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Member "PDL-2.080/GENERATED/PDL/GSLSF/LEGENDRE.pm" (28 May 2022, 10644 Bytes) of package /linux/misc/PDL-2.080.tar.gz:


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    1 #
    2 # GENERATED WITH PDL::PP! Don't modify!
    3 #
    4 package PDL::GSLSF::LEGENDRE;
    5 
    6 our @EXPORT_OK = qw(gsl_sf_legendre_Pl gsl_sf_legendre_Pl_array gsl_sf_legendre_Ql gsl_sf_legendre_Plm gsl_sf_legendre_array gsl_sf_legendre_array_index gsl_sf_legendre_sphPlm gsl_sf_conicalP_half gsl_sf_conicalP_mhalf gsl_sf_conicalP_0 gsl_sf_conicalP_1 gsl_sf_conicalP_sph_reg gsl_sf_conicalP_cyl_reg_e gsl_sf_legendre_H3d gsl_sf_legendre_H3d_array );
    7 our %EXPORT_TAGS = (Func=>\@EXPORT_OK);
    8 
    9 use PDL::Core;
   10 use PDL::Exporter;
   11 use DynaLoader;
   12 
   13 
   14    
   15    our @ISA = ( 'PDL::Exporter','DynaLoader' );
   16    push @PDL::Core::PP, __PACKAGE__;
   17    bootstrap PDL::GSLSF::LEGENDRE ;
   18 
   19 
   20 
   21 
   22 
   23 
   24 #line 5 "gsl_sf_legendre.pd"
   25 
   26 use strict;
   27 use warnings;
   28 
   29 =head1 NAME
   30 
   31 PDL::GSLSF::LEGENDRE - PDL interface to GSL Special Functions
   32 
   33 =head1 DESCRIPTION
   34 
   35 This is an interface to the Special Function package present in the GNU Scientific Library. 
   36 
   37 =cut
   38 #line 39 "LEGENDRE.pm"
   39 
   40 
   41 
   42 
   43 
   44 
   45 =head1 FUNCTIONS
   46 
   47 =cut
   48 
   49 
   50 
   51 
   52 #line 948 "../../../../blib/lib/PDL/PP.pm"
   53 
   54 
   55 
   56 =head2 gsl_sf_legendre_Pl
   57 
   58 =for sig
   59 
   60   Signature: (double x(); double [o]y(); double [o]e(); int l)
   61 
   62 =for ref
   63 
   64 P_l(x)
   65 
   66 =for bad
   67 
   68 gsl_sf_legendre_Pl does not process bad values.
   69 It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
   70 
   71 
   72 =cut
   73 #line 74 "LEGENDRE.pm"
   74 
   75 
   76 
   77 #line 950 "../../../../blib/lib/PDL/PP.pm"
   78 
   79 *gsl_sf_legendre_Pl = \&PDL::gsl_sf_legendre_Pl;
   80 #line 81 "LEGENDRE.pm"
   81 
   82 
   83 
   84 #line 948 "../../../../blib/lib/PDL/PP.pm"
   85 
   86 
   87 
   88 =head2 gsl_sf_legendre_Pl_array
   89 
   90 =for sig
   91 
   92   Signature: (double x(); double [o]y(num); int l=>num)
   93 
   94 =for ref
   95 
   96 P_l(x) from 0 to n-1.
   97 
   98 =for bad
   99 
  100 gsl_sf_legendre_Pl_array does not process bad values.
  101 It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
  102 
  103 
  104 =cut
  105 #line 106 "LEGENDRE.pm"
  106 
  107 
  108 
  109 #line 950 "../../../../blib/lib/PDL/PP.pm"
  110 
  111 *gsl_sf_legendre_Pl_array = \&PDL::gsl_sf_legendre_Pl_array;
  112 #line 113 "LEGENDRE.pm"
  113 
  114 
  115 
  116 #line 948 "../../../../blib/lib/PDL/PP.pm"
  117 
  118 
  119 
  120 =head2 gsl_sf_legendre_Ql
  121 
  122 =for sig
  123 
  124   Signature: (double x(); double [o]y(); double [o]e(); int l)
  125 
  126 =for ref
  127 
  128 Q_l(x)
  129 
  130 =for bad
  131 
  132 gsl_sf_legendre_Ql does not process bad values.
