Mercurial > octave
annotate libinterp/corefcn/quad.cc @ 30564:796f54d4ddbf stable
update Octave Project Developers copyright for the new year
In files that have the "Octave Project Developers" copyright notice,
update for 2021.
In all .txi and .texi files except gpl.txi and gpl.texi in the
doc/liboctave and doc/interpreter directories, change the copyright
to "Octave Project Developers", the same as used for other source
files. Update copyright notices for 2022 (not done since 2019). For
gpl.txi and gpl.texi, change the copyright notice to be "Free Software
Foundation, Inc." and leave the date at 2007 only because this file
only contains the text of the GPL, not anything created by the Octave
Project Developers.
Add Paul Thomas to contributors.in.
author | John W. Eaton <jwe@octave.org> |
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date | Tue, 28 Dec 2021 18:22:40 -0500 |
parents | 7d6709900da7 |
children | c9788d7f6e65 |
rev | line source |
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1 //////////////////////////////////////////////////////////////////////// |
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2 // |
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3 // Copyright (C) 1996-2022 The Octave Project Developers |
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4 // |
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5 // See the file COPYRIGHT.md in the top-level directory of this |
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6 // distribution or <https://octave.org/copyright/>. |
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7 // |
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8 // This file is part of Octave. |
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9 // |
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10 // Octave is free software: you can redistribute it and/or modify it |
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11 // under the terms of the GNU General Public License as published by |
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12 // the Free Software Foundation, either version 3 of the License, or |
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13 // (at your option) any later version. |
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14 // |
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15 // Octave is distributed in the hope that it will be useful, but |
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16 // WITHOUT ANY WARRANTY; without even the implied warranty of |
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17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 // GNU General Public License for more details. |
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19 // |
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20 // You should have received a copy of the GNU General Public License |
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21 // along with Octave; see the file COPYING. If not, see |
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22 // <https://www.gnu.org/licenses/>. |
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23 // |
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24 //////////////////////////////////////////////////////////////////////// |
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26 #if defined (HAVE_CONFIG_H) |
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27 # include "config.h" |
2928 | 28 #endif |
29 | |
30 #include <string> | |
31 | |
32 #include "Quad.h" | |
33 #include "lo-mappers.h" | |
34 | |
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35 #include "defun.h" |
2928 | 36 #include "error.h" |
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37 #include "errwarn.h" |
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38 #include "interpreter-private.h" |
2928 | 39 #include "pager.h" |
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40 #include "parse.h" |
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41 #include "ov.h" |
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42 #include "ovl.h" |
3243 | 43 #include "unwind-prot.h" |
2928 | 44 #include "utils.h" |
45 #include "variables.h" | |
46 | |
3998 | 47 #include "Quad-opts.cc" |
48 | |
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49 OCTAVE_NAMESPACE_BEGIN |
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50 |
2928 | 51 // Global pointer for user defined function required by quadrature functions. |
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52 static octave_value 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 | |
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60 static double |
2928 | 61 quad_user_function (double x) |
62 { | |
63 double retval = 0.0; | |
64 | |
65 octave_value_list args; | |
66 args(0) = x; | |
67 | |
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68 if (quad_fcn.is_defined ()) |
2928 | 69 { |
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70 octave_value_list tmp; |
2928 | 71 |
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72 try |
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73 { |
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74 tmp = feval (quad_fcn, args, 1); |
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75 } |
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76 catch (execution_exception& ee) |
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77 { |
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78 err_user_supplied_eval (ee, "quad"); |
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79 } |
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81 if (! tmp.length () || ! tmp(0).is_defined ()) |
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82 err_user_supplied_eval ("quad"); |
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83 |
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84 if (! warned_imaginary && tmp(0).iscomplex ()) |
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85 { |
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86 warning ("quad: ignoring imaginary part returned from user-supplied function"); |
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87 warned_imaginary = true; |
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88 } |
4140 | 89 |
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90 retval = tmp(0).xdouble_value ("quad: expecting user supplied function to return numeric value"); |
2928 | 91 } |
92 | |
93 return retval; | |
94 } | |
95 | |
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96 static float |
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97 quad_float_user_function (float x) |
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98 { |
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99 float retval = 0.0; |
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100 |
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101 octave_value_list args; |
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102 args(0) = x; |
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103 |
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104 if (quad_fcn.is_defined ()) |
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105 { |
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106 octave_value_list tmp; |
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107 |
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108 try |
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109 { |
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110 tmp = feval (quad_fcn, args, 1); |
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111 } |
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112 catch (execution_exception& ee) |
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113 { |
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114 err_user_supplied_eval (ee, "quad"); |
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115 } |
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116 |
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117 if (! tmp.length () || ! tmp(0).is_defined ()) |
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118 err_user_supplied_eval ("quad"); |
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119 |
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120 if (! warned_imaginary && tmp(0).iscomplex ()) |
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121 { |
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122 warning ("quad: ignoring imaginary part returned from user-supplied function"); |
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123 warned_imaginary = true; |
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124 } |
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125 |
