octave: libinterp/corefcn/psi.cc annotate

annotate libinterp/corefcn/psi.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	32d2b6604a9f
children	aac27ad79be6

rev	line source
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	1 ////////////////////////////////////////////////////////////////////////
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	2 //
30564 796f54d4ddbf update Octave Project Developers copyright for the new year John W. Eaton <jwe@octave.org> parents: 29961 diff changeset	3 // Copyright (C) 2016-2022 The Octave Project Developers
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	4 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	5 // See the file COPYRIGHT.md in the top-level directory of this
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	6 // distribution or <https://octave.org/copyright/>.
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	7 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	8 // This file is part of Octave.
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	9 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	10 // Octave is free software: you can redistribute it and/or modify it
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	11 // under the terms of the GNU General Public License as published by
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	12 // the Free Software Foundation, either version 3 of the License, or
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	13 // (at your option) any later version.
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	14 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	15 // Octave is distributed in the hope that it will be useful, but
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	16 // WITHOUT ANY WARRANTY; without even the implied warranty of
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	18 // GNU General Public License for more details.
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	19 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	20 // You should have received a copy of the GNU General Public License
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	21 // along with Octave; see the file COPYING. If not, see
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	22 // <https://www.gnu.org/licenses/>.
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	23 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	24 ////////////////////////////////////////////////////////////////////////
20154 45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	25
21724 aba2e6293dd8 use "#if ..." consistently instead of "#ifdef" and "#ifndef" John W. Eaton <jwe@octave.org> parents: 21580 diff changeset	26 #if defined (HAVE_CONFIG_H)
21301 40de9f8f23a6 Use '#include "config.h"' rather than <config.h>. Rik <rik@octave.org> parents: 21200 diff changeset	27 # include "config.h"
20154 45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	28 #endif
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	29
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	30 #include "ov.h"
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	31 #include "defun.h"
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	32 #include "error.h"
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	33 #include "dNDArray.h"
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	34 #include "fNDArray.h"
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	35
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	36 #include "lo-specfun.h"
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	37
31605 e88a07dec498 maint: Use macros to begin/end C++ namespaces. Rik <rik@octave.org> parents: 30888 diff changeset	38 OCTAVE_BEGIN_NAMESPACE(octave)
29958 32c3a5805893 move DEFUN and DEFMETHOD functions inside octave namespace John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	39
20154 45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	40 DEFUN (psi, args, ,
21966 112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	41 doc: /* -- texinfo --
30888 32d2b6604a9f doc: Ensure documentation lists output argument when it exists for functions in libinterp/ Rik <rik@octave.org> parents: 30565 diff changeset	42 @deftypefn {} {@var{y} =} psi (@var{z})
32d2b6604a9f doc: Ensure documentation lists output argument when it exists for functions in libinterp/ Rik <rik@octave.org> parents: 30565 diff changeset	43 @deftypefnx {} {@var{y} =} psi (@var{k}, @var{z})
21966 112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	44 Compute the psi (polygamma) function.
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	45
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	46 The polygamma functions are the @var{k}th derivative of the logarithm
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	47 of the gamma function. If unspecified, @var{k} defaults to zero. A value
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	48 of zero computes the digamma function, a value of 1, the trigamma function,
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	49 and so on.
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	50
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	51 The digamma function is defined:
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	52
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	53 @tex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	54 $$
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	55 \Psi (z) = {d (log (\Gamma (z))) \over dx}
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	56 $$
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	57 @end tex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	58 @ifnottex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	59
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	60 @example
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	61 @group
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	62 psi (z) = d (log (gamma (z))) / dx
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	63 @end group
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	64 @end example
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	65
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	66 @end ifnottex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	67
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	68 When computing the digamma function (when @var{k} equals zero), @var{z}
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	69 can have any value real or complex value. However, for polygamma functions
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	70 (@var{k} higher than 0), @var{z} must be real and non-negative.
