Gabriele Cosmo
105 lines
4.7 KiB
C++
105 lines
4.7 KiB
C++
/*
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# <<BEGIN-copyright>>
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# <<END-copyright>>
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*/
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#include "nf_Legendre.h"
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#if defined __cplusplus
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namespace GIDI {
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using namespace GIDI;
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#endif
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struct nf_Legendre_GaussianQuadrature_degree {
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int n;
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double *weights;
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double *xis;
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};
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static double sqrt_inv3 = 0.57735026918962576451; /* sqrt( 1. / 3. ); */
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#define n_3 3
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static double weights_3[(n_3 + 1)/2] = { 8. / 9., 5. / 9. };
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static double xis_3[(n_3 + 1)/2] = { 0., 0.77459666924148337704 };
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#define n_4 4
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static double weights_4[(n_4 + 1)/2] = { 0.65214515486254614263, 0.34785484513745385737 };
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static double xis_4[(n_4 + 1)/2] = { 0.33998104358485626480, 0.86113631159405257522 };
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#define n_5 5
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static double weights_5[(n_5 + 1)/2] = { 0.568888888888889, 0.478628670499366, 0.236926885056189 };
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static double xis_5[(n_5 + 1)/2] = { 0.0, 0.538469310105683, 0.906179845938664 };
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#define n_10 10
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static double weights_10[(n_10 + 1)/2] = { 0.295524224714752870, 0.269266719309996355, 0.219086362515982044, 0.149451349150580593, 0.066671344308688138 };
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static double xis_10[(n_10 + 1)/2] = { 0.148874338981631211, 0.433395394129247191, 0.679409568299024406, 0.865063366688984511, 0.973906528517171720 };
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#define n_20 20
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static double weights_20[(n_20 + 1)/2] = {
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0.152753387130725850698, 0.149172986472603746788, 0.142096109318382051329, 0.131688638449176626898, 0.118194531961518417312,
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0.101930119817240435037, 0.083276741576704748725, 0.062672048334109063570, 0.040601429800386941331, 0.017614007139152118312 };
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static double xis_20[(n_20 + 1)/2] = {
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0.076526521133497333755, 0.227785851141645078080, 0.373706088715419560673, 0.510867001950827098004, 0.636053680726515025453,
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0.746331906460150792614, 0.839116971822218823395, 0.912234428251325905868, 0.963971927277913791268, 0.993128599185094924786 };
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#define n_40 40
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static double weights_40[(n_40 + 1)/2] = {
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0.077505947978424811264, 0.077039818164247965588, 0.076110361900626242372, 0.074723169057968264200, 0.072886582395804059061,
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0.070611647391286779696, 0.067912045815233903826, 0.064804013456601038075, 0.061306242492928939167, 0.057439769099391551367,
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0.053227846983936824355, 0.048695807635072232061, 0.043870908185673271992, 0.038782167974472017640, 0.033460195282547847393,
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0.027937006980023401099, 0.022245849194166957262, 0.016421058381907888713, 0.010498284531152813615, 0.004521277098533191258 };
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static double xis_40[(n_40 + 1)/2] = {
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0.038772417506050821933, 0.116084070675255208483, 0.192697580701371099716, 0.268152185007253681141, 0.341994090825758473007,
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0.413779204371605001525, 0.483075801686178712909, 0.549467125095128202076, 0.612553889667980237953, 0.671956684614179548379,
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0.727318255189927103281, 0.778305651426519387695, 0.824612230833311663196, 0.865959503212259503821, 0.902098806968874296728,
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0.932812808278676533361, 0.957916819213791655805, 0.977259949983774262663, 0.990726238699457006453, 0.998237709710559200350 };
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#define nSets 6
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static struct nf_Legendre_GaussianQuadrature_degree GaussianQuadrature_degrees[nSets] = { { n_3, weights_3, xis_3 }, { n_4, weights_4, xis_4 },
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{ n_5, weights_5, xis_5 }, { n_10, weights_10, xis_10 }, { n_20, weights_20, xis_20 }, { n_40, weights_40, xis_40 } };
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/*
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************************************************************
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*/
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nfu_status nf_Legendre_GaussianQuadrature( int degree, double x1, double x2, nf_Legendre_GaussianQuadrature_callback func, void *argList, double *integral ) {
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int i, n;
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double x, mu, sum, *weights, *xis;
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nfu_status status = nfu_Okay;
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*integral = 0;
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if( degree < 2 ) {
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status = func( 0.5 * ( x1 + x2 ), integral, argList );
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*integral *= 2.; }
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else if( degree < 4 ) {
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x = 0.5 * ( -sqrt_inv3 * ( x2 - x1 ) + x1 + x2 );
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if( ( status = func( x, integral, argList ) ) == nfu_Okay ) {
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x = 0.5 * ( sqrt_inv3 * ( x2 - x1 ) + x1 + x2 );
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status = func( x, &sum, argList );
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*integral += sum;
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} }
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else {
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for( i = 0; i < nSets - 1; i++ ) {
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if( GaussianQuadrature_degrees[i].n > ( degree + 1 ) / 2 ) break;
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}
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n = ( GaussianQuadrature_degrees[i].n + 1 ) / 2;
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weights = GaussianQuadrature_degrees[i].weights;
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xis = GaussianQuadrature_degrees[i].xis;
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for( i = 0; i < n; i++ ) {
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mu = xis[i];
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x = 0.5 * ( x1 * ( 1 - mu ) + x2 * ( mu + 1 ) );
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if( ( status = func( x, &sum, argList ) ) != nfu_Okay ) break;
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*integral += sum * weights[i];
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if( mu == 0 ) continue;
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x = x1 + x2 - x;
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if( ( status = func( x, &sum, argList ) ) != nfu_Okay ) break;
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*integral += sum * weights[i];
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}
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}
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*integral *= 0.5 * ( x2 - x1 );
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return( status );
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}
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#if defined __cplusplus
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}
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#endif
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