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126 retval = tmp(0).xfloat_value ("quad: expecting user supplied function to return numeric value"); |
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127 } |
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128 |
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129 return retval; |
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130 } |
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131 |
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132 DEFMETHODX ("quad", Fquad, interp, args, , |
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133 doc: /* -*- texinfo -*- |
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134 @deftypefn {} {@var{q} =} quad (@var{f}, @var{a}, @var{b}) |
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135 @deftypefnx {} {@var{q} =} quad (@var{f}, @var{a}, @var{b}, @var{tol}) |
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136 @deftypefnx {} {@var{q} =} quad (@var{f}, @var{a}, @var{b}, @var{tol}, @var{sing}) |
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137 @deftypefnx {} {[@var{q}, @var{ier}, @var{nfun}, @var{err}] =} quad (@dots{}) |
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138 Numerically evaluate the integral of @var{f} from @var{a} to @var{b} using |
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139 Fortran routines from @w{@sc{quadpack}}. |
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140 |
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141 @var{f} is a function handle, inline function, or a string containing the |
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142 name of the function to evaluate. The function must have the form @code{y = |
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143 f (x)} where @var{y} and @var{x} are scalars. |
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144 |
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145 @var{a} and @var{b} are the lower and upper limits of integration. Either |
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146 or both may be infinite. |
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147 |
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148 The optional argument @var{tol} is a vector that specifies the desired |
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149 accuracy of the result. The first element of the vector is the desired |
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150 absolute tolerance, and the second element is the desired relative |
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151 tolerance. To choose a relative test only, set the absolute |
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152 tolerance to zero. To choose an absolute test only, set the relative |
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153 tolerance to zero. Both tolerances default to @code{sqrt (eps)} or |
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154 approximately 1.5e-8. |
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155 |
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156 The optional argument @var{sing} is a vector of values at which the |
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157 integrand is known to be singular. |
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158 |
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159 The result of the integration is returned in @var{q}. |
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160 |
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161 @var{ier} contains an integer error code (0 indicates a successful |
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162 integration). |
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163 |
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164 @var{nfun} indicates the number of function evaluations that were |
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165 made. |
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166 |
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167 @var{err} contains an estimate of the error in the solution. |
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168 |
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169 The function @code{quad_options} can set other optional parameters for |
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170 @code{quad}. |
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171 |
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172 Note: because @code{quad} is written in Fortran it cannot be called |
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173 recursively. This prevents its use in integrating over more than one |
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174 variable by routines @code{dblquad} and @code{triplequad}. |
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175 @seealso{quad_options, quadv, quadl, quadgk, quadcc, trapz, dblquad, triplequad} |
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176 @end deftypefn */) |
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178 int nargin = args.length (); |
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180 if (nargin < 3 || nargin > 5) |
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181 print_usage (); |
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184 | |
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185 unwind_protect_var<int> restore_var (call_depth); |
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187 | |
188 if (call_depth > 1) | |
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189 error ("quad: invalid recursive call"); |
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191 quad_fcn = get_function_handle (interp, args(0), "x"); |
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192 |
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193 octave_value_list retval; |
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194 |
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195 if (args(1).is_single_type () || args(2).is_single_type ()) |
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196 { |
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197 float a = args(1).xfloat_value ("quad: lower limit of integration A must be a scalar"); |
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198 float b = args(2).xfloat_value ("quad: upper limit of integration B must be a scalar"); |
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199 |
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200 int indefinite = 0; |
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201 FloatIndefQuad::IntegralType indef_type |
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202 = FloatIndefQuad::doubly_infinite; |
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203 float bound = 0.0; |
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204 if (math::isinf (a) && math::isinf (b)) |
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205 { |
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206 indefinite = 1; |
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207 indef_type = FloatIndefQuad::doubly_infinite; |
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208 } |
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209 else if (math::isinf (a)) |
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210 { |
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211 indefinite = 1; |
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212 bound = b; |
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213 indef_type = FloatIndefQuad::neg_inf_to_bound; |
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214 } |
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215 else if (math::isinf (b)) |
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216 { |
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217 indefinite = 1; |
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218 bound = a; |
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219 indef_type = FloatIndefQuad::bound_to_inf; |
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220 } |
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222 octave_idx_type ier = 0; |
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223 octave_idx_type nfun = 0; |
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224 float abserr = 0.0; |
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225 float val = 0.0; |
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226 bool have_sing = false; |
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227 FloatColumnVector sing; |
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228 FloatColumnVector tol; |
3243 | 229 |
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230 switch (nargin) |
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231 { |
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232 case 5: |
