Mercurial > octave
annotate scripts/general/integral3.m @ 28907:11f1207111c5
maint: Don't use semicolon at end of single-line BIST tests.
* Cell.cc, colamd.cc, mappers.cc, sparse.cc, strfns.cc, sub2ind.cc, tril.cc,
variables.cc, ov-cell.cc, integral3.m, quadv.m, import.m, isosurface.m,
betainc.m, cosint.m, gammainc.m, native2unicode.m, bug-50014.tst,
package-function.tst, static-method.tst, func.tst, if.tst, bug-51725.tst,
mk-sparse-tst.sh, nest.tst, pkg.tst:
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author | Rik <rik@octave.org> |
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date | Tue, 13 Oct 2020 14:23:39 -0700 |
parents | bd51beb6205e |
children | 0de38a6ef693 |
rev | line source |
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1 ######################################################################## |
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2 ## |
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3 ## Copyright (C) 2017-2020 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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25 |
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26 ## -*- texinfo -*- |
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27 ## @deftypefn {} {@var{q} =} integral3 (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{za}, @var{zb}) |
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28 ## @deftypefnx {} {@var{q} =} integral3 (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{za}, @var{zb}, @var{prop}, @var{val}, @dots{}) |
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29 ## |
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30 ## Numerically evaluate the three-dimensional integral of @var{f} using |
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31 ## adaptive quadrature over the three-dimensional domain defined by |
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32 ## @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{za}, @var{zb} (scalars may |
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33 ## be finite or infinite). Additionally, @var{ya} and @var{yb} may be |
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34 ## scalar functions of @var{x} and @var{za}, and @var{zb} maybe be scalar |
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35 ## functions of @var{x} and @var{y}, allowing for integration over |
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36 ## non-rectangular domains. |
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37 ## |
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38 ## @var{f} is a function handle, inline function, or string containing the name |
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39 ## of the function to evaluate. The function @var{f} must be of the form |
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40 ## @math{z = f(x,y)} where @var{x} is a vector and @var{y} is a scalar. It |
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41 ## should return a vector of the same length and orientation as @var{x}. |
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42 ## |
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43 ## Additional optional parameters can be specified using |
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44 ## @qcode{"@var{property}", @var{value}} pairs. Valid properties are: |
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45 ## |
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46 ## @table @code |
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47 ## @item AbsTol |
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48 ## Define the absolute error tolerance for the quadrature. The default |
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49 ## value is 1e-10 (1e-5 for single). |
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50 ## |
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51 ## @item RelTol |
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52 ## Define the relative error tolerance for the quadrature. The default |
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53 ## value is 1e-6 (1e-4 for single). |
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54 ## |
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55 ## @item Method |
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56 ## Specify the two-dimensional integration method to be used, with valid |
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57 ## options being @qcode{"auto"} (default), @qcode{"tiled"}, or |
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58 ## @qcode{"iterated"}. When using @qcode{"auto"}, Octave will choose the |
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59 ## @qcode{"tiled"} method unless any of the integration limits are infinite. |
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60 ## |
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61 ## @item Vectorized |
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62 ## Enable or disable vectorized integration. A value of @code{false} forces |
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63 ## Octave to use only scalar inputs when calling the integrand, which enables |
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64 ## integrands @math{f(x,y)} that have not been vectorized and only accept |
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65 ## @var{x} and @var{y} as scalars to be used. The default value is |
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66 ## @code{true}. |
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67 ## @end table |
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68 ## |
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69 ## Adaptive quadrature is used to minimize the estimate of error until the |
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70 ## following is satisfied: |
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71 ## @tex |
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72 ## $$error \leq \max \left( AbsTol, RelTol\cdot\vert q\vert \right)$$ |
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73 ## @end tex |
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74 ## @ifnottex |
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75 ## |
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76 ## @example |
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77 ## @group |
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78 ## @var{error} <= max (@var{AbsTol}, @var{RelTol}*|@var{q}|) |
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79 ## @end group |
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80 ## @end example |
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81 ## |
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82 ## @end ifnottex |
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83 ## |
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84 ## @var{err} is an approximate bound on the error in the integral |
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85 ## @code{abs (@var{q} - @var{I})}, where @var{I} is the exact value of the |
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86 ## integral. |
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87 ## |
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88 ## Example 1 : integrate over a rectangular volume |
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89 ## |
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90 ## @example |
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91 ## @group |
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92 ## @var{f} = @@(@var{x},@var{y},@var{z}) ones (size (@var{x})); |
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93 ## @var{q} = integral3 (@var{f}, 0, 1, 0, 1, 0, 1) |
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94 ## @result{} @var{q} = 1.00000 |
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95 ## @end group |
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96 ## @end example |
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97 ## |
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98 ## For this constant-value integrand, the result is a volume which is just |
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99 ## @code{@var{Length} * @var{Width} * @var{Height}}. |
