Mercurial > octave
annotate libinterp/corefcn/psi.cc @ 20801:a542a9bf177e
eliminate return statements after calls to print_usage
* graphics.cc, hess.cc, input.cc, kron.cc, load-save.cc, lsode.cc,
luinc.cc, matrix_type.cc, md5sum.cc, nproc.cc, pager.cc, pr-output.cc,
psi.cc, quadcc.cc, rand.cc, regexp.cc, sighandlers.cc, sqrtm.cc,
strfind.cc, sub2ind.cc, sylvester.cc:
Eliminate return statements after calls to print_usage.
author | John W. Eaton <jwe@octave.org> |
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date | Thu, 03 Dec 2015 19:22:54 -0500 |
parents | 571508c1ed06 |
children | 35241c4b696c |
rev | line source |
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1 /* |
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2 |
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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 |
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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 @deftypefnx {Function File} {} psi (@var{k}, @var{z})\n\ |
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39 Compute the psi (polygamma) function.\n\ |
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40 \n\ |
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41 The polygamma functions are the @var{k}th derivative of the logarithm\n\ |
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42 of the gamma function. If unspecified, @var{k} defaults to zero. A value\n\ |
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43 of zero computes the digamma function, a value of 1, the trigamma function,\n\ |
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44 and so on.\n\ |
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45 \n\ |
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46 The digamma function is defined:\n\ |
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47 \n\ |
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48 @tex\n\ |
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49 $$\n\ |
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50 \\Psi (z) = {d (log (\\Gamma (z))) \\over dx}\n\ |
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51 $$\n\ |
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52 @end tex\n\ |
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53 @ifnottex\n\ |
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54 @example\n\ |
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55 @group\n\ |
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56 psi (z) = d (log (gamma (z))) / dx\n\ |
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57 @end group\n\ |
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58 @end example\n\ |
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59 @end ifnottex\n\ |
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60 \n\ |
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61 When computing the digamma function (when @var{k} equals zero), @var{z}\n\ |
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62 can have any value real or complex value. However, for polygamma functions\n\ |
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63 (@var{k} higher than 0), @var{z} must be real and non-negative.\n\ |
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64 \n\ |
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65 @seealso{gamma, gammainc, gammaln}\n\ |
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66 @end deftypefn") |
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67 { |
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68 octave_value retval; |
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69 |
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70 const octave_idx_type nargin = args.length (); |
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71 if (nargin < 1 || nargin > 2) |
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72 print_usage (); |
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73 |
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74 const octave_value oct_z = (nargin == 1) ? args(0) : args(1); |
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75 const octave_idx_type k = (nargin == 1) ? 0 : args(0).idx_type_value ("psi: K must be an integer"); |
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76 if (k < 0) |
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77 { |
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78 error ("psi: K must be non-negative"); |
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79 return retval; |
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80 } |
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81 else if (k == 0) |
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82 { |
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83 #define FLOAT_BRANCH(T, A, M, E) \ |
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84 if (oct_z.is_ ## T ##_type ()) \ |
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85 { \ |
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86 const A ## NDArray z = oct_z.M ## array_value (); \ |
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87 A ## NDArray psi_z (z.dims ()); \ |
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88 \ |
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89 const E* zv = z.data (); \ |
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90 E* psi_zv = psi_z.fortran_vec (); \ |
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91 const octave_idx_type n = z.numel (); \ |
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92 for (octave_idx_type i = 0; i < n; i++) \ |
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93 *psi_zv++ = psi (*zv++); \ |
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94 \ |
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95 retval = psi_z; \ |
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96 } |
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97 |
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98 if (oct_z.is_complex_type ()) |
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99 { |
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100 FLOAT_BRANCH(double, Complex, complex_, Complex) |
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101 else FLOAT_BRANCH(single, FloatComplex, float_complex_, FloatComplex) |
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102 else |
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103 { |
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104 error ("psi: Z must be a floating point"); |
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105 } |
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106 } |
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107 else |
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108 { |
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109 FLOAT_BRANCH(double, , , double) |
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110 else FLOAT_BRANCH(single, Float, float_, float) |
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111 else |
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112 { |
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113 error ("psi: Z must be a floating point"); |
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114 } |
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115 } |
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116 |
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117 #undef FLOAT_BRANCH |
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118 } |
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119 else |
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120 { |
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121 if (! oct_z.is_real_type ()) |
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122 { |
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123 error ("psi: Z must be real value for polygamma (K > 0)"); |
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124 return retval; |
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125 } |
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126 |
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127 #define FLOAT_BRANCH(T, A, M, E) \ |
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128 if (oct_z.is_ ## T ##_type ()) \ |
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129 { \ |
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130 const A ## NDArray z = oct_z.M ## array_value (); \ |
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131 A ## NDArray psi_z (z.dims ()); \ |
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132 \ |
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133 const E* zv = z.data (); \ |
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134 E* psi_zv = psi_z.fortran_vec (); \ |
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135 const octave_idx_type n = z.numel (); \ |
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136 for (octave_idx_type i = 0; i < n; i++) \ |
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137 { \ |
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138 if (*zv < 0) \ |
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139 { \ |
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140 error ("psi: Z must be non-negative for polygamma (K > 0)"); \ |
