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annotate src/DLD-FUNCTIONS/quad.cc @ 10846:a4f482e66b65
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author | Rik <octave@nomad.inbox5.com> |
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date | Sun, 01 Aug 2010 20:22:17 -0700 |
parents | 89f4d7e294cc |
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2928 | 1 /* |
2 | |
7017 | 3 Copyright (C) 1996, 1997, 1998, 1999, 2000, 2002, 2004, 2005, 2006, |
8920 | 4 2007, 2008, 2009 John W. Eaton |
2928 | 5 |
6 This file is part of Octave. | |
7 | |
8 Octave is free software; you can redistribute it and/or modify it | |
9 under the terms of the GNU General Public License as published by the | |
7016 | 10 Free Software Foundation; either version 3 of the License, or (at your |
11 option) any later version. | |
2928 | 12 |
13 Octave is distributed in the hope that it will be useful, but WITHOUT | |
14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
16 for more details. | |
17 | |
18 You should have received a copy of the GNU General Public License | |
7016 | 19 along with Octave; see the file COPYING. If not, see |
20 <http://www.gnu.org/licenses/>. | |
2928 | 21 |
22 */ | |
23 | |
24 #ifdef HAVE_CONFIG_H | |
25 #include <config.h> | |
26 #endif | |
27 | |
28 #include <string> | |
29 | |
3567 | 30 #include <iomanip> |
3523 | 31 #include <iostream> |
2928 | 32 |
33 #include "Quad.h" | |
34 #include "lo-mappers.h" | |
35 | |
36 #include "defun-dld.h" | |
37 #include "error.h" | |
38 #include "gripes.h" | |
39 #include "pager.h" | |
40 #include "oct-obj.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) |
49 #undef quad | |
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 { | |
3544 | 71 octave_value_list tmp = quad_fcn->do_multi_index_op (1, args); |
2928 | 72 |
73 if (error_state) | |
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74 { |
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75 quad_integration_error = 1; // FIXME |
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76 gripe_user_supplied_eval ("quad"); |
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77 return retval; |
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78 } |
2928 | 79 |
80 if (tmp.length () && tmp(0).is_defined ()) | |
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81 { |
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82 if (! warned_imaginary && tmp(0).is_complex_type ()) |
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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).double_value (); |
2928 | 89 |
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90 if (error_state) |
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91 { |
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92 quad_integration_error = 1; // FIXME |
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93 gripe_user_supplied_eval ("quad"); |
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94 } |
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95 } |
2928 | 96 else |
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97 { |
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98 quad_integration_error = 1; // FIXME |
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99 gripe_user_supplied_eval ("quad"); |
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100 } |
2928 | 101 } |
102 | |
103 return retval; | |
104 } | |
105 | |
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106 float |
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107 quad_float_user_function (float x) |
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108 { |
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109 float retval = 0.0; |
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110 |
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111 octave_value_list args; |
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112 args(0) = x; |
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113 |
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114 if (quad_fcn) |
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115 { |
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116 octave_value_list tmp = quad_fcn->do_multi_index_op (1, args); |
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117 |
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118 if (error_state) |
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119 { |
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120 quad_integration_error = 1; // FIXME |
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121 gripe_user_supplied_eval ("quad"); |
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122 return retval; |
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123 } |
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124 |
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125 if (tmp.length () && tmp(0).is_defined ()) |
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126 { |
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127 if (! warned_imaginary && tmp(0).is_complex_type ()) |
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128 { |
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129 warning ("quad: ignoring imaginary part returned from user-supplied function"); |
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130 warned_imaginary = true; |
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131 } |
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132 |
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133 retval = tmp(0).float_value (); |
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134 |
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135 if (error_state) |
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136 { |
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137 quad_integration_error = 1; // FIXME |
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138 gripe_user_supplied_eval ("quad"); |
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139 } |
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140 } |
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141 else |
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142 { |
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143 quad_integration_error = 1; // FIXME |
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144 gripe_user_supplied_eval ("quad"); |
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145 } |
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146 } |
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147 |
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148 return retval; |
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149 } |
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150 |
3323 | 151 #define QUAD_ABORT() \ |
152 do \ | |
153 { \ | |
4954 | 154 if (fcn_name.length()) \ |
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155 clear_function (fcn_name); \ |
3323 | 156 return retval; \ |
157 } \ | |
158 while (0) | |
159 | |
160 #define QUAD_ABORT1(msg) \ | |
161 do \ | |
162 { \ | |
3747 | 163 ::error ("quad: " msg); \ |
3323 | 164 QUAD_ABORT (); \ |
165 } \ | |
166 while (0) | |
167 | |
168 #define QUAD_ABORT2(fmt, arg) \ | |
169 do \ | |
170 { \ | |
3747 | 171 ::error ("quad: " fmt, arg); \ |
3323 | 172 QUAD_ABORT (); \ |
173 } \ | |
174 while (0) | |
175 | |
2928 | 176 DEFUN_DLD (quad, args, nargout, |
3368 | 177 "-*- texinfo -*-\n\ |
178 @deftypefn {Loadable Function} {[@var{v}, @var{ier}, @var{nfun}, @var{err}] =} quad (@var{f}, @var{a}, @var{b}, @var{tol}, @var{sing})\n\ | |
