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<h3 class="section">16.8 QAWS adaptive integration for singular functions</h3>
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<p><a name="index-singular-functions_002c-numerical-integration-of-1359"></a>The QAWS algorithm is designed for integrands with algebraic-logarithmic
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singularities at the end-points of an integration region. In order to
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work efficiently the algorithm requires a precomputed table of
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— Function: gsl_integration_qaws_table * <b>gsl_integration_qaws_table_alloc</b> (<var>double alpha, double beta, int mu, int nu</var>)<var><a name="index-gsl_005fintegration_005fqaws_005ftable_005falloc-1360"></a></var><br>
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<p>This function allocates space for a <code>gsl_integration_qaws_table</code>
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struct and associated workspace describing a singular weight function
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W(x) with the parameters (\alpha, \beta, \mu, \nu),
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where \alpha > -1, \beta > -1, and \mu = 0, 1,
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\nu = 0, 1. The weight function can take four different forms
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depending on the values of \mu and \nu,
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The singular points (a,b) do not have to be specified until the
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integral is computed, where they are the endpoints of the integration
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<p>The function returns a pointer to the newly allocated
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<code>gsl_integration_qaws_table</code> if no errors were detected, and 0 in
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</p></blockquote></div>
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— Function: int <b>gsl_integration_qaws_table_set</b> (<var>gsl_integration_qaws_table * t, double alpha, double beta, int mu, int nu</var>)<var><a name="index-gsl_005fintegration_005fqaws_005ftable_005fset-1361"></a></var><br>
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<blockquote><p>This function modifies the parameters (\alpha, \beta, \mu, \nu) of
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an existing <code>gsl_integration_qaws_table</code> struct <var>t</var>.
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</p></blockquote></div>
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— Function: void <b>gsl_integration_qaws_table_free</b> (<var>gsl_integration_qaws_table * t</var>)<var><a name="index-gsl_005fintegration_005fqaws_005ftable_005ffree-1362"></a></var><br>
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<blockquote><p>This function frees all the memory associated with the
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<code>gsl_integration_qaws_table</code> struct <var>t</var>.
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</p></blockquote></div>
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— Function: int <b>gsl_integration_qaws</b> (<var>gsl_function * f, const double a, const double b, gsl_integration_qaws_table * t, const double epsabs, const double epsrel, const size_t limit, gsl_integration_workspace * workspace, double * result, double * abserr</var>)<var><a name="index-gsl_005fintegration_005fqaws-1363"></a></var><br>
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<p>This function computes the integral of the function f(x) over the
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interval (a,b) with the singular weight function
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(x-a)^\alpha (b-x)^\beta \log^\mu (x-a) \log^\nu (b-x). The parameters
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of the weight function (\alpha, \beta, \mu, \nu) are taken from the
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table <var>t</var>. The integral is,
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The adaptive bisection algorithm of QAG is used. When a subinterval
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contains one of the endpoints then a special 25-point modified
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Clenshaw-Curtis rule is used to control the singularities. For
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subintervals which do not include the endpoints an ordinary 15-point
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Gauss-Kronrod integration rule is used.
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