Mercurial > octave
annotate libinterp/corefcn/quad.cc @ 20687:5f04bfc7c17a
backout changeset 18f38ed43962
author | John W. Eaton <jwe@octave.org> |
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date | Sun, 08 Nov 2015 16:14:27 -0500 |
parents | 18f38ed43962 |
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2928 | 1 /* |
2 | |
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3 Copyright (C) 1996-2015 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 | |
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35 #include "defun.h" |
2928 | 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 { \ | |
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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 { \ | |
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162 error ("quad: " msg); \ |
3323 | 163 QUAD_ABORT (); \ |
164 } \ | |
165 while (0) | |
166 | |
167 #define QUAD_ABORT2(fmt, arg) \ | |
168 do \ | |
169 { \ | |
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170 error ("quad: " fmt, arg); \ |
3323 | 171 QUAD_ABORT (); \ |
172 } \ | |
173 while (0) | |
174 | |
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175 DEFUN (quad, args, nargout, |
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176 "-*- texinfo -*-\n\ |
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177 @deftypefn {Built-in Function} {@var{q} =} quad (@var{f}, @var{a}, @var{b})\n\ |
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178 @deftypefnx {Built-in Function} {@var{q} =} quad (@var{f}, @var{a}, @var{b}, @var{tol})\n\ |
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179 @deftypefnx {Built-in Function} {@var{q} =} quad (@var{f}, @var{a}, @var{b}, @var{tol}, @var{sing})\n\ |
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180 @deftypefnx {Built-in 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}}.\n\ |
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183 \n\ |
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184 @var{f} is a function handle, inline function, or a string containing the\n\ |
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185 name of the function to evaluate. The function must have the form @code{y =\n\ |
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186 f (x)} where @var{y} and @var{x} are scalars.\n\ |
2928 | 187 \n\ |
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188 @var{a} and @var{b} are the lower and upper limits of integration. Either\n\ |
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189 or both may be infinite.\n\ |
2928 | 190 \n\ |
3368 | 191 The optional argument @var{tol} is a vector that specifies the desired\n\ |
2928 | 192 accuracy of the result. The first element of the vector is the desired\n\ |
193 absolute tolerance, and the second element is the desired relative\n\ | |
3368 | 194 tolerance. To choose a relative test only, set the absolute\n\ |
195 tolerance to zero. To choose an absolute test only, set the relative\n\ | |
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196 tolerance to zero. Both tolerances default to @code{sqrt (eps)} or\n\ |
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197 approximately @math{1.5e^{-8}}.\n\ |
2928 | 198 \n\ |
199 The optional argument @var{sing} is a vector of values at which the\n\ | |
3368 | 200 integrand is known to be singular.\n\ |
201 \n\ | |
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202 The result of the integration is returned in @var{q}.\n\ |
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203 \n\ |
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204 @var{ier} contains an integer error code (0 indicates a successful\n\ |
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205 integration).\n\ |
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206 \n\ |
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207 @var{nfun} indicates the number of function evaluations that were\n\ |
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208 made.\n\ |
3964 | 209 \n\ |
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210 @var{err} contains an estimate of the error in the solution.\n\ |
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211 \n\ |
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212 The function @code{quad_options} can set other optional parameters for\n\ |
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213 @code{quad}.\n\ |
6741 | 214 \n\ |
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215 Note: because @code{quad} is written in Fortran it cannot be called\n\ |
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216 recursively. This prevents its use in integrating over more than one\n\ |
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217 variable by routines @code{dblquad} and @code{triplequad}.\n\ |
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218 @seealso{quad_options, quadv, quadl, quadgk, quadcc, trapz, dblquad, triplequad}\n\ |
3368 | 219 @end deftypefn") |
2928 | 220 { |
221 octave_value_list retval; | |
222 | |
4954 | 223 std::string fcn_name; |
224 | |
4140 | 225 warned_imaginary = false; |
226 | |
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227 unwind_protect frame; |
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229 frame.protect_var (call_depth); |
3243 | 230 call_depth++; |
231 | |
232 if (call_depth > 1) | |
3323 | 233 QUAD_ABORT1 ("invalid recursive call"); |
3243 | 234 |
2928 | 235 int nargin = args.length (); |
236 | |
3243 | 237 if (nargin > 2 && nargin < 6 && nargout < 5) |
238 { | |
4954 | 239 if (args(0).is_function_handle () || args(0).is_inline_function ()) |
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240 quad_fcn = args(0).function_value (); |
4954 | 241 else |
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242 { |
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243 fcn_name = unique_symbol_name ("__quad_fcn__"); |
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244 std::string fname = "function y = "; |
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245 fname.append (fcn_name); |
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246 fname.append ("(x) y = "); |
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247 quad_fcn = extract_function (args(0), "quad", fcn_name, fname, |
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248 "; endfunction"); |
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249 } |
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3243 | 251 if (! quad_fcn) |
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252 QUAD_ABORT (); |
3243 | 253 |
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254 if (args(1).is_single_type () || args(2).is_single_type ()) |
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255 { |
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256 float a = args(1).float_value (); |
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258 if (error_state) |
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259 QUAD_ABORT1 ("expecting second argument to be a scalar"); |
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261 float b = args(2).float_value (); |
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263 if (error_state) |
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264 QUAD_ABORT1 ("expecting third argument to be a scalar"); |
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266 int indefinite = 0; |
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267 FloatIndefQuad::IntegralType indef_type |
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268 = FloatIndefQuad::doubly_infinite; |
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269 float bound = 0.0; |
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270 if (xisinf (a) && xisinf (b)) |
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271 { |
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272 indefinite = 1; |
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273 indef_type = FloatIndefQuad::doubly_infinite; |
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274 } |
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275 else if (xisinf (a)) |
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276 { |
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277 indefinite = 1; |
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278 bound = b; |
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279 indef_type = FloatIndefQuad::neg_inf_to_bound; |
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280 } |
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281 else if (xisinf (b)) |
