/* integration/laguerre.c

 * 

 * Copyright (C) 2017 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

laguerre_check(const size_t n, const gsl_integration_fixed_params * params)

{

  (void) n;

  if (params->b <= 0.0)

    {

      GSL_ERROR("b must be positive", GSL_EDOM);

    }

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

    {

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

    }

  else

    {

      return GSL_SUCCESS;

    }

}

static int

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

{

  size_t i;

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

  for (i = 0; i < n; i++)

    {

      diag[i] = 2.0 * i + 1.0 + params->alpha;

      subdiag[i] = sqrt ((i + 1.0) * (params->alpha + i + 1.0));

    }

  params->zemu = gsl_sf_gamma(params->alpha + 1.0);

  params->shft = params->a;

  params->slp = 1.0 / params->b;

  params->al = params->alpha;

  params->be = 0.0;

  return GSL_SUCCESS;

}

static const gsl_integration_fixed_type laguerre_type =

{

  laguerre_check,

  laguerre_init

};

const gsl_integration_fixed_type *gsl_integration_fixed_laguerre = &laguerre_type;