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233 if (indefinite) |
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234 error ("quad: singularities not allowed on infinite intervals"); |
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235 |
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236 have_sing = true; |
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237 |
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238 sing = args(4).xfloat_vector_value ("quad: fifth argument SING must be a vector of singularities"); |
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239 OCTAVE_FALLTHROUGH; |
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240 |
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241 case 4: |
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242 tol = args(3).xfloat_vector_value ("quad: TOL must be a 1 or 2-element vector"); |
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244 switch (tol.numel ()) |
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245 { |
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246 case 2: |
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247 quad_opts.set_single_precision_relative_tolerance (tol (1)); |
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248 OCTAVE_FALLTHROUGH; |
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249 |
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250 case 1: |
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251 quad_opts.set_single_precision_absolute_tolerance (tol (0)); |
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252 break; |
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254 default: |
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255 error ("quad: TOL must be a 1 or 2-element vector"); |
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256 } |
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257 OCTAVE_FALLTHROUGH; |
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259 case 3: |
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260 if (indefinite) |
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261 { |
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262 FloatIndefQuad iq (quad_float_user_function, bound, |
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263 indef_type); |
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264 iq.set_options (quad_opts); |
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265 val = iq.float_integrate (ier, nfun, abserr); |
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266 } |
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267 else |
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268 { |
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269 if (have_sing) |
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270 { |
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271 FloatDefQuad dq (quad_float_user_function, a, b, sing); |
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272 dq.set_options (quad_opts); |
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273 val = dq.float_integrate (ier, nfun, abserr); |
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274 } |
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275 else |
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276 { |
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277 FloatDefQuad dq (quad_float_user_function, a, b); |
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278 dq.set_options (quad_opts); |
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279 val = dq.float_integrate (ier, nfun, abserr); |
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280 } |
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281 } |
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282 break; |
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283 |
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284 default: |
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285 panic_impossible (); |
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286 break; |
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287 } |
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288 |
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289 retval = ovl (val, ier, nfun, abserr); |
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290 |
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291 } |
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292 else |
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293 { |
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294 double a = args(1).xdouble_value ("quad: lower limit of integration A must be a scalar"); |
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295 double b = args(2).xdouble_value ("quad: upper limit of integration B must be a scalar"); |
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296 |
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297 int indefinite = 0; |
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298 IndefQuad::IntegralType indef_type = IndefQuad::doubly_infinite; |
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299 double bound = 0.0; |
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300 if (math::isinf (a) && math::isinf (b)) |
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301 { |
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302 indefinite = 1; |
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303 indef_type = IndefQuad::doubly_infinite; |
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304 } |
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305 else if (math::isinf (a)) |
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306 { |
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307 indefinite = 1; |
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308 bound = b; |
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309 indef_type = IndefQuad::neg_inf_to_bound; |
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310 } |
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311 else if (math::isinf (b)) |
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312 { |
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313 indefinite = 1; |
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314 bound = a; |
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315 indef_type = IndefQuad::bound_to_inf; |
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316 } |
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317 |
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318 octave_idx_type ier = 0; |
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319 octave_idx_type nfun = 0; |
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320 double abserr = 0.0; |
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321 double val = 0.0; |
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322 bool have_sing = false; |
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323 ColumnVector sing; |
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324 ColumnVector tol; |
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325 |
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326 switch (nargin) |
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327 { |
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328 case 5: |
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329 if (indefinite) |
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330 error ("quad: singularities not allowed on infinite intervals"); |
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331 |
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332 have_sing = true; |
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333 |
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334 sing = args(4).xvector_value ("quad: fifth argument SING must be a vector of singularities"); |
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335 OCTAVE_FALLTHROUGH; |
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336 |
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337 case 4: |
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338 tol = args(3).xvector_value ("quad: TOL must be a 1 or 2-element vector"); |
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339 |
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340 switch (tol.numel ()) |
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341 { |
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342 case 2: |
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343 quad_opts.set_relative_tolerance (tol (1)); |
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344 OCTAVE_FALLTHROUGH; |
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345 |
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346 case 1: |