10840 | 179 Integrate a nonlinear function of one variable using @sc{quadpack}.\n\ |
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180 The first argument is the name of the function, the function handle or\n\ |
4954 | 181 the inline function to call to compute the value of the integrand. It\n\ |
182 must have the form\n\ | |
2928 | 183 \n\ |
3368 | 184 @example\n\ |
185 y = f (x)\n\ | |
186 @end example\n\ | |
2928 | 187 \n\ |
3368 | 188 @noindent\n\ |
189 where @var{y} and @var{x} are scalars.\n\ | |
2928 | 190 \n\ |
191 The second and third arguments are limits of integration. Either or\n\ | |
192 both may be infinite.\n\ | |
193 \n\ | |
3368 | 194 The optional argument @var{tol} is a vector that specifies the desired\n\ |
2928 | 195 accuracy of the result. The first element of the vector is the desired\n\ |
196 absolute tolerance, and the second element is the desired relative\n\ | |
3368 | 197 tolerance. To choose a relative test only, set the absolute\n\ |
198 tolerance to zero. To choose an absolute test only, set the relative\n\ | |
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199 tolerance to zero. \n\ |
2928 | 200 \n\ |
201 The optional argument @var{sing} is a vector of values at which the\n\ | |
3368 | 202 integrand is known to be singular.\n\ |
203 \n\ | |
204 The result of the integration is returned in @var{v} and @var{ier}\n\ | |
205 contains an integer error code (0 indicates a successful integration).\n\ | |
206 The value of @var{nfun} indicates how many function evaluations were\n\ | |
207 required, and @var{err} contains an estimate of the error in the\n\ | |
208 solution.\n\ | |
3964 | 209 \n\ |
210 You can use the function @code{quad_options} to set optional\n\ | |
211 parameters for @code{quad}.\n\ | |
6741 | 212 \n\ |
213 It should be noted that since @code{quad} is written in Fortran it\n\ | |
214 cannot be called recursively.\n\ | |
3368 | 215 @end deftypefn") |
2928 | 216 { |
217 octave_value_list retval; | |
218 | |
4954 | 219 std::string fcn_name; |
220 | |
4140 | 221 warned_imaginary = false; |
222 | |
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223 unwind_protect frame; |
3243 | 224 |
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225 frame.protect_var (call_depth); |
3243 | 226 call_depth++; |
227 | |
228 if (call_depth > 1) | |
3323 | 229 QUAD_ABORT1 ("invalid recursive call"); |
3243 | 230 |
2928 | 231 int nargin = args.length (); |
232 | |
3243 | 233 if (nargin > 2 && nargin < 6 && nargout < 5) |
234 { | |
4954 | 235 if (args(0).is_function_handle () || args(0).is_inline_function ()) |
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236 quad_fcn = args(0).function_value (); |
4954 | 237 else |
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238 { |
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239 fcn_name = unique_symbol_name ("__quad_fcn_"); |
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240 std::string fname = "function y = "; |
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241 fname.append (fcn_name); |
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242 fname.append ("(x) y = "); |
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243 quad_fcn = extract_function (args(0), "quad", fcn_name, fname, |
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244 "; endfunction"); |
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245 } |
4954 | 246 |
3243 | 247 if (! quad_fcn) |
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248 QUAD_ABORT (); |
3243 | 249 |
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250 if (args(1).is_single_type () || args(2).is_single_type ()) |
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251 { |
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252 float a = args(1).float_value (); |
3243 | 253 |
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254 if (error_state) |
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255 QUAD_ABORT1 ("expecting second argument to be a scalar"); |
3998 | 256 |
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257 float b = args(2).float_value (); |
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259 if (error_state) |
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260 QUAD_ABORT1 ("expecting third argument to be a scalar"); |
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262 int indefinite = 0; |
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263 FloatIndefQuad::IntegralType indef_type = FloatIndefQuad::doubly_infinite; |
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264 float bound = 0.0; |
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265 if (xisinf (a) && xisinf (b)) |
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266 { |
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267 indefinite = 1; |
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268 indef_type = FloatIndefQuad::doubly_infinite; |
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269 } |
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270 else if (xisinf (a)) |
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271 { |
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272 indefinite = 1; |
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273 bound = b; |
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274 indef_type = FloatIndefQuad::neg_inf_to_bound; |
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275 } |
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276 else if (xisinf (b)) |
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277 { |
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278 indefinite = 1; |
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279 bound = a; |
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280 indef_type = FloatIndefQuad::bound_to_inf; |
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281 } |
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283 octave_idx_type ier = 0; |
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284 octave_idx_type nfun = 0; |
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285 float abserr = 0.0; |
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286 float val = 0.0; |
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287 bool have_sing = false; |
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288 FloatColumnVector sing; |
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289 FloatColumnVector tol; |
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290 |
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291 switch (nargin) |
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292 { |
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293 case 5: |
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294 if (indefinite) |
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295 QUAD_ABORT1 ("singularities not allowed on infinite intervals"); |
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296 |
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297 have_sing = true; |
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298 |
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299 sing = FloatColumnVector (args(4).float_vector_value ()); |
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301 if (error_state) |
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302 QUAD_ABORT1 ("expecting vector of singularities as fourth argument"); |
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303 |
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304 case 4: |
