Mercurial > octave
annotate libinterp/corefcn/psi.cc @ 29961:7d6709900da7
eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more
Files affected: __betainc__.cc, __contourc__.cc, __eigs__.cc,
__expint__.cc, __ftp__.cc, __gammainc__.cc, __ichol__.cc, __ilu__.cc,
__magick_read__.cc, __pchip_deriv__.cc, __qp__.cc, amd.cc, balance.cc,
besselj.cc, bsxfun.cc, call-stack.cc, ccolamd.cc, cellfun.cc, chol.cc,
colamd.cc, colloc.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc,
defaults.cc, dirfns.cc, display.cc, dlmread.cc, dmperm.cc, dot.cc,
eig.cc, ellipj.cc, environment.cc, error.cc, event-manager.cc, fft.cc,
fft2.cc, fftn.cc, file-io.cc, find.cc, gcd.cc, getgrent.cc,
getpwent.cc, getrusage.cc, gsvd.cc, hash.cc, help.cc, hess.cc,
hex2num.cc, input.cc, inv.cc, jsondecode.cc, jsonencode.cc,
load-path.cc, load-save.cc, lookup.cc, lsode.cc, lu.cc, max.cc,
mgorth.cc, oct-hist.cc, ordqz.cc, ordschur.cc, pager.cc, pr-output.cc,
psi.cc, qr.cc, quad.cc, quadcc.cc, qz.cc, rand.cc, regexp.cc,
schur.cc, settings.cc, sighandlers.cc, sparse.cc, spparms.cc,
sqrtm.cc, stream-euler.cc, strfind.cc, strfns.cc, sub2ind.cc, svd.cc,
symbfact.cc, symtab.cc, syscalls.cc, sysdep.cc, time.cc, toplev.cc,
tril.cc, typecast.cc, urlwrite.cc, utils.cc, variables.cc,
__delaunayn__.cc, __fltk_uigetfile__.cc, __glpk__.cc,
__init_gnuplot__.cc, __ode15__.cc, __voronoi__.cc, audiodevinfo.cc,
audioread.cc, convhulln.cc, fftw.cc, gzip.cc, ov-cell.cc, ov-class.cc,
ov-classdef.cc, ov-fcn-handle.cc, ov-struct.cc, ov-typeinfo.cc,
ov-usr-fcn.cc, octave.cc, lex.ll, oct-parse.yy, profiler.cc,
andpt-eval.cc.
author | John W. Eaton <jwe@octave.org> |
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date | Sat, 14 Aug 2021 22:48:52 -0400 |
parents | 32c3a5805893 |
children | 91c6288781ba 796f54d4ddbf |
rev | line source |
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1 //////////////////////////////////////////////////////////////////////// |
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2 // |
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3 // Copyright (C) 2016-2021 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 //////////////////////////////////////////////////////////////////////// |
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25 |
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26 #if defined (HAVE_CONFIG_H) |
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27 # include "config.h" |
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28 #endif |
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29 |
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30 #include "ov.h" |
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31 #include "defun.h" |
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32 #include "error.h" |
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33 #include "dNDArray.h" |
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34 #include "fNDArray.h" |
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35 |
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36 #include "lo-specfun.h" |
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37 |
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38 OCTAVE_NAMESPACE_BEGIN |
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39 |
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40 DEFUN (psi, args, , |
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41 doc: /* -*- texinfo -*- |
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42 @deftypefn {} {} psi (@var{z}) |
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43 @deftypefnx {} {} psi (@var{k}, @var{z}) |
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44 Compute the psi (polygamma) function. |
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45 |
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46 The polygamma functions are the @var{k}th derivative of the logarithm |
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47 of the gamma function. If unspecified, @var{k} defaults to zero. A value |
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48 of zero computes the digamma function, a value of 1, the trigamma function, |
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49 and so on. |
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50 |
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51 The digamma function is defined: |
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52 |
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53 @tex |
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54 $$ |
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55 \Psi (z) = {d (log (\Gamma (z))) \over dx} |
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56 $$ |
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57 @end tex |
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58 @ifnottex |
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59 |
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60 @example |
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61 @group |
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62 psi (z) = d (log (gamma (z))) / dx |
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63 @end group |
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64 @end example |
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65 |
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66 @end ifnottex |
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67 |
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68 When computing the digamma function (when @var{k} equals zero), @var{z} |
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69 can have any value real or complex value. However, for polygamma functions |
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70 (@var{k} higher than 0), @var{z} must be real and non-negative. |
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71 |
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72 @seealso{gamma, gammainc, gammaln} |
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73 @end deftypefn */) |
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74 { |
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75 int nargin = args.length (); |
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76 |
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77 if (nargin < 1 || nargin > 2) |
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78 print_usage (); |
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79 |
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80 const octave_value oct_z = (nargin == 1) ? args(0) : args(1); |
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81 const octave_idx_type k = (nargin == 1) ? 0 : args(0).xidx_type_value ("psi: K must be an integer"); |