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347 quad_opts.set_absolute_tolerance (tol (0)); |
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348 break; |
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350 default: |
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351 error ("quad: TOL must be a 1 or 2-element vector"); |
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352 } |
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353 OCTAVE_FALLTHROUGH; |
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355 case 3: |
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356 if (indefinite) |
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357 { |
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358 IndefQuad iq (quad_user_function, bound, indef_type); |
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359 iq.set_options (quad_opts); |
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360 val = iq.integrate (ier, nfun, abserr); |
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361 } |
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362 else |
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363 { |
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364 if (have_sing) |
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365 { |
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366 DefQuad dq (quad_user_function, a, b, sing); |
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367 dq.set_options (quad_opts); |
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368 val = dq.integrate (ier, nfun, abserr); |
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369 } |
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370 else |
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371 { |
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372 DefQuad dq (quad_user_function, a, b); |
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373 dq.set_options (quad_opts); |
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374 val = dq.integrate (ier, nfun, abserr); |
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375 } |
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376 } |
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377 break; |
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378 |
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379 default: |
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380 panic_impossible (); |
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381 break; |
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382 } |
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384 retval = ovl (val, ier, nfun, abserr); |
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386 |
2928 | 387 return retval; |
388 } | |
389 | |
390 /* | |
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391 %!function y = __f (x) |
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392 %! y = x + 1; |
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393 %!endfunction |
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394 |
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395 %!test |
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396 %! [v, ier, nfun, err] = quad ("__f", 0, 5); |
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397 %! assert (ier, 0); |
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398 %! assert (v, 17.5, sqrt (eps)); |
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399 %! assert (nfun > 0); |
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400 %! assert (err < sqrt (eps)); |
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401 |
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402 %!test |
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403 %! [v, ier, nfun, err] = quad ("__f", single (0), single (5)); |
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404 %! assert (ier, 0); |
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405 %! assert (v, 17.5, sqrt (eps ("single"))); |
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406 %! assert (nfun > 0); |
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407 %! assert (err < sqrt (eps ("single"))); |
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408 |
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409 %!function y = __f (x) |
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410 %! y = x .* sin (1 ./ x) .* sqrt (abs (1 - x)); |
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411 %!endfunction |
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412 |
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413 %!test |
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414 %! [v, ier, nfun, err] = quad ("__f", 0.001, 3); |
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415 %! assert (ier == 0 || ier == 1); |
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416 %! assert (v, 1.98194120273598, sqrt (eps)); |
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417 %! assert (nfun > 0); |
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418 |
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419 %!test |
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420 %! [v, ier, nfun, err] = quad (@__f, 0.001, 3); |
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421 %! assert (ier == 0 || ier == 1); |
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422 %! assert (v, 1.98194120273598, sqrt (eps)); |
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423 %! assert (nfun > 0); |
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424 |
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425 %!test |
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426 %! fstr = "x .* sin (1 ./ x) .* sqrt (abs (1 - x))"; |
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427 %! [v, ier, nfun, err] = quad (fstr, 0.001, 3); |
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428 %! assert (ier == 0 || ier == 1); |
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429 %! assert (v, 1.98194120273598, sqrt (eps)); |
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430 %! assert (nfun > 0); |
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431 |
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432 %!test |
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433 %! anon_fcn = @(x) x .* sin (1 ./ x) .* sqrt (abs (1 - x)); |
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434 %! [v, ier, nfun, err] = quad (anon_fcn, 0.001, 3); |
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435 %! assert (ier == 0 || ier == 1); |
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436 %! assert (v, 1.98194120273598, sqrt (eps)); |
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437 %! assert (nfun > 0); |
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438 |
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439 %!test |
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440 %! inline_fcn = inline ("x .* sin (1 ./ x) .* sqrt (abs (1 - x))", "x"); |
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441 %! [v, ier, nfun, err] = quad (inline_fcn, 0.001, 3); |
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442 %! assert (ier == 0 || ier == 1); |
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443 %! assert (v, 1.98194120273598, sqrt (eps)); |
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444 %! assert (nfun > 0); |
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445 |
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446 %!test |
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447 %! [v, ier, nfun, err] = quad ("__f", single (0.001), single (3)); |
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448 %! assert (ier == 0 || ier == 1); |
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449 %! assert (v, 1.98194120273598, sqrt (eps ("single"))); |
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450 %! assert (nfun > 0); |
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451 |
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452 %!error quad () |
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453 %!error quad ("__f", 1, 2, 3, 4, 5) |
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454 |
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455 %!test |
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456 %! quad_options ("absolute tolerance", eps); |
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457 %! assert (quad_options ("absolute tolerance") == eps); |
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458 |
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459 %!error quad_options (1, 2, 3) |
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460 */ |
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461 |
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462 OCTAVE_NAMESPACE_END |