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	71
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	72 @seealso{gamma, gammainc, gammaln}
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21830 diff changeset	73 @end deftypefn */)
20154 45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	74 {
20939 b17fda023ca6 maint: Use new C++ archetype in more files. Rik <rik@octave.org> parents: 20853 diff changeset	75 int nargin = args.length ();
20154 45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	76
20161 65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	77 if (nargin < 1 \|\| nargin > 2)
20801 a542a9bf177e eliminate return statements after calls to print_usage John W. Eaton <jwe@octave.org> parents: 20704 diff changeset	78 print_usage ();
20154 45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	79
20161 65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	80 const octave_value oct_z = (nargin == 1) ? args(0) : args(1);
26355 bb3ebaa9460e psi.cc: Fix static analyzer detected issues (bug #55347). Rik <rik@octave.org> parents: 25054 diff changeset	81 const octave_idx_type k = (nargin == 1) ? 0 : args(0).xidx_type_value ("psi: K must be an integer");
20704 571508c1ed06 eliminate more uses of error_state John W. Eaton <jwe@octave.org> parents: 20424 diff changeset	82 if (k < 0)
20831 35241c4b696c eliminate return statements after calls to error John W. Eaton <jwe@octave.org> parents: 20801 diff changeset	83 error ("psi: K must be non-negative");
20939 b17fda023ca6 maint: Use new C++ archetype in more files. Rik <rik@octave.org> parents: 20853 diff changeset	84
b17fda023ca6 maint: Use new C++ archetype in more files. Rik <rik@octave.org> parents: 20853 diff changeset	85 octave_value retval;
b17fda023ca6 maint: Use new C++ archetype in more files. Rik <rik@octave.org> parents: 20853 diff changeset	86
b17fda023ca6 maint: Use new C++ archetype in more files. Rik <rik@octave.org> parents: 20853 diff changeset	87 if (k == 0)
20161 65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	88 {
22197 e43d83253e28 refill multi-line macro definitions John W. Eaton <jwe@octave.org> parents: 21966 diff changeset	89 #define FLOAT_BRANCH(T, A, M, E) \
e43d83253e28 refill multi-line macro definitions John W. Eaton <jwe@octave.org> parents: 21966 diff changeset	90 if (oct_z.is_ ## T ##_type ()) \
e43d83253e28 refill multi-line macro definitions John W. Eaton <jwe@octave.org> parents: 21966 diff changeset	91 { \
e43d83253e28 refill multi-line macro definitions John W. Eaton <jwe@octave.org> parents: 21966 diff changeset	92 const A ## NDArray z = oct_z.M ## array_value (); \
e43d83253e28 refill multi-line macro definitions John W. Eaton <jwe@octave.org> parents: 21966 diff changeset	93 A ## NDArray psi_z (z.dims ()); \
e43d83253e28 refill multi-line macro definitions John W. Eaton <jwe@octave.org> parents: 21966 diff changeset	94 \
23449 c763214a8260 maint: Use convention 'int x' for naming pointers. Rik <rik@octave.org>* parents: 23220 diff changeset	95 const E *zv = z.data (); \
c763214a8260 maint: Use convention 'int x' for naming pointers. Rik <rik@octave.org>* parents: 23220 diff changeset	96 E *psi_zv = psi_z.fortran_vec (); \
22197 e43d83253e28 refill multi-line macro definitions John W. Eaton <jwe@octave.org> parents: 21966 diff changeset	97 const octave_idx_type n = z.numel (); \
e43d83253e28 refill multi-line macro definitions John W. Eaton <jwe@octave.org> parents: 21966 diff changeset	98 for (octave_idx_type i = 0; i < n; i++) \
29961 7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more John W. Eaton <jwe@octave.org> parents: 29958 diff changeset	99 psi_zv++ = math::psi (zv++); \
22197 e43d83253e28 refill multi-line macro definitions John W. Eaton <jwe@octave.org> parents: 21966 diff changeset	100 \
e43d83253e28 refill multi-line macro definitions John W. Eaton <jwe@octave.org> parents: 21966 diff changeset	101 retval = psi_z; \
20161 65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	102 }
20154 45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	103
23581 c3075ae020e1 maint: Deprecate is_complex_type and replace with iscomplex. Rik <rik@octave.org> parents: 23449 diff changeset	104 if (oct_z.iscomplex ())