  133 It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
  134 
  135 
  136 =cut
  137 #line 138 "LEGENDRE.pm"
  138 
  139 
  140 
  141 #line 950 "../../../../blib/lib/PDL/PP.pm"
  142 
  143 *gsl_sf_legendre_Ql = \&PDL::gsl_sf_legendre_Ql;
  144 #line 145 "LEGENDRE.pm"
  145 
  146 
  147 
  148 #line 948 "../../../../blib/lib/PDL/PP.pm"
  149 
  150 
  151 
  152 =head2 gsl_sf_legendre_Plm
  153 
  154 =for sig
  155 
  156   Signature: (double x(); double [o]y(); double [o]e(); int l; int m)
  157 
  158 =for ref
  159 
  160 P_lm(x)
  161 
  162 =for bad
  163 
  164 gsl_sf_legendre_Plm does not process bad values.
  165 It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
  166 
  167 
  168 =cut
  169 #line 170 "LEGENDRE.pm"
  170 
  171 
  172 
  173 #line 950 "../../../../blib/lib/PDL/PP.pm"
  174 
  175 *gsl_sf_legendre_Plm = \&PDL::gsl_sf_legendre_Plm;
  176 #line 177 "LEGENDRE.pm"
  177 
  178 
  179 
  180 #line 948 "../../../../blib/lib/PDL/PP.pm"
  181 
  182 
  183 
  184 =head2 gsl_sf_legendre_array
  185 
  186 =for sig
  187 
  188   Signature: (double x(); double [o]y(n); double [t]work(wn); char norm;  int lmax; int csphase)
  189 
  190 =for ref
  191 
  192 Calculate all normalized associated Legendre polynomials.
  193 
  194 =for usage
  195 
  196 $Plm = gsl_sf_legendre_array($x,'P',4,-1);
  197 
  198 The calculation is done for degree 0 <= l <= lmax and order 0 <= m <= l on the range abs(x)<=1.
  199 
  200 The parameter norm should be:
  201 
  202 =over 3
  203 
  204 =item 'S' for Schmidt semi-normalized associated Legendre polynomials S_l^m(x),
  205 
  206 =item 'Y' for spherical harmonic associated Legendre polynomials Y_l^m(x), or
  207 
  208 =item 'N' for fully normalized associated Legendre polynomials N_l^m(x).
  209 
  210 =item 'P' (or any other) for unnormalized associated Legendre polynomials P_l^m(x),
  211 
  212 =back
  213 
  214 lmax is the maximum degree l.
  215 csphase should be (-1) to INCLUDE the Condon-Shortley phase factor (-1)^m, or (+1) to EXCLUDE it.
  216 
  217 See L</gsl_sf_legendre_array_index> to get the value of C<l> and C<m> in the returned vector.
  218 
  219 
  220 =for bad
  221 
  222 gsl_sf_legendre_array processes bad values.
  223 It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
  224 
  225 
  226 =cut
  227 #line 228 "LEGENDRE.pm"
  228 
  229 
  230 
  231 #line 950 "../../../../blib/lib/PDL/PP.pm"
  232 
  233 *gsl_sf_legendre_array = \&PDL::gsl_sf_legendre_array;
  234 #line 235 "LEGENDRE.pm"
  235 
  236 
  237 
  238 #line 948 "../../../../blib/lib/PDL/PP.pm"
  239 
  240 
  241 
  242 =head2 gsl_sf_legendre_array_index
  243 
  244 =for sig
  245 
  246   Signature: (int [o]l(n); int [o]m(n); int lmax)
  247 
  248 =for ref
  249 
  250 Calculate the relation between gsl_sf_legendre_arrays index and l and m values.
  251 
  252 =for usage
  253 ($l,$m) = gsl_sf_legendre_array_index($lmax);
  254 
  255 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 C<gsl_sf_legendre_array> and it calculates all l and m values.
  256 
  257 =for bad
  258 
  259 gsl_sf_legendre_array_index does not process bad values.
  260 It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
  261 
  262 
  263 =cut
  264 #line 265 "LEGENDRE.pm"
  265 
  266 
  267 
  268 #line 950 "../../../../blib/lib/PDL/PP.pm"
  269 
  270 *gsl_sf_legendre_array_index = \&PDL::gsl_sf_legendre_array_index;
  271 #line 272 "LEGENDRE.pm"
  272 
  273 
  274 
  275 #line 948 "../../../../blib/lib/PDL/PP.pm"
  276 
  277 
  278 
  279 =head2 gsl_sf_legendre_sphPlm
  280 
  281 =for sig
  282 
  283   Signature: (double x(); double [o]y(); double [o]e(); int l; int m)
  284 
  285 =for ref
  286 
  287 P_lm(x), normalized properly for use in spherical harmonics
  288 
  289 =for bad
  290 
  291 gsl_sf_legendre_sphPlm does not process bad values.