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82 if (k < 0) |
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83 error ("psi: K must be non-negative"); |
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84 |
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85 octave_value retval; |
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86 |
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87 if (k == 0) |
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88 { |
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89 #define FLOAT_BRANCH(T, A, M, E) \ |
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90 if (oct_z.is_ ## T ##_type ()) \ |
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91 { \ |
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92 const A ## NDArray z = oct_z.M ## array_value (); \ |
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93 A ## NDArray psi_z (z.dims ()); \ |
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94 \ |
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95 const E *zv = z.data (); \ |
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96 E *psi_zv = psi_z.fortran_vec (); \ |
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97 const octave_idx_type n = z.numel (); \ |
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98 for (octave_idx_type i = 0; i < n; i++) \ |
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99 *psi_zv++ = math::psi (*zv++); \ |
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100 \ |
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101 retval = psi_z; \ |
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102 } |
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103 |
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104 if (oct_z.iscomplex ()) |
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105 { |
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106 FLOAT_BRANCH(double, Complex, complex_, Complex) |
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107 else FLOAT_BRANCH(single, FloatComplex, float_complex_, FloatComplex) |
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108 else |
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109 error ("psi: Z must be a floating point"); |
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110 } |
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111 else |
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112 { |
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113 FLOAT_BRANCH(double, , , double) |
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114 else FLOAT_BRANCH(single, Float, float_, float) |
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115 else |
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116 error ("psi: Z must be a floating point"); |
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117 } |
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118 |
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119 #undef FLOAT_BRANCH |
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120 } |
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121 else |
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122 { |
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123 if (! oct_z.isreal ()) |
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124 error ("psi: Z must be real value for polygamma (K > 0)"); |
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125 |
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126 #define FLOAT_BRANCH(T, A, M, E) \ |
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127 if (oct_z.is_ ## T ##_type ()) \ |
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128 { \ |
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129 const A ## NDArray z = oct_z.M ## array_value (); \ |
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130 A ## NDArray psi_z (z.dims ()); \ |
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131 \ |
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132 const E *zv = z.data (); \ |
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133 E *psi_zv = psi_z.fortran_vec (); \ |
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134 const octave_idx_type n = z.numel (); \ |
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135 for (octave_idx_type i = 0; i < n; i++) \ |
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136 { \ |
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137 if (*zv < 0) \ |
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138 error ("psi: Z must be non-negative for polygamma (K > 0)"); \ |
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139 \ |
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140 *psi_zv++ = math::psi (k, *zv++); \ |
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141 } \ |
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142 retval = psi_z; \ |
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143 } |
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144 |
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145 FLOAT_BRANCH(double, , , double) |
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146 else FLOAT_BRANCH(single, Float, float_, float) |
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147 else |
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148 error ("psi: Z must be a floating point for polygamma (K > 0)"); |
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149 |
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150 #undef FLOAT_BRANCH |
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151 } |
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152 |
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153 return retval; |
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154 } |
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155 |
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156 /* |
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157 %!shared em |
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158 %! em = 0.577215664901532860606512090082402431042; # Euler-Mascheroni Constant |
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159 |
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160 %!assert (psi (ones (7, 3, 5)), repmat (-em, [7 3 5])) |
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161 %!assert (psi ([0 1]), [-Inf -em]) |
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162 %!assert (psi ([-20:1]), [repmat(-Inf, [1 21]) -em]) |
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163 %!assert (psi (single ([0 1])), single ([-Inf -em])) |
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164 |
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165 ## Abramowitz and Stegun, page 258, eq 6.3.5 |
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166 %!test |
