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/* specfunc/mathieu_angfunc.c
*
* Copyright (C) 2002 Lowell Johnson
*
* 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., 675 Mass Ave, Cambridge, MA 02139, USA.
*/
/* Author: L. Johnson */
#include <config.h>
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_sf_mathieu.h>
int gsl_sf_mathieu_ce_e(int order, double qq, double zz, gsl_sf_result *result)
{
int even_odd, ii, status;
double coeff[GSL_SF_MATHIEU_COEFF], norm, fn, factor;
gsl_sf_result aa;
norm = 0.0;
even_odd = 0;
if (order % 2 != 0)
even_odd = 1;
/* Handle the trivial case where q = 0. */
if (qq == 0.0)
{
norm = 1.0;
if (order == 0)
norm = sqrt(2.0);
fn = cos(order*zz)/norm;
result->val = fn;
result->err = 2.0*GSL_DBL_EPSILON;
factor = fabs(fn);
if (factor > 1.0)
result->err *= factor;
return GSL_SUCCESS;
}
/* Use symmetry characteristics of the functions to handle cases with
negative order. */
if (order < 0)
order *= -1;
/* Compute the characteristic value. */
status = gsl_sf_mathieu_a_e(order, qq, &aa);
if (status != GSL_SUCCESS)
{
return status;
}
/* Compute the series coefficients. */
status = gsl_sf_mathieu_a_coeff(order, qq, aa.val, coeff);
if (status != GSL_SUCCESS)
{
return status;
}
if (even_odd == 0)
{
fn = 0.0;
norm = coeff[0]*coeff[0];
for (ii=0; ii<GSL_SF_MATHIEU_COEFF; ii++)
{
fn += coeff[ii]*cos(2.0*ii*zz);
norm += coeff[ii]*coeff[ii];
}
}
else
{
fn = 0.0;
for (ii=0; ii<GSL_SF_MATHIEU_COEFF; ii++)
{
fn += coeff[ii]*cos((2.0*ii + 1.0)*zz);
norm += coeff[ii]*coeff[ii];
}
}
norm = sqrt(norm);
fn /= norm;
result->val = fn;
result->err = 2.0*GSL_DBL_EPSILON;
factor = fabs(fn);
if (factor > 1.0)
result->err *= factor;
return GSL_SUCCESS;
}
int gsl_sf_mathieu_se_e(int order, double qq, double zz, gsl_sf_result *result)
{
int even_odd, ii, status;
double coeff[GSL_SF_MATHIEU_COEFF], norm, fn, factor;
gsl_sf_result aa;
norm = 0.0;
even_odd = 0;
if (order % 2 != 0)
even_odd = 1;
/* Handle the trivial cases where order = 0 and/or q = 0. */
if (order == 0)
{
result->val = 0.0;
result->err = 0.0;
return GSL_SUCCESS;
}
if (qq == 0.0)
{
norm = 1.0;
fn = sin(order*zz);
result->val = fn;
result->err = 2.0*GSL_DBL_EPSILON;
factor = fabs(fn);
if (factor > 1.0)
result->err *= factor;
return GSL_SUCCESS;
}
/* Use symmetry characteristics of the functions to handle cases with
negative order. */
if (order < 0)
order *= -1;
/* Compute the characteristic value. */
status = gsl_sf_mathieu_b_e(order, qq, &aa);
if (status != GSL_SUCCESS)
{
return status;
}
/* Compute the series coefficients. */
status = gsl_sf_mathieu_b_coeff(order, qq, aa.val, coeff);
if (status != GSL_SUCCESS)
{
return status;
}
if (even_odd == 0)
{
fn = 0.0;
for (ii=0; ii<GSL_SF_MATHIEU_COEFF; ii++)
{
norm += coeff[ii]*coeff[ii];
fn += coeff[ii]*sin(2.0*(ii + 1)*zz);
}
}
else
{
fn = 0.0;
for (ii=0; ii<GSL_SF_MATHIEU_COEFF; ii++)
{
norm += coeff[ii]*coeff[ii];
fn += coeff[ii]*sin((2.0*ii + 1)*zz);
}
}
norm = sqrt(norm);
fn /= norm;
result->val = fn;
result->err = 2.0*GSL_DBL_EPSILON;
factor = fabs(fn);
if (factor > 1.0)
result->err *= factor;
return GSL_SUCCESS;
}
int gsl_sf_mathieu_ce_array(int nmin, int nmax, double qq, double zz,
