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<definition>int libecpint::GCQuadrature::maxN</definition>
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<para>Maximum number of points to use in quadrature. </para>
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<para>Index of midpoint. </para>
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<para>Weights. </para>
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<para>Abscissae. </para>
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<para>Integral value. </para>
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<definition>GCTYPE libecpint::GCQuadrature::t</definition>
<argsstring></argsstring>
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<para>Algorithm type to be used. </para>
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<type>double</type>
<definition>double libecpint::GCQuadrature::sumTerms</definition>
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<name>sumTerms</name>
<param>
<type>const std::function< double(double, const double *, int)> &</type>
<declname>f</declname>
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<param>
<type>const double *</type>
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<param>
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<param>
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<para>Worker function for integration routines, should not be called directly. <linebreak/>
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<para>Default constructor, creates empty object. </para>
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<definition>void libecpint::GCQuadrature::initGrid</definition>
<argsstring>(int points, GCTYPE t)</argsstring>
<name>initGrid</name>
<param>
<type>int</type>
<declname>points</declname>
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<param>
<type><ref refid="namespacelibecpint_1a61c66c38649b648ca25caaff9ebc6c3f" kindref="member">GCTYPE</ref></type>
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<para>Intialises the integration grid to the given number of points, and integration type. ONEPOINT will choose N = 2^n - 1 closest to the given number of points, whilst TWOPOINT will choose N= 3*2^n - 1 in the same way.</para>
<para><parameterlist kind="param"><parameteritem>
<parameternamelist>
<parametername>points</parametername>
</parameternamelist>
<parameterdescription>
<para>- maximum number of quadrature points to be used </para>
</parameterdescription>
</parameteritem>
<parameteritem>
<parameternamelist>
<parametername>t</parametername>
</parameternamelist>
<parameterdescription>
<para>- the algorithm to be used (ONEPOINT / TWOPOINT) </para>
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<param>
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<param>
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<param>
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<param>
<type>int</type>
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<para>Integrates the given function (over [-1, 1] by default) to within the given tolerance. <parameterlist kind="param"><parameteritem>
<parameternamelist>
<parametername>f</parametername>
</parameternamelist>
<parameterdescription>
<para>- the function to be integrated </para>
</parameterdescription>
</parameteritem>
<parameteritem>
<parameternamelist>
<parametername>params</parametername>
</parameternamelist>
<parameterdescription>
<para>- array of parameters for the function to be integrated </para>
</parameterdescription>
</parameteritem>
<parameteritem>
<parameternamelist>
<parametername>tolerance</parametername>
</parameternamelist>
<parameterdescription>
<para>- change below which convergenced is considered to be achieved </para>
</parameterdescription>
</parameteritem>
<parameteritem>
<parameternamelist>
<parametername>start</parametername>
</parameternamelist>
<parameterdescription>
<para>- the index of the first point used in the integration </para>
</parameterdescription>
</parameteritem>
<parameteritem>
<parameternamelist>
<parametername>end</parametername>
</parameternamelist>
<parameterdescription>
<para>- the index of the last point used in the integration </para>
</parameterdescription>
</parameteritem>
</parameterlist>
<simplesect kind="return"><para>the integral (first) and true if integration converged, false otherwise (second) </para>
</simplesect>
</para>
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<inbodydescription>
</inbodydescription>
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<para>Transforms the region of integration to [0, inf) using the logarithmic transformation of Krack98 </para>
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<inbodydescription>
</inbodydescription>
<location file="/Users/robertshaw/devfiles/libecpint/include/libecpint/gaussquad.hpp" line="102" column="6" bodyfile="/Users/robertshaw/devfiles/libecpint/src/lib/gaussquad.cpp" bodystart="245" bodyend="254"/>
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<type>double</type>
<declname>z</declname>
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<param>
<type>double</type>
<declname>p</declname>
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<para>Transforms region of integration to [rmin, rmax] using the linear transformation from Flores06, assuming a Gaussian envelope. rmin/rmax are the distances from the centre of the envelope such that the integrand is effectively zero. <parameterlist kind="param"><parameteritem>
<parameternamelist>
<parametername>z</parametername>
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<parameterdescription>
<para>- the exponent of the Gaussian envelope </para>
</parameterdescription>
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<parameteritem>
<parameternamelist>
<parametername>p</parametername>
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<para>- the centre of the Gaussian envelope </para>
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<type>double</type>
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<type>double</type>
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<para><simplesect kind="return"><para>the maximum number of quadrature points </para>
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<para><simplesect kind="return"><para>a reference to the abscissae </para>
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<type>const std::vector< double > &</type>
<definition>const std::vector<double>& libecpint::GCQuadrature::getX</definition>
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<briefdescription>
<para>Performs adaptive Gauss-Chebyshev quadrature of the second kind for any given function. </para>
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<detaileddescription>
<para>Stores the weights and abscissae for the quadrature, and provides two different methods to integrate on [-1, 1] Also contains means to transform the region of integration to [0, infinity) and [rmin, rmax]</para>
<para>REFERENCES: (Perez92) J.M. Perez-Jorda et al., Comput. Phys. Comm. 70 (1992), 271-284 (Perez93) J.M. Perez-Jorda et al., Comput. Phys. Comm. 77 (1993), 46-56 (Krack98) M. Krack, A.M. Koster, J. Chem. Phys. 108 (1998), 3226 - 3234 (Flores06) R. Flores-Moreno et al., J. Comput. Chem. 27 (2006), 1009-1019 </para>
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