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100 ## |
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101 ## Example 2 : integrate over a spherical volume |
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102 ## |
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103 ## @example |
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104 ## @group |
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105 ## @var{f} = @@(@var{x},@var{y}) ones (size (@var{x})); |
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106 ## @var{ymax} = @@(@var{x}) sqrt (1 - @var{x}.^2); |
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107 ## @var{zmax} = @@(@var{x},@var{y}) sqrt (1 - @var{x}.^2 - @var{y}.^2); |
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108 ## @var{q} = integral3 (@var{f}, 0, 1, 0, @var{ymax}, 0, @var{zmax}) |
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109 ## @result{} @var{q} = 0.52360 |
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110 ## @end group |
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111 ## @end example |
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112 ## |
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113 ## For this constant-value integrand, the result is a volume which is 1/8th |
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114 ## of a unit sphere or @code{1/8 * 4/3 * pi}. |
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115 ## |
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116 ## Programming Notes: If there are singularities within the integration region |
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117 ## it is best to split the integral and place the singularities on the |
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118 ## boundary. |
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119 ## |
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120 ## Known @sc{matlab} incompatibility: If tolerances are left unspecified, and |
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121 ## any integration limits are of type @code{single}, then Octave's integral |
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122 ## functions automatically reduce the default absolute and relative error |
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123 ## tolerances as specified above. If tighter tolerances are desired they |
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124 ## must be specified. @sc{matlab} leaves the tighter tolerances appropriate |
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125 ## for @code{double} inputs in place regardless of the class of the |
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126 ## integration limits. |
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127 ## |
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128 ## Reference: @nospell{L.F. Shampine}, |
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129 ## @cite{@sc{matlab} program for quadrature in 2D}, Applied Mathematics and |
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130 ## Computation, pp.@: 266--274, Vol 1, 2008. |
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131 ## |
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132 ## @seealso{triplequad, integral, quad, quadgk, quadv, quadl, |
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133 ## quadcc, trapz, integral2, quad2d, dblquad} |
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134 ## @end deftypefn |
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135 |
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136 function q = integral3 (f, xa, xb, ya, yb, za, zb, varargin) |
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137 |
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138 if (nargin < 7 || mod (nargin, 2) == 0) |
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139 print_usage (); |
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140 endif |
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141 |
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142 if (! is_function_handle (f)) |
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143 print_usage (); |
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144 endif |
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145 |
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146 if (! (isreal (xa) && isscalar (xa) && isreal (xb) && isscalar (xb))) |
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147 print_usage (); |
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148 endif |
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149 |
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150 ## Check for single or double limits to set appropriate default tolerance. |
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151 issingle = (isa ([xa, xb], "single") |
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152 || (! is_function_handle (ya) && isa (ya, "single")) |
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153 || (! is_function_handle (yb) && isa (yb, "single")) |
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154 || (! is_function_handle (za) && isa (za, "single")) |
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155 || (! is_function_handle (zb) && isa (zb, "single"))); |
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156 |
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157 ## Communicate to downstream quadrature routines that at least one limit of |
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158 ## integration was of single type by casting xa, xb to single. |
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159 if (issingle) |
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160 xa = single (xa); |
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161 xb = single (xb); |
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162 endif |
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163 |
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164 ## Set default tolerances, and then update with any specified parameters. |
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165 if (issingle) |
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166 abstol = 1e-5; |
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167 reltol = 1e-4; |
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168 else |
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169 abstol = 1e-10; |
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170 reltol = 1e-6; |
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171 endif |
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172 |
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173 method = "auto"; |
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174 vectorized = true; |
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175 idx = 1; |
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176 while (idx < nargin - 7) |
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177 prop = varargin{idx++}; |
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178 if (! ischar (prop)) |
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179 error ("integral3: property PROP must be a string"); |
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180 endif |
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181 |
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182 switch (tolower (prop)) |
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183 case "abstol" |
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184 abstol = varargin{idx++}; |
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185 if (! (isnumeric (abstol) && isscalar (abstol) && abstol >= 0)) |
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186 error ("integral3: AbsTol value must be a numeric scalar >= 0"); |
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187 endif |
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188 |
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189 case "reltol" |
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190 reltol = varargin{idx++}; |
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191 if (! (isnumeric (reltol) && isscalar (reltol) && reltol >= 0)) |
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192 error ("integral3: RelTol value must be a numeric scalar >= 0"); |
