Mercurial > octave
annotate src/DLD-FUNCTIONS/quad.cc @ 14138:72c96de7a403 stable
maint: update copyright notices for 2012
author | John W. Eaton <jwe@octave.org> |
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date | Mon, 02 Jan 2012 14:25:41 -0500 |
parents | 4e8f23ccadce |
children | 60e5cf354d80 |
rev | line source |
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2928 | 1 /* |
2 | |
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3 Copyright (C) 1996-2012 John W. Eaton |
2928 | 4 |
5 This file is part of Octave. | |
6 | |
7 Octave is free software; you can redistribute it and/or modify it | |
8 under the terms of the GNU General Public License as published by the | |
7016 | 9 Free Software Foundation; either version 3 of the License, or (at your |
10 option) any later version. | |
2928 | 11 |
12 Octave is distributed in the hope that it will be useful, but WITHOUT | |
13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
15 for more details. | |
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 |
19 <http://www.gnu.org/licenses/>. | |
2928 | 20 |
21 */ | |
22 | |
23 #ifdef HAVE_CONFIG_H | |
24 #include <config.h> | |
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 | |
35 #include "defun-dld.h" | |
36 #include "error.h" | |
37 #include "gripes.h" | |
38 #include "pager.h" | |
39 #include "oct-obj.h" | |
2968 | 40 #include "ov-fcn.h" |
3243 | 41 #include "unwind-prot.h" |
2928 | 42 #include "utils.h" |
43 #include "variables.h" | |
44 | |
3998 | 45 #include "Quad-opts.cc" |
46 | |
2928 | 47 #if defined (quad) |
48 #undef quad | |
49 #endif | |
50 | |
51 // Global pointer for user defined function required by quadrature functions. | |
2968 | 52 static octave_function *quad_fcn; |
2928 | 53 |
4140 | 54 // Have we warned about imaginary values returned from user function? |
55 static bool warned_imaginary = false; | |
56 | |
3243 | 57 // Is this a recursive call? |
58 static int call_depth = 0; | |
59 | |
2928 | 60 double |
61 quad_user_function (double x) | |
62 { | |
63 double retval = 0.0; | |
64 | |
65 octave_value_list args; | |
66 args(0) = x; | |
67 | |
68 if (quad_fcn) | |
69 { | |
3544 | 70 octave_value_list tmp = quad_fcn->do_multi_index_op (1, args); |
2928 | 71 |
72 if (error_state) | |
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73 { |
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74 quad_integration_error = 1; // FIXME |
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75 gripe_user_supplied_eval ("quad"); |
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76 return retval; |
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77 } |
2928 | 78 |
79 if (tmp.length () && tmp(0).is_defined ()) | |
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80 { |
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81 if (! warned_imaginary && tmp(0).is_complex_type ()) |
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82 { |
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83 warning ("quad: ignoring imaginary part returned from user-supplied function"); |
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84 warned_imaginary = true; |
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85 } |
4140 | 86 |
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87 retval = tmp(0).double_value (); |
2928 | 88 |
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89 if (error_state) |
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90 { |
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91 quad_integration_error = 1; // FIXME |
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92 gripe_user_supplied_eval ("quad"); |
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93 } |
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94 } |
2928 | 95 else |
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96 { |
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97 quad_integration_error = 1; // FIXME |
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98 gripe_user_supplied_eval ("quad"); |
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99 } |
2928 | 100 } |
101 | |
102 return retval; | |
103 } | |
104 | |
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105 float |
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106 quad_float_user_function (float x) |
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107 { |
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108 float retval = 0.0; |
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109 |
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110 octave_value_list args; |
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111 args(0) = x; |
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112 |
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113 if (quad_fcn) |
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114 { |
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115 octave_value_list tmp = quad_fcn->do_multi_index_op (1, args); |
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116 |
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117 if (error_state) |
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118 { |
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119 quad_integration_error = 1; // FIXME |
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120 gripe_user_supplied_eval ("quad"); |
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121 return retval; |
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122 } |
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123 |
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124 if (tmp.length () && tmp(0).is_defined ()) |
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125 { |
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126 if (! warned_imaginary && tmp(0).is_complex_type ()) |
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127 { |
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128 warning ("quad: ignoring imaginary part returned from user-supplied function"); |
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129 warned_imaginary = true; |
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130 } |
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131 |
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132 retval = tmp(0).float_value (); |
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133 |
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134 if (error_state) |
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135 { |
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136 quad_integration_error = 1; // FIXME |
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137 gripe_user_supplied_eval ("quad"); |
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138 } |
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139 } |
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140 else |
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141 { |
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142 quad_integration_error = 1; // FIXME |
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143 gripe_user_supplied_eval ("quad"); |
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144 } |
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145 } |
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146 |
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147 return retval; |
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148 } |
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149 |
3323 | 150 #define QUAD_ABORT() \ |
151 do \ | |
152 { \ | |
4954 | 153 if (fcn_name.length()) \ |
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154 clear_function (fcn_name); \ |
3323 | 155 return retval; \ |
156 } \ | |
157 while (0) | |
158 | |
159 #define QUAD_ABORT1(msg) \ | |
160 do \ | |
161 { \ | |
3747 | 162 ::error ("quad: " msg); \ |
3323 | 163 QUAD_ABORT (); \ |
164 } \ | |
165 while (0) | |
166 | |
167 #define QUAD_ABORT2(fmt, arg) \ | |
168 do \ | |
169 { \ | |
3747 | 170 ::error ("quad: " fmt, arg); \ |
3323 | 171 QUAD_ABORT (); \ |
172 } \ | |
173 while (0) | |
174 | |
2928 | 175 DEFUN_DLD (quad, args, nargout, |
3368 | 176 "-*- texinfo -*-\n\ |
