Mercurial > octave
annotate libinterp/corefcn/quad.cc @ 29359:7854d5752dd2
maint: merge stable to default.
author | John W. Eaton <jwe@octave.org> |
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date | Wed, 10 Feb 2021 10:10:40 -0500 |
parents | 8f67ad8b3103 0a5b15007766 |
children | 32c3a5805893 |
rev | line source |
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1 //////////////////////////////////////////////////////////////////////// |
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2 // |
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3 // Copyright (C) 1996-2021 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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26 #if defined (HAVE_CONFIG_H) |
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27 # include "config.h" |
2928 | 28 #endif |
29 | |
30 #include <string> | |
31 | |
32 #include "Quad.h" | |
33 #include "lo-mappers.h" | |
34 | |
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35 #include "defun.h" |
2928 | 36 #include "error.h" |
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37 #include "errwarn.h" |
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38 #include "interpreter-private.h" |
2928 | 39 #include "pager.h" |
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40 #include "parse.h" |
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41 #include "ov.h" |
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42 #include "ovl.h" |
3243 | 43 #include "unwind-prot.h" |
2928 | 44 #include "utils.h" |
45 #include "variables.h" | |
46 | |
3998 | 47 #include "Quad-opts.cc" |
48 | |
2928 | 49 // Global pointer for user defined function required by quadrature functions. |
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50 static octave_value quad_fcn; |
2928 | 51 |
4140 | 52 // Have we warned about imaginary values returned from user function? |
53 static bool warned_imaginary = false; | |
54 | |
3243 | 55 // Is this a recursive call? |
56 static int call_depth = 0; | |
57 | |
2928 | 58 double |
59 quad_user_function (double x) | |
60 { | |
61 double retval = 0.0; | |
62 | |
63 octave_value_list args; | |
64 args(0) = x; | |
65 | |
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66 if (quad_fcn.is_defined ()) |
2928 | 67 { |
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68 octave_value_list tmp; |
2928 | 69 |
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70 try |
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71 { |
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72 tmp = octave::feval (quad_fcn, args, 1); |
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73 } |
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74 catch (octave::execution_exception& ee) |
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75 { |
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76 err_user_supplied_eval (ee, "quad"); |
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77 } |
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79 if (! tmp.length () || ! tmp(0).is_defined ()) |
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80 err_user_supplied_eval ("quad"); |
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81 |
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82 if (! warned_imaginary && tmp(0).iscomplex ()) |
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83 { |
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84 warning ("quad: ignoring imaginary part returned from user-supplied function"); |
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85 warned_imaginary = true; |
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86 } |
4140 | 87 |
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88 retval = tmp(0).xdouble_value ("quad: expecting user supplied function to return numeric value"); |
2928 | 89 } |
90 | |
91 return retval; | |
92 } | |
93 | |
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94 float |
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95 quad_float_user_function (float x) |
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96 { |
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97 float retval = 0.0; |
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98 |
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99 octave_value_list args; |
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100 args(0) = x; |
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101 |
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102 if (quad_fcn.is_defined ()) |
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103 { |
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104 octave_value_list tmp; |
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105 |
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106 try |
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107 { |
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108 tmp = octave::feval (quad_fcn, args, 1); |
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109 } |
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110 catch (octave::execution_exception& ee) |
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111 { |
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112 err_user_supplied_eval (ee, "quad"); |
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113 } |
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114 |
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115 if (! tmp.length () || ! tmp(0).is_defined ()) |
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116 err_user_supplied_eval ("quad"); |
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117 |
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118 if (! warned_imaginary && tmp(0).iscomplex ()) |
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119 { |
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120 warning ("quad: ignoring imaginary part returned from user-supplied function"); |
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121 warned_imaginary = true; |
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122 } |
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123 |
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124 retval = tmp(0).xfloat_value ("quad: expecting user supplied function to return numeric value"); |
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125 } |
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126 |
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127 return retval; |
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128 } |
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129 |
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130 DEFMETHODX ("quad", Fquad, interp, args, , |
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131 doc: /* -*- texinfo -*- |
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132 @deftypefn {} {@var{q} =} quad (@var{f}, @var{a}, @var{b}) |
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133 @deftypefnx {} {@var{q} =} quad (@var{f}, @var{a}, @var{b}, @var{tol}) |
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134 @deftypefnx {} {@var{q} =} quad (@var{f}, @var{a}, @var{b}, @var{tol}, @var{sing}) |
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135 @deftypefnx {} {[@var{q}, @var{ier}, @var{nfun}, @var{err}] =} quad (@dots{}) |
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136 Numerically evaluate the integral of @var{f} from @var{a} to @var{b} using |
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137 Fortran routines from @w{@sc{quadpack}}. |
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138 |
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139 @var{f} is a function handle, inline function, or a string containing the |
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140 name of the function to evaluate. The function must have the form @code{y = |
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141 f (x)} where @var{y} and @var{x} are scalars. |
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142 |
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143 @var{a} and @var{b} are the lower and upper limits of integration. Either |