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167 %! z = [-100:-1 1:200] ./ 10; # drop the 0 |
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168 %! assert (psi (z + 1), psi (z) + 1 ./ z, eps*1000); |
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169 |
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170 ## Abramowitz and Stegun, page 258, eq 6.3.2 |
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171 %!assert (psi (1), -em) |
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172 |
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173 ## Abramowitz and Stegun, page 258, eq 6.3.3 |
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174 %!assert (psi (1/2), -em - 2 * log (2)) |
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175 |
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176 ## The following tests are from Pascal Sebah and Xavier Gourdon (2002) |
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177 ## "Introduction to the Gamma Function" |
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178 |
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179 ## Interesting identities of the digamma function, in section of 5.1.3 |
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180 %!assert (psi (1/3), - em - (3/2) * log (3) - ((sqrt (3) / 6) * pi), eps*10) |
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181 %!assert (psi (1/4), - em -3 * log (2) - pi/2, eps*10) |
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182 %!assert (psi (1/6), - em -2 * log (2) - (3/2) * log (3) - ((sqrt (3) / 2) * pi), eps*10) |
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183 |
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184 ## First 6 zeros of the digamma function, in section of 5.1.5 (and also on |
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185 ## Abramowitz and Stegun, page 258, eq 6.3.19) |
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186 %!assert (psi ( 1.46163214496836234126265954232572132846819620400644), 0, eps) |
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187 %!assert (psi (-0.504083008264455409258269304533302498955385182368579), 0, eps*2) |
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188 %!assert (psi (-1.573498473162390458778286043690434612655040859116846), 0, eps*2) |
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189 %!assert (psi (-2.610720868444144650001537715718724207951074010873480), 0, eps*10) |
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190 %!assert (psi (-3.635293366436901097839181566946017713948423861193530), 0, eps*10) |
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191 %!assert (psi (-4.653237761743142441714598151148207363719069416133868), 0, eps*100) |
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192 |
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193 ## Tests for complex values |
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194 %!shared z |
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195 %! z = [-100:-1 1:200] ./ 10; # drop the 0 |
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196 |
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197 ## Abramowitz and Stegun, page 259 eq 6.3.10 |
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198 %!assert (real (psi (i*z)), real (psi (1 - i*z))) |
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199 |
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200 ## Abramowitz and Stegun, page 259 eq 6.3.11 |
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201 %!assert (imag (psi (i*z)), 1/2 .* 1./z + 1/2 * pi * coth (pi * z), eps *10) |
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202 |
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203 ## Abramowitz and Stegun, page 259 eq 6.3.12 |
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204 %!assert (imag (psi (1/2 + i*z)), 1/2 * pi * tanh (pi * z), eps*10) |
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205 |
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206 ## Abramowitz and Stegun, page 259 eq 6.3.13 |
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207 %!assert (imag (psi (1 + i*z)), - 1./(2*z) + 1/2 * pi * coth (pi * z), eps*10) |
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208 |
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209 ## Abramowitz and Stegun, page 260 eq 6.4.5 |
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210 %!test |
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211 %! for z = 0:20 |
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212 %! assert (psi (1, z + 0.5), |
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213 %! 0.5 * (pi^2) - 4 * sum ((2*(1:z) -1) .^(-2)), |
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214 %! eps*10); |
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215 %! endfor |
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216 |
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217 ## Abramowitz and Stegun, page 260 eq 6.4.6 |
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218 %!test |
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219 %! z = 0.1:0.1:20; |
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220 %! for n = 0:8 |
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221 %! ## our precision goes down really quick when computing n is too high. |
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222 %! assert (psi (n, z+1), |
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223 %! psi (n, z) + ((-1)^n) * factorial (n) * (z.^(-n-1)), 0.1); |
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224 %! endfor |
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225 |
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226 ## Test input validation |
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227 %!error psi () |
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228 %!error psi (1, 2, 3) |
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229 %!error <Z must be> psi ("non numeric") |
26359 | 230 %!error <K must be an integer> psi ({5.3}, 1) |
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231 %!error <K must be non-negative> psi (-5, 1) |
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232 %!error <Z must be non-negative for polygamma> psi (5, -1) |
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233 %!error <Z must be a floating point> psi (5, uint8 (-1)) |
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234 %!error <Z must be real value for polygamma> psi (5, 5i) |
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235 |
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236 */ |
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237 |
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238 OCTAVE_NAMESPACE_END |