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annotate libinterp/corefcn/__expint__.cc @ 29958:32c3a5805893

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move DEFUN and DEFMETHOD functions inside octave namespace * mk-opts.pl: Surround emitted function definitions with OCTAVE_NAMESPACE_BEGIN and OCTAVE_NAMESPACE_END tags. * mk-builtins.pl: Surround emitted function declarations with OCTAVE_NAMESPACE_BEGIN and OCTAVE_NAMESPACE_END tags. Emit deprecated global inline functions. * __betainc__.cc, __contourc__.cc, __dsearchn__.cc, __eigs__.cc, __expint__.cc, __ftp__.cc, __gammainc__.cc, __ichol__.cc, __ilu__.cc, __lin_interpn__.cc, __magick_read__.cc, __pchip_deriv__.cc, __qp__.cc, amd.cc, balance.cc, besselj.cc, bitfcns.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, debug.cc, defaults.cc, defun.cc, det.cc, dirfns.cc, display.cc, dlmread.cc, dmperm.cc, dot.cc, eig.cc, ellipj.cc, environment.cc, error.cc, event-manager.cc, fcn-info.cc, fft.cc, fft2.cc, fftn.cc, file-io.cc, filter.cc, find.cc, gcd.cc, getgrent.cc, getpwent.cc, getrusage.cc, givens.cc, graphics.cc, gsvd.cc, hash.cc, help.cc, hess.cc, hex2num.cc, input.cc, interpreter.cc, inv.cc, jsondecode.cc, jsonencode.cc, kron.cc, load-path.cc, load-save.cc, lookup.cc, ls-oct-text.cc, lsode.cc, lu.cc, mappers.cc, matrix_type.cc, max.cc, mgorth.cc, nproc.cc, oct-hist.cc, ordqz.cc, ordschur.cc, pager.cc, pinv.cc, pr-flt-fmt.cc, pr-output.cc, psi.cc, qr.cc, quad.cc, quadcc.cc, qz.cc, rand.cc, rcond.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, sylvester.cc, symbfact.cc, symrcm.cc, symtab.cc, syscalls.cc, sysdep.cc, time.cc, toplev.cc, tril.cc, tsearch.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-base.cc, ov-bool-mat.cc, ov-cell.cc, ov-class.cc, ov-classdef.cc, ov-fcn-handle.cc, ov-java.cc, ov-null-mat.cc, ov-oncleanup.cc, ov-struct.cc, ov-typeinfo.cc, ov-usr-fcn.cc, ov.cc, octave.cc, lex.ll, oct-parse.yy, profiler.cc, pt-eval.cc: Surround DEFUN and DEFMETHOD function defnitions with OCTAVE_NAMESPACE_BEGIN and OCTAVE_NAMESPACE_END tags.
author John W. Eaton <jwe@octave.org>
date Fri, 13 Aug 2021 21:53:51 -0400
parents 7854d5752dd2
children 7d6709900da7
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1 ////////////////////////////////////////////////////////////////////////
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2 //
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3 // Copyright (C) 2018-2021 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 "CNDArray.h"
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31 #include "defun.h"
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32 #include "fCNDArray.h"
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33
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34 OCTAVE_NAMESPACE_BEGIN
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35
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36 DEFUN (__expint__, args, ,
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37 doc: /* -*- texinfo -*-
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38 @deftypefn {} {@var{y} =} __expint__ (@var{x})
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39 Continued fraction expansion for the exponential integral.