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282 { |
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283 indefinite = 1; |
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284 bound = a; |
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285 indef_type = FloatIndefQuad::bound_to_inf; |
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286 } |
3243 | 287 |
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288 octave_idx_type ier = 0; |
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289 octave_idx_type nfun = 0; |
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290 float abserr = 0.0; |
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291 float val = 0.0; |
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292 bool have_sing = false; |
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293 FloatColumnVector sing; |
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294 FloatColumnVector tol; |
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295 |
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296 switch (nargin) |
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297 { |
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298 case 5: |
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299 if (indefinite) |
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300 QUAD_ABORT1 ("singularities not allowed on infinite intervals"); |
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301 |
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302 have_sing = true; |
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303 |
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304 sing = FloatColumnVector (args(4).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 singularities as fourth argument"); |
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308 |
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309 case 4: |
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310 tol = FloatColumnVector (args(3).float_vector_value ()); |
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311 |
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312 if (error_state) |
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313 QUAD_ABORT1 ("expecting vector of tolerances as fifth argument"); |
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314 |
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315 switch (tol.numel ()) |
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316 { |
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317 case 2: |
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318 quad_opts.set_single_precision_relative_tolerance (tol (1)); |
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319 |
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320 case 1: |
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321 quad_opts.set_single_precision_absolute_tolerance (tol (0)); |
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322 break; |
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323 |
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324 default: |
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325 QUAD_ABORT1 ("expecting tol to contain no more than two values"); |
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326 } |
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328 case 3: |
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329 if (indefinite) |
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330 { |
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331 FloatIndefQuad iq (quad_float_user_function, bound, |
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332 indef_type); |
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333 iq.set_options (quad_opts); |
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334 val = iq.float_integrate (ier, nfun, abserr); |
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335 } |
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336 else |
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337 { |
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338 if (have_sing) |
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339 { |
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340 FloatDefQuad dq (quad_float_user_function, a, b, sing); |
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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 else |
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345 { |
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346 FloatDefQuad dq (quad_float_user_function, a, b); |
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347 dq.set_options (quad_opts); |
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348 val = dq.float_integrate (ier, nfun, abserr); |
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349 } |
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350 } |
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351 break; |
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353 default: |
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354 panic_impossible (); |
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355 break; |
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356 } |
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357 |
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358 retval(3) = abserr; |
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359 retval(2) = nfun; |
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360 retval(1) = ier; |
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361 retval(0) = val; |
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362 |
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363 } |
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364 else |
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365 { |
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366 double a = args(1).double_value (); |
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367 |
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368 if (error_state) |
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369 QUAD_ABORT1 ("expecting second argument to be a scalar"); |
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370 |
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371 double b = args(2).double_value (); |
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372 |
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373 if (error_state) |
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374 QUAD_ABORT1 ("expecting third argument to be a scalar"); |
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375 |
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376 int indefinite = 0; |
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377 IndefQuad::IntegralType indef_type = IndefQuad::doubly_infinite; |
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378 double bound = 0.0; |
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379 if (xisinf (a) && xisinf (b)) |
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380 { |
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381 indefinite = 1; |
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382 indef_type = IndefQuad::doubly_infinite; |
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383 } |
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384 else if (xisinf (a)) |
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385 { |
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386 indefinite = 1; |
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387 bound = b; |
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388 indef_type = IndefQuad::neg_inf_to_bound; |
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389 } |
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390 else if (xisinf (b)) |
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391 { |
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392 indefinite = 1; |
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393 bound = a; |
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394 indef_type = IndefQuad::bound_to_inf; |
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395 } |
3243 | 396 |
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397 octave_idx_type ier = 0; |
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398 octave_idx_type nfun = 0; |
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399 double abserr = 0.0; |
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400 double val = 0.0; |
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401 bool have_sing = false; |
