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/* integration/gsl_integration.h
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*
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* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Brian Gough
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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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#ifndef __GSL_INTEGRATION_H__
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#define __GSL_INTEGRATION_H__
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#include <stdlib.h>
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#include <gsl/gsl_math.h>
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#undef __BEGIN_DECLS
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#undef __END_DECLS
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#ifdef __cplusplus
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# define __BEGIN_DECLS extern "C" {
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# define __END_DECLS }
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#else
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# define __BEGIN_DECLS /* empty */
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# define __END_DECLS /* empty */
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#endif
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__BEGIN_DECLS
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/* Workspace for adaptive integrators */
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typedef struct
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{
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size_t limit;
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size_t size;
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size_t nrmax;
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size_t i;
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size_t maximum_level;
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double *alist;
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double *blist;
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double *rlist;
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double *elist;
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size_t *order;
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size_t *level;
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}
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gsl_integration_workspace;
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gsl_integration_workspace *
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gsl_integration_workspace_alloc (const size_t n);
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void
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gsl_integration_workspace_free (gsl_integration_workspace * w);
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/* Workspace for QAWS integrator */
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typedef struct
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{
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double alpha;
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double beta;
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int mu;
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int nu;
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double ri[25];
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double rj[25];
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double rg[25];
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double rh[25];
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}
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gsl_integration_qaws_table;
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gsl_integration_qaws_table *
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gsl_integration_qaws_table_alloc (double alpha, double beta, int mu, int nu);
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int
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gsl_integration_qaws_table_set (gsl_integration_qaws_table * t,
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double alpha, double beta, int mu, int nu);
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void
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gsl_integration_qaws_table_free (gsl_integration_qaws_table * t);
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/* Workspace for QAWO integrator */
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enum gsl_integration_qawo_enum { GSL_INTEG_COSINE, GSL_INTEG_SINE };
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typedef struct
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{
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size_t n;
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double omega;
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double L;
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double par;
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enum gsl_integration_qawo_enum sine;
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double *chebmo;
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}
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gsl_integration_qawo_table;
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gsl_integration_qawo_table *
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gsl_integration_qawo_table_alloc (double omega, double L,
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enum gsl_integration_qawo_enum sine,
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size_t n);
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int
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gsl_integration_qawo_table_set (gsl_integration_qawo_table * t,
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double omega, double L,
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enum gsl_integration_qawo_enum sine);
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int
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gsl_integration_qawo_table_set_length (gsl_integration_qawo_table * t,
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double L);
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void
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gsl_integration_qawo_table_free (gsl_integration_qawo_table * t);
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/* Definition of an integration rule */
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typedef void gsl_integration_rule (const gsl_function * f,
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double a, double b,
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double *result, double *abserr,
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double *defabs, double *resabs);
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void gsl_integration_qk15 (const gsl_function * f, double a, double b,
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double *result, double *abserr,
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double *resabs, double *resasc);
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void gsl_integration_qk21 (const gsl_function * f, double a, double b,
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double *result, double *abserr,
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double *resabs, double *resasc);
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void gsl_integration_qk31 (const gsl_function * f, double a, double b,
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double *result, double *abserr,
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double *resabs, double *resasc);
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void gsl_integration_qk41 (const gsl_function * f, double a, double b,
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double *result, double *abserr,
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double *resabs, double *resasc);
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void gsl_integration_qk51 (const gsl_function * f, double a, double b,
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double *result, double *abserr,
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double *resabs, double *resasc);
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void gsl_integration_qk61 (const gsl_function * f, double a, double b,
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double *result, double *abserr,
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double *resabs, double *resasc);
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void gsl_integration_qcheb (gsl_function * f, double a, double b,