  292 It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
  293 
  294 
  295 =cut
  296 #line 297 "LEGENDRE.pm"
  297 
  298 
  299 
  300 #line 950 "../../../../blib/lib/PDL/PP.pm"
  301 
  302 *gsl_sf_legendre_sphPlm = \&PDL::gsl_sf_legendre_sphPlm;
  303 #line 304 "LEGENDRE.pm"
  304 
  305 
  306 
  307 #line 948 "../../../../blib/lib/PDL/PP.pm"
  308 
  309 
  310 
  311 =head2 gsl_sf_conicalP_half
  312 
  313 =for sig
  314 
  315   Signature: (double x(); double [o]y(); double [o]e(); double lambda)
  316 
  317 =for ref
  318 
  319 Irregular Spherical Conical Function P^{1/2}_{-1/2 + I lambda}(x)
  320 
  321 =for bad
  322 
  323 gsl_sf_conicalP_half does not process bad values.
  324 It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
  325 
  326 
  327 =cut
  328 #line 329 "LEGENDRE.pm"
  329 
  330 
  331 
  332 #line 950 "../../../../blib/lib/PDL/PP.pm"
  333 
  334 *gsl_sf_conicalP_half = \&PDL::gsl_sf_conicalP_half;
  335 #line 336 "LEGENDRE.pm"
  336 
  337 
  338 
  339 #line 948 "../../../../blib/lib/PDL/PP.pm"
  340 
  341 
  342 
  343 =head2 gsl_sf_conicalP_mhalf
  344 
  345 =for sig
  346 
  347   Signature: (double x(); double [o]y(); double [o]e(); double lambda)
  348 
  349 =for ref
  350 
  351 Regular Spherical Conical Function P^{-1/2}_{-1/2 + I lambda}(x)
  352 
  353 =for bad
  354 
  355 gsl_sf_conicalP_mhalf does not process bad values.
  356 It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
  357 
  358 
  359 =cut
  360 #line 361 "LEGENDRE.pm"
  361 
  362 
  363 
  364 #line 950 "../../../../blib/lib/PDL/PP.pm"
  365 
  366 *gsl_sf_conicalP_mhalf = \&PDL::gsl_sf_conicalP_mhalf;
  367 #line 368 "LEGENDRE.pm"
  368 
  369 
  370 
  371 #line 948 "../../../../blib/lib/PDL/PP.pm"
  372 
  373 
  374 
  375 =head2 gsl_sf_conicalP_0
  376 
  377 =for sig
  378 
  379   Signature: (double x(); double [o]y(); double [o]e(); double lambda)
  380 
  381 =for ref
  382 
  383 Conical Function P^{0}_{-1/2 + I lambda}(x)
  384 
  385 =for bad
  386 
  387 gsl_sf_conicalP_0 does not process bad values.
  388 It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
  389 
  390 
  391 =cut
  392 #line 393 "LEGENDRE.pm"
  393 
  394 
  395 
  396 #line 950 "../../../../blib/lib/PDL/PP.pm"
  397 
  398 *gsl_sf_conicalP_0 = \&PDL::gsl_sf_conicalP_0;
  399 #line 400 "LEGENDRE.pm"
  400 
  401 
  402 
  403 #line 948 "../../../../blib/lib/PDL/PP.pm"
  404 
  405 
  406 
  407 =head2 gsl_sf_conicalP_1
  408 
  409 =for sig
  410 
  411   Signature: (double x(); double [o]y(); double [o]e(); double lambda)
  412 
  413 =for ref
  414 
  415 Conical Function P^{1}_{-1/2 + I lambda}(x)
  416 
  417 =for bad
  418 
  419 gsl_sf_conicalP_1 does not process bad values.