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40 @end deftypefn */)
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41 {
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42 if (args.length () != 1)
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43 print_usage ();
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44
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45 octave_value_list retval;
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46
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47 bool is_single = args(0).is_single_type ();
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48
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49 int numel_x = args(0).numel ();
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50
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51 // Initialize output dimension vector
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52 dim_vector output_dv (numel_x, 1);
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53
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54 // Lentz's algorithm in two cases: single and double precision
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55 if (is_single)
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56 {
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57 // Initialize output and inputs
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58 FloatComplexColumnVector output (output_dv);
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59 FloatComplexNDArray x;
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60
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61 if (numel_x == 1)
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62 x = FloatComplexNDArray (output_dv, args(0).float_complex_value ());
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63 else
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64 x = args(0).float_complex_array_value ();
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65
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66 // Initialize variables used in algorithm
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67 static const FloatComplex tiny = octave::math::exp2 (-50.0f);
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68 static const float eps = std::numeric_limits<float>::epsilon ();
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69 const FloatComplex cone (1.0, 0.0);
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70 const FloatComplex czero (0.0, 0.0);
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71 const int maxit = 100;
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72
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73 // Loop over all elements
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74 for (octave_idx_type i = 0; i < numel_x; ++i)
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75 {
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76 // Catch Ctrl+C
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77 OCTAVE_QUIT;
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78
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79 // Variable initialization for the current element
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80 FloatComplex xj = x(i);
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81 FloatComplex y = tiny;
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82 FloatComplex Cj = y;
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83 FloatComplex Dj = czero;
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84 FloatComplex alpha_j = cone;
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85 FloatComplex beta_j = xj;
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86 FloatComplex Deltaj = czero;
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87 int j = 1;
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88
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89 // Lentz's algorithm
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90 while ((std::abs (Deltaj - cone) > eps) && (j < maxit))
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91 {
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92 Dj = beta_j + alpha_j * Dj;
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93 if (Dj == czero)
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94 Dj = tiny;
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95 Cj = beta_j + alpha_j / Cj;
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96 if (Cj == czero)
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97 Cj = tiny;
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98 Dj = cone / Dj;
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99 Deltaj = Cj * Dj;
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100 y *= Deltaj;
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101 alpha_j = (j + 1) / 2;
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102 if ((j % 2) == 0)
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103 beta_j = xj;
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104 else
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105 beta_j = cone;
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106 j++;
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107 }
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108
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109 output(i) = y;
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110 }
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111 retval(0) = output;
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112 }
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113 else
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114 {
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115 // Initialize output and inputs
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116 ComplexColumnVector output (output_dv);
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117 ComplexNDArray x;
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118
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119 if (numel_x == 1)
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120 x = ComplexNDArray (output_dv, args(0).complex_value ());
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121 else
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122 x = args(0).complex_array_value ();
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123
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124 // Initialize variables used in algorithm
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125 static const Complex tiny = octave::math::exp2 (-100.0);
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126 static const double eps = std::numeric_limits<double>::epsilon ();
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127 const Complex cone (1.0, 0.0);
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128 const Complex czero (0.0, 0.0);
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129 const int maxit = 200;
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130
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131 // Loop over all scenarios
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132 for (octave_idx_type i = 0; i < numel_x; ++i)
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133 {
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134 // Catch Ctrl+C
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135 OCTAVE_QUIT;
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136
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137 // Variable initialization for the current element
25052
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138 Complex xj = x(i);
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139 Complex y = tiny;
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140 Complex Cj = y;
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141 Complex Dj = czero;
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142 Complex alpha_j = cone;
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143 Complex beta_j = xj;
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144 Complex Deltaj = czero;
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145 int j = 1;
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146
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147 // Lentz's algorithm
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148 while ((std::abs (Deltaj - cone) > eps) && (j < maxit))
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149 {
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150 Dj = beta_j + alpha_j * Dj;
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151 if (Dj == czero)
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152 Dj = tiny;
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153 Cj = beta_j + alpha_j / Cj;
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154 if (Cj == czero)
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155 Cj = tiny;
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156 Dj = cone / Dj;
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157 Deltaj = Cj * Dj;
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158 y *= Deltaj;
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159 alpha_j = (j + 1) / 2;
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160 if ((j % 2) == 0)
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161 beta_j = xj;
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162 else
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163 beta_j = cone;
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164 j++;
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165 }
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166
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167 output(i) = y;
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168 }
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169
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170 retval(0) = output;
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171 }
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172
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173 return retval;
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174 }
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175
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176 OCTAVE_NAMESPACE_END