Mercurial > octave
annotate libinterp/corefcn/besselj.cc @ 31605:e88a07dec498 stable
maint: Use macros to begin/end C++ namespaces.
* oct-conf-post-public.in.h: Define two macros (OCTAVE_BEGIN_NAMESPACE,
OCTAVE_END_NAMESPACE) that can be used to start/end a namespace.
* mk-opts.pl, build-env.h, build-env.in.cc, __betainc__.cc, __contourc__.cc,
__dsearchn__.cc, __eigs__.cc, __expint__.cc, __ftp__.cc, __gammainc__.cc,
__ichol__.cc, __ilu__.cc, __isprimelarge__.cc, __lin_interpn__.cc,
__magick_read__.cc, __pchip_deriv__.cc, __qp__.cc, amd.cc, auto-shlib.cc,
auto-shlib.h, balance.cc, base-text-renderer.cc, base-text-renderer.h,
besselj.cc, bitfcns.cc, bsxfun.cc, c-file-ptr-stream.cc, c-file-ptr-stream.h,
call-stack.cc, call-stack.h, ccolamd.cc, cellfun.cc, chol.cc, colamd.cc,
colloc.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc, data.h, debug.cc,
defaults.cc, defaults.h, defun-int.h, defun.cc, det.cc, dirfns.cc, display.cc,
display.h, dlmread.cc, dmperm.cc, dot.cc, dynamic-ld.cc, dynamic-ld.h, eig.cc,
ellipj.cc, environment.cc, environment.h, error.cc, error.h, errwarn.h,
event-manager.cc, event-manager.h, event-queue.cc, event-queue.h, fcn-info.cc,
fcn-info.h, fft.cc, fft2.cc, fftn.cc, file-io.cc, filter.cc, find.cc,
ft-text-renderer.cc, ft-text-renderer.h, gcd.cc, getgrent.cc, getpwent.cc,
getrusage.cc, givens.cc, gl-render.cc, gl-render.h, gl2ps-print.cc,
gl2ps-print.h, graphics-toolkit.cc, graphics-toolkit.h, graphics.cc,
graphics.in.h, gsvd.cc, gtk-manager.cc, gtk-manager.h, hash.cc, help.cc,
help.h, hess.cc, hex2num.cc, hook-fcn.cc, hook-fcn.h, input.cc, input.h,
interpreter-private.cc, interpreter-private.h, interpreter.cc, interpreter.h,
inv.cc, jsondecode.cc, jsonencode.cc, kron.cc, latex-text-renderer.cc,
latex-text-renderer.h, load-path.cc, load-path.h, load-save.cc, load-save.h,
lookup.cc, ls-ascii-helper.cc, ls-ascii-helper.h, ls-oct-text.cc, ls-utils.cc,
ls-utils.h, lsode.cc, lu.cc, mappers.cc, matrix_type.cc, max.cc, mex-private.h,
mex.cc, mgorth.cc, nproc.cc, oct-fstrm.cc, oct-fstrm.h, oct-hdf5-types.cc,
oct-hdf5-types.h, oct-hist.cc, oct-hist.h, oct-iostrm.cc, oct-iostrm.h,
oct-opengl.h, oct-prcstrm.cc, oct-prcstrm.h, oct-procbuf.cc, oct-procbuf.h,
oct-process.cc, oct-process.h, oct-stdstrm.h, oct-stream.cc, oct-stream.h,
oct-strstrm.cc, oct-strstrm.h, oct-tex-lexer.in.ll, oct-tex-parser.yy,
ordqz.cc, ordschur.cc, pager.cc, pager.h, pinv.cc, pow2.cc, pr-flt-fmt.cc,
pr-output.cc, procstream.cc, procstream.h, psi.cc, qr.cc, quad.cc, quadcc.cc,
qz.cc, rand.cc, rcond.cc, regexp.cc, schur.cc, settings.cc, settings.h,
sighandlers.cc, sighandlers.h, sparse-xdiv.cc, sparse-xdiv.h, sparse-xpow.cc,
sparse-xpow.h, sparse.cc, spparms.cc, sqrtm.cc, stack-frame.cc, stack-frame.h,
stream-euler.cc, strfind.cc, strfns.cc, sub2ind.cc, svd.cc, sylvester.cc,
symbfact.cc, syminfo.cc, syminfo.h, symrcm.cc, symrec.cc, symrec.h,
symscope.cc, symscope.h, symtab.cc, symtab.h, syscalls.cc, sysdep.cc, sysdep.h,
text-engine.cc, text-engine.h, text-renderer.cc, text-renderer.h, time.cc,
toplev.cc, tril.cc, tsearch.cc, typecast.cc, url-handle-manager.cc,
url-handle-manager.h, urlwrite.cc, utils.cc, utils.h, variables.cc,
variables.h, xdiv.cc, xdiv.h, xnorm.cc, xnorm.h, xpow.cc, xpow.h,
__delaunayn__.cc, __fltk_uigetfile__.cc, __glpk__.cc, __init_fltk__.cc,
__init_gnuplot__.cc, __ode15__.cc, __voronoi__.cc, audiodevinfo.cc,
audioread.cc, convhulln.cc, fftw.cc, gzip.cc, mk-build-env-features.sh,
mk-builtins.pl, cdef-class.cc, cdef-class.h, cdef-fwd.h, cdef-manager.cc,
cdef-manager.h, cdef-method.cc, cdef-method.h, cdef-object.cc, cdef-object.h,
cdef-package.cc, cdef-package.h, cdef-property.cc, cdef-property.h,
cdef-utils.cc, cdef-utils.h, ov-base.cc, ov-base.h, ov-bool-mat.cc,
ov-builtin.h, ov-cell.cc, ov-class.cc, ov-class.h, ov-classdef.cc,
ov-classdef.h, ov-complex.cc, ov-fcn-handle.cc, ov-fcn-handle.h, ov-fcn.h,
ov-java.cc, ov-java.h, ov-mex-fcn.h, ov-null-mat.cc, ov-oncleanup.cc,
ov-struct.cc, ov-typeinfo.cc, ov-typeinfo.h, ov-usr-fcn.cc, ov-usr-fcn.h,
ov.cc, ov.h, octave.cc, octave.h, mk-ops.sh, op-b-b.cc, op-b-bm.cc,
op-b-sbm.cc, op-bm-b.cc, op-bm-bm.cc, op-bm-sbm.cc, op-cdm-cdm.cc, op-cell.cc,
op-chm.cc, op-class.cc, op-cm-cm.cc, op-cm-cs.cc, op-cm-m.cc, op-cm-s.cc,
op-cm-scm.cc, op-cm-sm.cc, op-cs-cm.cc, op-cs-cs.cc, op-cs-m.cc, op-cs-s.cc,
op-cs-scm.cc, op-cs-sm.cc, op-dm-dm.cc, op-dm-scm.cc, op-dm-sm.cc,
op-dm-template.cc, op-dms-template.cc, op-fcdm-fcdm.cc, op-fcm-fcm.cc,
op-fcm-fcs.cc, op-fcm-fm.cc, op-fcm-fs.cc, op-fcn.cc, op-fcs-fcm.cc,
op-fcs-fcs.cc, op-fcs-fm.cc, op-fcs-fs.cc, op-fdm-fdm.cc, op-fm-fcm.cc,
op-fm-fcs.cc, op-fm-fm.cc, op-fm-fs.cc, op-fs-fcm.cc, op-fs-fcs.cc,
op-fs-fm.cc, op-fs-fs.cc, op-i16-i16.cc, op-i32-i32.cc, op-i64-i64.cc,
op-i8-i8.cc, op-int-concat.cc, op-m-cm.cc, op-m-cs.cc, op-m-m.cc, op-m-s.cc,
op-m-scm.cc, op-m-sm.cc, op-mi.cc, op-pm-pm.cc, op-pm-scm.cc, op-pm-sm.cc,
op-pm-template.cc, op-range.cc, op-s-cm.cc, op-s-cs.cc, op-s-m.cc, op-s-s.cc,
op-s-scm.cc, op-s-sm.cc, op-sbm-b.cc, op-sbm-bm.cc, op-sbm-sbm.cc,
op-scm-cm.cc, op-scm-cs.cc, op-scm-m.cc, op-scm-s.cc, op-scm-scm.cc,
op-scm-sm.cc, op-sm-cm.cc, op-sm-cs.cc, op-sm-m.cc, op-sm-s.cc, op-sm-scm.cc,
op-sm-sm.cc, op-str-m.cc, op-str-s.cc, op-str-str.cc, op-struct.cc,
op-ui16-ui16.cc, op-ui32-ui32.cc, op-ui64-ui64.cc, op-ui8-ui8.cc, ops.h,
anon-fcn-validator.cc, anon-fcn-validator.h, bp-table.cc, bp-table.h,
comment-list.cc, comment-list.h, filepos.h, lex.h, lex.ll, oct-lvalue.cc,
oct-lvalue.h, oct-parse.yy, parse.h, profiler.cc, profiler.h,
pt-anon-scopes.cc, pt-anon-scopes.h, pt-arg-list.cc, pt-arg-list.h,
pt-args-block.cc, pt-args-block.h, pt-array-list.cc, pt-array-list.h,
pt-assign.cc, pt-assign.h, pt-binop.cc, pt-binop.h, pt-bp.cc, pt-bp.h,
pt-cbinop.cc, pt-cbinop.h, pt-cell.cc, pt-cell.h, pt-check.cc, pt-check.h,
pt-classdef.cc, pt-classdef.h, pt-cmd.h, pt-colon.cc, pt-colon.h, pt-const.cc,
pt-const.h, pt-decl.cc, pt-decl.h, pt-eval.cc, pt-eval.h, pt-except.cc,
pt-except.h, pt-exp.cc, pt-exp.h, pt-fcn-handle.cc, pt-fcn-handle.h, pt-id.cc,
pt-id.h, pt-idx.cc, pt-idx.h, pt-jump.h, pt-loop.cc, pt-loop.h, pt-mat.cc,
pt-mat.h, pt-misc.cc, pt-misc.h, pt-pr-code.cc, pt-pr-code.h, pt-select.cc,
pt-select.h, pt-spmd.cc, pt-spmd.h, pt-stmt.cc, pt-stmt.h, pt-tm-const.cc,
pt-tm-const.h, pt-unop.cc, pt-unop.h, pt-vm-eval.cc, pt-walk.cc, pt-walk.h,
pt.cc, pt.h, token.cc, token.h, Range.cc, Range.h, idx-vector.cc, idx-vector.h,
range-fwd.h, CollocWt.cc, CollocWt.h, aepbalance.cc, aepbalance.h, chol.cc,
chol.h, gepbalance.cc, gepbalance.h, gsvd.cc, gsvd.h, hess.cc, hess.h,
lo-mappers.cc, lo-mappers.h, lo-specfun.cc, lo-specfun.h, lu.cc, lu.h,
oct-convn.cc, oct-convn.h, oct-fftw.cc, oct-fftw.h, oct-norm.cc, oct-norm.h,
oct-rand.cc, oct-rand.h, oct-spparms.cc, oct-spparms.h, qr.cc, qr.h, qrp.cc,
qrp.h, randgamma.cc, randgamma.h, randmtzig.cc, randmtzig.h, randpoisson.cc,
randpoisson.h, schur.cc, schur.h, sparse-chol.cc, sparse-chol.h, sparse-lu.cc,
sparse-lu.h, sparse-qr.cc, sparse-qr.h, svd.cc, svd.h, child-list.cc,
child-list.h, dir-ops.cc, dir-ops.h, file-ops.cc, file-ops.h, file-stat.cc,
file-stat.h, lo-sysdep.cc, lo-sysdep.h, lo-sysinfo.cc, lo-sysinfo.h,
mach-info.cc, mach-info.h, oct-env.cc, oct-env.h, oct-group.cc, oct-group.h,
oct-password.cc, oct-password.h, oct-syscalls.cc, oct-syscalls.h, oct-time.cc,
oct-time.h, oct-uname.cc, oct-uname.h, action-container.cc, action-container.h,
base-list.h, cmd-edit.cc, cmd-edit.h, cmd-hist.cc, cmd-hist.h, f77-fcn.h,
file-info.cc, file-info.h, lo-array-errwarn.cc, lo-array-errwarn.h, lo-hash.cc,
lo-hash.h, lo-ieee.h, lo-regexp.cc, lo-regexp.h, lo-utils.cc, lo-utils.h,
oct-base64.cc, oct-base64.h, oct-glob.cc, oct-glob.h, oct-inttypes.h,
oct-mutex.cc, oct-mutex.h, oct-refcount.h, oct-shlib.cc, oct-shlib.h,
oct-sparse.cc, oct-sparse.h, oct-string.h, octave-preserve-stream-state.h,
pathsearch.cc, pathsearch.h, quit.cc, quit.h, unwind-prot.cc, unwind-prot.h,
url-transfer.cc, url-transfer.h : Use new macros to begin/end C++ namespaces.