20161 65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	105 {
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	106 FLOAT_BRANCH(double, Complex, complex_, Complex)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	107 else FLOAT_BRANCH(single, FloatComplex, float_complex_, FloatComplex)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	108 else
20831 35241c4b696c eliminate return statements after calls to error John W. Eaton <jwe@octave.org> parents: 20801 diff changeset	109 error ("psi: Z must be a floating point");
20161 65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	110 }
20155 1fae49e34a1a psi: add support for complex numbers. Carnë Draug <carandraug@octave.org> parents: 20154 diff changeset	111 else
1fae49e34a1a psi: add support for complex numbers. Carnë Draug <carandraug@octave.org> parents: 20154 diff changeset	112 {
20161 65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	113 FLOAT_BRANCH(double, , , double)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	114 else FLOAT_BRANCH(single, Float, float_, float)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	115 else
20831 35241c4b696c eliminate return statements after calls to error John W. Eaton <jwe@octave.org> parents: 20801 diff changeset	116 error ("psi: Z must be a floating point");
20155 1fae49e34a1a psi: add support for complex numbers. Carnë Draug <carandraug@octave.org> parents: 20154 diff changeset	117 }
20161 65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	118
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	119 #undef FLOAT_BRANCH
20155 1fae49e34a1a psi: add support for complex numbers. Carnë Draug <carandraug@octave.org> parents: 20154 diff changeset	120 }
20154 45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	121 else
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	122 {
23582 0cc2011d800e maint: Deprecate is_real_type and replace with isreal. Rik <rik@octave.org> parents: 23581 diff changeset	123 if (! oct_z.isreal ())
20831 35241c4b696c eliminate return statements after calls to error John W. Eaton <jwe@octave.org> parents: 20801 diff changeset	124 error ("psi: Z must be real value for polygamma (K > 0)");
20161 65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	125
22197 e43d83253e28 refill multi-line macro definitions John W. Eaton <jwe@octave.org> parents: 21966 diff changeset	126 #define FLOAT_BRANCH(T, A, M, E) \
e43d83253e28 refill multi-line macro definitions John W. Eaton <jwe@octave.org> parents: 21966 diff changeset	127 if (oct_z.is_ ## T ##_type ()) \
e43d83253e28 refill multi-line macro definitions John W. Eaton <jwe@octave.org> parents: 21966 diff changeset	128 { \
e43d83253e28 refill multi-line macro definitions John W. Eaton <jwe@octave.org> parents: 21966 diff changeset	129 const A ## NDArray z = oct_z.M ## array_value (); \
e43d83253e28 refill multi-line macro definitions John W. Eaton <jwe@octave.org> parents: 21966 diff changeset	130 A ## NDArray psi_z (z.dims ()); \
e43d83253e28 refill multi-line macro definitions John W. Eaton <jwe@octave.org> parents: 21966 diff changeset	131 \
23449 c763214a8260 maint: Use convention 'int x' for naming pointers. Rik <rik@octave.org>* parents: 23220 diff changeset	132 const E *zv = z.data (); \
c763214a8260 maint: Use convention 'int x' for naming pointers. Rik <rik@octave.org>* parents: 23220 diff changeset	133 E *psi_zv = psi_z.fortran_vec (); \
22197 e43d83253e28 refill multi-line macro definitions John W. Eaton <jwe@octave.org> parents: 21966 diff changeset	134 const octave_idx_type n = z.numel (); \
e43d83253e28 refill multi-line macro definitions John W. Eaton <jwe@octave.org> parents: 21966 diff changeset	135 for (octave_idx_type i = 0; i < n; i++) \
e43d83253e28 refill multi-line macro definitions John W. Eaton <jwe@octave.org> parents: 21966 diff changeset	136 { \
e43d83253e28 refill multi-line macro definitions John W. Eaton <jwe@octave.org> parents: 21966 diff changeset	137 if (*zv < 0) \
20831 35241c4b696c eliminate return statements after calls to error John W. Eaton <jwe@octave.org> parents: 20801 diff changeset	138 error ("psi: Z must be non-negative for polygamma (K > 0)"); \
