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annotate libinterp/corefcn/psi.cc @ 20154:45565ecec019

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New function psi to compute the digamma function. * libinterp/corefcn/psi.cc: file for the new function file (implementation is actually in lo-specfun.cc). * liboctave/numeric/lo-specfun.cc, liboctave/numeric/lo-specfun.h: added implementation of the digamma (psi )function. Partly based on diGamma() from XLiFE++ 1.1 (file gammaFunctions.cpp which was previously melina++) which is under GPL 3 or later and why D. Martin is also added to copyright. * doc/interpreter/arith.txi: add function entry to the manual. * libinterp/corefcn/module.mk: add file to the build system. * NEWS: note new function.
author Carnë Draug <carandraug@octave.org>
date Sun, 15 Mar 2015 03:31:16 +0000
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children 1fae49e34a1a
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20154
45565ecec019 New function psi to compute the digamma function.
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1 /*
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2
45565ecec019 New function psi to compute the digamma function.
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3 Copyright (C) 2015 Carnë Draug
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4
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5 This file is part of Octave.
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6
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7 Octave is free software; you can redistribute it and/or modify it
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8 under the terms of the GNU General Public License as published by the
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9 Free Software Foundation; either version 3 of the License, or (at your
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10 option) any later version.
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11
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12 Octave is distributed in the hope that it will be useful, but WITHOUT
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13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
45565ecec019 New function psi to compute the digamma function.
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15 for more details.
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16
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17 You should have received a copy of the GNU General Public License
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18 along with Octave; see the file COPYING. If not, see
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19 <http://www.gnu.org/licenses/>.
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20
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21 */
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22
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23 #ifdef HAVE_CONFIG_H
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24 #include <config.h>
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25 #endif
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26
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27 #include "ov.h"
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28 #include "defun.h"
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29 #include "error.h"
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30 #include "dNDArray.h"
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31 #include "fNDArray.h"
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32
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33 #include "lo-specfun.h"
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34
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35 DEFUN (psi, args, ,
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36 "-*- texinfo -*-\n\
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37 @deftypefn {Function File} {} psi (@var{z})\n\
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38 Compute the psi (digamma) function.\n\
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39 \n\
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40 @tex\n\
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41 $$\n\
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42 \\Psi (z) = {d (log (\\Gamma (z))) \\over dx}\n\
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43 $$\n\
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44 @end tex\n\
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45 @ifnottex\n\
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46 @example\n\
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47 @group\n\
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48 psi (z) = d (log (gamma (z))) / dx\n\
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49 @end group\n\
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50 @end example\n\
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51 @end ifnottex\n\
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52 \n\
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53 @seealso{gamma, gammainc, gammaln}\n\
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54 @end deftypefn")
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55 {
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56 octave_value retval;
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57
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58 const octave_idx_type nargin = args.length ();
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59
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60 if (nargin != 1)
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61 {
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62 print_usage ();
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63 return retval;
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64 }
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65
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66 #define FLOAT_BRANCH(T, A, M, E) \
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67 if (args(0).is_ ## T ##_type ()) \
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68 { \
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69 const A ## NDArray z = args(0).M ## array_value (); \
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70 A ## NDArray psi_z (z.dims ()); \
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71 \
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72 const E* zv = z.data (); \
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73 E* psi_zv = psi_z.fortran_vec (); \
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74 const octave_idx_type n = z.numel (); \
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75 for (octave_idx_type i = 0; i < n; i++) \
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76 psi_zv[i] = psi<E> (zv[i]); \
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77 \
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78 retval = psi_z; \
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79 }
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80
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81 FLOAT_BRANCH(double, , , double)
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82 else FLOAT_BRANCH(single, Float, float_, float)
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83 else
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84 {
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85 error ("psi: Z must be a floating point");
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86 }
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87
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88 #undef FLOAT_BRANCH
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89
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90 return retval;
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91 }
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92
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93 /*
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94 %!shared em
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95 %! em = 0.577215664901532860606512090082402431042; # Euler-Mascheroni Constant
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96
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97 %!assert (psi (ones (7, 3, 5)), repmat (-em, [7 3 5]))
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98 %!assert (psi ([0 1]), [-Inf -em])
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99 %!assert (psi ([-20:1]), [repmat(-Inf, [1 21]) -em])
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100 %!assert (psi (single ([0 1])), single ([-Inf -em]))
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101
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102 ## Abramowitz and Stegun, page 258, eq 6.3.5
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103 %!test
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104 %! z = [-10:.1:-.1 .1:.1:20]; # drop the 0
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105 %! assert (psi (z + 1), psi (z) + 1 ./ z, eps*1000)
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106
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107 ## Abramowitz and Stegun, page 258, eq 6.3.2
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108 %!assert (psi (1), -em)
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109
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110 ## Abramowitz and Stegun, page 258, eq 6.3.3
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111 %!assert (psi (1/2), -em - 2 * log (2))
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112
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113 ## The following tests are from Pascal Sebah and Xavier Gourdon (2002)
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114 ## "Introduction to the Gamma Function"
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115
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116 ## Interesting identities of the digamma function, in section of 5.1.3
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117 %!assert (psi (1/3), - em - (3/2) * log(3) - ((sqrt (3) / 6) * pi), eps*10)
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118 %!assert (psi (1/4), - em -3 * log (2) - pi /2, eps*10)
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119 %!assert (psi (1/6), - em -2 * log (2) - (3/2) * log (3) - ((sqrt (3) / 2) * pi), eps*10)
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120
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121 ## First 6 zeros of the digamma function, in section of 5.1.5 (and also on
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122 ## Abramowitz and Stegun, page 258, eq 6.3.19)
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123 %!assert (psi ( 1.46163214496836234126265954232572132846819620400644), 0, eps)
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124 %!assert (psi (-0.504083008264455409258269304533302498955385182368579), 0, eps*10)
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125 %!assert (psi (-1.573498473162390458778286043690434612655040859116846), 0, eps)
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126 %!assert (psi (-2.610720868444144650001537715718724207951074010873480), 0, eps*10)
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127 %!assert (psi (-3.635293366436901097839181566946017713948423861193530), 0, eps)
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128 %!assert (psi (-4.653237761743142441714598151148207363719069416133868), 0, eps*100)
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129 */
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130