author | Rik <rik@octave.org> |
---|---|
date | Thu, 01 Dec 2022 14:23:45 -0800 |
parents | ed7b17c7ddf3 |
children | aac27ad79be6 |
rev | line source |
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1 //////////////////////////////////////////////////////////////////////// |
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2 // |
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3 // Copyright (C) 1997-2022 The Octave Project Developers |
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4 // |
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5 // See the file COPYRIGHT.md in the top-level directory of this |
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6 // distribution or <https://octave.org/copyright/>. |
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7 // |
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8 // This file is part of Octave. |
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9 // |
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10 // Octave is free software: you can redistribute it and/or modify it |
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11 // under the terms of the GNU General Public License as published by |
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12 // the Free Software Foundation, either version 3 of the License, or |
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13 // (at your option) any later version. |
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14 // |
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15 // Octave is distributed in the hope that it will be useful, but |
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16 // WITHOUT ANY WARRANTY; without even the implied warranty of |
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17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 // GNU General Public License for more details. |
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19 // |
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20 // You should have received a copy of the GNU General Public License |
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21 // along with Octave; see the file COPYING. If not, see |
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22 // <https://www.gnu.org/licenses/>. |
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23 // |
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24 //////////////////////////////////////////////////////////////////////// |
3155 | 25 |
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26 #if defined (HAVE_CONFIG_H) |
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27 # include "config.h" |
3155 | 28 #endif |
29 | |
30 #include "lo-specfun.h" | |
4153 | 31 #include "quit.h" |
3155 | 32 |
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33 #include "defun.h" |
3155 | 34 #include "error.h" |
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35 #include "ovl.h" |
3155 | 36 #include "utils.h" |
37 | |
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38 OCTAVE_BEGIN_NAMESPACE(octave) |
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39 |
3220 | 40 enum bessel_type |
41 { | |
42 BESSEL_J, | |
43 BESSEL_Y, | |
44 BESSEL_I, | |
45 BESSEL_K, | |
46 BESSEL_H1, | |
47 BESSEL_H2 | |
48 }; | |
49 | |
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50 #define DO_BESSEL(type, alpha, x, scaled, ierr, result) \ |
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51 do \ |
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52 { \ |
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53 switch (type) \ |
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54 { \ |
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55 case BESSEL_J: \ |
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56 result = math::besselj (alpha, x, scaled, ierr); \ |
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57 break; \ |
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58 \ |
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59 case BESSEL_Y: \ |
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60 result = math::bessely (alpha, x, scaled, ierr); \ |
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61 break; \ |
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62 \ |
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63 case BESSEL_I: \ |
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64 result = math::besseli (alpha, x, scaled, ierr); \ |
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65 break; \ |
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66 \ |
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67 case BESSEL_K: \ |
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68 result = math::besselk (alpha, x, scaled, ierr); \ |
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69 break; \ |
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70 \ |
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71 case BESSEL_H1: \ |
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72 result = math::besselh1 (alpha, x, scaled, ierr); \ |
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73 break; \ |
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74 \ |
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75 case BESSEL_H2: \ |
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76 result = math::besselh2 (alpha, x, scaled, ierr); \ |
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77 break; \ |
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78 \ |
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79 default: \ |
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80 break; \ |
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81 } \ |
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82 } \ |
3155 | 83 while (0) |
84 | |
85 octave_value_list | |
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86 do_bessel (enum bessel_type type, const char *fcn, |
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87 const octave_value_list& args, int nargout) |
3155 | 88 { |
89 int nargin = args.length (); | |
90 | |
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91 if (nargin < 2 || nargin > 3) |
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92 print_usage (); |
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93 |
20892 | 94 octave_value_list retval (nargout > 1 ? 2 : 1); |
95 | |
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96 bool scaled = false; |
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97 if (nargin == 3) |
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99 octave_value opt_arg = args(2); |
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100 bool rpt_error = false; |
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101 |
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102 if (! opt_arg.is_scalar_type ()) |
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103 rpt_error = true; |
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104 else if (opt_arg.isnumeric ()) |
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105 { |
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106 double opt_val = opt_arg.double_value (); |
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107 if (opt_val != 0.0 && opt_val != 1.0) |
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108 rpt_error = true; |
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109 scaled = (opt_val == 1.0); |
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110 } |
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111 else if (opt_arg.islogical ()) |
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112 scaled = opt_arg.bool_value (); |
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113 |
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114 if (rpt_error) |
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115 error ("%s: OPT must be 0 (or false) or 1 (or true)", fcn); |
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116 } |
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117 |
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118 octave_value alpha_arg = args(0); |
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119 octave_value x_arg = args(1); |
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120 |
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121 if (alpha_arg.is_single_type () || x_arg.is_single_type ()) |
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122 { |
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123 if (alpha_arg.is_scalar_type ()) |
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124 { |
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125 float alpha = args(0).xfloat_value ("%s: ALPHA must be a scalar or matrix", fcn); |
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126 |
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127 if (x_arg.is_scalar_type ()) |
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128 { |
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129 FloatComplex x = x_arg.xfloat_complex_value ("%s: X must be a scalar or matrix", fcn); |
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130 |
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131 octave_idx_type ierr; |
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132 octave_value result; |
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133 |
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134 DO_BESSEL (type, alpha, x, scaled, ierr, result); |
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135 |
20892 | 136 retval(0) = result; |
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137 if (nargout > 1) |
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138 retval(1) = static_cast<float> (ierr); |
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139 } |
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140 else |
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141 { |
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142 FloatComplexNDArray x = x_arg.xfloat_complex_array_value ("%s: X must be a scalar or matrix", fcn); |
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143 |
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144 Array<octave_idx_type> ierr; |
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145 octave_value result; |
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146 |
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147 DO_BESSEL (type, alpha, x, scaled, ierr, result); |
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148 |
20892 | 149 retval(0) = result; |
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150 if (nargout > 1) |
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151 retval(1) = NDArray (ierr); |
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152 } |
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153 } |
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154 else |
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155 { |
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156 dim_vector dv0 = args(0).dims (); |
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157 dim_vector dv1 = args(1).dims (); |
3220 | 158 |
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159 bool args0_is_row_vector = (dv0(1) == dv0.numel ()); |
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160 bool args1_is_col_vector = (dv1(0) == dv1.numel ()); |
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161 |
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162 if (args0_is_row_vector && args1_is_col_vector) |
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163 { |
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164 FloatRowVector ralpha = args(0).xfloat_row_vector_value ("%s: ALPHA must be a scalar or matrix", fcn); |
3155 | 165 |
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166 FloatComplexColumnVector cx |
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167 = x_arg.xfloat_complex_column_vector_value ("%s: X must be a scalar or matrix", fcn); |
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168 |
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169 Array<octave_idx_type> ierr; |
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170 octave_value result; |
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171 |
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172 DO_BESSEL (type, ralpha, cx, scaled, ierr, result); |
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173 |
20892 | 174 retval(0) = result; |
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175 if (nargout > 1) |
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176 retval(1) = NDArray (ierr); |
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177 } |
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178 else |
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179 { |
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180 FloatNDArray alpha = args(0).xfloat_array_value ("%s: ALPHA must be a scalar or matrix", fcn); |
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181 |
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182 if (x_arg.is_scalar_type ()) |
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183 { |
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184 FloatComplex x = x_arg.xfloat_complex_value ("%s: X must be a scalar or matrix", fcn); |
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186 Array<octave_idx_type> ierr; |
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187 octave_value result; |
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188 |
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189 DO_BESSEL (type, alpha, x, scaled, ierr, result); |
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190 |
20892 | 191 retval(0) = result; |
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192 if (nargout > 1) |
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193 retval(1) = NDArray (ierr); |
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194 } |
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195 else |
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196 { |
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197 FloatComplexNDArray x = x_arg.xfloat_complex_array_value ("%s: X must be a scalar or matrix", fcn); |
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198 |
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199 Array<octave_idx_type> ierr; |
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200 octave_value result; |
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201 |
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202 DO_BESSEL (type, alpha, x, scaled, ierr, result); |
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203 |
20892 | 204 retval(0) = result; |
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205 if (nargout > 1) |
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206 retval(1) = NDArray (ierr); |
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207 } |
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208 } |
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209 } |
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210 } |
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211 else |
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212 { |
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213 if (alpha_arg.is_scalar_type ()) |
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214 { |
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215 double alpha = args(0).xdouble_value ("%s: ALPHA must be a scalar or matrix", fcn); |
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216 |
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217 if (x_arg.is_scalar_type ()) |
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218 { |
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219 Complex x = x_arg.xcomplex_value ("%s: X must be a scalar or matrix", fcn); |
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220 |
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221 octave_idx_type ierr; |
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222 octave_value result; |
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223 |
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224 DO_BESSEL (type, alpha, x, scaled, ierr, result); |
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225 |
20892 | 226 retval(0) = result; |
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227 if (nargout > 1) |
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228 retval(1) = static_cast<double> (ierr); |
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229 } |
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230 else |
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231 { |
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232 ComplexNDArray x = x_arg.xcomplex_array_value ("%s: X must be a scalar or matrix", fcn); |
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233 |
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234 Array<octave_idx_type> ierr; |
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235 octave_value result; |
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236 |
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237 DO_BESSEL (type, alpha, x, scaled, ierr, result); |
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238 |
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240 if (nargout > 1) |
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241 retval(1) = NDArray (ierr); |
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242 } |
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243 } |
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244 else |
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245 { |
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246 dim_vector dv0 = args(0).dims (); |
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247 dim_vector dv1 = args(1).dims (); |
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248 |
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249 bool args0_is_row_vector = (dv0(1) == dv0.numel ()); |
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250 bool args1_is_col_vector = (dv1(0) == dv1.numel ()); |
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251 |
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252 if (args0_is_row_vector && args1_is_col_vector) |
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253 { |
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254 RowVector ralpha = args(0).xrow_vector_value ("%s: ALPHA must be a scalar or matrix", fcn); |