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193 endif |
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194 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
195 case "method" |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
196 method = tolower (varargin{idx++}); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
197 if (! any (strcmp (method, {"auto", "iterated", "tiled"}))) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
198 error ("integral3 : unrecognized method '%s'", method); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
199 endif |
24102
c723faa56ab4
Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
200 |
24148
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
201 case "vectorized" |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
202 vectorized = varargin{idx++}; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
203 if (! (isscalar (vectorized) && isreal (vectorized))) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
204 error ('integral3: Vectorized must be a logical value'); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
205 endif |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
206 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
207 otherwise |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
208 error ("integral3: unknown property '%s'", prop); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
209 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
210 endswitch |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
211 endwhile |
24102
c723faa56ab4
Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
212 |
24148
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
213 if (strcmp (method, "auto")) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
214 if (isinf (xa) || isinf (xb) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
215 || (! is_function_handle (ya) && isinf (ya)) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
216 || (! is_function_handle (yb) && isinf (yb)) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
217 || (! is_function_handle (za) && isinf (za)) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
218 || (! is_function_handle (zb) && isinf (zb))) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
219 method = "iterated"; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
220 else |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
221 method = "tiled"; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
222 endif |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
223 endif |
24102
c723faa56ab4
Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
224 |
24148
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
225 ## check upper and lower bounds of y |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
226 if (! is_function_handle (ya)) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
227 if (! (isreal (ya) && isscalar (ya))) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
228 error ("integral3: YA must be a real scalar or a function"); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
229 endif |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
230 ya = @(x) ya * ones (size (x)); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
231 endif |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
232 if (! is_function_handle (yb)) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
233 if (! (isreal (yb) && isscalar (yb))) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
234 error ("integral3: YB must be a real scalar or a function"); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
235 endif |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
236 yb = @(x) yb * ones (size (x)); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
237 endif |
24102
c723faa56ab4
Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
238 |
24148
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
239 ## check upper and lower bounds of z |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
240 if (! is_function_handle (za)) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
241 if (! (isreal (za) && isscalar (za))) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
242 error ("integral3: ZA must be a real scalar or a function"); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
243 endif |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
244 za = @(x, y) za * ones (size(y)); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
245 endif |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
246 if (! is_function_handle (zb)) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
247 if (! (isreal (zb) && isscalar (zb))) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
248 error ("integral3: ZB must be a real scalar or a function") |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
249 endif |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
250 zb = @(x, y) zb * ones (size (y)); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
251 endif |
24102
c723faa56ab4
Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
252 |
24148
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
253 finner = @(x) inner (x, f, ya, yb, za, zb, vectorized, method, abstol, reltol); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
254 q = quadcc (finner, xa, xb, [abstol, reltol]); |
24102
c723faa56ab4
Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
255 |
c723faa56ab4
Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
256 endfunction |
c723faa56ab4
Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
257 |
24148
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
258 function q = inner (x, f, ya, yb, za, zb, vectorized, method, abstol, reltol) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
259 q = zeros (size (x)); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
260 for i = 1 : length (x) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
261 za2 = @(y) za(x(i), y); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
262 zb2 = @(y) zb(x(i), y); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
263 f2 = @(y, z) f(x(i), y, z); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
264 if (! vectorized) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
265 f2 = @(y, z) arrayfun (f2, y, z); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
266 endif |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
267 if (strcmp (method, "iterated")) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
268 finner_iter = @(y) inner_iterated (y, f2, za2, zb2, abstol, reltol); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
269 q(i) = quadcc (finner_iter, ya(x(i)), yb(x(i)), [abstol, reltol]); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
270 else |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
271 q(i) = quad2d (f2, ya(x(i)), yb(x(i)), za2, zb2, |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
272 "AbsTol", abstol, "RelTol", reltol); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
273 endif |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
274 endfor |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
275 endfunction |
24102
c723faa56ab4
Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
276 |
24148
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
277 function q = inner_iterated (y, f2, za2, zb2, abstol, reltol) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
278 q = zeros (size (y)); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
279 for i = 1 : length (y) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
280 q(i) = quadcc (@(z) f2(y(i), z), za2(y(i)), zb2(y(i)), [abstol, reltol]); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
281 endfor |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
282 endfunction |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
283 |
24102
c723faa56ab4
Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
284 |
24148
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
285 ## method tests |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
286 %!shared f |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
287 %! f = @(x, y, z) x .* y .* z; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
288 |
28907
11f1207111c5
maint: Don't use semicolon at end of single-line BIST tests.
