/* integration/jacobi.c

 * 

 * Copyright (C) 2017 Konrad Griessinger, Patrick Alken

 * 

 * This program is free software; you can redistribute it and/or modify

 * it under the terms of the GNU General Public License as published by

 * the Free Software Foundation; either version 3 of the License, or (at

 * your option) any later version.

 * 

 * This program is distributed in the hope that it will be useful, but

 * WITHOUT ANY WARRANTY; without even the implied warranty of

 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

 * General Public License for more details.

 * 

 * You should have received a copy of the GNU General Public License

 * along with this program; if not, write to the Free Software

 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.

 */

/*

 * The code in this module is based on IQPACK, specifically the LGPL

 * implementation found in HERMITE_RULE:

 * https://people.sc.fsu.edu/~jburkardt/c_src/hermite_rule/hermite_rule.html

 */

#include <stdio.h>

#include <gsl/gsl_errno.h>

#include <gsl/gsl_math.h>

#include <gsl/gsl_integration.h>

#include <gsl/gsl_sf_gamma.h>

static int

jacobi_check(const size_t n, const gsl_integration_fixed_params * params)

{

  (void) n;

  if (fabs(params->b - params->a) <= GSL_DBL_EPSILON)

    {

      GSL_ERROR("|b - a| too small", GSL_EDOM);

    }

  else if (params->a >= params->b)

    {

      GSL_ERROR("lower integration limit must be smaller than upper limit", GSL_EDOM);

    }

  else if (params->alpha <= -1.0 || params->beta <= -1.0)

    {

      GSL_ERROR("alpha and beta must be > -1", GSL_EDOM);

    }

  else

    {

      return GSL_SUCCESS;

    }

}

static int

jacobi_init(const size_t n, double * diag, double * subdiag, gsl_integration_fixed_params * params)

{

  const double absum = params->beta + params->alpha;

  const double abdiff = params->beta - params->alpha;

  const double a2b2 = absum * abdiff; /* beta^2 - alpha^2 */

  size_t i;

  /* construct the diagonal and subdiagonal elements of Jacobi matrix */

  diag[0] = abdiff/(absum + 2.0);

  subdiag[0] = 2.0*sqrt((params->alpha + 1.0)*(params->beta + 1.0)/(absum + 3.0))/(absum + 2.0);

  for (i = 1; i < n; i++)

    {

      diag[i] = a2b2 / ( (absum + 2.0*i) * (absum + 2.0*i + 2.0) );

      subdiag[i] = sqrt ( 4.0*(i + 1.0) * (params->alpha + i + 1.0) * (params->beta + i + 1.0) * (absum + i + 1.0) / ( pow((absum + 2.0*i + 2.0), 2.0) - 1.0 ) ) / ( absum + 2.0*i + 2.0 );

    }

  params->zemu = pow(2.0, absum + 1.0) * gsl_sf_gamma(params->alpha + 1.0) * gsl_sf_gamma(params->beta + 1.0) / gsl_sf_gamma(absum + 2.0);

  params->shft = 0.5*(params->b + params->a);

  params->slp = 0.5*(params->b - params->a);

  params->al = params->alpha;

  params->be = params->beta;

  return GSL_SUCCESS;

}

static const gsl_integration_fixed_type jacobi_type =

{

  jacobi_check,

  jacobi_init

};

const gsl_integration_fixed_type *gsl_integration_fixed_jacobi = &jacobi_type;