22197 e43d83253e28 refill multi-line macro definitions John W. Eaton <jwe@octave.org> parents: 21966 diff changeset	139 \
29961 7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more John W. Eaton <jwe@octave.org> parents: 29958 diff changeset	140 psi_zv++ = math::psi (k, zv++); \
22197 e43d83253e28 refill multi-line macro definitions John W. Eaton <jwe@octave.org> parents: 21966 diff changeset	141 } \
e43d83253e28 refill multi-line macro definitions John W. Eaton <jwe@octave.org> parents: 21966 diff changeset	142 retval = psi_z; \
20161 65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	143 }
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	144
20155 1fae49e34a1a psi: add support for complex numbers. Carnë Draug <carandraug@octave.org> parents: 20154 diff changeset	145 FLOAT_BRANCH(double, , , double)
1fae49e34a1a psi: add support for complex numbers. Carnë Draug <carandraug@octave.org> parents: 20154 diff changeset	146 else FLOAT_BRANCH(single, Float, float_, float)
1fae49e34a1a psi: add support for complex numbers. Carnë Draug <carandraug@octave.org> parents: 20154 diff changeset	147 else
20831 35241c4b696c eliminate return statements after calls to error John W. Eaton <jwe@octave.org> parents: 20801 diff changeset	148 error ("psi: Z must be a floating point for polygamma (K > 0)");
20154 45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	149
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	150 #undef FLOAT_BRANCH
20161 65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	151 }
20154 45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	152
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	153 return retval;
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	154 }
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	155
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	156 /*
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	157 %!shared em
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	158 %! em = 0.577215664901532860606512090082402431042; # Euler-Mascheroni Constant
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	159
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	160 %!assert (psi (ones (7, 3, 5)), repmat (-em, [7 3 5]))
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	161 %!assert (psi ([0 1]), [-Inf -em])
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	162 %!assert (psi ([-20:1]), [repmat(-Inf, [1 21]) -em])
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	163 %!assert (psi (single ([0 1])), single ([-Inf -em]))
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	164
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	165 ## Abramowitz and Stegun, page 258, eq 6.3.5
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	166 %!test
20424 099bdf98f724 psi: Fix failing unit tests on 32-bit systems Mike Miller <mtmiller@octave.org> parents: 20161 diff changeset	167 %! z = [-100:-1 1:200] ./ 10; # drop the 0
21580 ecce63c99c3f maint: Add semicolons to terminate code in %! blocks. Rik <rik@octave.org> parents: 21316 diff changeset	168 %! assert (psi (z + 1), psi (z) + 1 ./ z, eps*1000);
20154 45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	169
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	170 ## Abramowitz and Stegun, page 258, eq 6.3.2
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	171 %!assert (psi (1), -em)
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	172
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	173 ## Abramowitz and Stegun, page 258, eq 6.3.3
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	174 %!assert (psi (1/2), -em - 2 * log (2))
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	175
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	176 ## The following tests are from Pascal Sebah and Xavier Gourdon (2002)
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	177 ## "Introduction to the Gamma Function"
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	178
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	179 ## Interesting identities of the digamma function, in section of 5.1.3