Rik <rik@octave.org>
parents:
27923
diff
changeset
|
289 %!assert (integral3 (f, 0, 1, 0, 1, 0, 1), 0.125, 1e-10) |
11f1207111c5
maint: Don't use semicolon at end of single-line BIST tests.
Rik <rik@octave.org>
parents:
27923
diff
changeset
|
290 %!assert (integral3 (f, 0, 1, 0, 1, 0, 1, "method", "tiled"), 0.125, 1e-10) |
11f1207111c5
maint: Don't use semicolon at end of single-line BIST tests.
Rik <rik@octave.org>
parents:
27923
diff
changeset
|
291 %!assert (integral3 (f, 0, 1, 0, 1, 0, 1, "method", "iterated"), 0.125, 1e-10) |
11f1207111c5
maint: Don't use semicolon at end of single-line BIST tests.
Rik <rik@octave.org>
parents:
27923
diff
changeset
|
292 %!assert (integral3 (f, 0, 1, 0, 1, 0, 1, "method", "auto"), 0.125, 1e-10) |
24148
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
293 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
294 ## vectorized = false test |
24102
c723faa56ab4
Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
295 %!test |
24148
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
296 %! f = @(x, y, z) x * y * z; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
297 %! assert (integral3 (f, 0, 1, 0, 1, 0, 1, "vectorized", false), 0.125, 1e-10); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
298 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
299 ## tolerance tests |
24149
1a3229a2f1ab
integral2.m, integral3.m: Clean up BIST tests.
Rik <rik@octave.org>
parents:
24148
diff
changeset
|
300 %!test |
24148
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
301 %! f = @(x, y, z) 2 * x.^2 + 3 * y.^2 + 4 * z.^2; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
302 %!assert (integral3 (f, 0, 5, -5, 0, 0, 5, "AbsTol", 1e-9), 9375, 1e-9) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
303 %!assert (integral3 (f, 0, 5, -5, 0, 0, 5, "RelTol", 1e-5), 9375, -1e-5) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
304 %!assert (integral3 (f, 0, 5, -5, 0, 0, 5, "RelTol", 1e-6, "AbsTol", 1e-9), |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
305 %! 9375, 1e-9) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
306 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
307 ## non-rectangular region |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
308 ## This test is too slow with "iterated" method |
24149
1a3229a2f1ab
integral2.m, integral3.m: Clean up BIST tests.
Rik <rik@octave.org>
parents:
24148
diff
changeset
|
309 %!test |
1a3229a2f1ab
integral2.m, integral3.m: Clean up BIST tests.
Rik <rik@octave.org>
parents:
24148
diff
changeset
|
310 %! f = @(x,y,z) 1 ./ (x + y + z); |
1a3229a2f1ab
integral2.m, integral3.m: Clean up BIST tests.
Rik <rik@octave.org>
parents:
24148
diff
changeset
|
311 %! ymax = @(x) 1 - x; |
1a3229a2f1ab
integral2.m, integral3.m: Clean up BIST tests.
Rik <rik@octave.org>
parents:
24148
diff
changeset
|
312 %! zmax = @(x, y) 1 - x - y; |
1a3229a2f1ab
integral2.m, integral3.m: Clean up BIST tests.
