NAME
PDL::GSLSF::LEGENDRE - PDL interface to GSL Special Functions
DESCRIPTION
This is an interface to the Special Function package present in the GNU Scientific Library.
SYNOPSIS
Calculate all normalized associated Legendre polynomials.
$Plm = gsl_sf_legendre_array($x,'P',4,-1);
The calculation is done for degree 0 <= l <= lmax and order 0 <= m <= l on the range abs(x)<=1.
The parameter norm should be:
- 'P' for unnormalized associated Legendre polynomials P_l^m(x),
- 'S' for Schmidt semi-normalized associated Legendre polynomials S_l^m(x),
- 'Y' for spherical harmonic associated Legendre polynomials Y_l^m(x), or
- 'N' for fully normalized associated Legendre polynomials N_l^m(x).
lmax is the maximum degree l. csphase should be (-1) to INCLUDE the Condon-Shortley phase factor (-1)^m, or (+1) to EXCLUDE it.
See "gsl_sf_legendre_array_index" to get the value of l and m in the returned vector.
EOD
);
pp_def('gsl_sf_legendre_array_index',
OtherPars => 'int lmax',
Pars => 'int [o]l(n); int [o]m(n)',
RedoDimsCode => '$SIZE(n)=$COMP(lmax)*($COMP(lmax)+1)/2+$COMP(lmax)+1;',
Code => q/
int ell, em, index;
for (ell=0; ell<=$COMP(lmax); ell++){
for (em=0; em<=ell; em++){
index = gsl_sf_legendre_array_index(ell,em);
$l(n=>index)=ell;
$m(n=>index)=em;
}
}/,
Doc =>'=for refCalculate the relation between gsl_sf_legendre_arrays index and l and m values.
Note that this function is called differently than the corresponding GSL function, to make it more useful for PDL: here you just input the maximum l (lmax) that was used in gsl_sf_legendre_array and it calculates all l and m values.' );
} elsif (defined($v) && $v<2.0) {
pp_def('gsl_sf_legendre_Plm_array', GenericTypes => [D], OtherPars =>'int l=>num; int m', Pars=>'double x(); double [o]y(num)', Code =>' GSLERR(gsl_sf_legendre_Plm_array,($COMP(l)-2+$COMP(m),$COMP(m),$x(),$P(y))) ', Doc =>'P_lm(x) for l from 0 to n-2+m. gsl_sf_legendre_Plm_array has been deprecated in GSL version 2.0. It is included here for backwards compatability and may be removed in a future release. New code should use "gsl_sf_legendre_array" instead.' );
pp_def('gsl_sf_legendre_sphPlm_array', GenericTypes => [D], OtherPars =>'int n=>num; int m', Pars=>'double x(); double [o]y(num)', Code =>' GSLERR(gsl_sf_legendre_sphPlm_array,($COMP(n)-2+$COMP(m),$COMP(m),$x(),$P(y))) ', Doc =>'P_lm(x), normalized properly for use in spherical harmonics for l from 0 to n-2+m. gsl_sf_legendre_sphPlm_array has been deprecated in GSL version 2.0. It is included here for backwards compatability and may be removed in a future release. New code should use "gsl_sf_legendre_array" instead.' );
} else { die("Could not determine GSL version from gsl-config, so can not determine which legendre array functions to define."); }
pp_def('gsl_sf_legendre_sphPlm', GenericTypes => [D], OtherPars =>'int l; int m', Pars=>'double x(); double [o]y(); double [o]e()', Code =>' gsl_sf_result r; GSLERR(gsl_sf_legendre_sphPlm_e,($COMP(l),$COMP(m),$x(),&r)) $y() = r.val; $e() = r.err; ', Doc =>'P_lm(x), normalized properly for use in spherical harmonics' );