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double *cheb12, double *cheb24);
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/* The low-level integration rules in QUADPACK are identified by small
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integers (1-6). We'll use symbolic constants to refer to them. */
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enum
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{
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GSL_INTEG_GAUSS15 = 1, /* 15 point Gauss-Kronrod rule */
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GSL_INTEG_GAUSS21 = 2, /* 21 point Gauss-Kronrod rule */
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GSL_INTEG_GAUSS31 = 3, /* 31 point Gauss-Kronrod rule */
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GSL_INTEG_GAUSS41 = 4, /* 41 point Gauss-Kronrod rule */
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GSL_INTEG_GAUSS51 = 5, /* 51 point Gauss-Kronrod rule */
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GSL_INTEG_GAUSS61 = 6 /* 61 point Gauss-Kronrod rule */
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};
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void
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gsl_integration_qk (const int n, const double xgk[],
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const double wg[], const double wgk[],
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double fv1[], double fv2[],
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const gsl_function *f, double a, double b,
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double * result, double * abserr,
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double * resabs, double * resasc);
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int gsl_integration_qng (const gsl_function * f,
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double a, double b,
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double epsabs, double epsrel,
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double *result, double *abserr,
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size_t * neval);
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int gsl_integration_qag (const gsl_function * f,
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double a, double b,
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double epsabs, double epsrel, size_t limit,
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int key,
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gsl_integration_workspace * workspace,
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double *result, double *abserr);
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int gsl_integration_qagi (gsl_function * f,
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double epsabs, double epsrel, size_t limit,
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gsl_integration_workspace * workspace,
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double *result, double *abserr);
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int gsl_integration_qagiu (gsl_function * f,
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double a,
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double epsabs, double epsrel, size_t limit,
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gsl_integration_workspace * workspace,
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double *result, double *abserr);
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int gsl_integration_qagil (gsl_function * f,
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double b,
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double epsabs, double epsrel, size_t limit,
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gsl_integration_workspace * workspace,
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double *result, double *abserr);
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int gsl_integration_qags (const gsl_function * f,
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double a, double b,
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double epsabs, double epsrel, size_t limit,
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gsl_integration_workspace * workspace,
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double *result, double *abserr);
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int gsl_integration_qagp (const gsl_function * f,
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double *pts, size_t npts,
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double epsabs, double epsrel, size_t limit,
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gsl_integration_workspace * workspace,
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double *result, double *abserr);
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int gsl_integration_qawc (gsl_function *f,
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const double a, const double b, const double c,
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const double epsabs, const double epsrel, const size_t limit,
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gsl_integration_workspace * workspace,
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double * result, double * abserr);
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int gsl_integration_qaws (gsl_function * f,
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const double a, const double b,
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gsl_integration_qaws_table * t,
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const double epsabs, const double epsrel,
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const size_t limit,
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gsl_integration_workspace * workspace,
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double *result, double *abserr);
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int gsl_integration_qawo (gsl_function * f,
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const double a,
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const double epsabs, const double epsrel,
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const size_t limit,
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gsl_integration_workspace * workspace,
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gsl_integration_qawo_table * wf,
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double *result, double *abserr);
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int gsl_integration_qawf (gsl_function * f,
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const double a,
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const double epsabs,
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const size_t limit,
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gsl_integration_workspace * workspace,
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gsl_integration_workspace * cycle_workspace,
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gsl_integration_qawo_table * wf,
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double *result, double *abserr);
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/* Workspace for fixed-order Gauss-Legendre integration */
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typedef struct
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{
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size_t n; /* number of points */
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double *x; /* Gauss abscissae/points */
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double *w; /* Gauss weights for each abscissae */
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int precomputed; /* high precision abscissae/weights precomputed? */
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}
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gsl_integration_glfixed_table;
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gsl_integration_glfixed_table * gsl_integration_glfixed_table_alloc (size_t n);
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void gsl_integration_glfixed_table_free (gsl_integration_glfixed_table * t);
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/* Routine for fixed-order Gauss-Legendre integration */
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double gsl_integration_glfixed (const gsl_function *f,
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double a,
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double b,
