is used, and when
the <code>lower</code> prefix is specified, the lower triangle is used. If the <code>unit</code>
prefix is specified, then the diagonal elements of the matrix <var>T</var> are taken as
unity and are not referenced. Otherwise the diagonal elements are used in the inversion.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005flinalg_005ftri_005fupper_005frcond"></a>Function: <em>int</em> <strong>gsl_linalg_tri_upper_rcond</strong> <em>(const gsl_matrix * <var>T</var>, double * <var>rcond</var>, gsl_vector * <var>work</var>)</em></dt>
<dt><a name="index-gsl_005flinalg_005ftri_005flower_005frcond"></a>Function: <em>int</em> <strong>gsl_linalg_tri_lower_rcond</strong> <em>(const gsl_matrix * <var>T</var>, double * <var>rcond</var>, gsl_vector * <var>work</var>)</em></dt>
<dd><p>These functions estimate the reciprocal condition number, in the 1-norm, of the upper or lower
<em>N</em>-by-<em>N</em> triangular matrix <var>T</var>. The reciprocal condition number
is stored in <var>rcond</var> on output, and is defined by <em>1 / (||T||_1 \cdot ||T^{-1}||_1)</em>.
Additional workspace of size <em>3 N</em> is required in <var>work</var>.
</p></dd></dl>




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