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255 |
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256 ComplexColumnVector cx |
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257 = x_arg.xcomplex_column_vector_value ("%s: X must be a scalar or matrix", fcn); |
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258 |
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259 Array<octave_idx_type> ierr; |
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260 octave_value result; |
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261 |
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262 DO_BESSEL (type, ralpha, cx, scaled, ierr, result); |
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263 |
20892 | 264 retval(0) = result; |
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265 if (nargout > 1) |
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266 retval(1) = NDArray (ierr); |
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267 } |
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268 else |
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269 { |
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270 NDArray alpha = args(0).xarray_value ("%s: ALPHA must be a scalar or matrix", fcn); |
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272 if (x_arg.is_scalar_type ()) |
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273 { |
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274 Complex x = x_arg.xcomplex_value ("%s: X must be a scalar or matrix", fcn); |
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275 |
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276 Array<octave_idx_type> ierr; |
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277 octave_value result; |
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278 |
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279 DO_BESSEL (type, alpha, x, scaled, ierr, result); |
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280 |
20892 | 281 retval(0) = result; |
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282 if (nargout > 1) |
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283 retval(1) = NDArray (ierr); |
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284 } |
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285 else |
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286 { |
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287 ComplexNDArray x = x_arg.xcomplex_array_value ("%s: X must be a scalar or matrix", fcn); |
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288 |
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289 Array<octave_idx_type> ierr; |
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290 octave_value result; |
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291 |
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292 DO_BESSEL (type, alpha, x, scaled, ierr, result); |
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293 |
20892 | 294 retval(0) = result; |
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295 if (nargout > 1) |
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296 retval(1) = NDArray (ierr); |
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297 } |
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298 } |
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299 } |
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301 | |
302 return retval; | |
303 } | |
304 | |
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305 DEFUN (besselj, args, nargout, |
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306 doc: /* -*- texinfo -*- |
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307 @deftypefn {} {@var{J} =} besselj (@var{alpha}, @var{x}) |
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308 @deftypefnx {} {@var{J} =} besselj (@var{alpha}, @var{x}, @var{opt}) |
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309 @deftypefnx {} {[@var{J}, @var{ierr}] =} besselj (@dots{}) |
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310 Compute Bessel functions of the first kind. |
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311 |
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312 The order of the Bessel function @var{alpha} must be real. The points for |
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313 evaluation @var{x} may be complex. |
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314 |
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315 If the optional argument @var{opt} is 1 or true, the result @var{J} is |
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316 multiplied by @w{@code{exp (-abs (imag (@var{x})))}}. |
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317 |
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318 If @var{alpha} is a scalar, the result is the same size as @var{x}. If @var{x} |
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319 is a scalar, the result is the same size as @var{alpha}. If @var{alpha} is a |
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320 row vector and @var{x} is a column vector, the result is a matrix with |
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321 @code{length (@var{x})} rows and @code{length (@var{alpha})} columns. |
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322 Otherwise, @var{alpha} and @var{x} must conform and the result will be the same |
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323 size. |
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324 |
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325 If requested, @var{ierr} contains the following status information and is the |
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326 same size as the result. |
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327 |
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328 @enumerate 0 |
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329 @item |
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330 Normal return. |
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331 |
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332 @item |
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333 Input error, return @code{NaN}. |
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334 |
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335 @item |
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336 Overflow, return @code{Inf}. |
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337 |
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338 @item |
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339 Loss of significance by argument reduction results in less than half of machine |
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340 accuracy. |
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341 |
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342 @item |
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343 Loss of significance by argument reduction, output may be inaccurate. |
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344 |
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345 @item |
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346 Error---no computation, algorithm termination condition not met, return |
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347 @code{NaN}. |
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348 @end enumerate |
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349 |
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350 @seealso{bessely, besseli, besselk, besselh} |
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351 @end deftypefn */) |
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352 { |
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353 return do_bessel (BESSEL_J, "besselj", args, nargout); |
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354 } |
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355 |
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356 /* |
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357 %!# Function besselj is tested along with other bessels at the end of this file |
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358 |
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359 ## besselj specific BIST |
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360 %!assert <*48316> (! any (isnan (besselj (1, 10.^[5:12])))) |
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361 |
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362 */ |
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363 |
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364 DEFUN (bessely, args, nargout, |
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365 doc: /* -*- texinfo -*- |
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366 @deftypefn {} {@var{Y} =} bessely (@var{alpha}, @var{x}) |
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367 @deftypefnx {} {@var{Y} =} bessely (@var{alpha}, @var{x}, @var{opt}) |
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368 @deftypefnx {} {[@var{Y}, @var{ierr}] =} bessely (@dots{}) |
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369 Compute Bessel functions of the second kind. |
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370 |
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371 The order of the Bessel function @var{alpha} must be real. The points for |
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372 evaluation @var{x} may be complex. |
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373 |
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374 If the optional argument @var{opt} is 1 or true, the result @var{Y} is |
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375 multiplied by @w{@code{exp (-abs (imag (@var{x})))}}. |
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376 |
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377 If @var{alpha} is a scalar, the result is the same size as @var{x}. If @var{x} |
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378 is a scalar, the result is the same size as @var{alpha}. If @var{alpha} is a |
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379 row vector and @var{x} is a column vector, the result is a matrix with |
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380 @code{length (@var{x})} rows and @code{length (@var{alpha})} columns. |
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381 Otherwise, @var{alpha} and @var{x} must conform and the result will be the same |
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382 size. |
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383 |
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384 If requested, @var{ierr} contains the following status information and is the |
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385 same size as the result. |
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386 |
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387 @enumerate 0 |
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388 @item |
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389 Normal return. |
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390 |
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391 @item |
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392 Input error, return @code{NaN}. |
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393 |
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394 @item |
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395 Overflow, return @code{Inf}. |
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396 |
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397 @item |
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398 Loss of significance by argument reduction results in less than half of machine |
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399 accuracy. |
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400 |
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401 @item |
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402 Complete loss of significance by argument reduction, return @code{NaN}. |
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403 |
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404 @item |
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405 Error---no computation, algorithm termination condition not met, return |
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406 @code{NaN}. |
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407 @end enumerate |
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409 @seealso{besselj, besseli, besselk, besselh} |
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410 @end deftypefn */) |
3155 | 411 { |
3220 | 412 return do_bessel (BESSEL_Y, "bessely", args, nargout); |
3155 | 413 } |
414 | |
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415 /* |
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416 %!# Function bessely is tested along with other bessels at the end of this file |
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417 */ |
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418 |
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419 DEFUN (besseli, args, nargout, |
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420 doc: /* -*- texinfo -*- |
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421 @deftypefn {} {@var{I} =} besseli (@var{alpha}, @var{x}) |
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422 @deftypefnx {} {@var{I} =} besseli (@var{alpha}, @var{x}, @var{opt}) |
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423 @deftypefnx {} {[@var{I}, @var{ierr}] =} besseli (@dots{}) |
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424 Compute modified Bessel functions of the first kind. |
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425 |
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426 The order of the Bessel function @var{alpha} must be real. The points for |
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427 evaluation @var{x} may be complex. |
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428 |
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429 If the optional argument @var{opt} is 1 or true, the result @var{I} is |
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430 multiplied by @w{@code{exp (-abs (real (@var{x})))}}. |
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431 |
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432 If @var{alpha} is a scalar, the result is the same size as @var{x}. If @var{x} |
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433 is a scalar, the result is the same size as @var{alpha}. If @var{alpha} is a |
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434 row vector and @var{x} is a column vector, the result is a matrix with |
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435 @code{length (@var{x})} rows and @code{length (@var{alpha})} columns. |
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436 Otherwise, @var{alpha} and @var{x} must conform and the result will be the same |
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437 size. |
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438 |
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439 If requested, @var{ierr} contains the following status information and is the |
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440 same size as the result. |
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441 |
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442 @enumerate 0 |
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443 @item |
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444 Normal return. |
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445 |
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446 @item |
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447 Input error, return @code{NaN}. |
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448 |
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449 @item |
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450 Overflow, return @code{Inf}. |
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451 |
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452 @item |
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453 Loss of significance by argument reduction results in less than half of machine |
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454 accuracy. |
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455 |
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456 @item |
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457 Complete loss of significance by argument reduction, return @code{NaN}. |
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458 |
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459 @item |
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460 Error---no computation, algorithm termination condition not met, return |
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461 @code{NaN}. |
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462 @end enumerate |
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463 |
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464 @seealso{besselk, besselj, bessely, besselh} |
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465 @end deftypefn */) |
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466 |
3155 | 467 { |
3220 | 468 return do_bessel (BESSEL_I, "besseli", args, nargout); |
3155 | 469 } |
470 | |
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471 /* |
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472 %!# Function besseli is tested along with other bessels at the end of this file |
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473 |
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474 ## besseli specific BIST |
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475 %!assert (! isinf (besseli (0, 700))) |
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476 |
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477 */ |
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478 |
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479 DEFUN (besselk, args, nargout, |
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480 doc: /* -*- texinfo -*- |
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481 @deftypefn {} {@var{K} =} besselk (@var{alpha}, @var{x}) |
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482 @deftypefnx {} {@var{K} =} besselk (@var{alpha}, @var{x}, @var{opt}) |
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483 @deftypefnx {} {[@var{K}, @var{ierr}] =} besselk (@dots{}) |