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177 @deftypefn {Loadable Function} {@var{q} =} quad (@var{f}, @var{a}, @var{b})\n\ |
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178 @deftypefnx {Loadable Function} {@var{q} =} quad (@var{f}, @var{a}, @var{b}, @var{tol})\n\ |
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179 @deftypefnx {Loadable Function} {@var{q} =} quad (@var{f}, @var{a}, @var{b}, @var{tol}, @var{sing})\n\ |
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180 @deftypefnx {Loadable Function} {[@var{q}, @var{ier}, @var{nfun}, @var{err}] =} quad (@dots{})\n\ |
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181 Numerically evaluate the integral of @var{f} from @var{a} to @var{b} using\n\ |
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182 Fortran routines from @w{@sc{quadpack}}. @var{f} is a function handle,\n\ |
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183 inline function, or a string containing the name of the function to\n\ |
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184 evaluate. The function must have the form @code{y = f (x)} where @var{y} and\n\ |
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185 @var{x} are scalars.\n\ |
2928 | 186 \n\ |
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187 @var{a} and @var{b} are the lower and upper limits of integration. Either\n\ |
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188 or both may be infinite.\n\ |
2928 | 189 \n\ |
3368 | 190 The optional argument @var{tol} is a vector that specifies the desired\n\ |
2928 | 191 accuracy of the result. The first element of the vector is the desired\n\ |
192 absolute tolerance, and the second element is the desired relative\n\ | |
3368 | 193 tolerance. To choose a relative test only, set the absolute\n\ |
194 tolerance to zero. To choose an absolute test only, set the relative\n\ | |
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195 tolerance to zero. Both tolerances default to @code{sqrt(eps)} or\n\ |
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196 approximately @math{1.5e^{-8}}.\n\ |
2928 | 197 \n\ |
198 The optional argument @var{sing} is a vector of values at which the\n\ | |
3368 | 199 integrand is known to be singular.\n\ |
200 \n\ | |
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201 The result of the integration is returned in @var{q}. @var{ier}\n\ |
3368 | 202 contains an integer error code (0 indicates a successful integration).\n\ |
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203 @var{nfun} indicates the number of function evaluations that were\n\ |
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204 made, and @var{err} contains an estimate of the error in the\n\ |
3368 | 205 solution.\n\ |
3964 | 206 \n\ |
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207 The function @code{quad_options} can set other optional\n\ |
3964 | 208 parameters for @code{quad}.\n\ |
6741 | 209 \n\ |
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210 Note: because @code{quad} is written in Fortran it cannot be called\n\ |
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211 recursively. This prevents its use in integrating over more than one\n\ |
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212 variable by routines @code{dblquad} and @code{triplequad}.\n\ |
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213 @seealso{quad_options, quadv, quadl, quadgk, quadcc, trapz, dblquad, triplequad}\n\ |
3368 | 214 @end deftypefn") |
2928 | 215 { |
216 octave_value_list retval; | |
217 | |
4954 | 218 std::string fcn_name; |
219 | |
4140 | 220 warned_imaginary = false; |
221 | |
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222 unwind_protect frame; |
3243 | 223 |
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224 frame.protect_var (call_depth); |
3243 | 225 call_depth++; |
226 | |
227 if (call_depth > 1) | |
3323 | 228 QUAD_ABORT1 ("invalid recursive call"); |
3243 | 229 |
2928 | 230 int nargin = args.length (); |
231 | |
3243 | 232 if (nargin > 2 && nargin < 6 && nargout < 5) |
233 { | |
4954 | 234 if (args(0).is_function_handle () || args(0).is_inline_function ()) |
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235 quad_fcn = args(0).function_value (); |
4954 | 236 else |
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237 { |
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238 fcn_name = unique_symbol_name ("__quad_fcn_"); |
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239 std::string fname = "function y = "; |
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240 fname.append (fcn_name); |
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241 fname.append ("(x) y = "); |
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242 quad_fcn = extract_function (args(0), "quad", fcn_name, fname, |
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243 "; endfunction"); |
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244 } |
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3243 | 246 if (! quad_fcn) |
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247 QUAD_ABORT (); |
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249 if (args(1).is_single_type () || args(2).is_single_type ()) |
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250 { |
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251 float a = args(1).float_value (); |
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253 if (error_state) |
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254 QUAD_ABORT1 ("expecting second argument to be a scalar"); |
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256 float b = args(2).float_value (); |
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258 if (error_state) |
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259 QUAD_ABORT1 ("expecting third argument to be a scalar"); |
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261 int indefinite = 0; |
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262 FloatIndefQuad::IntegralType indef_type = FloatIndefQuad::doubly_infinite; |
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263 float bound = 0.0; |
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264 if (xisinf (a) && xisinf (b)) |
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265 { |
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266 indefinite = 1; |
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267 indef_type = FloatIndefQuad::doubly_infinite; |
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268 } |
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269 else if (xisinf (a)) |
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270 { |
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271 indefinite = 1; |
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272 bound = b; |
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273 indef_type = FloatIndefQuad::neg_inf_to_bound; |
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274 } |
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275 else if (xisinf (b)) |
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276 { |
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277 indefinite = 1; |
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278 bound = a; |
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279 indef_type = FloatIndefQuad::bound_to_inf; |
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280 } |
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282 octave_idx_type ier = 0; |
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283 octave_idx_type nfun = 0; |
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284 float abserr = 0.0; |
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285 float val = 0.0; |
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286 bool have_sing = false; |
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287 FloatColumnVector sing; |
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288 FloatColumnVector tol; |
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289 |
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290 switch (nargin) |
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291 { |