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402 ColumnVector sing; |
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403 ColumnVector tol; |
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404 |
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405 switch (nargin) |
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406 { |
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407 case 5: |
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408 if (indefinite) |
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409 QUAD_ABORT1 ("singularities not allowed on infinite intervals"); |
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410 |
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411 have_sing = true; |
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412 |
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413 sing = ColumnVector (args(4).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 singularities as fourth argument"); |
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417 |
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418 case 4: |
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419 tol = ColumnVector (args(3).vector_value ()); |
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420 |
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421 if (error_state) |
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422 QUAD_ABORT1 ("expecting vector of tolerances as fifth argument"); |
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423 |
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424 switch (tol.numel ()) |
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425 { |
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426 case 2: |
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427 quad_opts.set_relative_tolerance (tol (1)); |
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428 |
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429 case 1: |
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430 quad_opts.set_absolute_tolerance (tol (0)); |
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431 break; |
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432 |
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433 default: |
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434 QUAD_ABORT1 ("expecting tol to contain no more than two values"); |
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435 } |
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436 |
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437 case 3: |
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438 if (indefinite) |
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439 { |
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440 IndefQuad iq (quad_user_function, bound, indef_type); |
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441 iq.set_options (quad_opts); |
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442 val = iq.integrate (ier, nfun, abserr); |
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443 } |
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444 else |
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445 { |
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446 if (have_sing) |
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447 { |
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448 DefQuad dq (quad_user_function, a, b, sing); |
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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 else |
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453 { |
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454 DefQuad dq (quad_user_function, a, b); |
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455 dq.set_options (quad_opts); |
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456 val = dq.integrate (ier, nfun, abserr); |
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457 } |
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458 } |
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459 break; |
3243 | 460 |
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461 default: |
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462 panic_impossible (); |
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463 break; |
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464 } |
3243 | 465 |
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466 retval(3) = abserr; |
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467 retval(2) = nfun; |
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468 retval(1) = ier; |
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469 retval(0) = val; |
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470 } |
4954 | 471 |
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472 if (fcn_name.length ()) |
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473 clear_function (fcn_name); |
3243 | 474 } |
475 else | |
5823 | 476 print_usage (); |
2928 | 477 |
478 return retval; | |
479 } | |
480 | |
481 /* | |
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482 %!function y = __f (x) |
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483 %! y = x + 1; |
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484 %!endfunction |
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485 |
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486 %!test |
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487 %! [v, ier, nfun, err] = quad ("__f", 0, 5); |
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488 %! assert (ier, 0); |
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489 %! assert (v, 17.5, sqrt (eps)); |
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490 %! assert (nfun > 0); |
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491 %! assert (err < sqrt (eps)); |
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492 |
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493 %!test |
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494 %! [v, ier, nfun, err] = quad ("__f", single (0), single (5)); |
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495 %! assert (ier, 0); |
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496 %! assert (v, 17.5, sqrt (eps ("single"))); |
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497 %! assert (nfun > 0); |
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498 %! assert (err < sqrt (eps ("single"))); |
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499 |
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500 %!function y = __f (x) |
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501 %! y = x .* sin (1 ./ x) .* sqrt (abs (1 - x)); |
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502 %!endfunction |
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503 |
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504 %!test |
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505 %! [v, ier, nfun, err] = quad ("__f", 0.001, 3); |
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506 %! assert (ier == 0 || ier == 1); |
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507 %! assert (v, 1.98194120273598, sqrt (eps)); |
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508 %! assert (nfun > 0); |
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509 |
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510 %!test |
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511 %! [v, ier, nfun, err] = quad ("__f", single (0.001), single (3)); |
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512 %! assert (ier == 0 || ier == 1); |
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513 %! assert (v, 1.98194120273598, sqrt (eps ("single"))); |
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514 %! assert (nfun > 0); |
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515 |
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516 %!error quad () |
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517 %!error quad ("__f", 1, 2, 3, 4, 5) |
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518 |
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519 %!test |
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520 %! quad_options ("absolute tolerance", eps); |
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521 %! assert (quad_options ("absolute tolerance") == eps); |
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522 |
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523 %!error quad_options (1, 2, 3) |
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524 */ |