Mercurial > hg > octave-lyh
annotate src/DLD-FUNCTIONS/quad.cc @ 9377:610bf90fce2a
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author | Jaroslav Hajek <highegg@gmail.com> |
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date | Tue, 23 Jun 2009 08:22:13 +0200 |
parents | 7c02ec148a3c |
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rev | line source |
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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) | |
74 { | |
5775 | 75 quad_integration_error = 1; // FIXME |
2928 | 76 gripe_user_supplied_eval ("quad"); |
77 return retval; | |
78 } | |
79 | |
80 if (tmp.length () && tmp(0).is_defined ()) | |
81 { | |
4140 | 82 if (! warned_imaginary && tmp(0).is_complex_type ()) |
83 { | |
84 warning ("quad: ignoring imaginary part returned from user-supplied function"); | |
85 warned_imaginary = true; | |
86 } | |
87 | |
2928 | 88 retval = tmp(0).double_value (); |
89 | |
90 if (error_state) | |
91 { | |
5775 | 92 quad_integration_error = 1; // FIXME |
2928 | 93 gripe_user_supplied_eval ("quad"); |
94 } | |
95 } | |
96 else | |
97 { | |
5775 | 98 quad_integration_error = 1; // FIXME |
2928 | 99 gripe_user_supplied_eval ("quad"); |
100 } | |
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()) \ |
155 clear_function (fcn_name); \ | |
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156 unwind_protect::run_frame (uwp_frame); \ |
3323 | 157 return retval; \ |
158 } \ | |
159 while (0) | |
160 | |
161 #define QUAD_ABORT1(msg) \ | |
162 do \ | |
163 { \ | |
3747 | 164 ::error ("quad: " msg); \ |
3323 | 165 QUAD_ABORT (); \ |
166 } \ | |
167 while (0) | |
168 | |
169 #define QUAD_ABORT2(fmt, arg) \ | |
170 do \ | |
171 { \ | |
3747 | 172 ::error ("quad: " fmt, arg); \ |
3323 | 173 QUAD_ABORT (); \ |
174 } \ | |
175 while (0) | |
176 | |
2928 | 177 DEFUN_DLD (quad, args, nargout, |
3368 | 178 "-*- texinfo -*-\n\ |
179 @deftypefn {Loadable Function} {[@var{v}, @var{ier}, @var{nfun}, @var{err}] =} quad (@var{f}, @var{a}, @var{b}, @var{tol}, @var{sing})\n\ | |
180 Integrate a nonlinear function of one variable using Quadpack.\n\ | |
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181 The first argument is the name of the function, the function handle or\n\ |
4954 | 182 the inline function to call to compute the value of the integrand. It\n\ |
183 must have the form\n\ | |
2928 | 184 \n\ |
3368 | 185 @example\n\ |
186 y = f (x)\n\ | |
187 @end example\n\ | |
2928 | 188 \n\ |
3368 | 189 @noindent\n\ |
190 where @var{y} and @var{x} are scalars.\n\ | |
2928 | 191 \n\ |
192 The second and third arguments are limits of integration. Either or\n\ | |
193 both may be infinite.\n\ | |
194 \n\ | |
3368 | 195 The optional argument @var{tol} is a vector that specifies the desired\n\ |
2928 | 196 accuracy of the result. The first element of the vector is the desired\n\ |
197 absolute tolerance, and the second element is the desired relative\n\ | |
3368 | 198 tolerance. To choose a relative test only, set the absolute\n\ |
199 tolerance to zero. To choose an absolute test only, set the relative\n\ | |
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200 tolerance to zero. \n\ |
2928 | 201 \n\ |
202 The optional argument @var{sing} is a vector of values at which the\n\ | |
3368 | 203 integrand is known to be singular.\n\ |
204 \n\ | |
205 The result of the integration is returned in @var{v} and @var{ier}\n\ | |
206 contains an integer error code (0 indicates a successful integration).\n\ | |
207 The value of @var{nfun} indicates how many function evaluations were\n\ | |
208 required, and @var{err} contains an estimate of the error in the\n\ | |
209 solution.\n\ | |
3964 | 210 \n\ |
211 You can use the function @code{quad_options} to set optional\n\ | |
212 parameters for @code{quad}.\n\ | |
6741 | 213 \n\ |
214 It should be noted that since @code{quad} is written in Fortran it\n\ | |
215 cannot be called recursively.\n\ | |
3368 | 216 @end deftypefn") |
2928 | 217 { |
218 octave_value_list retval; | |
219 | |
4954 | 220 std::string fcn_name; |
221 | |
4140 | 222 warned_imaginary = false; |
223 | |
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224 unwind_protect::frame_id_t uwp_frame = unwind_protect::begin_frame (); |
3243 | 225 |
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226 unwind_protect::protect_var (call_depth); |
3243 | 227 call_depth++; |
228 | |
229 if (call_depth > 1) | |
3323 | 230 QUAD_ABORT1 ("invalid recursive call"); |
3243 | 231 |
2928 | 232 int nargin = args.length (); |
233 | |
3243 | 234 if (nargin > 2 && nargin < 6 && nargout < 5) |
235 { | |
4954 | 236 if (args(0).is_function_handle () || args(0).is_inline_function ()) |
237 quad_fcn = args(0).function_value (); | |
238 else | |
239 { | |
4962 | 240 fcn_name = unique_symbol_name ("__quad_fcn_"); |
4954 | 241 std::string fname = "function y = "; |
242 fname.append (fcn_name); | |
243 fname.append ("(x) y = "); | |
244 quad_fcn = extract_function (args(0), "quad", fcn_name, fname, | |
245 "; endfunction"); | |
246 } | |
247 | |
3243 | 248 if (! quad_fcn) |
3323 | 249 QUAD_ABORT (); |
3243 | 250 |
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251 if (args(1).is_single_type () || args(2).is_single_type ()) |
3243 | 252 { |
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253 float a = args(1).float_value (); |
3243 | 254 |
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255 if (error_state) |
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256 QUAD_ABORT1 ("expecting second argument to be a scalar"); |
3998 | 257 |
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258 float b = args(2).float_value (); |
3243 | 259 |
260 if (error_state) | |
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261 QUAD_ABORT1 ("expecting third argument to be a scalar"); |
3243 | 262 |
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263 int indefinite = 0; |
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264 FloatIndefQuad::IntegralType indef_type = FloatIndefQuad::doubly_infinite; |
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265 float bound = 0.0; |
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266 if (xisinf (a) && xisinf (b)) |
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267 { |
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268 indefinite = 1; |
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269 indef_type = FloatIndefQuad::doubly_infinite; |
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270 } |
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271 else if (xisinf (a)) |
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272 { |
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273 indefinite = 1; |
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274 bound = b; |
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275 indef_type = FloatIndefQuad::neg_inf_to_bound; |
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276 } |
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277 else if (xisinf (b)) |
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278 { |
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279 indefinite = 1; |
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280 bound = a; |
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281 indef_type = FloatIndefQuad::bound_to_inf; |
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282 } |
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284 octave_idx_type ier = 0; |
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285 octave_idx_type nfun = 0; |