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484 |
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485 Compute modified Bessel functions of the second kind. |
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486 |
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487 The order of the Bessel function @var{alpha} must be real. The points for |
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488 evaluation @var{x} may be complex. |
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489 |
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490 If the optional argument @var{opt} is 1 or true, the result @var{K} is |
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491 multiplied by @w{@code{exp (@var{x})}}. |
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492 |
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493 If @var{alpha} is a scalar, the result is the same size as @var{x}. If @var{x} |
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494 is a scalar, the result is the same size as @var{alpha}. If @var{alpha} is a |
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495 row vector and @var{x} is a column vector, the result is a matrix with |
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496 @code{length (@var{x})} rows and @code{length (@var{alpha})} columns. |
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497 Otherwise, @var{alpha} and @var{x} must conform and the result will be the same |
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498 size. |
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499 |
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500 If requested, @var{ierr} contains the following status information and is the |
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501 same size as the result. |
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502 |
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503 @enumerate 0 |
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504 @item |
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505 Normal return. |
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506 |
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507 @item |
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508 Input error, return @code{NaN}. |
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509 |
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510 @item |
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511 Overflow, return @code{Inf}. |
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512 |
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513 @item |
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514 Loss of significance by argument reduction results in less than half of machine |
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515 accuracy. |
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516 |
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517 @item |
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518 Complete loss of significance by argument reduction, return @code{NaN}. |
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519 |
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520 @item |
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521 Error---no computation, algorithm termination condition not met, return |
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522 @code{NaN}. |
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523 @end enumerate |
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524 |
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525 @seealso{besseli, besselj, bessely, besselh} |
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526 @end deftypefn */) |
3220 | 527 { |
528 return do_bessel (BESSEL_K, "besselk", args, nargout); | |
529 } | |
530 | |
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531 /* |
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532 %!# Function besselk is tested along with other bessels at the end of this file |
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533 */ |
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534 |
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535 DEFUN (besselh, args, nargout, |
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536 doc: /* -*- texinfo -*- |
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537 @deftypefn {} {@var{H} =} besselh (@var{alpha}, @var{x}) |
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538 @deftypefnx {} {@var{H} =} besselh (@var{alpha}, @var{k}, @var{x}) |
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539 @deftypefnx {} {@var{H} =} besselh (@var{alpha}, @var{k}, @var{x}, @var{opt}) |
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540 @deftypefnx {} {[@var{H}, @var{ierr}] =} besselh (@dots{}) |
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541 Compute Bessel functions of the third kind (Hankel functions). |
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542 |
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543 The order of the Bessel function @var{alpha} must be real. The kind of Hankel |
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544 function is specified by @var{k} and may be either first (@var{k} = 1) or |
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545 second (@var{k} = 2). The default is Hankel functions of the first kind. The |
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546 points for evaluation @var{x} may be complex. |
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547 |
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548 If the optional argument @var{opt} is 1 or true, the result is multiplied |
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549 by @code{exp (-I*@var{x})} for @var{k} = 1 or @code{exp (I*@var{x})} for |
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550 @var{k} = 2. |
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551 |
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552 If @var{alpha} is a scalar, the result is the same size as @var{x}. If @var{x} |
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553 is a scalar, the result is the same size as @var{alpha}. If @var{alpha} is a |
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554 row vector and @var{x} is a column vector, the result is a matrix with |
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555 @code{length (@var{x})} rows and @code{length (@var{alpha})} columns. |
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556 Otherwise, @var{alpha} and @var{x} must conform and the result will be the same |
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557 size. |
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558 |
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559 If requested, @var{ierr} contains the following status information and is the |
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560 same size as the result. |
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561 |
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562 @enumerate 0 |
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563 @item |
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564 Normal return. |
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565 |
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566 @item |
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567 Input error, return @code{NaN}. |
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568 |
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569 @item |
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570 Overflow, return @code{Inf}. |
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571 |
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572 @item |
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573 Loss of significance by argument reduction results in less than half of machine |
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574 accuracy. |
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575 |
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576 @item |
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577 Complete loss of significance by argument reduction, return @code{NaN}. |
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578 |
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579 @item |
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580 Error---no computation, algorithm termination condition not met, return |
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581 @code{NaN}. |
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582 @end enumerate |
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583 |
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584 @seealso{besselj, bessely, besseli, besselk} |
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585 @end deftypefn */) |
3220 | 586 { |
587 int nargin = args.length (); | |
588 | |
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589 if (nargin < 2 || nargin > 4) |
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590 print_usage (); |
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591 |
20892 | 592 octave_value_list retval; |
593 | |
3220 | 594 if (nargin == 2) |
595 { | |
596 retval = do_bessel (BESSEL_H1, "besselh", args, nargout); | |
597 } | |
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598 else |
3220 | 599 { |
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600 octave_idx_type kind = args(1).xint_value ("besselh: invalid value of K"); |
3220 | 601 |
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602 octave_value_list tmp_args; |
3220 | 603 |
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604 if (nargin == 4) |
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605 tmp_args(2) = args(3); |
3220 | 606 |
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607 tmp_args(1) = args(2); |
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608 tmp_args(0) = args(0); |
3220 | 609 |
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610 if (kind == 1) |
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611 retval = do_bessel (BESSEL_H1, "besselh", tmp_args, nargout); |
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612 else if (kind == 2) |
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613 retval = do_bessel (BESSEL_H2, "besselh", tmp_args, nargout); |
3220 | 614 else |
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615 error ("besselh: K must be 1 or 2"); |
3220 | 616 } |
617 | |
618 return retval; | |
619 } | |
620 | |
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621 /* |
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622 %!# Function besselh is tested along with other bessels at the end of this file |
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623 */ |
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624 |
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625 DEFUN (airy, args, nargout, |
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626 doc: /* -*- texinfo -*- |
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627 @deftypefn {} {@var{a} =} airy (@var{z}) |
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628 @deftypefnx {} {@var{a} =} airy (@var{k}, @var{z}) |
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629 @deftypefnx {} {@var{a} =} airy (@var{k}, @var{z}, @var{scale}) |
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630 @deftypefnx {} {[@var{a}, @var{ierr}] =} airy (@dots{}) |
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631 |
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632 Compute Airy functions of the first and second kind, and their derivatives. |
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633 |
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634 @example |
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635 @group |
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636 K Function Scale factor (if @var{scale} is true) |
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637 --- -------- --------------------------------------- |
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638 0 Ai (Z) exp ((2/3) * Z * sqrt (Z)) |
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639 1 dAi(Z)/dZ exp ((2/3) * Z * sqrt (Z)) |
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640 2 Bi (Z) exp (-abs (real ((2/3) * Z * sqrt (Z)))) |
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641 3 dBi(Z)/dZ exp (-abs (real ((2/3) * Z * sqrt (Z)))) |
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642 @end group |
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643 @end example |
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644 |
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645 The function call @code{airy (@var{z})} is equivalent to |
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646 @code{airy (0, @var{z})}. |
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647 |
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648 The optional third input @var{scale} determines whether to |
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649 apply scaling as described above. It is false by default. |
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650 |
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651 The result @var{a} is the same size as @var{z}. |
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652 |
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653 The optional output @var{ierr} contains the following status information and |
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654 is the same size as the result. |
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655 |
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656 @enumerate 0 |
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657 @item |
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658 Normal return. |
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659 |
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660 @item |
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661 Input error, return @code{NaN}. |
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662 |
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663 @item |
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664 Overflow, return @code{Inf}. |
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665 |
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666 @item |
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667 Loss of significance by argument reduction results in less than half |
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668 of machine accuracy. |
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669 |
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670 @item |
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671 Loss of significance by argument reduction, output may be inaccurate. |
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672 |
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673 @item |
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674 Error---no computation, algorithm termination condition not met, |
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675 return @code{NaN}. |
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676 @end enumerate |
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677 @end deftypefn */) |
3155 | 678 { |
3220 | 679 int nargin = args.length (); |
680 | |
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681 if (nargin < 1 || nargin > 3) |
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682 print_usage (); |
3220 | 683 |
20892 | 684 octave_value_list retval (nargout > 1 ? 2 : 1); |
3220 | 685 |
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686 int kind = 0; |
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687 if (nargin > 1) |
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688 { |
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689 kind = args(0).xint_value ("airy: K must be an integer value"); |
3220 | 690 |
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691 if (kind < 0 || kind > 3) |
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692 error ("airy: K must be 0, 1, 2, or 3"); |
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693 } |
3220 | 694 |
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695 bool scale = (nargin == 3) && args(2).xbool_value ("airy: scale option must be a logical value"); |
20892 | 696 |
697 int idx = (nargin == 1 ? 0 : 1); | |
3220 | 698 |
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699 Array<octave_idx_type> ierr; |
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700 octave_value result; |
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701 |
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702 if (args(idx).is_single_type ()) |
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703 { |
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704 FloatComplexNDArray z = args(idx).xfloat_complex_array_value ("airy: Z must be a complex matrix"); |
3220 | 705 |
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706 if (kind > 1) |
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707 result = math::biry (z, kind == 3, scale, ierr); |
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708 else |
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709 result = math::airy (z, kind == 1, scale, ierr); |
3220 | 710 } |
711 else | |
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712 { |
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713 ComplexNDArray z = args(idx).xcomplex_array_value ("airy: Z must be a complex matrix"); |
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714 |
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715 if (kind > 1) |
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716 result = math::biry (z, kind == 3, scale, ierr); |
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717 else |
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718 result = math::airy (z, kind == 1, scale, ierr); |
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719 } |
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720 |
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721 retval(0) = result; |
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722 if (nargout > 1) |
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723 retval(1) = NDArray (ierr); |
3220 | 724 |
725 return retval; | |
3155 | 726 } |
727 | |
728 /* | |
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729 %!test <*62321> |
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730 %! assert (airy (0, +1, false), 0.1352924163128814, 1e-15); |