28915 c40a367a84c0 maint: Use Octave convention of space after function name in libinterp/. Rik <rik@octave.org> parents: 28888 diff changeset	180 %!assert (psi (1/3), - em - (3/2) * log (3) - ((sqrt (3) / 6) * pi), eps*10)
20424 099bdf98f724 psi: Fix failing unit tests on 32-bit systems Mike Miller <mtmiller@octave.org> parents: 20161 diff changeset	181 %!assert (psi (1/4), - em -3 * log (2) - pi/2, eps*10)
30346 91c6288781ba maint: Shorten some long lines in libinterp to <= 80 characters (bug #57599) Rik <rik@octave.org> parents: 29961 diff changeset	182 %!assert (psi (1/6),
91c6288781ba maint: Shorten some long lines in libinterp to <= 80 characters (bug #57599) Rik <rik@octave.org> parents: 29961 diff changeset	183 %! - em -2 * log (2) - (3/2) * log (3) - ((sqrt (3) / 2) * pi), eps*10)
20154 45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	184
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	185 ## First 6 zeros of the digamma function, in section of 5.1.5 (and also on
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	186 ## Abramowitz and Stegun, page 258, eq 6.3.19)
45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	187 %!assert (psi ( 1.46163214496836234126265954232572132846819620400644), 0, eps)
21762 289ee97765ad psi: Adjust tolerances for failing tests on i386 systems (bug #47965) Mike Miller <mtmiller@octave.org> parents: 21724 diff changeset	188 %!assert (psi (-0.504083008264455409258269304533302498955385182368579), 0, eps*2)
289ee97765ad psi: Adjust tolerances for failing tests on i386 systems (bug #47965) Mike Miller <mtmiller@octave.org> parents: 21724 diff changeset	189 %!assert (psi (-1.573498473162390458778286043690434612655040859116846), 0, eps*2)
20154 45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	190 %!assert (psi (-2.610720868444144650001537715718724207951074010873480), 0, eps*10)
20156 bd565f3e0ecb psi: refactor to reduce code duplication. Carnë Draug <carandraug@octave.org> parents: 20155 diff changeset	191 %!assert (psi (-3.635293366436901097839181566946017713948423861193530), 0, eps*10)
20154 45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	192 %!assert (psi (-4.653237761743142441714598151148207363719069416133868), 0, eps*100)
20155 1fae49e34a1a psi: add support for complex numbers. Carnë Draug <carandraug@octave.org> parents: 20154 diff changeset	193
1fae49e34a1a psi: add support for complex numbers. Carnë Draug <carandraug@octave.org> parents: 20154 diff changeset	194 ## Tests for complex values
1fae49e34a1a psi: add support for complex numbers. Carnë Draug <carandraug@octave.org> parents: 20154 diff changeset	195 %!shared z
20424 099bdf98f724 psi: Fix failing unit tests on 32-bit systems Mike Miller <mtmiller@octave.org> parents: 20161 diff changeset	196 %! z = [-100:-1 1:200] ./ 10; # drop the 0
20155 1fae49e34a1a psi: add support for complex numbers. Carnë Draug <carandraug@octave.org> parents: 20154 diff changeset	197
1fae49e34a1a psi: add support for complex numbers. Carnë Draug <carandraug@octave.org> parents: 20154 diff changeset	198 ## Abramowitz and Stegun, page 259 eq 6.3.10
1fae49e34a1a psi: add support for complex numbers. Carnë Draug <carandraug@octave.org> parents: 20154 diff changeset	199 %!assert (real (psi (iz)), real (psi (1 - iz)))
1fae49e34a1a psi: add support for complex numbers. Carnë Draug <carandraug@octave.org> parents: 20154 diff changeset	200
1fae49e34a1a psi: add support for complex numbers. Carnë Draug <carandraug@octave.org> parents: 20154 diff changeset	201 ## Abramowitz and Stegun, page 259 eq 6.3.11
1fae49e34a1a psi: add support for complex numbers. Carnë Draug <carandraug@octave.org> parents: 20154 diff changeset	202 %!assert (imag (psi (iz)), 1/2 . 1./z + 1/2 * pi * coth (pi * z), eps *10)
1fae49e34a1a psi: add support for complex numbers. Carnë Draug <carandraug@octave.org> parents: 20154 diff changeset	203
1fae49e34a1a psi: add support for complex numbers. Carnë Draug <carandraug@octave.org> parents: 20154 diff changeset	204 ## Abramowitz and Stegun, page 259 eq 6.3.12
20424 099bdf98f724 psi: Fix failing unit tests on 32-bit systems Mike Miller <mtmiller@octave.org> parents: 20161 diff changeset	205 %!assert (imag (psi (1/2 + iz)), 1/2 pi * tanh (pi * z), eps*10)
