Mercurial > octave
annotate libinterp/corefcn/quad.cc @ 24546:d3a507ca2d5d
maint: merge stable to default.
author | Rik <rik@octave.org> |
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date | Sun, 07 Jan 2018 09:57:32 -0800 |
parents | 194eb4bd202b ba8b828ee4f2 |
children | af11cc7cd336 |
rev | line source |
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2928 | 1 /* |
2 | |
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3 Copyright (C) 1996-2017 John W. Eaton |
2928 | 4 |
5 This file is part of Octave. | |
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 |
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9 the Free Software Foundation, either version 3 of the License, or |
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10 (at your option) any later version. |
2928 | 11 |
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12 Octave is distributed in the hope that it will be useful, but |
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13 WITHOUT ANY WARRANTY; without even the implied warranty of |
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14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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15 GNU General Public License for more details. |
2928 | 16 |
17 You should have received a copy of the GNU General Public License | |
7016 | 18 along with Octave; see the file COPYING. If not, see |
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19 <https://www.gnu.org/licenses/>. |
2928 | 20 |
21 */ | |
22 | |
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23 #if defined (HAVE_CONFIG_H) |
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24 # include "config.h" |
2928 | 25 #endif |
26 | |
27 #include <string> | |
28 | |
3567 | 29 #include <iomanip> |
3523 | 30 #include <iostream> |
2928 | 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" |
2928 | 38 #include "pager.h" |
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39 #include "parse.h" |
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40 #include "ovl.h" |
2968 | 41 #include "ov-fcn.h" |
3243 | 42 #include "unwind-prot.h" |
2928 | 43 #include "utils.h" |
44 #include "variables.h" | |
45 | |
3998 | 46 #include "Quad-opts.cc" |
47 | |
2928 | 48 #if defined (quad) |
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49 # undef quad |
2928 | 50 #endif |
51 | |
52 // Global pointer for user defined function required by quadrature functions. | |
2968 | 53 static octave_function *quad_fcn; |
2928 | 54 |
4140 | 55 // Have we warned about imaginary values returned from user function? |
56 static bool warned_imaginary = false; | |
57 | |
3243 | 58 // Is this a recursive call? |
59 static int call_depth = 0; | |
60 | |
2928 | 61 double |
62 quad_user_function (double x) | |
63 { | |
64 double retval = 0.0; | |
65 | |
66 octave_value_list args; | |
67 args(0) = x; | |
68 | |
69 if (quad_fcn) | |
70 { | |
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71 octave_value_list tmp; |
2928 | 72 |
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73 try |
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74 { |
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75 tmp = octave::feval (quad_fcn, args, 1); |
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76 } |
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77 catch (octave::execution_exception& e) |
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78 { |
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79 err_user_supplied_eval (e, "quad"); |
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80 } |
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82 if (! tmp.length () || ! tmp(0).is_defined ()) |
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83 err_user_supplied_eval ("quad"); |
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84 |
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85 if (! warned_imaginary && tmp(0).iscomplex ()) |
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86 { |
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87 warning ("quad: ignoring imaginary part returned from user-supplied function"); |
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88 warned_imaginary = true; |
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89 } |
4140 | 90 |
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91 retval = tmp(0).xdouble_value ("quad: expecting user supplied function to return numeric value"); |
2928 | 92 } |
93 | |
94 return retval; | |
95 } | |
96 | |
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97 float |
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98 quad_float_user_function (float x) |
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99 { |
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100 float retval = 0.0; |
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101 |
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102 octave_value_list args; |
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103 args(0) = x; |
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104 |
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105 if (quad_fcn) |
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106 { |
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107 octave_value_list tmp; |
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108 |
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109 try |
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110 { |
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111 tmp = octave::feval (quad_fcn, args, 1); |
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112 } |
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113 catch (octave::execution_exception& e) |
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114 { |
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115 err_user_supplied_eval (e, "quad"); |
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116 } |
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117 |
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118 if (! tmp.length () || ! tmp(0).is_defined ()) |
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119 err_user_supplied_eval ("quad"); |
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120 |
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121 if (! warned_imaginary && tmp(0).iscomplex ()) |
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122 { |
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123 warning ("quad: ignoring imaginary part returned from user-supplied function"); |
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124 warned_imaginary = true; |
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125 } |
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126 |
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127 retval = tmp(0).xfloat_value ("quad: expecting user supplied function to return numeric value"); |
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128 } |
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129 |
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130 return retval; |
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131 } |
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132 |
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133 DEFMETHOD (quad, interp, args, , |
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134 doc: /* -*- texinfo -*- |
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135 @deftypefn {} {@var{q} =} quad (@var{f}, @var{a}, @var{b}) |
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136 @deftypefnx {} {@var{q} =} quad (@var{f}, @var{a}, @var{b}, @var{tol}) |
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137 @deftypefnx {} {@var{q} =} quad (@var{f}, @var{a}, @var{b}, @var{tol}, @var{sing}) |
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138 @deftypefnx {} {[@var{q}, @var{ier}, @var{nfun}, @var{err}] =} quad (@dots{}) |