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731 %! assert (airy (0, -1, false), 0.5355608832923521, 1e-15); |
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732 %! assert (airy (0, +i, false), 0.3314933054321411 - 0.3174498589684437i, 1e-15); |
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|
733 %! assert (airy (0, -i, false), 0.3314933054321411 + 0.3174498589684437i, 1e-15); |
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734 %! assert (airy (0, +1, true), 0.2635136447491401, 1e-15); |
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|
735 %! assert (airy (0, -1, true), 0.4208904755499093 - 0.3311746779333462i, 1e-15); |
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736 %! assert (airy (0, +i, true), 0.2743053542644657 - 0.0825606941400591i, 1e-15); |
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737 %! assert (airy (0, -i, true), 0.2743053542644657 + 0.0825606941400591i, 1e-15); |
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738 %! assert (airy (1, +1, false), -0.1591474412967932, 1e-15); |
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739 %! assert (airy (1, -1, false), -0.0101605671166451, 1e-15); |
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740 %! assert (airy (1, +i, false), -0.4324926598418070 + 0.0980478562292432i, 1e-15); |
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741 %! assert (airy (1, -i, false), -0.4324926598418070 - 0.0980478562292432i, 1e-15); |
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742 %! assert (airy (1, +1, true), -0.3099768889605148, 1e-15); |
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743 %! assert (airy (1, -1, true), -0.0079850602592406 + 0.0062829878869967i, 1e-15); |
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744 %! assert (airy (1, +i, true), -0.2682792317254506 - 0.0680655016581369i, 1e-15); |
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745 %! assert (airy (1, -i, true), -0.2682792317254506 + 0.0680655016581369i, 1e-15); |
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746 %! assert (airy (2, +1, false), 1.2074235949528715, 1e-15); |
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747 %! assert (airy (2, -1, false), 0.1039973894969446, 1e-15); |
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748 %! assert (airy (2, +i, false), 0.6488582083303949 + 0.3449586347680484i, 1e-15); |
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749 %! assert (airy (2, -i, false), 0.6488582083303949 - 0.3449586347680484i, 1e-15); |
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750 %! assert (airy (2, +1, true), 0.6199119435726786, 1e-15); |
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751 %! assert (airy (2, -1, true), 0.1039973894969446, 1e-15); |
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752 %! assert (airy (2, +i, true), 0.4049686654663902 + 0.2152973271658010i, 1e-15); |
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753 %! assert (airy (2, -i, true), 0.4049686654663902 - 0.2152973271658010i, 1e-15); |
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754 %! assert (airy (3, +1, false), 0.9324359333927754, 1e-15); |
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755 %! assert (airy (3, -1, false), 0.5923756264227923, 1e-15); |
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756 %! assert (airy (3, +i, false), 0.1350266467108190 - 0.1288373867812549i, 1e-15); |
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757 %! assert (airy (3, -i, false), 0.1350266467108190 + 0.1288373867812549i, 1e-15); |
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758 %! assert (airy (3, +1, true), 0.4787285706049846, 1e-15); |
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759 %! assert (airy (3, -1, true), 0.5923756264227923, 1e-15); |
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760 %! assert (airy (3, +i, true), 0.0842735134099415 - 0.0804106412111761i, 1e-15); |
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761 %! assert (airy (3, -i, true), 0.0842735134099415 + 0.0804106412111761i, 1e-15); |
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|
762 %! z = -1 - 1e-6i; |
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763 %! s1 = exp (2/3 * z * sqrt(z)); |
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|
764 %! s2 = exp (-abs (real (2/3 * z * sqrt(z)))); |
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765 %! assert (airy (0, z, true), s1 * airy (0, z, false), 1e-15); |
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766 %! assert (airy (1, z, true), s1 * airy (1, z, false), 1e-15); |
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767 %! assert (airy (2, z, true), s2 * airy (2, z, false), 1e-15); |
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768 %! assert (airy (3, z, true), s2 * airy (3, z, false), 1e-15); |
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|
769 |
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770 Input validation tests |
30944
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771 %!error airy () |
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772 %!error airy (0, 1, 2, 3) |
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773 %!error <K must be an integer value> airy ("foo", 2, false) |
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774 %!error <K must be 0, 1, 2, or 3> airy (3743, 2, false) |
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775 %!error <scale option must be a logical value> airy (0, 2, "foo") |
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776 %!error <Z must be a complex matrix> airy (0, "foo", false) |
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777 */ |
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|
778 |
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|
779 |
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780 /* |
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781 ## Test values computed with GP/PARI version 2.3.3 |
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782 %!shared alpha, x, jx, yx, ix, kx, nix |
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783 %! |
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784 %! ## Bessel functions, even order, positive and negative x |
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785 %! alpha = 2; x = 1.25; |
8278
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786 %! jx = 0.1710911312405234823613091417; |
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787 %! yx = -1.193199310178553861283790424; |
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788 %! ix = 0.2220184483766341752692212604; |
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|
789 %! kx = 0.9410016167388185767085460540; |
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|
790 %! |
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791 %!assert (besselj (alpha,x), jx, 100*eps) |
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792 %!assert (bessely (alpha,x), yx, 100*eps) |
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793 %!assert (besseli (alpha,x), ix, 100*eps) |
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794 %!assert (besselk (alpha,x), kx, 100*eps) |
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795 %!assert (besselh (alpha,1,x), jx + I*yx, 100*eps) |
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796 %!assert (besselh (alpha,2,x), jx - I*yx, 100*eps) |
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797 %! |
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798 %!assert (besselj (alpha,x,1), jx*exp (-abs (imag (x))), 100*eps) |
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799 %!assert (bessely (alpha,x,1), yx*exp (-abs (imag (x))), 100*eps) |
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800 %!assert (besseli (alpha,x,1), ix*exp (-abs (real (x))), 100*eps) |
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801 %!assert (besselk (alpha,x,1), kx*exp (x), 100*eps) |
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802 %!assert (besselh (alpha,1,x,1), (jx + I*yx)*exp (-I*x), 100*eps) |
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803 %!assert (besselh (alpha,2,x,1), (jx - I*yx)*exp (I*x), 100*eps) |
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804 %! |
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805 %!assert (besselj (-alpha,x), jx, 100*eps) |
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806 %!assert (bessely (-alpha,x), yx, 100*eps) |
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807 %!assert (besseli (-alpha,x), ix, 100*eps) |
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808 %!assert (besselk (-alpha,x), kx, 100*eps) |
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809 %!assert (besselh (-alpha,1,x), jx + I*yx, 100*eps) |
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810 %!assert (besselh (-alpha,2,x), jx - I*yx, 100*eps) |
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|
811 %! |
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812 %!assert (besselj (-alpha,x,1), jx*exp (-abs (imag (x))), 100*eps) |
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813 %!assert (bessely (-alpha,x,1), yx*exp (-abs (imag (x))), 100*eps) |
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814 %!assert (besseli (-alpha,x,1), ix*exp (-abs (real (x))), 100*eps) |
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815 %!assert (besselk (-alpha,x,1), kx*exp (x), 100*eps) |
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816 %!assert (besselh (-alpha,1,x,1), (jx + I*yx)*exp (-I*x), 100*eps) |
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817 %!assert (besselh (-alpha,2,x,1), (jx - I*yx)*exp (I*x), 100*eps) |
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818 %! |
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|
819 %! x *= -1; |
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820 %! yx = -1.193199310178553861283790424 + 0.3421822624810469647226182835*I; |
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821 %! kx = 0.9410016167388185767085460540 - 0.6974915263814386815610060884*I; |
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822 %! |
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823 %!assert (besselj (alpha,x), jx, 100*eps) |
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824 %!assert (bessely (alpha,x), yx, 100*eps) |
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825 %!assert (besseli (alpha,x), ix, 100*eps) |
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|
826 %!assert (besselk (alpha,x), kx, 100*eps) |
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|
827 %!assert (besselh (alpha,1,x), jx + I*yx, 100*eps) |
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|
828 %!assert (besselh (alpha,2,x), jx - I*yx, 100*eps) |
8278
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|
829 %! |
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830 %!assert (besselj (alpha,x,1), jx*exp (-abs (imag (x))), 100*eps) |
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|
831 %!assert (bessely (alpha,x,1), yx*exp (-abs (imag (x))), 100*eps) |
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|
832 %!assert (besseli (alpha,x,1), ix*exp (-abs (real (x))), 100*eps) |
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|
833 %!assert (besselk (alpha,x,1), kx*exp (x), 100*eps) |
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|
834 %!assert (besselh (alpha,1,x,1), (jx + I*yx)*exp (-I*x), 100*eps) |
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|
835 %!assert (besselh (alpha,2,x,1), (jx - I*yx)*exp (I*x), 100*eps) |
8278
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|
836 %! |
17336
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|
837 %! ## Bessel functions, odd order, positive and negative x |
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838 %! alpha = 3; x = 2.5; |
8278
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839 %! jx = 0.2166003910391135247666890035; |
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|
840 %! yx = -0.7560554967536709968379029772; |
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841 %! ix = 0.4743704087780355895548240179; |
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|
842 %! kx = 0.2682271463934492027663765197; |
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|
843 %! |
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|
844 %!assert (besselj (alpha,x), jx, 100*eps) |
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845 %!assert (bessely (alpha,x), yx, 100*eps) |
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846 %!assert (besseli (alpha,x), ix, 100*eps) |
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847 %!assert (besselk (alpha,x), kx, 100*eps) |
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848 %!assert (besselh (alpha,1,x), jx + I*yx, 100*eps) |
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849 %!assert (besselh (alpha,2,x), jx - I*yx, 100*eps) |
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850 %! |
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851 %!assert (besselj (alpha,x,1), jx*exp (-abs (imag (x))), 100*eps) |
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852 %!assert (bessely (alpha,x,1), yx*exp (-abs (imag (x))), 100*eps) |
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853 %!assert (besseli (alpha,x,1), ix*exp (-abs (real (x))), 100*eps) |
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854 %!assert (besselk (alpha,x,1), kx*exp (x), 100*eps) |
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855 %!assert (besselh (alpha,1,x,1), (jx + I*yx)*exp (-I*x), 100*eps) |
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856 %!assert (besselh (alpha,2,x,1), (jx - I*yx)*exp (I*x), 100*eps) |
8278
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857 %! |
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858 %!assert (besselj (-alpha,x), -jx, 100*eps) |
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859 %!assert (bessely (-alpha,x), -yx, 100*eps) |
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860 %!assert (besseli (-alpha,x), ix, 100*eps) |
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861 %!assert (besselk (-alpha,x), kx, 100*eps) |
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862 %!assert (besselh (-alpha,1,x), -(jx + I*yx), 100*eps) |
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863 %!assert (besselh (-alpha,2,x), -(jx - I*yx), 100*eps) |
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864 %! |
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865 %!assert (besselj (-alpha,x,1), -jx*exp (-abs (imag (x))), 100*eps) |
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866 %!assert (bessely (-alpha,x,1), -yx*exp (-abs (imag (x))), 100*eps) |
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867 %!assert (besseli (-alpha,x,1), ix*exp (-abs (real (x))), 100*eps) |
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868 %!assert (besselk (-alpha,x,1), kx*exp (x), 100*eps) |
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869 %!assert (besselh (-alpha,1,x,1), -(jx + I*yx)*exp (-I*x), 100*eps) |
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870 %!assert (besselh (-alpha,2,x,1), -(jx - I*yx)*exp (I*x), 100*eps) |
8278
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871 %! |
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872 %! x *= -1; |
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873 %! jx = -jx; |
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874 %! yx = 0.7560554967536709968379029772 - 0.4332007820782270495333780070*I; |
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875 %! ix = -ix; |
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876 %! kx = -0.2682271463934492027663765197 - 1.490278591297463775542004240*I; |
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877 %! |
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878 %!assert (besselj (alpha,x), jx, 100*eps) |
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879 %!assert (bessely (alpha,x), yx, 100*eps) |
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880 %!assert (besseli (alpha,x), ix, 100*eps) |
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881 %!assert (besselk (alpha,x), kx, 100*eps) |
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882 %!assert (besselh (alpha,1,x), jx + I*yx, 100*eps) |
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883 %!assert (besselh (alpha,2,x), jx - I*yx, 100*eps) |
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884 %! |
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885 %!assert (besselj (alpha,x,1), jx*exp (-abs (imag (x))), 100*eps) |
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886 %!assert (bessely (alpha,x,1), yx*exp (-abs (imag (x))), 100*eps) |
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887 %!assert (besseli (alpha,x,1), ix*exp (-abs (real (x))), 100*eps) |
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888 %!assert (besselk (alpha,x,1), kx*exp (x), 100*eps) |
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889 %!assert (besselh (alpha,1,x,1), (jx + I*yx)*exp (-I*x), 100*eps) |
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890 %!assert (besselh (alpha,2,x,1), (jx - I*yx)*exp (I*x), 100*eps) |
8278
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891 %! |
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892 %! ## Bessel functions, fractional order, positive and negative x |
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893 %! |
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894 %! alpha = 3.5; x = 2.75; |
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895 %! jx = 0.1691636439842384154644784389; |
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896 %! yx = -0.8301381935499356070267953387; |
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897 %! ix = 0.3930540878794826310979363668; |
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898 %! kx = 0.2844099013460621170288192503; |
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|
899 %! |
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900 %!assert (besselj (alpha,x), jx, 100*eps) |
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901 %!assert (bessely (alpha,x), yx, 100*eps) |
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902 %!assert (besseli (alpha,x), ix, 100*eps) |
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903 %!assert (besselk (alpha,x), kx, 100*eps) |
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904 %!assert (besselh (alpha,1,x), jx + I*yx, 100*eps) |
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905 %!assert (besselh (alpha,2,x), jx - I*yx, 100*eps) |