20155 1fae49e34a1a psi: add support for complex numbers. Carnë Draug <carandraug@octave.org> parents: 20154 diff changeset	206
1fae49e34a1a psi: add support for complex numbers. Carnë Draug <carandraug@octave.org> parents: 20154 diff changeset	207 ## Abramowitz and Stegun, page 259 eq 6.3.13
1fae49e34a1a psi: add support for complex numbers. Carnë Draug <carandraug@octave.org> parents: 20154 diff changeset	208 %!assert (imag (psi (1 + iz)), - 1./(2z) + 1/2 * pi * coth (pi * z), eps*10)
1fae49e34a1a psi: add support for complex numbers. Carnë Draug <carandraug@octave.org> parents: 20154 diff changeset	209
20161 65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	210 ## Abramowitz and Stegun, page 260 eq 6.4.5
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	211 %!test
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	212 %! for z = 0:20
21580 ecce63c99c3f maint: Add semicolons to terminate code in %! blocks. Rik <rik@octave.org> parents: 21316 diff changeset	213 %! assert (psi (1, z + 0.5),
ecce63c99c3f maint: Add semicolons to terminate code in %! blocks. Rik <rik@octave.org> parents: 21316 diff changeset	214 %! 0.5 * (pi^2) - 4 * sum ((2*(1:z) -1) .^(-2)),
ecce63c99c3f maint: Add semicolons to terminate code in %! blocks. Rik <rik@octave.org> parents: 21316 diff changeset	215 %! eps*10);
20161 65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	216 %! endfor
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	217
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	218 ## Abramowitz and Stegun, page 260 eq 6.4.6
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	219 %!test
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	220 %! z = 0.1:0.1:20;
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	221 %! for n = 0:8
21580 ecce63c99c3f maint: Add semicolons to terminate code in %! blocks. Rik <rik@octave.org> parents: 21316 diff changeset	222 %! ## our precision goes down really quick when computing n is too high.
ecce63c99c3f maint: Add semicolons to terminate code in %! blocks. Rik <rik@octave.org> parents: 21316 diff changeset	223 %! assert (psi (n, z+1),
ecce63c99c3f maint: Add semicolons to terminate code in %! blocks. Rik <rik@octave.org> parents: 21316 diff changeset	224 %! psi (n, z) + ((-1)^n) * factorial (n) * (z.^(-n-1)), 0.1);
20161 65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	225 %! endfor
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	226
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	227 ## Test input validation
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	228 %!error psi ()
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	229 %!error psi (1, 2, 3)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	230 %!error <Z must be> psi ("non numeric")
26359 cd44edea6a31 psi.cc: Fix BIST test. Rik <rik@octave.org> parents: 26355 diff changeset	231 %!error <K must be an integer> psi ({5.3}, 1)
20704 571508c1ed06 eliminate more uses of error_state John W. Eaton <jwe@octave.org> parents: 20424 diff changeset	232 %!error <K must be non-negative> psi (-5, 1)
20161 65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	233 %!error <Z must be non-negative for polygamma> psi (5, -1)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	234 %!error <Z must be a floating point> psi (5, uint8 (-1))
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	235 %!error <Z must be real value for polygamma> psi (5, 5i)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative). Carnë Draug <carandraug@octave.org> parents: 20156 diff changeset	236
20154 45565ecec019 New function psi to compute the digamma function. Carnë Draug <carandraug@octave.org> parents: diff changeset	237 */
29958 32c3a5805893 move DEFUN and DEFMETHOD functions inside octave namespace John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	238
31605 e88a07dec498 maint: Use macros to begin/end C++ namespaces. Rik <rik@octave.org> parents: 30888 diff changeset	239 OCTAVE_END_NAMESPACE(octave)

Mercurial > octave

annotate libinterp/corefcn/psi.cc @ 31605:e88a07dec498 stable