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305 tol = FloatColumnVector (args(3).float_vector_value ()); |
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306 |
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307 if (error_state) |
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308 QUAD_ABORT1 ("expecting vector of tolerances as fifth argument"); |
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309 |
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310 switch (tol.capacity ()) |
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311 { |
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312 case 2: |
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313 quad_opts.set_single_precision_relative_tolerance (tol (1)); |
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314 |
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315 case 1: |
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316 quad_opts.set_single_precision_absolute_tolerance (tol (0)); |
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317 break; |
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318 |
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319 default: |
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320 QUAD_ABORT1 ("expecting tol to contain no more than two values"); |
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321 } |
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323 case 3: |
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324 if (indefinite) |
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325 { |
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326 FloatIndefQuad iq (quad_float_user_function, bound, |
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327 indef_type); |
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328 iq.set_options (quad_opts); |
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329 val = iq.float_integrate (ier, nfun, abserr); |
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330 } |
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331 else |
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332 { |
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333 if (have_sing) |
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334 { |
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335 FloatDefQuad dq (quad_float_user_function, a, b, sing); |
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336 dq.set_options (quad_opts); |
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337 val = dq.float_integrate (ier, nfun, abserr); |
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338 } |
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339 else |
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340 { |
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341 FloatDefQuad dq (quad_float_user_function, a, b); |
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342 dq.set_options (quad_opts); |
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343 val = dq.float_integrate (ier, nfun, abserr); |
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344 } |
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345 } |
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346 break; |
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348 default: |
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349 panic_impossible (); |
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350 break; |
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351 } |
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352 |
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353 retval(3) = abserr; |
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354 retval(2) = nfun; |
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355 retval(1) = ier; |
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356 retval(0) = val; |
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357 |
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358 } |
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359 else |
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360 { |
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361 double a = args(1).double_value (); |
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362 |
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363 if (error_state) |
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364 QUAD_ABORT1 ("expecting second argument to be a scalar"); |
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365 |
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366 double b = args(2).double_value (); |
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367 |
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368 if (error_state) |
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369 QUAD_ABORT1 ("expecting third argument to be a scalar"); |
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370 |
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371 int indefinite = 0; |
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372 IndefQuad::IntegralType indef_type = IndefQuad::doubly_infinite; |
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373 double bound = 0.0; |
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374 if (xisinf (a) && xisinf (b)) |
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375 { |
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376 indefinite = 1; |
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377 indef_type = IndefQuad::doubly_infinite; |
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378 } |
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379 else if (xisinf (a)) |
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380 { |
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381 indefinite = 1; |
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382 bound = b; |
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383 indef_type = IndefQuad::neg_inf_to_bound; |
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384 } |
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385 else if (xisinf (b)) |
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386 { |
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387 indefinite = 1; |
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388 bound = a; |
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389 indef_type = IndefQuad::bound_to_inf; |
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390 } |
3243 | 391 |
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392 octave_idx_type ier = 0; |
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393 octave_idx_type nfun = 0; |
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394 double abserr = 0.0; |
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395 double val = 0.0; |
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396 bool have_sing = false; |
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397 ColumnVector sing; |
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398 ColumnVector tol; |
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399 |
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400 switch (nargin) |
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401 { |
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402 case 5: |
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403 if (indefinite) |
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404 QUAD_ABORT1 ("singularities not allowed on infinite intervals"); |
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405 |