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139 Numerically evaluate the integral of @var{f} from @var{a} to @var{b} using |
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140 Fortran routines from @w{@sc{quadpack}}. |
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141 |
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142 @var{f} is a function handle, inline function, or a string containing the |
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143 name of the function to evaluate. The function must have the form @code{y = |
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144 f (x)} where @var{y} and @var{x} are scalars. |
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145 |
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146 @var{a} and @var{b} are the lower and upper limits of integration. Either |
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147 or both may be infinite. |
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148 |
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149 The optional argument @var{tol} is a vector that specifies the desired |
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150 accuracy of the result. The first element of the vector is the desired |
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151 absolute tolerance, and the second element is the desired relative |
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152 tolerance. To choose a relative test only, set the absolute |
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153 tolerance to zero. To choose an absolute test only, set the relative |
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154 tolerance to zero. Both tolerances default to @code{sqrt (eps)} or |
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155 approximately 1.5e-8. |
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156 |
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157 The optional argument @var{sing} is a vector of values at which the |
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158 integrand is known to be singular. |
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159 |
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160 The result of the integration is returned in @var{q}. |
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161 |
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162 @var{ier} contains an integer error code (0 indicates a successful |
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163 integration). |
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164 |
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165 @var{nfun} indicates the number of function evaluations that were |
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166 made. |
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167 |
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168 @var{err} contains an estimate of the error in the solution. |
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169 |
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170 The function @code{quad_options} can set other optional parameters for |
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171 @code{quad}. |
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172 |
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173 Note: because @code{quad} is written in Fortran it cannot be called |
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174 recursively. This prevents its use in integrating over more than one |
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175 variable by routines @code{dblquad} and @code{triplequad}. |
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176 @seealso{quad_options, quadv, quadl, quadgk, quadcc, trapz, dblquad, triplequad} |
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177 @end deftypefn */) |
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179 int nargin = args.length (); |
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181 if (nargin < 3 || nargin > 5) |
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182 print_usage (); |
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185 | |
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186 octave::unwind_protect frame; |
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188 frame.protect_var (call_depth); |
3243 | 189 call_depth++; |
190 | |
191 if (call_depth > 1) | |
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192 error ("quad: invalid recursive call"); |
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194 std::string fcn_name; |
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195 |
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196 if (args(0).is_function_handle () || args(0).is_inline_function ()) |
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197 quad_fcn = args(0).function_value (); |
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198 else |
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200 fcn_name = unique_symbol_name ("__quad_fcn__"); |
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201 std::string fname = "function y = "; |
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202 fname.append (fcn_name); |
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203 fname.append ("(x) y = "); |
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204 quad_fcn = extract_function (args(0), "quad", fcn_name, fname, |
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205 "; endfunction"); |
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206 octave::symbol_table& symtab = interp.get_symbol_table (); |
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207 frame.add_method (symtab, &octave::symbol_table::clear_function, fcn_name); |
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208 } |
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209 |
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210 if (! quad_fcn) |
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211 error ("quad: FCN argument is not a valid function name or handle"); |
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212 |
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213 octave_value_list retval; |
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214 |
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215 if (args(1).is_single_type () || args(2).is_single_type ()) |
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216 { |
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217 float a = args(1).xfloat_value ("quad: lower limit of integration A must be a scalar"); |
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218 float b = args(2).xfloat_value ("quad: upper limit of integration B must be a scalar"); |
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219 |
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220 int indefinite = 0; |
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221 FloatIndefQuad::IntegralType indef_type |
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222 = FloatIndefQuad::doubly_infinite; |
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223 float bound = 0.0; |
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224 if (octave::math::isinf (a) && octave::math::isinf (b)) |
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225 { |
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226 indefinite = 1; |
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227 indef_type = FloatIndefQuad::doubly_infinite; |
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228 } |
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229 else if (octave::math::isinf (a)) |
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230 { |
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231 indefinite = 1; |
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232 bound = b; |
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233 indef_type = FloatIndefQuad::neg_inf_to_bound; |