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const gsl_integration_glfixed_table * t);
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/* Routine to retrieve the i-th Gauss-Legendre point and weight from t */
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int gsl_integration_glfixed_point (double a,
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double b,
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size_t i,
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double *xi,
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double *wi,
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const gsl_integration_glfixed_table * t);
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/* Cquad integration - Pedro Gonnet */
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/* Data of a single interval */
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typedef struct
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{
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double a, b;
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double c[64];
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double fx[33];
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double igral, err;
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int depth, rdepth, ndiv;
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} gsl_integration_cquad_ival;
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/* The workspace is just a collection of intervals */
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typedef struct
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{
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size_t size;
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gsl_integration_cquad_ival *ivals;
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size_t *heap;
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} gsl_integration_cquad_workspace;
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gsl_integration_cquad_workspace *
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gsl_integration_cquad_workspace_alloc (const size_t n);
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void
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gsl_integration_cquad_workspace_free (gsl_integration_cquad_workspace * w);
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int
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gsl_integration_cquad (const gsl_function * f, double a, double b,
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double epsabs, double epsrel,
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gsl_integration_cquad_workspace * ws,
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double *result, double *abserr, size_t * nevals);
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/* Romberg integration workspace and routines */
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typedef struct
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{
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size_t n; /* maximum number of steps */
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double *work1; /* workspace for a row of R matrix, size n */
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double *work2; /* workspace for a row of R matrix, size n */
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} gsl_integration_romberg_workspace;
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gsl_integration_romberg_workspace *gsl_integration_romberg_alloc(const size_t n);
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void gsl_integration_romberg_free(gsl_integration_romberg_workspace * w);
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int gsl_integration_romberg(const gsl_function * f, const double a, const double b,
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const double epsabs, const double epsrel, double * result,
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size_t * neval, gsl_integration_romberg_workspace * w);
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/* IQPACK related structures and routines */
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typedef struct
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{
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double alpha;
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double beta;
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double a;
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double b;
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double zemu;
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double shft;
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double slp;
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double al;
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double be;
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} gsl_integration_fixed_params;
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typedef struct
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{
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int (*check)(const size_t n, const gsl_integration_fixed_params * params);
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int (*init)(const size_t n, double * diag, double * subdiag, gsl_integration_fixed_params * params);
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} gsl_integration_fixed_type;
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typedef struct
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{
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size_t n; /* number of nodes/weights */
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double *weights; /* quadrature weights */
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double *x; /* quadrature nodes */
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double *diag; /* diagonal of Jacobi matrix */
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double *subdiag; /* subdiagonal of Jacobi matrix */
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const gsl_integration_fixed_type * type;
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} gsl_integration_fixed_workspace;
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/* IQPACK integral types */
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GSL_VAR const gsl_integration_fixed_type * gsl_integration_fixed_legendre;
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GSL_VAR const gsl_integration_fixed_type * gsl_integration_fixed_chebyshev;
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GSL_VAR const gsl_integration_fixed_type * gsl_integration_fixed_gegenbauer;
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GSL_VAR const gsl_integration_fixed_type * gsl_integration_fixed_jacobi;
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GSL_VAR const gsl_integration_fixed_type * gsl_integration_fixed_laguerre;
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GSL_VAR const gsl_integration_fixed_type * gsl_integration_fixed_hermite;
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GSL_VAR const gsl_integration_fixed_type * gsl_integration_fixed_exponential;
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GSL_VAR const gsl_integration_fixed_type * gsl_integration_fixed_rational;
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GSL_VAR const gsl_integration_fixed_type * gsl_integration_fixed_chebyshev2;
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gsl_integration_fixed_workspace *
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gsl_integration_fixed_alloc(const gsl_integration_fixed_type * type, const size_t n,
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const double a, const double b, const double alpha, const double beta);
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void gsl_integration_fixed_free(gsl_integration_fixed_workspace * w);
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size_t gsl_integration_fixed_n(const gsl_integration_fixed_workspace * w);
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double *gsl_integration_fixed_nodes(const gsl_integration_fixed_workspace * w);
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double *gsl_integration_fixed_weights(const gsl_integration_fixed_workspace * w);
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int gsl_integration_fixed(const gsl_function * func, double * result,
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const gsl_integration_fixed_workspace * w);
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__END_DECLS
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#endif /* __GSL_INTEGRATION_H__ */
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