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144 or both may be infinite. |
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145 |
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146 The optional argument @var{tol} is a vector that specifies the desired |
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147 accuracy of the result. The first element of the vector is the desired |
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148 absolute tolerance, and the second element is the desired relative |
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149 tolerance. To choose a relative test only, set the absolute |
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150 tolerance to zero. To choose an absolute test only, set the relative |
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151 tolerance to zero. Both tolerances default to @code{sqrt (eps)} or |
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152 approximately 1.5e-8. |
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153 |
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154 The optional argument @var{sing} is a vector of values at which the |
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155 integrand is known to be singular. |
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156 |
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157 The result of the integration is returned in @var{q}. |
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158 |
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159 @var{ier} contains an integer error code (0 indicates a successful |
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160 integration). |
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161 |
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162 @var{nfun} indicates the number of function evaluations that were |
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163 made. |
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164 |
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165 @var{err} contains an estimate of the error in the solution. |
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166 |
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167 The function @code{quad_options} can set other optional parameters for |
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168 @code{quad}. |
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169 |
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170 Note: because @code{quad} is written in Fortran it cannot be called |
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171 recursively. This prevents its use in integrating over more than one |
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172 variable by routines @code{dblquad} and @code{triplequad}. |
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173 @seealso{quad_options, quadv, quadl, quadgk, quadcc, trapz, dblquad, triplequad} |
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174 @end deftypefn */) |
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176 int nargin = args.length (); |
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178 if (nargin < 3 || nargin > 5) |
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179 print_usage (); |
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4140 | 181 warned_imaginary = false; |
182 | |
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183 octave::unwind_protect_var<int> restore_var (call_depth); |
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186 if (call_depth > 1) | |
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187 error ("quad: invalid recursive call"); |
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189 quad_fcn = octave::get_function_handle (interp, args(0), "x"); |
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190 |
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191 octave_value_list retval; |
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192 |
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193 if (args(1).is_single_type () || args(2).is_single_type ()) |
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194 { |
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195 float a = args(1).xfloat_value ("quad: lower limit of integration A must be a scalar"); |
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196 float b = args(2).xfloat_value ("quad: upper limit of integration B must be a scalar"); |
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197 |
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198 int indefinite = 0; |
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199 FloatIndefQuad::IntegralType indef_type |
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200 = FloatIndefQuad::doubly_infinite; |
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201 float bound = 0.0; |
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202 if (octave::math::isinf (a) && octave::math::isinf (b)) |
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203 { |
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204 indefinite = 1; |
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205 indef_type = FloatIndefQuad::doubly_infinite; |
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206 } |
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207 else if (octave::math::isinf (a)) |
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208 { |
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209 indefinite = 1; |
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210 bound = b; |
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211 indef_type = FloatIndefQuad::neg_inf_to_bound; |
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212 } |
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213 else if (octave::math::isinf (b)) |
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214 { |
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215 indefinite = 1; |
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216 bound = a; |
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217 indef_type = FloatIndefQuad::bound_to_inf; |
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218 } |
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220 octave_idx_type ier = 0; |
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221 octave_idx_type nfun = 0; |
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222 float abserr = 0.0; |
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223 float val = 0.0; |
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224 bool have_sing = false; |
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225 FloatColumnVector sing; |
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226 FloatColumnVector tol; |
3243 | 227 |
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228 switch (nargin) |
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229 { |
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230 case 5: |
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231 if (indefinite) |
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232 error ("quad: singularities not allowed on infinite intervals"); |
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233 |
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234 have_sing = true; |
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235 |
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236 sing = args(4).xfloat_vector_value ("quad: fifth argument SING must be a vector of singularities"); |
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237 OCTAVE_FALLTHROUGH; |
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238 |
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239 case 4: |
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240 tol = args(3).xfloat_vector_value ("quad: TOL must be a 1 or 2-element vector"); |
3243 | 241 |
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242 switch (tol.numel ()) |
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243 { |
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244 case 2: |
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245 quad_opts.set_single_precision_relative_tolerance (tol (1)); |