gsl_sf_mathieu_workspace *work,
double result_array[])
{
int even_odd, order, ii, jj, status;
double coeff[GSL_SF_MATHIEU_COEFF], *aa = work->aa, norm;
/* Initialize the result array to zeroes. */
for (ii=0; ii<nmax-nmin+1; ii++)
result_array[ii] = 0.0;
/* Ensure that the workspace is large enough to accomodate. */
if (work->size < (unsigned int)nmax)
{
GSL_ERROR("Work space not large enough", GSL_EINVAL);
}
if (nmin < 0 || nmax < nmin)
{
GSL_ERROR("domain error", GSL_EDOM);
}
/* Compute all of the eigenvalues up to nmax. */
gsl_sf_mathieu_a_array(0, nmax, qq, work, aa);
for (ii=0, order=nmin; order<=nmax; ii++, order++)
{
norm = 0.0;
even_odd = 0;
if (order % 2 != 0)
even_odd = 1;
/* Handle the trivial case where q = 0. */
if (qq == 0.0)
{
norm = 1.0;
if (order == 0)
norm = sqrt(2.0);
result_array[ii] = cos(order*zz)/norm;
continue;
}
/* Compute the series coefficients. */
status = gsl_sf_mathieu_a_coeff(order, qq, aa[order], coeff);
if (status != GSL_SUCCESS)
return status;
if (even_odd == 0)
{
norm = coeff[0]*coeff[0];
for (jj=0; jj<GSL_SF_MATHIEU_COEFF; jj++)
{
result_array[ii] += coeff[jj]*cos(2.0*jj*zz);
norm += coeff[jj]*coeff[jj];
}
}
else
{
for (jj=0; jj<GSL_SF_MATHIEU_COEFF; jj++)
{
result_array[ii] += coeff[jj]*cos((2.0*jj + 1.0)*zz);
norm += coeff[jj]*coeff[jj];
}
}
norm = sqrt(norm);
result_array[ii] /= norm;
}
return GSL_SUCCESS;
}
int gsl_sf_mathieu_se_array(int nmin, int nmax, double qq, double zz,
gsl_sf_mathieu_workspace *work,
double result_array[])
{
int even_odd, order, ii, jj, status;
double coeff[GSL_SF_MATHIEU_COEFF], *bb = work->bb, norm;
/* Initialize the result array to zeroes. */
for (ii=0; ii<nmax-nmin+1; ii++)
result_array[ii] = 0.0;
/* Ensure that the workspace is large enough to accomodate. */
if (work->size < (unsigned int)nmax)
{
GSL_ERROR("Work space not large enough", GSL_EINVAL);
}
if (nmin < 0 || nmax < nmin)
{
GSL_ERROR("domain error", GSL_EDOM);
}
/* Compute all of the eigenvalues up to nmax. */
gsl_sf_mathieu_b_array(0, nmax, qq, work, bb);
for (ii=0, order=nmin; order<=nmax; ii++, order++)
{
norm = 0.0;
even_odd = 0;
if (order % 2 != 0)
even_odd = 1;
/* Handle the trivial cases where order = 0 and/or q = 0. */
if (order == 0)
{
norm = 1.0;
result_array[ii] = 0.0;
continue;
}
if (qq == 0.0)
{
norm = 1.0;
result_array[ii] = sin(order*zz);
continue;
}
/* Compute the series coefficients. */
status = gsl_sf_mathieu_b_coeff(order, qq, bb[order], coeff);
if (status != GSL_SUCCESS)
{
return status;
}
if (even_odd == 0)
{
for (jj=0; jj<GSL_SF_MATHIEU_COEFF; jj++)
{
result_array[ii] += coeff[jj]*sin(2.0*(jj + 1)*zz);
norm += coeff[jj]*coeff[jj];
}
}
else
{
for (jj=0; jj<GSL_SF_MATHIEU_COEFF; jj++)
{
result_array[ii] += coeff[jj]*sin((2.0*jj + 1.0)*zz);
norm += coeff[jj]*coeff[jj];
}
}
norm = sqrt(norm);
result_array[ii] /= norm;
}
return GSL_SUCCESS;
}
/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
#include "eval.h"
double gsl_sf_mathieu_ce(int order, double qq, double zz)
{
EVAL_RESULT(gsl_sf_mathieu_ce_e(order, qq, zz, &result));
}
double gsl_sf_mathieu_se(int order, double qq, double zz)
{
EVAL_RESULT(gsl_sf_mathieu_se_e(order, qq, zz, &result));
}
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