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906 %! |
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|
907 %!assert (besselj (alpha,x,1), jx*exp (-abs (imag (x))), 100*eps) |
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908 %!assert (bessely (alpha,x,1), yx*exp (-abs (imag (x))), 100*eps) |
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909 %!assert (besseli (alpha,x,1), ix*exp (-abs (real (x))), 100*eps) |
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910 %!assert (besselk (alpha,x,1), kx*exp (x), 100*eps) |
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911 %!assert (besselh (alpha,1,x,1), (jx + I*yx)*exp (-I*x), 100*eps) |
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912 %!assert (besselh (alpha,2,x,1), (jx - I*yx)*exp (I*x), 100*eps) |
8278
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913 %! |
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914 %! nix = 0.2119931212254662995364461998; |
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915 %! |
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916 %!assert (besselj (-alpha,x), yx, 100*eps) |
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917 %!assert (bessely (-alpha,x), -jx, 100*eps) |
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918 %!assert (besseli (-alpha,x), nix, 100*eps) |
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919 %!assert (besselk (-alpha,x), kx, 100*eps) |
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920 %!assert (besselh (-alpha,1,x), -I*(jx + I*yx), 100*eps) |
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|
921 %!assert (besselh (-alpha,2,x), I*(jx - I*yx), 100*eps) |
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|
922 %! |
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|
923 %!assert (besselj (-alpha,x,1), yx*exp (-abs (imag (x))), 100*eps) |
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|
924 %!assert (bessely (-alpha,x,1), -jx*exp (-abs (imag (x))), 100*eps) |
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|
925 %!assert (besseli (-alpha,x,1), nix*exp (-abs (real (x))), 100*eps) |
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|
926 %!assert (besselk (-alpha,x,1), kx*exp (x), 100*eps) |
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|
927 %!assert (besselh (-alpha,1,x,1), -I*(jx + I*yx)*exp (-I*x), 100*eps) |
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|
928 %!assert (besselh (-alpha,2,x,1), I*(jx - I*yx)*exp (I*x), 100*eps) |
8278
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|
929 %! |
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|
930 %! x *= -1; |
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|
931 %! jx *= -I; |
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|
932 %! yx = -0.8301381935499356070267953387*I; |
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Brian Gough <bjg@gnu.org>
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|
933 %! ix *= -I; |
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Brian Gough <bjg@gnu.org>
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|
934 %! kx = -0.9504059335995575096509874508*I; |
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Brian Gough <bjg@gnu.org>
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|
935 %! |
14501
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|
936 %!assert (besselj (alpha,x), jx, 100*eps) |
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937 %!assert (bessely (alpha,x), yx, 100*eps) |
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|
938 %!assert (besseli (alpha,x), ix, 100*eps) |
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|
939 %!assert (besselk (alpha,x), kx, 100*eps) |
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|
940 %!assert (besselh (alpha,1,x), jx + I*yx, 100*eps) |
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|
941 %!assert (besselh (alpha,2,x), jx - I*yx, 100*eps) |
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|
942 %! |
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|
943 %!assert (besselj (alpha,x,1), jx*exp (-abs (imag (x))), 100*eps) |
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|
944 %!assert (bessely (alpha,x,1), yx*exp (-abs (imag (x))), 100*eps) |
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|
945 %!assert (besseli (alpha,x,1), ix*exp (-abs (real (x))), 100*eps) |
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|
946 %!assert (besselk (alpha,x,1), kx*exp (x), 100*eps) |
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|
947 %!assert (besselh (alpha,1,x,1), (jx + I*yx)*exp (-I*x), 100*eps) |
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|
948 %!assert (besselh (alpha,2,x,1), (jx - I*yx)*exp (I*x), 100*eps) |
8278
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|
949 %! |
17336
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950 %! ## Bessel functions, even order, complex x |
8278
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951 %! |
14501
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952 %! alpha = 2; x = 1.25 + 3.625 * I; |
8278
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953 %! jx = -1.299533366810794494030065917 + 4.370833116012278943267479589*I; |
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|
954 %! yx = -4.370357232383223896393056727 - 1.283083391453582032688834041*I; |
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|
955 %! ix = -0.6717801680341515541002273932 - 0.2314623443930774099910228553*I; |
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|
956 %! kx = -0.01108009888623253515463783379 + 0.2245218229358191588208084197*I; |
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|
957 %! |
14501
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958 %!assert (besselj (alpha,x), jx, 100*eps) |
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959 %!assert (bessely (alpha,x), yx, 100*eps) |
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960 %!assert (besseli (alpha,x), ix, 100*eps) |
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|
961 %!assert (besselk (alpha,x), kx, 100*eps) |
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|
962 %!assert (besselh (alpha,1,x), jx + I*yx, 100*eps) |
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963 %!assert (besselh (alpha,2,x), jx - I*yx, 100*eps) |
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964 %! |
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965 %!assert (besselj (alpha,x,1), jx*exp (-abs (imag (x))), 100*eps) |
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|
966 %!assert (bessely (alpha,x,1), yx*exp (-abs (imag (x))), 100*eps) |
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967 %!assert (besseli (alpha,x,1), ix*exp (-abs (real (x))), 100*eps) |
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|
968 %!assert (besselk (alpha,x,1), kx*exp (x), 100*eps) |
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969 %!assert (besselh (alpha,1,x,1), (jx + I*yx)*exp (-I*x), 100*eps) |
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970 %!assert (besselh (alpha,2,x,1), (jx - I*yx)*exp (I*x), 100*eps) |
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971 %! |
14501
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972 %!assert (besselj (-alpha,x), jx, 100*eps) |
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973 %!assert (bessely (-alpha,x), yx, 100*eps) |
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974 %!assert (besseli (-alpha,x), ix, 100*eps) |
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975 %!assert (besselk (-alpha,x), kx, 100*eps) |
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976 %!assert (besselh (-alpha,1,x), jx + I*yx, 100*eps) |
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977 %!assert (besselh (-alpha,2,x), jx - I*yx, 100*eps) |
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978 %! |
28915
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|
979 %!assert (besselj (-alpha,x,1), jx*exp (-abs (imag (x))), 100*eps) |
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980 %!assert (bessely (-alpha,x,1), yx*exp (-abs (imag (x))), 100*eps) |
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981 %!assert (besseli (-alpha,x,1), ix*exp (-abs (real (x))), 100*eps) |
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982 %!assert (besselk (-alpha,x,1), kx*exp (x), 100*eps) |
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983 %!assert (besselh (-alpha,1,x,1), (jx + I*yx)*exp (-I*x), 100*eps) |
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984 %!assert (besselh (-alpha,2,x,1), (jx - I*yx)*exp (I*x), 100*eps) |
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985 %! |
17336
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986 %! ## Bessel functions, odd order, complex x |
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987 %! |
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988 %! alpha = 3; x = 2.5 + 1.875 * I; |
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989 %! jx = 0.1330721523048277493333458596 + 0.5386295217249660078754395597*I; |
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990 %! yx = -0.6485072392105829901122401551 + 0.2608129289785456797046996987*I; |
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991 %! ix = -0.6182064685486998097516365709 + 0.4677561094683470065767989920*I; |
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992 %! kx = -0.1568585587733540007867882337 - 0.05185853709490846050505141321*I; |
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993 %! |
14501
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994 %!assert (besselj (alpha,x), jx, 100*eps) |
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995 %!assert (bessely (alpha,x), yx, 100*eps) |
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996 %!assert (besseli (alpha,x), ix, 100*eps) |
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997 %!assert (besselk (alpha,x), kx, 100*eps) |
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998 %!assert (besselh (alpha,1,x), jx + I*yx, 100*eps) |
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|
999 %!assert (besselh (alpha,2,x), jx - I*yx, 100*eps) |
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1000 %! |
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1001 %!assert (besselj (alpha,x,1), jx*exp (-abs (imag (x))), 100*eps) |
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1002 %!assert (bessely (alpha,x,1), yx*exp (-abs (imag (x))), 100*eps) |
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1003 %!assert (besseli (alpha,x,1), ix*exp (-abs (real (x))), 100*eps) |
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1004 %!assert (besselk (alpha,x,1), kx*exp (x), 100*eps) |
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1005 %!assert (besselh (alpha,1,x,1), (jx + I*yx)*exp (-I*x), 100*eps) |
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1006 %!assert (besselh (alpha,2,x,1), (jx - I*yx)*exp (I*x), 100*eps) |
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1007 %! |
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1008 %!assert (besselj (-alpha,x), -jx, 100*eps) |
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1009 %!assert (bessely (-alpha,x), -yx, 100*eps) |
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1010 %!assert (besseli (-alpha,x), ix, 100*eps) |
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1011 %!assert (besselk (-alpha,x), kx, 100*eps) |
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1012 %!assert (besselh (-alpha,1,x), -(jx + I*yx), 100*eps) |
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1013 %!assert (besselh (-alpha,2,x), -(jx - I*yx), 100*eps) |
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1014 %! |
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1015 %!assert (besselj (-alpha,x,1), -jx*exp (-abs (imag (x))), 100*eps) |
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1016 %!assert (bessely (-alpha,x,1), -yx*exp (-abs (imag (x))), 100*eps) |
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1017 %!assert (besseli (-alpha,x,1), ix*exp (-abs (real (x))), 100*eps) |
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1018 %!assert (besselk (-alpha,x,1), kx*exp (x), 100*eps) |
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1019 %!assert (besselh (-alpha,1,x,1), -(jx + I*yx)*exp (-I*x), 100*eps) |
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1020 %!assert (besselh (-alpha,2,x,1), -(jx - I*yx)*exp (I*x), 100*eps) |
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1021 %! |
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1022 %! ## Bessel functions, fractional order, complex x |
8278
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1023 %! |
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1024 %! alpha = 3.5; x = 1.75 + 4.125 * I; |
8278
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1025 %! jx = -3.018566131370455929707009100 - 0.7585648436793900607704057611*I; |
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1026 %! yx = 0.7772278839106298215614791107 - 3.018518722313849782683792010*I; |
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1027 %! ix = 0.2100873577220057189038160913 - 0.6551765604618246531254970926*I; |
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1028 %! kx = 0.1757147290513239935341488069 + 0.08772348296883849205562558311*I; |
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1029 %! |
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1030 %!assert (besselj (alpha,x), jx, 100*eps) |
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1031 %!assert (bessely (alpha,x), yx, 100*eps) |
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1032 %!assert (besseli (alpha,x), ix, 100*eps) |
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1033 %!assert (besselk (alpha,x), kx, 100*eps) |
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1034 %!assert (besselh (alpha,1,x), jx + I*yx, 100*eps) |
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1035 %!assert (besselh (alpha,2,x), jx - I*yx, 100*eps) |
8278
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1036 %! |
28915
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1037 %!assert (besselj (alpha,x,1), jx*exp (-abs (imag (x))), 100*eps) |
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1038 %!assert (bessely (alpha,x,1), yx*exp (-abs (imag (x))), 100*eps) |
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1039 %!assert (besseli (alpha,x,1), ix*exp (-abs (real (x))), 100*eps) |
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1040 %!assert (besselk (alpha,x,1), kx*exp (x), 100*eps) |
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1041 %!assert (besselh (alpha,1,x,1), (jx + I*yx)*exp (-I*x), 100*eps) |
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1042 %!assert (besselh (alpha,2,x,1), (jx - I*yx)*exp (I*x), 100*eps) |
8278
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|
1043 %! |
17337
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1044 %! nix = 0.09822388691172060573913739253 - 0.7110230642207380127317227407*I; |
8278
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1045 %! |
14501
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1046 %!assert (besselj (-alpha,x), yx, 100*eps) |
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1047 %!assert (bessely (-alpha,x), -jx, 100*eps) |
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1048 %!assert (besseli (-alpha,x), nix, 100*eps) |
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1049 %!assert (besselk (-alpha,x), kx, 100*eps) |
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1050 %!assert (besselh (-alpha,1,x), -I*(jx + I*yx), 100*eps) |
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1051 %!assert (besselh (-alpha,2,x), I*(jx - I*yx), 100*eps) |
8278
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1052 %! |
28915
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1053 %!assert (besselj (-alpha,x,1), yx*exp (-abs (imag (x))), 100*eps) |
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1054 %!assert (bessely (-alpha,x,1), -jx*exp (-abs (imag (x))), 100*eps) |
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1055 %!assert (besseli (-alpha,x,1), nix*exp (-abs (real (x))), 100*eps) |
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1056 %!assert (besselk (-alpha,x,1), kx*exp (x), 100*eps) |
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1057 %!assert (besselh (-alpha,1,x,1), -I*(jx + I*yx)*exp (-I*x), 100*eps) |
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1058 %!assert (besselh (-alpha,2,x,1), I*(jx - I*yx)*exp (I*x), 100*eps) |
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|
1059 |
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1060 Tests contributed by Robert T. Short. |
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1061 Tests are based on the properties and tables in A&S: |
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1062 Abramowitz and Stegun, "Handbook of Mathematical Functions", |
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|
1063 1972. |
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|
1064 |
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1065 For regular Bessel functions, there are 3 tests. These compare octave |
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1066 results against Tables 9.1, 9.2, and 9.4 in A&S. Tables 9.1 and 9.2 |
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1067 are good to only a few decimal places, so any failures should be |
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1068 considered a broken implementation. Table 9.4 is an extended table |
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1069 for larger orders and arguments. There are some differences between |
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1070 Octave and Table 9.4, mostly in the last decimal place but in a very |
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1071 few instances the errors are in the last two places. The comparison |
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1072 tolerance has been changed to reflect this. |
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1073 |
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1074 Similarly for modified Bessel functions, there are 3 tests. These |
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1075 compare octave results against Tables 9.8, 9.9, and 9.11 in A&S. |
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1076 Tables 9.8 and 9.9 are good to only a few decimal places, so any |
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1077 failures should be considered a broken implementation. Table 9.11 is |
