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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 "gsl__config.h"
- #include <stdlib.h>
- #include <stdio.h>
- #include <math.h>
- #include "gsl_math.h"
- #include "gsl_sf_mathieu.h"
- int gsl_sf_mathieu_ce(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(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(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(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 case where q = 0. */
- 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;
- }
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