pp_def('gsl_sf_conicalP_half', GenericTypes => [D], OtherPars =>'double lambda', Pars=>'double x(); double [o]y(); double [o]e()', Code =>' gsl_sf_result r; GSLERR(gsl_sf_conicalP_half_e,($COMP(lambda),$x(),&r)) $y() = r.val; $e() = r.err; ', Doc =>'Irregular Spherical Conical Function P^{1/2}_{-1/2 + I lambda}(x)' );
pp_def('gsl_sf_conicalP_mhalf', GenericTypes => [D], OtherPars =>'double lambda', Pars=>'double x(); double [o]y(); double [o]e()', Code =>' gsl_sf_result r; GSLERR(gsl_sf_conicalP_mhalf_e,($COMP(lambda),$x(),&r)) $y() = r.val; $e() = r.err; ', Doc =>'Regular Spherical Conical Function P^{-1/2}_{-1/2 + I lambda}(x)' );
pp_def('gsl_sf_conicalP_0', GenericTypes => [D], OtherPars =>'double lambda', Pars=>'double x(); double [o]y(); double [o]e()', Code =>' gsl_sf_result r; GSLERR(gsl_sf_conicalP_0_e,($COMP(lambda),$x(),&r)) $y() = r.val; $e() = r.err; ', Doc =>'Conical Function P^{0}_{-1/2 + I lambda}(x)' );
pp_def('gsl_sf_conicalP_1', GenericTypes => [D], OtherPars =>'double lambda', Pars=>'double x(); double [o]y(); double [o]e()', Code =>' gsl_sf_result r; GSLERR(gsl_sf_conicalP_1_e,($COMP(lambda),$x(),&r)) $y() = r.val; $e() = r.err; ', Doc =>'Conical Function P^{1}_{-1/2 + I lambda}(x)' );
pp_def('gsl_sf_conicalP_sph_reg', GenericTypes => [D], OtherPars =>'int l; double lambda', Pars=>'double x(); double [o]y(); double [o]e()', Code =>' gsl_sf_result r; GSLERR(gsl_sf_conicalP_sph_reg_e,($COMP(l),$COMP(lambda),$x(),&r)) $y() = r.val; $e() = r.err; ', Doc =>'Regular Spherical Conical Function P^{-1/2-l}_{-1/2 + I lambda}(x)' );
pp_def('gsl_sf_conicalP_cyl_reg_e', GenericTypes => [D], OtherPars =>'int m; double lambda', Pars=>'double x(); double [o]y(); double [o]e()', Code =>' gsl_sf_result r; GSLERR(gsl_sf_conicalP_cyl_reg_e,($COMP(m),$COMP(lambda),$x(),&r)) $y() = r.val; $e() = r.err; ', Doc =>'Regular Cylindrical Conical Function P^{-m}_{-1/2 + I lambda}(x)' );
pp_def('gsl_sf_legendre_H3d', GenericTypes => [D], OtherPars =>'int l; double lambda; double eta', Pars=>'double [o]y(); double [o]e()', Code =>' gsl_sf_result r; GSLERR(gsl_sf_legendre_H3d_e,($COMP(l),$COMP(lambda),$COMP(eta),&r)) $y() = r.val; $e() = r.err; ', Doc =>'lth radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space.' );
pp_def('gsl_sf_legendre_H3d_array', GenericTypes => [D], OtherPars =>'int l=>num; double lambda; double eta', Pars=>'double [o]y(num)', Code =>' GSLERR(gsl_sf_legendre_H3d_array,($COMP(l)-1,$COMP(lambda),$COMP(eta),$P(y))) ', Doc =>'Array of H3d(ell), for l from 0 to n-1.' );
pp_addpm({At=>Bot},<<'EOD');
AUTHOR
This file copyright (C) 1999 Christian Pellegrin <chri@infis.univ.trieste.it> All rights reserved. There is no warranty. You are allowed to redistribute this software / documentation under certain conditions. For details, see the file COPYING in the PDL distribution. If this file is separated from the PDL distribution, the copyright notice should be included in the file.
The GSL SF modules were written by G. Jungman.