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286 float abserr = 0.0; |
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287 float val = 0.0; |
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288 bool have_sing = false; |
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289 FloatColumnVector sing; |
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290 FloatColumnVector tol; |
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291 |
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292 switch (nargin) |
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293 { |
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294 case 5: |
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295 if (indefinite) |
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296 QUAD_ABORT1 ("singularities not allowed on infinite intervals"); |
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297 |
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298 have_sing = true; |
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299 |
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300 sing = FloatColumnVector (args(4).float_vector_value ()); |
3243 | 301 |
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302 if (error_state) |
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303 QUAD_ABORT1 ("expecting vector of singularities as fourth argument"); |
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304 |
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305 case 4: |
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306 tol = FloatColumnVector (args(3).float_vector_value ()); |
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307 |
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308 if (error_state) |
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309 QUAD_ABORT1 ("expecting vector of tolerances as fifth argument"); |
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310 |
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311 switch (tol.capacity ()) |
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312 { |
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313 case 2: |
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314 quad_opts.set_single_precision_relative_tolerance (tol (1)); |
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315 |
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316 case 1: |
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317 quad_opts.set_single_precision_absolute_tolerance (tol (0)); |
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318 break; |
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319 |
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320 default: |
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321 QUAD_ABORT1 ("expecting tol to contain no more than two values"); |
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322 } |
3243 | 323 |
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324 case 3: |
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325 if (indefinite) |
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326 { |
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327 FloatIndefQuad iq (quad_float_user_function, bound, |
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328 indef_type); |
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329 iq.set_options (quad_opts); |
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330 val = iq.float_integrate (ier, nfun, abserr); |
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331 } |
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332 else |
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333 { |
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334 if (have_sing) |
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335 { |
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336 FloatDefQuad dq (quad_float_user_function, a, b, sing); |
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337 dq.set_options (quad_opts); |
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338 val = dq.float_integrate (ier, nfun, abserr); |
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339 } |
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340 else |
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341 { |
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342 FloatDefQuad dq (quad_float_user_function, a, b); |
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343 dq.set_options (quad_opts); |
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344 val = dq.float_integrate (ier, nfun, abserr); |
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345 } |
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346 } |
3243 | 347 break; |
348 | |
349 default: | |
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350 panic_impossible (); |
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351 break; |
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352 } |
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353 |
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354 retval(3) = abserr; |
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355 retval(2) = nfun; |
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356 retval(1) = ier; |
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357 retval(0) = val; |
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358 |
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359 } |
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360 else |
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361 { |
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362 double a = args(1).double_value (); |
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363 |
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364 if (error_state) |
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365 QUAD_ABORT1 ("expecting second argument to be a scalar"); |
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366 |
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367 double b = args(2).double_value (); |
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368 |
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369 if (error_state) |
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370 QUAD_ABORT1 ("expecting third argument to be a scalar"); |
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371 |
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372 int indefinite = 0; |
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373 IndefQuad::IntegralType indef_type = IndefQuad::doubly_infinite; |
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374 double bound = 0.0; |
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375 if (xisinf (a) && xisinf (b)) |
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376 { |
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377 indefinite = 1; |
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378 indef_type = IndefQuad::doubly_infinite; |
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379 } |
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380 else if (xisinf (a)) |
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381 { |
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382 indefinite = 1; |
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383 bound = b; |
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384 indef_type = IndefQuad::neg_inf_to_bound; |
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385 } |
