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/* integration/rational.c
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*
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* Copyright (C) 2017 Konrad Griessinger, Patrick Alken
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or (at
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* your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*/
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/*
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* The code in this module is based on IQPACK, specifically the LGPL
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* implementation found in HERMITE_RULE:
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* https://people.sc.fsu.edu/~jburkardt/c_src/hermite_rule/hermite_rule.html
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*/
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#include <stdio.h>
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#include <gsl/gsl_errno.h>
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#include <gsl/gsl_math.h>
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#include <gsl/gsl_integration.h>
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#include <gsl/gsl_sf_gamma.h>
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static int
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rational_check(const size_t n, const gsl_integration_fixed_params * params)
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{
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if (fabs(params->b - params->a) <= GSL_DBL_EPSILON)
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{
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GSL_ERROR("|b - a| too small", GSL_EDOM);
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}
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else if (params->alpha <= -1.0)
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{
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GSL_ERROR("alpha must be > -1", GSL_EDOM);
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}
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else if (params->beta >= 0.0 || params->alpha+params->beta+2*n >= 0.0 || 0.0 >= params->alpha+2*n)
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{
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GSL_ERROR("beta < alpha + beta + 2n < 0 is required", GSL_EDOM);
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}
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else if (params->a + params->b <= 0.0)
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{
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GSL_ERROR("a + b <= 0 is not allowed", GSL_EDOM);
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}
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else
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{
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return GSL_SUCCESS;
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}
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}
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static int
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rational_init(const size_t n, double * diag, double * subdiag, gsl_integration_fixed_params * params)
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{
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const double absum = params->beta + params->alpha;
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const double a1 = params->alpha + 1.0;
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const double aba1 = absum*a1;
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double ab2i = absum + 2.0;
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size_t i;
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/* construct the diagonal and subdiagonal elements of Jacobi matrix */
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diag[0] = -a1/(absum + 2.0);
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subdiag[0] = sqrt( -diag[0] * ( params->beta + 1.0 ) / ( (absum + 2.0)*(absum + 3.0) ) );
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for (i = 1; i < n-1; i++)
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{
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ab2i += 2.0;
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diag[i] = ( -aba1 - 2.0 * i * ( absum + i + 1.0 ) ) / ( ab2i * ( ab2i - 2.0 ) );
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subdiag[i] = sqrt( (i+1.0) * ( params->alpha + i + 1.0 ) / ( ab2i - 1.0 ) * ( params->beta + i + 1.0 ) / ( ab2i * ab2i ) * ( absum + i + 1.0 ) / ( ab2i + 1.0 ) );
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}
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diag[n-1] = ( -aba1 - 2.0 * (n-1.0) * ( absum + n ) ) / ( (absum + 2.0*n) * ( absum + 2.0*n - 2.0 ) );
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subdiag[n-1] = 0.0;
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params->zemu = gsl_sf_gamma(params->alpha + 1.0) * gsl_sf_gamma(-absum - 1.0) / gsl_sf_gamma(-params->beta);
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params->shft = params->a;
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params->slp = params->b + params->a;
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params->al = params->alpha;
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params->be = params->beta;
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return GSL_SUCCESS;
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}
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static const gsl_integration_fixed_type rational_type =
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{
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rational_check,
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rational_init
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};
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const gsl_integration_fixed_type *gsl_integration_fixed_rational = &rational_type;
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