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234 } |
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235 else if (octave::math::isinf (b)) |
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236 { |
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237 indefinite = 1; |
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238 bound = a; |
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239 indef_type = FloatIndefQuad::bound_to_inf; |
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240 } |
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242 octave_idx_type ier = 0; |
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243 octave_idx_type nfun = 0; |
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244 float abserr = 0.0; |
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245 float val = 0.0; |
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246 bool have_sing = false; |
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247 FloatColumnVector sing; |
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248 FloatColumnVector tol; |
3243 | 249 |
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250 switch (nargin) |
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251 { |
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252 case 5: |
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253 if (indefinite) |
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254 error ("quad: singularities not allowed on infinite intervals"); |
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255 |
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256 have_sing = true; |
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257 |
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258 sing = args(4).xfloat_vector_value ("quad: fifth argument SING must be a vector of singularities"); |
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259 OCTAVE_FALLTHROUGH; |
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260 |
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261 case 4: |
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262 tol = args(3).xfloat_vector_value ("quad: TOL must be a 1 or 2-element vector"); |
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264 switch (tol.numel ()) |
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265 { |
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266 case 2: |
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267 quad_opts.set_single_precision_relative_tolerance (tol (1)); |
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268 OCTAVE_FALLTHROUGH; |
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269 |
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270 case 1: |
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271 quad_opts.set_single_precision_absolute_tolerance (tol (0)); |
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272 break; |
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274 default: |
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275 error ("quad: TOL must be a 1 or 2-element vector"); |
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276 } |
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278 case 3: |
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279 if (indefinite) |
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280 { |
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281 FloatIndefQuad iq (quad_float_user_function, bound, |
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282 indef_type); |
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283 iq.set_options (quad_opts); |
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284 val = iq.float_integrate (ier, nfun, abserr); |
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285 } |
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286 else |
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287 { |
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288 if (have_sing) |
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289 { |
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290 FloatDefQuad dq (quad_float_user_function, a, b, sing); |
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291 dq.set_options (quad_opts); |
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292 val = dq.float_integrate (ier, nfun, abserr); |
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293 } |
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294 else |
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295 { |
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296 FloatDefQuad dq (quad_float_user_function, a, b); |
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297 dq.set_options (quad_opts); |
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298 val = dq.float_integrate (ier, nfun, abserr); |
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299 } |
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300 } |
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301 break; |
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302 |
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303 default: |
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304 panic_impossible (); |
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305 break; |
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306 } |
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307 |
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308 retval = ovl (val, ier, nfun, abserr); |
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309 |
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310 } |
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311 else |
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312 { |
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313 double a = args(1).xdouble_value ("quad: lower limit of integration A must be a scalar"); |
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314 double b = args(2).xdouble_value ("quad: upper limit of integration B must be a scalar"); |
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315 |
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316 int indefinite = 0; |
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317 IndefQuad::IntegralType indef_type = IndefQuad::doubly_infinite; |
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318 double bound = 0.0; |
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319 if (octave::math::isinf (a) && octave::math::isinf (b)) |
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320 { |
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321 indefinite = 1; |
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322 indef_type = IndefQuad::doubly_infinite; |
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323 } |
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324 else if (octave::math::isinf (a)) |
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325 { |
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326 indefinite = 1; |
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327 bound = b; |
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328 indef_type = IndefQuad::neg_inf_to_bound; |
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329 } |
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330 else if (octave::math::isinf (b)) |
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331 { |
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332 indefinite = 1; |
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333 bound = a; |
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334 indef_type = IndefQuad::bound_to_inf; |
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335 } |
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336 |
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337 octave_idx_type ier = 0; |
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338 octave_idx_type nfun = 0; |