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386 else if (xisinf (b)) |
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387 { |
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388 indefinite = 1; |
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389 bound = a; |
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390 indef_type = IndefQuad::bound_to_inf; |
3243 | 391 } |
392 | |
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393 octave_idx_type ier = 0; |
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394 octave_idx_type nfun = 0; |
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395 double abserr = 0.0; |
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396 double val = 0.0; |
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397 bool have_sing = false; |
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398 ColumnVector sing; |
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399 ColumnVector tol; |
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400 |
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401 switch (nargin) |
3243 | 402 { |
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403 case 5: |
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404 if (indefinite) |
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405 QUAD_ABORT1 ("singularities not allowed on infinite intervals"); |
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406 |
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407 have_sing = true; |
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408 |
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409 sing = ColumnVector (args(4).vector_value ()); |
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410 |
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411 if (error_state) |
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412 QUAD_ABORT1 ("expecting vector of singularities as fourth argument"); |
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413 |
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414 case 4: |
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415 tol = ColumnVector (args(3).vector_value ()); |
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416 |
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417 if (error_state) |
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418 QUAD_ABORT1 ("expecting vector of tolerances as fifth argument"); |
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419 |
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420 switch (tol.capacity ()) |
3243 | 421 { |
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422 case 2: |
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|
423 quad_opts.set_relative_tolerance (tol (1)); |
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424 |
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|
425 case 1: |
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|
426 quad_opts.set_absolute_tolerance (tol (0)); |
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427 break; |
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|
428 |
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|
429 default: |
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|
430 QUAD_ABORT1 ("expecting tol to contain no more than two values"); |
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431 } |
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|
432 |
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|
433 case 3: |
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|
434 if (indefinite) |
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435 { |
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|
436 IndefQuad iq (quad_user_function, bound, indef_type); |
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437 iq.set_options (quad_opts); |
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438 val = iq.integrate (ier, nfun, abserr); |
3243 | 439 } |
440 else | |
441 { | |
7805
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|
442 if (have_sing) |
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|
443 { |
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changeset
|
444 DefQuad dq (quad_user_function, a, b, sing); |
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|
445 dq.set_options (quad_opts); |
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|
446 val = dq.integrate (ier, nfun, abserr); |
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447 } |
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448 else |
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449 { |
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450 DefQuad dq (quad_user_function, a, b); |
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451 dq.set_options (quad_opts); |
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452 val = dq.integrate (ier, nfun, abserr); |
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453 } |
3243 | 454 } |
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455 break; |
3243 | 456 |
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457 default: |
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458 panic_impossible (); |
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459 break; |
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460 } |
3243 | 461 |
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462 retval(3) = abserr; |
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463 retval(2) = nfun; |
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464 retval(1) = ier; |
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465 retval(0) = val; |
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466 } |
4954 | 467 |
468 if (fcn_name.length()) | |
469 clear_function (fcn_name); | |
3243 | 470 } |
471 else | |
5823 | 472 print_usage (); |
2928 | 473 |
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474 unwind_protect::run_frame (uwp_frame); |
2928 | 475 |
476 return retval; | |
477 } | |
478 | |
479 /* | |
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480 |
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481 %!function y = f (x) |
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482 %! y = x + 1; |
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483 %!test |
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484 %! [v, ier, nfun, err] = quad ("f", 0, 5); |
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485 %! assert(ier == 0 && abs (v - 17.5) < sqrt (eps) && nfun > 0 && |
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486 %! err < sqrt (eps)) |
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487 %!test |
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488 %! [v, ier, nfun, err] = quad ("f", single(0), single(5)); |
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489 %! assert(ier == 0 && abs (v - 17.5) < sqrt (eps ("single")) && nfun > 0 && |
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490 %! err < sqrt (eps ("single"))) |
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491 |
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492 %!function y = f (x) |
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493 %! y = x .* sin (1 ./ x) .* sqrt (abs (1 - x)); |
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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 */ |
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512 |
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513 /* |
2928 | 514 ;;; Local Variables: *** |
515 ;;; mode: C++ *** | |
516 ;;; End: *** | |
517 */ |