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/* integration/hermite.c
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*
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* Copyright (C) 2017 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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hermite_check(const size_t n, const gsl_integration_fixed_params * params)
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{
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(void) n;
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if (params->b <= 0.0)
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{
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GSL_ERROR("b must be positive", 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
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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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hermite_init(const size_t n, double * diag, double * subdiag, gsl_integration_fixed_params * params)
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{
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size_t i;
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/* construct the diagonal and subdiagonal elements of Jacobi matrix */
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for (i = 1; i <= n; i++)
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{
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diag[i - 1] = 0.0;
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subdiag[i - 1] = sqrt (0.5 * (i + params->alpha * (i % 2)));
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}
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params->zemu = gsl_sf_gamma(0.5 * (params->alpha + 1.0));
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params->shft = params->a;
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params->slp = 1.0 / sqrt(params->b);
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params->al = params->alpha;
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params->be = 0.0;
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return GSL_SUCCESS;
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}
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static const gsl_integration_fixed_type hermite_type =
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{
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hermite_check,
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hermite_init
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};
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const gsl_integration_fixed_type *gsl_integration_fixed_hermite = &hermite_type;
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