  420 It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
  421 
  422 
  423 =cut
  424 #line 425 "LEGENDRE.pm"
  425 
  426 
  427 
  428 #line 950 "../../../../blib/lib/PDL/PP.pm"
  429 
  430 *gsl_sf_conicalP_1 = \&PDL::gsl_sf_conicalP_1;
  431 #line 432 "LEGENDRE.pm"
  432 
  433 
  434 
  435 #line 948 "../../../../blib/lib/PDL/PP.pm"
  436 
  437 
  438 
  439 =head2 gsl_sf_conicalP_sph_reg
  440 
  441 =for sig
  442 
  443   Signature: (double x(); double [o]y(); double [o]e(); int l; double lambda)
  444 
  445 =for ref
  446 
  447 Regular Spherical Conical Function P^{-1/2-l}_{-1/2 + I lambda}(x)
  448 
  449 =for bad
  450 
  451 gsl_sf_conicalP_sph_reg does not process bad values.
  452 It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
  453 
  454 
  455 =cut
  456 #line 457 "LEGENDRE.pm"
  457 
  458 
  459 
  460 #line 950 "../../../../blib/lib/PDL/PP.pm"
  461 
  462 *gsl_sf_conicalP_sph_reg = \&PDL::gsl_sf_conicalP_sph_reg;
  463 #line 464 "LEGENDRE.pm"
  464 
  465 
  466 
  467 #line 948 "../../../../blib/lib/PDL/PP.pm"
  468 
  469 
  470 
  471 =head2 gsl_sf_conicalP_cyl_reg_e
  472 
  473 =for sig
  474 
  475   Signature: (double x(); double [o]y(); double [o]e(); int m; double lambda)
  476 
  477 =for ref
  478 
  479 Regular Cylindrical Conical Function P^{-m}_{-1/2 + I lambda}(x)
  480 
  481 =for bad
  482 
  483 gsl_sf_conicalP_cyl_reg_e does not process bad values.
  484 It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
  485 
  486 
  487 =cut
  488 #line 489 "LEGENDRE.pm"
  489 
  490 
  491 
  492 #line 950 "../../../../blib/lib/PDL/PP.pm"
  493 
  494 *gsl_sf_conicalP_cyl_reg_e = \&PDL::gsl_sf_conicalP_cyl_reg_e;
  495 #line 496 "LEGENDRE.pm"
  496 
  497 
  498 
  499 #line 948 "../../../../blib/lib/PDL/PP.pm"
  500 
  501 
  502 
  503 =head2 gsl_sf_legendre_H3d
  504 
  505 =for sig
  506 
  507   Signature: (double [o]y(); double [o]e(); int l; double lambda; double eta)
  508 
  509 =for ref
  510 
  511 lth radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space.
  512 
  513 =for bad
  514 
  515 gsl_sf_legendre_H3d does not process bad values.
  516 It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
  517 
  518 
  519 =cut
  520 #line 521 "LEGENDRE.pm"
  521 
  522 
  523 
  524 #line 950 "../../../../blib/lib/PDL/PP.pm"
  525 
  526 *gsl_sf_legendre_H3d = \&PDL::gsl_sf_legendre_H3d;
  527 #line 528 "LEGENDRE.pm"
  528 
  529 
  530 
  531 #line 948 "../../../../blib/lib/PDL/PP.pm"
  532 
  533 
  534 
  535 =head2 gsl_sf_legendre_H3d_array
  536 
  537 =for sig
  538 
  539   Signature: (double [o]y(num); int l=>num; double lambda; double eta)
  540 
  541 =for ref
  542 
  543 Array of H3d(ell), for l from 0 to n-1.
  544 
  545 =for bad
  546 
  547 gsl_sf_legendre_H3d_array does not process bad values.
  548 It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
  549 
  550 
  551 =cut
  552 #line 553 "LEGENDRE.pm"
  553 
  554 
  555 
  556 #line 950 "../../../../blib/lib/PDL/PP.pm"
  557 
  558 *gsl_sf_legendre_H3d_array = \&PDL::gsl_sf_legendre_H3d_array;
  559 #line 560 "LEGENDRE.pm"
  560 
  561 
  562 
  563 
  564 
  565 #line 302 "gsl_sf_legendre.pd"
  566 
  567 
  568 =head1 AUTHOR
  569 
  570 This file copyright (C) 1999 Christian Pellegrin <chri@infis.univ.trieste.it>
  571 All rights reserved. There
  572 is no warranty. You are allowed to redistribute this software /
  573 documentation under certain conditions. For details, see the file
  574 COPYING in the PDL distribution. If this file is separated from the
  575 PDL distribution, the copyright notice should be included in the file.
  576 
  577 The GSL SF modules were written by G. Jungman.
  578 
  579 =cut
  580 #line 581 "LEGENDRE.pm"
  581 
  582 
  583 
  584 
  585 # Exit with OK status
  586 
  587 1;