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246 OCTAVE_FALLTHROUGH; |
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247 |
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248 case 1: |
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249 quad_opts.set_single_precision_absolute_tolerance (tol (0)); |
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250 break; |
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252 default: |
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253 error ("quad: TOL must be a 1 or 2-element vector"); |
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254 } |
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255 OCTAVE_FALLTHROUGH; |
3243 | 256 |
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257 case 3: |
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258 if (indefinite) |
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259 { |
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260 FloatIndefQuad iq (quad_float_user_function, bound, |
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261 indef_type); |
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262 iq.set_options (quad_opts); |
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263 val = iq.float_integrate (ier, nfun, abserr); |
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264 } |
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265 else |
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266 { |
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267 if (have_sing) |
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268 { |
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269 FloatDefQuad dq (quad_float_user_function, a, b, sing); |
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270 dq.set_options (quad_opts); |
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271 val = dq.float_integrate (ier, nfun, abserr); |
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272 } |
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273 else |
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274 { |
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275 FloatDefQuad dq (quad_float_user_function, a, b); |
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276 dq.set_options (quad_opts); |
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277 val = dq.float_integrate (ier, nfun, abserr); |
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278 } |
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279 } |
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280 break; |
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281 |
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282 default: |
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283 panic_impossible (); |
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284 break; |
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285 } |
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286 |
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287 retval = ovl (val, ier, nfun, abserr); |
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288 |
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289 } |
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290 else |
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291 { |
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292 double a = args(1).xdouble_value ("quad: lower limit of integration A must be a scalar"); |
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293 double b = args(2).xdouble_value ("quad: upper limit of integration B must be a scalar"); |
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294 |
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295 int indefinite = 0; |
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296 IndefQuad::IntegralType indef_type = IndefQuad::doubly_infinite; |
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297 double bound = 0.0; |
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298 if (octave::math::isinf (a) && octave::math::isinf (b)) |
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299 { |
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300 indefinite = 1; |
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301 indef_type = IndefQuad::doubly_infinite; |
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302 } |
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303 else if (octave::math::isinf (a)) |
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304 { |
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305 indefinite = 1; |
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306 bound = b; |
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307 indef_type = IndefQuad::neg_inf_to_bound; |
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308 } |
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309 else if (octave::math::isinf (b)) |
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310 { |
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311 indefinite = 1; |
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312 bound = a; |
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313 indef_type = IndefQuad::bound_to_inf; |
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314 } |
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315 |
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316 octave_idx_type ier = 0; |
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317 octave_idx_type nfun = 0; |
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318 double abserr = 0.0; |
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319 double val = 0.0; |
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320 bool have_sing = false; |
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321 ColumnVector sing; |
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322 ColumnVector tol; |
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323 |
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324 switch (nargin) |
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325 { |
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326 case 5: |
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327 if (indefinite) |
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328 error ("quad: singularities not allowed on infinite intervals"); |
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329 |
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330 have_sing = true; |
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331 |
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332 sing = args(4).xvector_value ("quad: fifth argument SING must be a vector of singularities"); |
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333 OCTAVE_FALLTHROUGH; |
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334 |
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335 case 4: |
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336 tol = args(3).xvector_value ("quad: TOL must be a 1 or 2-element vector"); |
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337 |
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338 switch (tol.numel ()) |
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339 { |
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340 case 2: |
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341 quad_opts.set_relative_tolerance (tol (1)); |
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342 OCTAVE_FALLTHROUGH; |
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343 |
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344 case 1: |
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345 quad_opts.set_absolute_tolerance (tol (0)); |
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346 break; |
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348 default: |
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349 error ("quad: TOL must be a 1 or 2-element vector"); |
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350 } |
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351 OCTAVE_FALLTHROUGH; |
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353 case 3: |