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141 return retval; \ |
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142 } \ |
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143 *psi_zv++ = psi (k, *zv++); \ |
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144 } \ |
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145 retval = psi_z; \ |
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146 } |
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147 |
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148 FLOAT_BRANCH(double, , , double) |
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149 else FLOAT_BRANCH(single, Float, float_, float) |
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150 else |
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151 { |
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152 error ("psi: Z must be a floating point for polygamma (K > 0)"); |
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153 } |
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154 |
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155 #undef FLOAT_BRANCH |
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156 } |
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157 |
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158 return retval; |
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159 } |
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160 |
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161 /* |
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162 %!shared em |
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163 %! em = 0.577215664901532860606512090082402431042; # Euler-Mascheroni Constant |
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164 |
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165 %!assert (psi (ones (7, 3, 5)), repmat (-em, [7 3 5])) |
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166 %!assert (psi ([0 1]), [-Inf -em]) |
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167 %!assert (psi ([-20:1]), [repmat(-Inf, [1 21]) -em]) |
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168 %!assert (psi (single ([0 1])), single ([-Inf -em])) |
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169 |
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170 ## Abramowitz and Stegun, page 258, eq 6.3.5 |
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171 %!test |
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172 %! z = [-100:-1 1:200] ./ 10; # drop the 0 |
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173 %! assert (psi (z + 1), psi (z) + 1 ./ z, eps*1000) |
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174 |
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175 ## Abramowitz and Stegun, page 258, eq 6.3.2 |
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176 %!assert (psi (1), -em) |
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177 |
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178 ## Abramowitz and Stegun, page 258, eq 6.3.3 |
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179 %!assert (psi (1/2), -em - 2 * log (2)) |
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180 |
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181 ## The following tests are from Pascal Sebah and Xavier Gourdon (2002) |
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182 ## "Introduction to the Gamma Function" |
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183 |
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184 ## Interesting identities of the digamma function, in section of 5.1.3 |
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185 %!assert (psi (1/3), - em - (3/2) * log(3) - ((sqrt (3) / 6) * pi), eps*10) |
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186 %!assert (psi (1/4), - em -3 * log (2) - pi/2, eps*10) |
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187 %!assert (psi (1/6), - em -2 * log (2) - (3/2) * log (3) - ((sqrt (3) / 2) * pi), eps*10) |
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188 |
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189 ## First 6 zeros of the digamma function, in section of 5.1.5 (and also on |
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190 ## Abramowitz and Stegun, page 258, eq 6.3.19) |
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191 %!assert (psi ( 1.46163214496836234126265954232572132846819620400644), 0, eps) |
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192 %!assert (psi (-0.504083008264455409258269304533302498955385182368579), 0, eps) |
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193 %!assert (psi (-1.573498473162390458778286043690434612655040859116846), 0, eps) |
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194 %!assert (psi (-2.610720868444144650001537715718724207951074010873480), 0, eps*10) |
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195 %!assert (psi (-3.635293366436901097839181566946017713948423861193530), 0, eps*10) |
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196 %!assert (psi (-4.653237761743142441714598151148207363719069416133868), 0, eps*100) |
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197 |
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198 ## Tests for complex values |
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199 %!shared z |
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200 %! z = [-100:-1 1:200] ./ 10; # drop the 0 |
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201 |
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202 ## Abramowitz and Stegun, page 259 eq 6.3.10 |
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203 %!assert (real (psi (i*z)), real (psi (1 - i*z))) |
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204 |
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205 ## Abramowitz and Stegun, page 259 eq 6.3.11 |
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206 %!assert (imag (psi (i*z)), 1/2 .* 1./z + 1/2 * pi * coth (pi * z), eps *10) |
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207 |
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208 ## Abramowitz and Stegun, page 259 eq 6.3.12 |
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209 %!assert (imag (psi (1/2 + i*z)), 1/2 * pi * tanh (pi * z), eps*10) |
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210 |
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211 ## Abramowitz and Stegun, page 259 eq 6.3.13 |
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212 %!assert (imag (psi (1 + i*z)), - 1./(2*z) + 1/2 * pi * coth (pi * z), eps*10) |
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213 |
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214 ## Abramowitz and Stegun, page 260 eq 6.4.5 |
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215 %!test |
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216 %! for z = 0:20 |
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217 %! assert (psi (1, z + 0.5), 0.5 * (pi^2) - 4 * sum ((2*(1:z) -1) .^(-2)), eps*10) |
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218 %! endfor |
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219 |
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220 ## Abramowitz and Stegun, page 260 eq 6.4.6 |
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221 %!test |
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222 %! z = 0.1:0.1:20; |
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223 %! for n = 0:8 |
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224 %! ## our precision goes down really quick when computing n is too high, |
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225 %! assert (psi (n, z+1), psi (n, z) + ((-1)^n) * factorial (n) * (z.^(-n-1)), 0.1) |
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226 %! endfor |
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227 |
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228 ## Test input validation |
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229 %!error psi () |
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230 %!error psi (1, 2, 3) |
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231 %!error <Z must be> psi ("non numeric") |
20704
571508c1ed06
eliminate more uses of error_state
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232 %!error <conversion of 5.3 to int value failed> psi (5.3, 1) |
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233 %!error <K must be non-negative> psi (-5, 1) |
20161
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234 %!error <Z must be non-negative for polygamma> psi (5, -1) |
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psi: add support to compute the polygamma function (kth-derivative).
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235 %!error <Z must be a floating point> psi (5, uint8 (-1)) |
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236 %!error <Z must be real value for polygamma> psi (5, 5i) |
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237 |
20154
45565ecec019
New function psi to compute the digamma function.
Carnë Draug <carandraug@octave.org>
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238 */ |