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292 case 5: |
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293 if (indefinite) |
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294 QUAD_ABORT1 ("singularities not allowed on infinite intervals"); |
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295 |
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296 have_sing = true; |
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297 |
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298 sing = FloatColumnVector (args(4).float_vector_value ()); |
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300 if (error_state) |
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301 QUAD_ABORT1 ("expecting vector of singularities as fourth argument"); |
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302 |
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303 case 4: |
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304 tol = FloatColumnVector (args(3).float_vector_value ()); |
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305 |
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306 if (error_state) |
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307 QUAD_ABORT1 ("expecting vector of tolerances as fifth argument"); |
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308 |
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309 switch (tol.capacity ()) |
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310 { |
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311 case 2: |
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312 quad_opts.set_single_precision_relative_tolerance (tol (1)); |
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313 |
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314 case 1: |
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315 quad_opts.set_single_precision_absolute_tolerance (tol (0)); |
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316 break; |
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317 |
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318 default: |
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319 QUAD_ABORT1 ("expecting tol to contain no more than two values"); |
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320 } |
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322 case 3: |
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323 if (indefinite) |
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324 { |
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325 FloatIndefQuad iq (quad_float_user_function, bound, |
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326 indef_type); |
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327 iq.set_options (quad_opts); |
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328 val = iq.float_integrate (ier, nfun, abserr); |
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329 } |
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330 else |
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331 { |
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332 if (have_sing) |
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333 { |
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334 FloatDefQuad dq (quad_float_user_function, a, b, sing); |
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335 dq.set_options (quad_opts); |
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336 val = dq.float_integrate (ier, nfun, abserr); |
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337 } |
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338 else |
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339 { |
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340 FloatDefQuad dq (quad_float_user_function, a, b); |
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341 dq.set_options (quad_opts); |
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342 val = dq.float_integrate (ier, nfun, abserr); |
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343 } |
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344 } |
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345 break; |
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347 default: |
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348 panic_impossible (); |
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349 break; |
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350 } |
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351 |
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352 retval(3) = abserr; |
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353 retval(2) = nfun; |
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354 retval(1) = ier; |
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355 retval(0) = val; |
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356 |
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357 } |
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358 else |
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359 { |
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360 double a = args(1).double_value (); |
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361 |
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362 if (error_state) |
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363 QUAD_ABORT1 ("expecting second argument to be a scalar"); |
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364 |
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365 double b = args(2).double_value (); |
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366 |
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367 if (error_state) |
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368 QUAD_ABORT1 ("expecting third argument to be a scalar"); |
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369 |
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370 int indefinite = 0; |
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371 IndefQuad::IntegralType indef_type = IndefQuad::doubly_infinite; |
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372 double bound = 0.0; |
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373 if (xisinf (a) && xisinf (b)) |
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374 { |
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375 indefinite = 1; |
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376 indef_type = IndefQuad::doubly_infinite; |
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377 } |
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378 else if (xisinf (a)) |
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379 { |
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380 indefinite = 1; |
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381 bound = b; |
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382 indef_type = IndefQuad::neg_inf_to_bound; |
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383 } |
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384 else if (xisinf (b)) |
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385 { |
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386 indefinite = 1; |
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387 bound = a; |
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388 indef_type = IndefQuad::bound_to_inf; |
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389 } |
3243 | 390 |
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391 octave_idx_type ier = 0; |
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392 octave_idx_type nfun = 0; |
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393 double abserr = 0.0; |
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394 double val = 0.0; |
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395 bool have_sing = false; |
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396 ColumnVector sing; |
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397 ColumnVector tol; |
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398 |
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399 switch (nargin) |
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400 { |