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354 if (indefinite) |
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355 { |
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356 IndefQuad iq (quad_user_function, bound, indef_type); |
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357 iq.set_options (quad_opts); |
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358 val = iq.integrate (ier, nfun, abserr); |
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359 } |
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360 else |
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361 { |
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362 if (have_sing) |
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363 { |
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364 DefQuad dq (quad_user_function, a, b, sing); |
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365 dq.set_options (quad_opts); |
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366 val = dq.integrate (ier, nfun, abserr); |
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367 } |
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368 else |
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369 { |
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370 DefQuad dq (quad_user_function, a, b); |
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371 dq.set_options (quad_opts); |
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372 val = dq.integrate (ier, nfun, abserr); |
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373 } |
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374 } |
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375 break; |
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376 |
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377 default: |
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378 panic_impossible (); |
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379 break; |
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380 } |
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382 retval = ovl (val, ier, nfun, abserr); |
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384 |
2928 | 385 return retval; |
386 } | |
387 | |
388 /* | |
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389 %!function y = __f (x) |
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390 %! y = x + 1; |
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391 %!endfunction |
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392 |
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393 %!test |
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394 %! [v, ier, nfun, err] = quad ("__f", 0, 5); |
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395 %! assert (ier, 0); |
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396 %! assert (v, 17.5, sqrt (eps)); |
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397 %! assert (nfun > 0); |
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398 %! assert (err < sqrt (eps)); |
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399 |
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400 %!test |
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401 %! [v, ier, nfun, err] = quad ("__f", single (0), single (5)); |
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402 %! assert (ier, 0); |
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403 %! assert (v, 17.5, sqrt (eps ("single"))); |
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404 %! assert (nfun > 0); |
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405 %! assert (err < sqrt (eps ("single"))); |
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406 |
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407 %!function y = __f (x) |
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408 %! y = x .* sin (1 ./ x) .* sqrt (abs (1 - x)); |
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409 %!endfunction |
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410 |
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411 %!test |
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412 %! [v, ier, nfun, err] = quad ("__f", 0.001, 3); |
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413 %! assert (ier == 0 || ier == 1); |
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414 %! assert (v, 1.98194120273598, sqrt (eps)); |
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415 %! assert (nfun > 0); |
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416 |
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417 %!test |
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418 %! [v, ier, nfun, err] = quad (@__f, 0.001, 3); |
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419 %! assert (ier == 0 || ier == 1); |
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420 %! assert (v, 1.98194120273598, sqrt (eps)); |
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421 %! assert (nfun > 0); |
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422 |
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423 %!test |
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424 %! fstr = "x .* sin (1 ./ x) .* sqrt (abs (1 - x))"; |
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425 %! [v, ier, nfun, err] = quad (fstr, 0.001, 3); |
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426 %! assert (ier == 0 || ier == 1); |
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427 %! assert (v, 1.98194120273598, sqrt (eps)); |
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428 %! assert (nfun > 0); |
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429 |
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430 %!test |
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431 %! anon_fcn = @(x) x .* sin (1 ./ x) .* sqrt (abs (1 - x)); |
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432 %! [v, ier, nfun, err] = quad (anon_fcn, 0.001, 3); |
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433 %! assert (ier == 0 || ier == 1); |
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434 %! assert (v, 1.98194120273598, sqrt (eps)); |
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435 %! assert (nfun > 0); |
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436 |
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437 %!test |
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438 %! inline_fcn = inline ("x .* sin (1 ./ x) .* sqrt (abs (1 - x))", "x"); |
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439 %! [v, ier, nfun, err] = quad (inline_fcn, 0.001, 3); |
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440 %! assert (ier == 0 || ier == 1); |
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441 %! assert (v, 1.98194120273598, sqrt (eps)); |
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442 %! assert (nfun > 0); |
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443 |
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444 %!test |
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445 %! [v, ier, nfun, err] = quad ("__f", single (0.001), single (3)); |
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446 %! assert (ier == 0 || ier == 1); |
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447 %! assert (v, 1.98194120273598, sqrt (eps ("single"))); |
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448 %! assert (nfun > 0); |
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449 |
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450 %!error quad () |
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451 %!error quad ("__f", 1, 2, 3, 4, 5) |
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452 |
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453 %!test |
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454 %! quad_options ("absolute tolerance", eps); |
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455 %! assert (quad_options ("absolute tolerance") == eps); |
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456 |
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457 %!error quad_options (1, 2, 3) |
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458 */ |