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1078 an extended table for larger orders and arguments. There are some |
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1079 differences between octave and Table 9.11, mostly in the last decimal |
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1080 place but in a very few instances the errors are in the last two |
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1081 places. The comparison tolerance has been changed to reflect this. |
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|
1082 |
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1083 For spherical Bessel functions, there are also three tests, comparing |
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1084 octave results to Tables 10.1, 10.2, and 10.4 in A&S. Very similar |
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1085 comments may be made here as in the previous lines. At this time, |
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1086 modified spherical Bessel function tests are not included. |
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1087 |
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1088 % Table 9.1 - J and Y for integer orders 0, 1, 2. |
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1089 % Compare against excerpts of Table 9.1, Abramowitz and Stegun. |
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1090 %!test |
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1091 %! n = 0:2; |
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1092 %! z = (0:2.5:17.5)'; |
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1093 %! |
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1094 %! Jt = [[ 1.000000000000000, 0.0000000000, 0.0000000000]; |
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1095 %! [-0.048383776468198, 0.4970941025, 0.4460590584]; |
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1096 %! [-0.177596771314338, -0.3275791376, 0.0465651163]; |
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1097 %! [ 0.266339657880378, 0.1352484276, -0.2302734105]; |
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1098 %! [-0.245935764451348, 0.0434727462, 0.2546303137]; |
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1099 %! [ 0.146884054700421, -0.1654838046, -0.1733614634]; |
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1100 %! [-0.014224472826781, 0.2051040386, 0.0415716780]; |
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1101 %! [-0.103110398228686, -0.1634199694, 0.0844338303]]; |
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1102 %! |
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1103 %! Yt = [[-Inf, -Inf, -Inf ]; |
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1104 %! [ 0.4980703596, 0.1459181380, -0.38133585 ]; |
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1105 %! [-0.3085176252, 0.1478631434, 0.36766288 ]; |
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1106 %! [ 0.1173132861, -0.2591285105, -0.18641422 ]; |
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1107 %! [ 0.0556711673, 0.2490154242, -0.00586808 ]; |
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|
1108 %! [-0.1712143068, -0.1538382565, 0.14660019 ]; |
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1109 %! [ 0.2054642960, 0.0210736280, -0.20265448 ]; |
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|
1110 %! [-0.1604111925, 0.0985727987, 0.17167666 ]]; |
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1111 %! |
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1112 %! J = besselj (n,z); |
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1113 %! Y = bessely (n,z); |
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1114 %! assert (Jt(:,1), J(:,1), 0.5e-10); |
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1115 %! assert (Yt(:,1), Y(:,1), 0.5e-10); |
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1116 %! assert (Jt(:,2:3), J(:,2:3), 0.5e-10); |
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|
1117 |
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|
1118 Table 9.2 - J and Y for integer orders 3-9. |
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|
1119 |
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|
1120 %!test |
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1121 %! n = (3:9); |
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1122 %! z = (0:2:20).'; |
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|
1123 %! |
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1124 %! Jt = [[ 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00]; |
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1125 %! [ 1.2894e-01, 3.3996e-02, 7.0396e-03, 1.2024e-03, 1.7494e-04, 2.2180e-05, 2.4923e-06]; |
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1126 %! [ 4.3017e-01, 2.8113e-01, 1.3209e-01, 4.9088e-02, 1.5176e-02, 4.0287e-03, 9.3860e-04]; |
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1127 %! [ 1.1477e-01, 3.5764e-01, 3.6209e-01, 2.4584e-01, 1.2959e-01, 5.6532e-02, 2.1165e-02]; |
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1128 %! [-2.9113e-01,-1.0536e-01, 1.8577e-01, 3.3758e-01, 3.2059e-01, 2.2345e-01, 1.2632e-01]; |
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1129 %! [ 5.8379e-02,-2.1960e-01,-2.3406e-01,-1.4459e-02, 2.1671e-01, 3.1785e-01, 2.9186e-01]; |
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1130 %! [ 1.9514e-01, 1.8250e-01,-7.3471e-02,-2.4372e-01,-1.7025e-01, 4.5095e-02, 2.3038e-01]; |
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1131 %! [-1.7681e-01, 7.6244e-02, 2.2038e-01, 8.1168e-02,-1.5080e-01,-2.3197e-01,-1.1431e-01]; |
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1132 %! [-4.3847e-02,-2.0264e-01,-5.7473e-02, 1.6672e-01, 1.8251e-01,-7.0211e-03,-1.8953e-01]; |
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1133 %! [ 1.8632e-01, 6.9640e-02,-1.5537e-01,-1.5596e-01, 5.1399e-02, 1.9593e-01, 1.2276e-01]; |
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1134 %! [-9.8901e-02, 1.3067e-01, 1.5117e-01,-5.5086e-02,-1.8422e-01,-7.3869e-02, 1.2513e-01]]; |
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|
1135 %! |
14501
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1136 %! Yt = [[ -Inf, -Inf, -Inf, -Inf, -Inf, -Inf, -Inf]; |
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1137 %! [-1.1278e+00,-2.7659e+00,-9.9360e+00,-4.6914e+01,-2.7155e+02,-1.8539e+03,-1.4560e+04]; |
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1138 %! [-1.8202e-01,-4.8894e-01,-7.9585e-01,-1.5007e+00,-3.7062e+00,-1.1471e+01,-4.2178e+01]; |
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1139 %! [ 3.2825e-01, 9.8391e-02,-1.9706e-01,-4.2683e-01,-6.5659e-01,-1.1052e+00,-2.2907e+00]; |
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1140 %! [ 2.6542e-02, 2.8294e-01, 2.5640e-01, 3.7558e-02,-2.0006e-01,-3.8767e-01,-5.7528e-01]; |
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|
1141 %! [-2.5136e-01,-1.4495e-01, 1.3540e-01, 2.8035e-01, 2.0102e-01, 1.0755e-03,-1.9930e-01]; |
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1142 %! [ 1.2901e-01,-1.5122e-01,-2.2982e-01,-4.0297e-02, 1.8952e-01, 2.6140e-01, 1.5902e-01]; |
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|
1143 %! [ 1.2350e-01, 2.0393e-01,-6.9717e-03,-2.0891e-01,-1.7209e-01, 3.6816e-02, 2.1417e-01]; |
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1144 %! [-1.9637e-01,-7.3222e-05, 1.9633e-01, 1.2278e-01,-1.0425e-01,-2.1399e-01,-1.0975e-01]; |
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1145 %! [ 3.3724e-02,-1.7722e-01,-1.1249e-01, 1.1472e-01, 1.8897e-01, 3.2253e-02,-1.6030e-01]; |
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1146 %! [ 1.4967e-01, 1.2409e-01,-1.0004e-01,-1.7411e-01,-4.4312e-03, 1.7101e-01, 1.4124e-01]]; |
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|
1147 %! |
14501
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1148 %! n = (3:9); |
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1149 %! z = (0:2:20).'; |
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1150 %! J = besselj (n,z); |
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|
1151 %! Y = bessely (n,z); |
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|
1152 %! |
14501
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1153 %! assert (J(1,:), zeros (1, columns (J))); |
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1154 %! assert (J(2:end,:), Jt(2:end,:), -5e-5); |
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1155 %! assert (Yt(1,:), Y(1,:)); |
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|
1156 %! assert (Y(2:end,:), Yt(2:end,:), -5e-5); |
14425
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Robert T. Short <octave@phaselockedsystems.com>
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|
1157 |
14426
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|
1158 Table 9.4 - J and Y for various integer orders and arguments. |
e28a1723d5a2
besselj: Style fixes on new tests due to Robert T. Short
Jordi Gutiérrez Hermoso <jordigh@octave.org>
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|
1159 |
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|
1160 %!test |
ab4676288414
Fix typos and errors in new bessel function tests
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|
1161 %! Jt = [[ 7.651976866e-01, 2.238907791e-01, -1.775967713e-01, -2.459357645e-01, 5.581232767e-02, 1.998585030e-02]; |
ab4676288414
Fix typos and errors in new bessel function tests
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|
1162 %! [ 2.497577302e-04, 7.039629756e-03, 2.611405461e-01, -2.340615282e-01, -8.140024770e-02, -7.419573696e-02]; |
ab4676288414
Fix typos and errors in new bessel function tests
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|
1163 %! [ 2.630615124e-10, 2.515386283e-07, 1.467802647e-03, 2.074861066e-01, -1.138478491e-01, -5.473217694e-02]; |
ab4676288414
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|
1164 %! [ 2.297531532e-17, 7.183016356e-13, 4.796743278e-07, 4.507973144e-03, -1.082255990e-01, 1.519812122e-02]; |
ab4676288414
Fix typos and errors in new bessel function tests
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|
1165 %! [ 3.873503009e-25, 3.918972805e-19, 2.770330052e-11, 1.151336925e-05, -1.167043528e-01, 6.221745850e-02]; |
ab4676288414
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|
1166 %! [ 3.482869794e-42, 3.650256266e-33, 2.671177278e-21, 1.551096078e-12, 4.843425725e-02, 8.146012958e-02]; |
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|
1167 %! [ 1.107915851e-60, 1.196077458e-48, 8.702241617e-33, 6.030895312e-21, -1.381762812e-01, 7.270175482e-02]; |
ab4676288414
Fix typos and errors in new bessel function tests
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|
1168 %! [ 2.906004948e-80, 3.224095839e-65, 2.294247616e-45, 1.784513608e-30, 1.214090219e-01, -3.869833973e-02]; |
ab4676288414
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1169 %! [ 8.431828790e-189, 1.060953112e-158, 6.267789396e-119, 6.597316064e-89, 1.115927368e-21, 9.636667330e-02]]; |
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|
1170 %! |
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|
1171 %! Yt = [[ 8.825696420e-02, 5.103756726e-01, -3.085176252e-01, 5.567116730e-02, -9.806499547e-02, -7.724431337e-02] |
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|
1172 %! [-2.604058666e+02, -9.935989128e+00, -4.536948225e-01, 1.354030477e-01, -7.854841391e-02, -2.948019628e-02] |
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|
1173 %! [-1.216180143e+08, -1.291845422e+05, -2.512911010e+01, -3.598141522e-01, 5.723897182e-03, 5.833157424e-02] |
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|
1174 %! [-9.256973276e+14, -2.981023646e+10, -4.694049564e+04, -6.364745877e+00, 4.041280205e-02, 7.879068695e-02] |
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|
1175 %! [-4.113970315e+22, -4.081651389e+16, -5.933965297e+08, -1.597483848e+03, 1.644263395e-02, 5.124797308e-02] |
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1176 %! [-3.048128783e+39, -2.913223848e+30, -4.028568418e+18, -7.256142316e+09, -1.164572349e-01, 6.138839212e-03] |
ab4676288414
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|
1177 %! [-7.184874797e+57, -6.661541235e+45, -9.216816571e+29, -1.362803297e+18, -4.530801120e-02, 4.074685217e-02] |
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|
1178 %! [-2.191142813e+77, -1.976150576e+62, -2.788837017e+42, -3.641066502e+27, -2.103165546e-01, 7.650526394e-02] |
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1179 %! [-3.775287810e+185, -3.000826049e+155, -5.084863915e+115, -4.849148271e+85, -3.293800188e+18, -1.669214114e-01]]; |
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|
1180 %! |
6646031e2450
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|
1181 %! n = [(0:5:20).';30;40;50;100]; |
6646031e2450
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|
1182 %! z = [1,2,5,10,50,100]; |
14501
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|
1183 %! J = besselj (n.', z.').'; |
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1184 %! Y = bessely (n.', z.').'; |
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|
1185 %! assert (J, Jt, -1e-9); |
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1186 %! assert (Y, Yt, -1e-9); |
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1187 |
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1188 Table 9.8 - I and K for integer orders 0, 1, 2. |
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1189 |
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1190 %!test |
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1191 %! n = 0:2; |
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1192 %! z1 = [0.1;2.5;5.0]; |
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1193 %! z2 = [7.5;10.0;15.0;20.0]; |
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1194 %! rtbl = [[ 0.9071009258 0.0452984468 0.1251041992 2.6823261023 10.890182683 1.995039646 ]; |
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1195 %! [ 0.2700464416 0.2065846495 0.2042345837 0.7595486903 0.9001744239 0.759126289 ]; |
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1196 %! [ 0.1835408126 0.1639722669 0.7002245988 0.5478075643 0.6002738588 0.132723593 ]; |
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1197 %! [ 0.1483158301 0.1380412115 0.111504840 0.4505236991 0.4796689336 0.57843541 ]; |
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1198 %! [ 0.1278333372 0.1212626814 0.103580801 0.3916319344 0.4107665704 0.47378525 ]; |
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1199 %! [ 0.1038995314 0.1003741751 0.090516308 0.3210023535 0.3315348950 0.36520701 ]; |
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1200 %! [ 0.0897803119 0.0875062222 0.081029690 0.2785448768 0.2854254970 0.30708743 ]]; |
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1201 %! |
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1202 %! tbl = [besseli(n,z1,1), besselk(n,z1,1)]; |
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1203 %! tbl(:,3) = tbl(:,3) .* (exp (z1) .* z1.^(-2)); |
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1204 %! tbl(:,6) = tbl(:,6) .* (exp (-z1) .* z1.^(2)); |
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1205 %! tbl = [tbl;[besseli(n,z2,1),besselk(n,z2,1)]]; |
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1206 %! |
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1207 %! assert (tbl, rtbl, -2e-8); |
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1208 |
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|
1209 Table 9.9 - I and K for orders 3-9. |
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1210 |
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1211 %!test |
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1212 %! It = [[ 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00]; |
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1213 %! [ 2.8791e-02 6.8654e-03 1.3298e-03 2.1656e-04 3.0402e-05 3.7487e-06 4.1199e-07]; |
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1214 %! [ 6.1124e-02 2.5940e-02 9.2443e-03 2.8291e-03 7.5698e-04 1.7968e-04 3.8284e-05]; |
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1215 %! [ 7.4736e-02 4.1238e-02 1.9752e-02 8.3181e-03 3.1156e-03 1.0484e-03 3.1978e-04]; |
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1216 %! [ 7.9194e-02 5.0500e-02 2.8694e-02 1.4633e-02 6.7449e-03 2.8292e-03 1.0866e-03]; |
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1217 %! [ 7.9830e-02 5.5683e-02 3.5284e-02 2.0398e-02 1.0806e-02 5.2694e-03 2.3753e-03]; |
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1218 %! [ 7.8848e-02 5.8425e-02 3.9898e-02 2.5176e-02 1.4722e-02 8.0010e-03 4.0537e-03]; |
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1219 %! [ 7.7183e-02 5.9723e-02 4.3056e-02 2.8969e-02 1.8225e-02 1.0744e-02 5.9469e-03]; |
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1220 %! [ 7.5256e-02 6.0155e-02 4.5179e-02 3.1918e-02 2.1240e-02 1.3333e-02 7.9071e-03]; |
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1221 %! [ 7.3263e-02 6.0059e-02 4.6571e-02 3.4186e-02 2.3780e-02 1.5691e-02 9.8324e-03]; |
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1222 %! [ 7.1300e-02 5.9640e-02 4.7444e-02 3.5917e-02 2.5894e-02 1.7792e-02 1.1661e-02]]; |
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1223 %! |
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1224 %! Kt = [[ Inf Inf Inf Inf Inf Inf Inf]; |
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1225 %! [ 4.7836e+00 1.6226e+01 6.9687e+01 3.6466e+02 2.2576e+03 1.6168e+04 1.3160e+05]; |
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1226 %! [ 1.6317e+00 3.3976e+00 8.4268e+00 2.4465e+01 8.1821e+01 3.1084e+02 1.3252e+03]; |
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1227 %! [ 9.9723e-01 1.6798e+00 3.2370e+00 7.0748e+00 1.7387e+01 4.7644e+01 1.4444e+02]; |
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1228 %! [ 7.3935e-01 1.1069e+00 1.8463e+00 3.4148e+00 6.9684e+00 1.5610e+01 3.8188e+01]; |
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1229 %! [ 6.0028e-01 8.3395e-01 1.2674e+00 2.1014e+00 3.7891e+00 7.4062e+00 1.5639e+01]; |
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1230 %! [ 5.1294e-01 6.7680e-01 9.6415e-01 1.4803e+00 2.4444e+00 4.3321e+00 8.2205e+00]; |
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1231 %! [ 4.5266e-01 5.7519e-01 7.8133e-01 1.1333e+00 1.7527e+00 2.8860e+00 5.0510e+00]; |
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1232 %! [ 4.0829e-01 5.0414e-01 6.6036e-01 9.1686e-01 1.3480e+00 2.0964e+00 3.4444e+00]; |