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401 case 5: |
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402 if (indefinite) |
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403 QUAD_ABORT1 ("singularities not allowed on infinite intervals"); |
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404 |
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405 have_sing = true; |
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406 |
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407 sing = ColumnVector (args(4).vector_value ()); |
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408 |
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409 if (error_state) |
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410 QUAD_ABORT1 ("expecting vector of singularities as fourth argument"); |
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411 |
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412 case 4: |
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413 tol = ColumnVector (args(3).vector_value ()); |
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414 |
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415 if (error_state) |
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416 QUAD_ABORT1 ("expecting vector of tolerances as fifth argument"); |
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417 |
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418 switch (tol.capacity ()) |
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419 { |
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420 case 2: |
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421 quad_opts.set_relative_tolerance (tol (1)); |
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422 |
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423 case 1: |
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424 quad_opts.set_absolute_tolerance (tol (0)); |
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425 break; |
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426 |
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427 default: |
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428 QUAD_ABORT1 ("expecting tol to contain no more than two values"); |
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429 } |
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430 |
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431 case 3: |
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432 if (indefinite) |
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433 { |
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434 IndefQuad iq (quad_user_function, bound, indef_type); |
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435 iq.set_options (quad_opts); |
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436 val = iq.integrate (ier, nfun, abserr); |
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437 } |
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438 else |
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439 { |
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440 if (have_sing) |
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441 { |
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442 DefQuad dq (quad_user_function, a, b, sing); |
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443 dq.set_options (quad_opts); |
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444 val = dq.integrate (ier, nfun, abserr); |
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445 } |
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446 else |
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447 { |
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448 DefQuad dq (quad_user_function, a, b); |
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449 dq.set_options (quad_opts); |
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450 val = dq.integrate (ier, nfun, abserr); |
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451 } |
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452 } |
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453 break; |
3243 | 454 |
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455 default: |
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456 panic_impossible (); |
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457 break; |
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458 } |
3243 | 459 |
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460 retval(3) = abserr; |
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461 retval(2) = nfun; |
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462 retval(1) = ier; |
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463 retval(0) = val; |
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464 } |
4954 | 465 |
466 if (fcn_name.length()) | |
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467 clear_function (fcn_name); |
3243 | 468 } |
469 else | |
5823 | 470 print_usage (); |
2928 | 471 |
472 return retval; | |
473 } | |
474 | |
475 /* | |
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476 |
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477 %!function y = __f (x) |
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478 %! y = x + 1; |
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479 %!endfunction |
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480 |
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481 %!test |
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482 %! [v, ier, nfun, err] = quad ("__f", 0, 5); |
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483 %! assert(ier == 0 && abs (v - 17.5) < sqrt (eps) && nfun > 0 && |
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484 %! err < sqrt (eps)) |
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485 %!test |
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486 %! [v, ier, nfun, err] = quad ("__f", single(0), single(5)); |
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487 %! assert(ier == 0 && abs (v - 17.5) < sqrt (eps ("single")) && nfun > 0 && |
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488 %! err < sqrt (eps ("single"))) |
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489 |
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490 %!function y = __f (x) |
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491 %! y = x .* sin (1 ./ x) .* sqrt (abs (1 - x)); |
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492 %!endfunction |
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493 |
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494 %!test |
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495 %! [v, ier, nfun, err] = quad ("__f", 0.001, 3); |
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496 %! assert((ier == 0 || ier == 1) && abs (v - 1.98194120273598) < sqrt (eps) && nfun > 0); |
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497 %!test |
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498 %! [v, ier, nfun, err] = quad ("__f", single(0.001), single(3)); |
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499 %! assert((ier == 0 || ier == 1) && abs (v - 1.98194120273598) < sqrt (eps ("single")) && nfun > 0); |
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500 |
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501 %!error <Invalid call to quad> quad (); |
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502 |
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503 %!error <Invalid call to quad> quad ("__f", 1, 2, 3, 4, 5); |
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504 |
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505 %!test |
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506 %! quad_options ("absolute tolerance", eps); |
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507 %! assert(quad_options ("absolute tolerance") == eps); |
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508 |
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509 %!error <Invalid call to quad_options> quad_options (1, 2, 3); |
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510 |
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511 */ |