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406 have_sing = true; |
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407 |
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408 sing = ColumnVector (args(4).vector_value ()); |
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409 |
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410 if (error_state) |
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411 QUAD_ABORT1 ("expecting vector of singularities as fourth argument"); |
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412 |
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413 case 4: |
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414 tol = ColumnVector (args(3).vector_value ()); |
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415 |
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416 if (error_state) |
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417 QUAD_ABORT1 ("expecting vector of tolerances as fifth argument"); |
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418 |
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419 switch (tol.capacity ()) |
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420 { |
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421 case 2: |
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422 quad_opts.set_relative_tolerance (tol (1)); |
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423 |
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424 case 1: |
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425 quad_opts.set_absolute_tolerance (tol (0)); |
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426 break; |
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427 |
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428 default: |
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429 QUAD_ABORT1 ("expecting tol to contain no more than two values"); |
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430 } |
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431 |
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432 case 3: |
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433 if (indefinite) |
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434 { |
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435 IndefQuad iq (quad_user_function, bound, indef_type); |
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436 iq.set_options (quad_opts); |
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437 val = iq.integrate (ier, nfun, abserr); |
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438 } |
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439 else |
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440 { |
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441 if (have_sing) |
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442 { |
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443 DefQuad dq (quad_user_function, a, b, sing); |
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444 dq.set_options (quad_opts); |
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445 val = dq.integrate (ier, nfun, abserr); |
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446 } |
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447 else |
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448 { |
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449 DefQuad dq (quad_user_function, a, b); |
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450 dq.set_options (quad_opts); |
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451 val = dq.integrate (ier, nfun, abserr); |
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452 } |
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453 } |
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454 break; |
3243 | 455 |
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456 default: |
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457 panic_impossible (); |
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458 break; |
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459 } |
3243 | 460 |
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461 retval(3) = abserr; |
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462 retval(2) = nfun; |
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463 retval(1) = ier; |
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464 retval(0) = val; |
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465 } |
4954 | 466 |
467 if (fcn_name.length()) | |
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468 clear_function (fcn_name); |
3243 | 469 } |
470 else | |
5823 | 471 print_usage (); |
2928 | 472 |
473 return retval; | |
474 } | |
475 | |
476 /* | |
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477 |
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478 %!function y = f (x) |
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479 %! y = x + 1; |
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480 %!test |
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481 %! [v, ier, nfun, err] = quad ("f", 0, 5); |
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482 %! assert(ier == 0 && abs (v - 17.5) < sqrt (eps) && nfun > 0 && |
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483 %! err < sqrt (eps)) |
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484 %!test |
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485 %! [v, ier, nfun, err] = quad ("f", single(0), single(5)); |
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486 %! assert(ier == 0 && abs (v - 17.5) < sqrt (eps ("single")) && nfun > 0 && |
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487 %! err < sqrt (eps ("single"))) |
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488 |
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489 %!function y = f (x) |
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490 %! y = x .* sin (1 ./ x) .* sqrt (abs (1 - x)); |
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491 %!test |
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492 %! [v, ier, nfun, err] = quad ("f", 0.001, 3); |
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493 %! assert((ier == 0 || ier == 1) && abs (v - 1.98194120273598) < sqrt (eps) && nfun > 0); |
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494 %!test |
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495 %! [v, ier, nfun, err] = quad ("f", single(0.001), single(3)); |
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496 %! assert((ier == 0 || ier == 1) && abs (v - 1.98194120273598) < sqrt (eps ("single")) && nfun > 0); |
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497 |
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498 %!error <Invalid call to quad.*> quad (); |
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499 |
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500 %!error <Invalid call to quad.*> quad ("f", 1, 2, 3, 4, 5); |
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501 |
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502 %!test |
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503 %! quad_options ("absolute tolerance", eps); |
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504 %! assert(quad_options ("absolute tolerance") == eps); |
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505 |
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506 %!error <Invalid call to quad_options.*> quad_options (1, 2, 3); |
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507 |
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508 */ |