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1233 %! [ 3.7411e-01 4.5162e-01 5.7483e-01 7.7097e-01 1.0888e+00 1.6178e+00 2.5269e+00]; |
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1234 %! [ 3.4684e-01 4.1114e-01 5.1130e-01 6.6679e-01 9.1137e-01 1.3048e+00 1.9552e+00]]; |
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1235 %! |
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1236 %! n = (3:9); |
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1237 %! z = (0:2:20).'; |
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1238 %! I = besseli (n,z,1); |
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1239 %! K = besselk (n,z,1); |
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1240 %! |
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1241 %! assert (abs (I(1,:)), zeros (1, columns (I))); |
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1242 %! assert (I(2:end,:), It(2:end,:), -5e-5); |
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1243 %! assert (Kt(1,:), K(1,:)); |
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1244 %! assert (K(2:end,:), Kt(2:end,:), -5e-5); |
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|
1245 |
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1246 Table 9.11 - I and K for various integer orders and arguments. |
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1247 |
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1248 %!test |
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1249 %! It = [[ 1.266065878e+00 2.279585302e+00 2.723987182e+01 2.815716628e+03 2.93255378e+20 1.07375171e+42 ]; |
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1250 %! [ 2.714631560e-04 9.825679323e-03 2.157974547e+00 7.771882864e+02 2.27854831e+20 9.47009387e+41 ]; |
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1251 %! [ 2.752948040e-10 3.016963879e-07 4.580044419e-03 2.189170616e+01 1.07159716e+20 6.49897552e+41 ]; |
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1252 %! [ 2.370463051e-17 8.139432531e-13 1.047977675e-06 1.043714907e-01 3.07376455e+19 3.47368638e+41 ]; |
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1253 %! [ 3.966835986e-25 4.310560576e-19 5.024239358e-11 1.250799736e-04 5.44200840e+18 1.44834613e+41 ]; |
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1254 %! [ 3.539500588e-42 3.893519664e-33 3.997844971e-21 7.787569783e-12 4.27499365e+16 1.20615487e+40 ]; |
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1255 %! [ 1.121509741e-60 1.255869192e-48 1.180426980e-32 2.042123274e-20 6.00717897e+13 3.84170550e+38 ]; |
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|
1256 %! [ 2.934635309e-80 3.353042830e-65 2.931469647e-45 4.756894561e-30 1.76508024e+10 4.82195809e+36 ]; |
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1257 %! [ 8.473674008e-189 1.082171475e-158 7.093551489e-119 1.082344202e-88 2.72788795e-16 4.64153494e+21 ]]; |
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1258 %! |
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1259 %! Kt = [[ 4.210244382e-01 1.138938727e-01 3.691098334e-03 1.778006232e-05 3.41016774e-23 4.65662823e-45 ]; |
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|
1260 %! [ 3.609605896e+02 9.431049101e+00 3.270627371e-02 5.754184999e-05 4.36718224e-23 5.27325611e-45 ]; |
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1261 %! [ 1.807132899e+08 1.624824040e+05 9.758562829e+00 1.614255300e-03 9.15098819e-23 7.65542797e-45 ]; |
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1262 %! [ 1.403066801e+15 4.059213332e+10 3.016976630e+04 2.656563849e-01 3.11621117e-22 1.42348325e-44 ]; |
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|
1263 %! [ 6.294369360e+22 5.770856853e+16 4.827000521e+08 1.787442782e+02 1.70614838e-21 3.38520541e-44 ]; |
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1264 %! [ 4.706145527e+39 4.271125755e+30 4.112132063e+18 2.030247813e+09 2.00581681e-19 3.97060205e-43 ]; |
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1265 %! [ 1.114220651e+58 9.940839886e+45 1.050756722e+30 5.938224681e+17 1.29986971e-16 1.20842080e-41 ]; |
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1266 %! [ 3.406896854e+77 2.979981740e+62 3.394322243e+42 2.061373775e+27 4.00601349e-13 9.27452265e-40 ]; |
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1267 %! [ 5.900333184e+185 4.619415978e+155 7.039860193e+115 4.596674084e+85 1.63940352e+13 7.61712963e-25 ]]; |
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1268 %! |
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1269 %! n = [(0:5:20).';30;40;50;100]; |
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1270 %! z = [1,2,5,10,50,100]; |
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1271 %! I = besseli (n.', z.').'; |
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1272 %! K = besselk (n.', z.').'; |
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1273 %! assert (I, It, -5e-9); |
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1274 %! assert (K, Kt, -5e-9); |
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1275 |
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1276 The next section checks that negative integer orders and positive |
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1277 integer orders are appropriately related. |
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1278 |
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1279 %!test |
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1280 %! n = (0:2:20); |
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1281 %! assert (besselj (n,1), besselj (-n,1), 1e-8); |
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1282 %! assert (-besselj (n+1,1), besselj (-n-1,1), 1e-8); |
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1283 |
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1284 besseli (n,z) = besseli (-n,z); |
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1285 |
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1286 %!test |
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1287 %! n = (0:2:20); |
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1288 %! assert (besseli (n,1), besseli (-n,1), 1e-8); |
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1289 |
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1290 Table 10.1 - j and y for integer orders 0, 1, 2. |
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1291 Compare against excerpts of Table 10.1, Abramowitz and Stegun. |
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1292 |
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1293 %!test |
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1294 %! n = (0:2); |
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1295 %! z = [0.1;(2.5:2.5:10.0).']; |
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1296 %! |
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1297 %! jt = [[ 9.9833417e-01 3.33000119e-02 6.6619061e-04 ]; |
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1298 %! [ 2.3938886e-01 4.16212989e-01 2.6006673e-01 ]; |
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1299 %! [-1.9178485e-01 -9.50894081e-02 1.3473121e-01 ]; |
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1300 %! [ 1.2507e-01 -2.9542e-02 -1.3688e-01 ]; |
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1301 %! [ -5.4402e-02 7.8467e-02 7.7942e-02 ]]; |
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1302 %! |
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1303 %! yt = [[-9.9500417e+00 -1.0049875e+02 -3.0050125e+03 ]; |
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1304 %! [ 3.2045745e-01 -1.1120588e-01 -4.5390450e-01 ]; |
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1305 %! [-5.6732437e-02 1.8043837e-01 1.6499546e-01 ]; |
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1306 %! [ -4.6218e-02 -1.3123e-01 -6.2736e-03 ]; |
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1307 %! [ 8.3907e-02 6.2793e-02 -6.5069e-02 ]]; |
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1308 %! |
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1309 %! j = sqrt ((pi/2)./z) .* besselj (n+1/2,z); |
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1310 %! y = sqrt ((pi/2)./z) .* bessely (n+1/2,z); |
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1311 %! assert (jt, j, -5e-5); |
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1312 %! assert (yt, y, -5e-5); |
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1313 |
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1314 Table 10.2 - j and y for orders 3-8. |
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1315 Compare against excerpts of Table 10.2, Abramowitzh and Stegun. |
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1316 |
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1317 Important note: In A&S, y_4(0.1) = -1.0507e+7, but Octave returns |
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1318 y_4(0.1) = -1.0508e+07 (-10507503.75). If I compute the same term using |
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1319 a series, the difference is in the eighth significant digit so I left |
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1320 the Octave results in place. |
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1321 |
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1322 %!test |
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1323 %! n = (3:8); |
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1324 %! z = (0:2.5:10).'; z(1) = 0.1; |
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1325 %! |
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1326 %! jt = [[ 9.5185e-06 1.0577e-07 9.6163e-10 7.3975e-12 4.9319e-14 2.9012e-16]; |
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1327 %! [ 1.0392e-01 3.0911e-02 7.3576e-03 1.4630e-03 2.5009e-04 3.7516e-05]; |
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1328 %! [ 2.2982e-01 1.8702e-01 1.0681e-01 4.7967e-02 1.7903e-02 5.7414e-03]; |
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1329 %! [-6.1713e-02 7.9285e-02 1.5685e-01 1.5077e-01 1.0448e-01 5.8188e-02]; |
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1330 %! [-3.9496e-02 -1.0559e-01 -5.5535e-02 4.4501e-02 1.1339e-01 1.2558e-01]]; |
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1331 %! |
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1332 %! yt = [[-1.5015e+05 -1.0508e+07 -9.4553e+08 -1.0400e+11 -1.3519e+13 -2.0277e+15]; |
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1333 %! [-7.9660e-01 -1.7766e+00 -5.5991e+00 -2.2859e+01 -1.1327e+02 -6.5676e+02]; |
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1334 %! [-1.5443e-02 -1.8662e-01 -3.2047e-01 -5.1841e-01 -1.0274e+00 -2.5638e+00]; |
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1335 %! [ 1.2705e-01 1.2485e-01 2.2774e-02 -9.1449e-02 -1.8129e-01 -2.7112e-01]; |
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1336 %! [-9.5327e-02 -1.6599e-03 9.3834e-02 1.0488e-01 4.2506e-02 -4.1117e-02]]; |
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1337 %! |
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1338 %! j = sqrt ((pi/2)./z) .* besselj (n+1/2,z); |
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1339 %! y = sqrt ((pi/2)./z) .* bessely (n+1/2,z); |
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1340 %! |
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1341 %! assert (jt, j, -5e-5); |
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1342 %! assert (yt, y, -5e-5); |
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1343 |
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1344 Table 10.4 - j and y for various integer orders and arguments. |
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1345 |
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1346 %!test |
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1347 %! jt = [[ 8.414709848e-01 4.546487134e-01 -1.917848549e-01 -5.440211109e-02 -5.247497074e-03 -5.063656411e-03]; |
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1348 %! [ 9.256115861e-05 2.635169770e-03 1.068111615e-01 -5.553451162e-02 -2.004830056e-02 -9.290148935e-03]; |
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1349 %! [ 7.116552640e-11 6.825300865e-08 4.073442442e-04 6.460515449e-02 -1.503922146e-02 -1.956578597e-04]; |
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|
1350 %! [ 5.132686115e-18 1.606982166e-13 1.084280182e-07 1.063542715e-03 -1.129084539e-02 7.877261748e-03]; |
6646031e2450
besselj.cc: Added tests to cover a broad range of arguments and orders.
Robert T. Short <octave@phaselockedsystems.com>
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1351 %! [ 7.537795722e-26 7.632641101e-20 5.427726761e-12 2.308371961e-06 -1.578502990e-02 1.010767128e-02]; |
6646031e2450
besselj.cc: Added tests to cover a broad range of arguments and orders.
Robert T. Short <octave@phaselockedsystems.com>
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|
1352 %! [ 5.566831267e-43 5.836617888e-34 4.282730217e-22 2.512057385e-13 -1.494673454e-03 8.700628514e-03]; |
6646031e2450
besselj.cc: Added tests to cover a broad range of arguments and orders.
Robert T. Short <octave@phaselockedsystems.com>
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1353 %! [ 1.538210374e-61 1.660978779e-49 1.210347583e-33 8.435671634e-22 -2.606336952e-02 1.043410851e-02]; |
6646031e2450
besselj.cc: Added tests to cover a broad range of arguments and orders.
Robert T. Short <octave@phaselockedsystems.com>
parents:
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1354 %! [ 3.615274717e-81 4.011575290e-66 2.857479350e-46 2.230696023e-31 1.882910737e-02 5.797140882e-04]; |
6646031e2450
besselj.cc: Added tests to cover a broad range of arguments and orders.
Robert T. Short <octave@phaselockedsystems.com>
parents:
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1355 %! [7.444727742e-190 9.367832591e-160 5.535650303e-120 5.832040182e-90 1.019012263e-22 1.088047701e-02]]; |
14426
e28a1723d5a2
besselj: Style fixes on new tests due to Robert T. Short
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents:
14425
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1356 %! |
14425
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Robert T. Short <octave@phaselockedsystems.com>
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1357 %! yt = [[ -5.403023059e-01 2.080734183e-01 -5.673243709e-02 8.390715291e-02 -1.929932057e-02 -8.623188723e-03] |
6646031e2450
besselj.cc: Added tests to cover a broad range of arguments and orders.
Robert T. Short <octave@phaselockedsystems.com>
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1358 %! [ -9.994403434e+02 -1.859144531e+01 -3.204650467e-01 9.383354168e-02 -6.971131965e-04 3.720678486e-03] |
6646031e2450
besselj.cc: Added tests to cover a broad range of arguments and orders.
Robert T. Short <octave@phaselockedsystems.com>
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1359 %! [ -6.722150083e+08 -3.554147201e+05 -2.665611441e+01 -1.724536721e-01 1.352468751e-02 1.002577737e-02] |
6646031e2450
besselj.cc: Added tests to cover a broad range of arguments and orders.
Robert T. Short <octave@phaselockedsystems.com>
parents:
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1360 %! [ -6.298007233e+15 -1.012182944e+11 -6.288146513e+04 -3.992071745e+00 1.712319725e-02 6.258641510e-03] |
6646031e2450
besselj.cc: Added tests to cover a broad range of arguments and orders.
Robert T. Short <octave@phaselockedsystems.com>
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1361 %! [ -3.239592219e+23 -1.605436493e+17 -9.267951403e+08 -1.211210605e+03 1.375953130e-02 5.631729379e-05] |
6646031e2450
besselj.cc: Added tests to cover a broad range of arguments and orders.
Robert T. Short <octave@phaselockedsystems.com>
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1362 %! [ -2.946428547e+40 -1.407393871e+31 -7.760717570e+18 -6.908318646e+09 -2.241226812e-02 -5.412929349e-03] |
6646031e2450
besselj.cc: Added tests to cover a broad range of arguments and orders.
Robert T. Short <octave@phaselockedsystems.com>
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1363 %! [ -8.028450851e+58 -3.720929322e+46 -2.055758716e+30 -1.510304919e+18 4.978797221e-05 -7.048420407e-04] |
6646031e2450
besselj.cc: Added tests to cover a broad range of arguments and orders.
Robert T. Short <octave@phaselockedsystems.com>
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1364 %! [ -2.739192285e+78 -1.235021944e+63 -6.964109188e+42 -4.528227272e+27 -4.190000150e-02 1.074782297e-02] |
6646031e2450
besselj.cc: Added tests to cover a broad range of arguments and orders.
Robert T. Short <octave@phaselockedsystems.com>
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1365 %! [-6.683079463e+186 -2.655955830e+156 -1.799713983e+116 -8.573226309e+85 -1.125692891e+18 -2.298385049e-02]]; |
6646031e2450
besselj.cc: Added tests to cover a broad range of arguments and orders.
Robert T. Short <octave@phaselockedsystems.com>
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1366 %! |
6646031e2450
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1367 %! n = [(0:5:20).';30;40;50;100]; |
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1368 %! z = [1,2,5,10,50,100]; |
14501
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Rik <octave@nomad.inbox5.com>
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1369 %! j = sqrt ((pi/2)./z) .* besselj ((n+1/2).', z.').'; |
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Rik <octave@nomad.inbox5.com>
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1370 %! y = sqrt ((pi/2)./z) .* bessely ((n+1/2).', z.').'; |
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Rik <octave@nomad.inbox5.com>
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1371 %! assert (j, jt, -1e-9); |
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Rik <octave@nomad.inbox5.com>
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1372 %! assert (y, yt, -1e-9); |
8278
ab0674a8b345
fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
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1373 */ |
29958
32c3a5805893
move DEFUN and DEFMETHOD functions inside octave namespace
John W. Eaton <jwe@octave.org>
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29359
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1374 |
31605
e88a07dec498
maint: Use macros to begin/end C++ namespaces.
Rik <rik@octave.org>
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31549
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1375 OCTAVE_END_NAMESPACE(octave) |