Rik <rik@octave.org>
parents:
24148
diff
changeset
|
313 %! assert (integral3 (f, 0, 1, 0, ymax, 0, zmax, "method", "tiled"), 0.25, 1e-6); |
24102
c723faa56ab4
Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
314 |
c723faa56ab4
Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
315 ## Test input validation |
24148
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
316 %!error integral3 |
24102
c723faa56ab4
Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
317 %!error integral3 (@plus) |
c723faa56ab4
Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
318 %!error integral3 (@plus, 1) |
c723faa56ab4
Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
319 %!error integral3 (@plus, 1, 2) |
c723faa56ab4
Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
320 %!error integral3 (@plus, 1, 2, 3) |
c723faa56ab4
Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
321 %!error integral3 (@plus, 1, 2, 3, 4) |
c723faa56ab4
Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
322 %!error integral3 (@plus, 1, 2, 3, 4, 5) |
c723faa56ab4
Add missing functions integral2.m and integral3.m (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
323 %!error integral3 (@plus, 1, 2, 3, 4, 5, 6, "foo") |
24148
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
324 %!error integral3 (0, 1, 2, 3, 4, 5, 6) # f must be a function handle |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
325 %!error integral3 (@plus, 1i, 2, 3, 4, 5, 6) # real limits |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
326 %!error integral3 (@plus, 1, 2i, 3, 4, 5, 6) # real limits |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
327 %!error integral3 (@plus, [1 1], 2, 3, 4, 5, 6) # scalar limits |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
328 %!error integral3 (@plus, 1, [2 2], 3, 4, 5, 6) # scalar limits |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
329 %!error <property PROP must be a string> |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
330 %! integral3 (@plus, 1, 2, 3, 4, 5, 6, 99, "bar"); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
331 %!error <AbsTol value must be a numeric> |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
332 %! integral3 (@plus, 1, 2, 3, 4, 5, 6, "AbsTol", "foo"); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
333 %!error <AbsTol value must be a .* scalar> |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
334 %! integral3 (@plus, 1, 2, 3, 4, 5, 6, "AbsTol", [1, 2]); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
335 %!error <AbsTol value must be.* .= 0> |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
336 %! integral3 (@plus, 1, 2, 3, 4, 5, 6, "AbsTol", -1); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
337 %!error <RelTol value must be a numeric> |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
338 %! integral3 (@plus, 1, 2, 3, 4, 5, 6, "RelTol", "foo"); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
339 %!error <RelTol value must be a .* scalar> |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
340 %! integral3 (@plus, 1, 2, 3, 4, 5, 6, "RelTol", [1, 2]); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
341 %!error <RelTol value must be.* .= 0> |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
342 %! integral3 (@plus, 1, 2, 3, 4, 5, 6, "RelTol", -1); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
343 %!error <unrecognized method 'foo'> |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
344 %! integral3 (@plus,1,2,3,4,5,6, "method", "foo"); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
345 %!error <Vectorized must be a logical value> |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
346 %! integral3 (@plus,1,2,3,4,5,6, "Vectorized", [0 1]); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
347 %!error <Vectorized must be a logical value> |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
348 %! integral3 (@plus,1,2,3,4,5,6, "Vectorized", {true}); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
349 %!error <unknown property 'foo'> |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
350 %! integral3 (@plus, 1, 2, 3, 4, 6, 6, "foo", "bar"); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
351 %!error <YA must be a real scalar> integral3 (@plus, 1, 2, 3i, 4, 5, 6) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
352 %!error <YA must be a real scalar> integral3 (@plus, 1, 2, [3 3], 4, 5, 6) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
353 %!error <YB must be a real scalar> integral3 (@plus, 1, 2, 3, 4i, 5, 6) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
354 %!error <YB must be a real scalar> integral3 (@plus, 1, 2, 3, [4 4], 5, 6) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
355 %!error <ZA must be a real scalar> integral3 (@plus, 1, 2, 3, 4, 5i, 6) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
356 %!error <ZA must be a real scalar> integral3 (@plus, 1, 2, 3, 4, [5 5], 6) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
357 %!error <ZB must be a real scalar> integral3 (@plus, 1, 2, 3, 4, 5, 6i) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
24102
diff
changeset
|
358 %!error <ZB must be a real scalar> integral3 (@plus, 1, 2, 3, 4, 5, [6 6]) |