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339 double abserr = 0.0; |
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340 double val = 0.0; |
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341 bool have_sing = false; |
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342 ColumnVector sing; |
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343 ColumnVector tol; |
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344 |
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345 switch (nargin) |
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346 { |
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347 case 5: |
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348 if (indefinite) |
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349 error ("quad: singularities not allowed on infinite intervals"); |
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350 |
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351 have_sing = true; |
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352 |
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353 sing = args(4).vector_value ("quad: fifth argument SING must be a vector of singularities"); |
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354 OCTAVE_FALLTHROUGH; |
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355 |
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356 case 4: |
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357 tol = args(3).xvector_value ("quad: TOL must be a 1 or 2-element vector"); |
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358 |
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359 switch (tol.numel ()) |
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360 { |
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361 case 2: |
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362 quad_opts.set_relative_tolerance (tol (1)); |
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363 OCTAVE_FALLTHROUGH; |
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364 |
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365 case 1: |
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366 quad_opts.set_absolute_tolerance (tol (0)); |
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367 break; |
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369 default: |
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370 error ("quad: TOL must be a 1 or 2-element vector"); |
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371 } |
3243 | 372 |
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373 case 3: |
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374 if (indefinite) |
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375 { |
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376 IndefQuad iq (quad_user_function, bound, indef_type); |
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377 iq.set_options (quad_opts); |
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378 val = iq.integrate (ier, nfun, abserr); |
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379 } |
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380 else |
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381 { |
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382 if (have_sing) |
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383 { |
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384 DefQuad dq (quad_user_function, a, b, sing); |
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385 dq.set_options (quad_opts); |
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386 val = dq.integrate (ier, nfun, abserr); |
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387 } |
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388 else |
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389 { |
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390 DefQuad dq (quad_user_function, a, b); |
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391 dq.set_options (quad_opts); |
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392 val = dq.integrate (ier, nfun, abserr); |
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393 } |
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394 } |
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395 break; |
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396 |
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397 default: |
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398 panic_impossible (); |
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399 break; |
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400 } |
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402 retval = ovl (val, ier, nfun, abserr); |
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404 |
2928 | 405 return retval; |
406 } | |
407 | |
408 /* | |
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409 %!function y = __f (x) |
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410 %! y = x + 1; |
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411 %!endfunction |
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412 |
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413 %!test |
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414 %! [v, ier, nfun, err] = quad ("__f", 0, 5); |
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415 %! assert (ier, 0); |
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416 %! assert (v, 17.5, sqrt (eps)); |
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417 %! assert (nfun > 0); |
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418 %! assert (err < sqrt (eps)); |
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419 |
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420 %!test |
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421 %! [v, ier, nfun, err] = quad ("__f", single (0), single (5)); |
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422 %! assert (ier, 0); |
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423 %! assert (v, 17.5, sqrt (eps ("single"))); |
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424 %! assert (nfun > 0); |
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425 %! assert (err < sqrt (eps ("single"))); |
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426 |
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427 %!function y = __f (x) |
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428 %! y = x .* sin (1 ./ x) .* sqrt (abs (1 - x)); |
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429 %!endfunction |
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430 |
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431 %!test |
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432 %! [v, ier, nfun, err] = quad ("__f", 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 %! [v, ier, nfun, err] = quad ("__f", single (0.001), single (3)); |
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439 %! assert (ier == 0 || ier == 1); |
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440 %! assert (v, 1.98194120273598, sqrt (eps ("single"))); |
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441 %! assert (nfun > 0); |
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442 |
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443 %!error quad () |
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444 %!error quad ("__f", 1, 2, 3, 4, 5) |
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445 |
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446 %!test |
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447 %! quad_options ("absolute tolerance", eps); |
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448 %! assert (quad_options ("absolute tolerance") == eps); |
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449 |
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450 %!error quad_options (1, 2, 3) |
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451 */ |