Mercurial > octave
annotate scripts/general/quad2d.m @ 27919:1891570abac8
update Octave Project Developers copyright for the new year
In files that have the "Octave Project Developers" copyright notice,
update for 2020.
author | John W. Eaton <jwe@octave.org> |
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date | Mon, 06 Jan 2020 22:29:51 -0500 |
parents | b442ec6dda5c |
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27919
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update Octave Project Developers copyright for the new year
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1 ## Copyright (C) 2017-2020 The Octave Project Developers |
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2 ## |
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3 ## See the file COPYRIGHT.md in the top-level directory of this distribution |
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4 ## or <https://octave.org/COPYRIGHT.html/>. |
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5 ## |
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6 ## |
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7 ## This file is part of Octave. |
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8 ## |
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9 ## Octave is free software: you can redistribute it and/or modify it |
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10 ## under the terms of the GNU General Public License as published by |
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11 ## the Free Software Foundation, either version 3 of the License, or |
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12 ## (at your option) any later version. |
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13 ## |
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14 ## Octave is distributed in the hope that it will be useful, but |
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15 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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16 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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17 ## GNU General Public License for more details. |
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18 ## |
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19 ## You should have received a copy of the GNU General Public License |
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20 ## along with Octave; see the file COPYING. If not, see |
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21 ## <https://www.gnu.org/licenses/>. |
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22 |
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23 ## -*- texinfo -*- |
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24 ## @deftypefn {} {@var{q} =} quad2d (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}) |
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25 ## @deftypefnx {} {@var{q} =} quad2d (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{prop}, @var{val}, @dots{}) |
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26 ## @deftypefnx {} {[@var{q}, @var{err}, @var{iter}] =} quad2d (@dots{}) |
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27 ## |
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28 ## Numerically evaluate the two-dimensional integral of @var{f} using adaptive |
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29 ## quadrature over the two-dimensional domain defined by @var{xa}, @var{xb}, |
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30 ## @var{ya}, @var{yb} using tiled integration. Additionally, @var{ya} and |
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31 ## @var{yb} may be scalar functions of @var{x}, allowing for the integration |
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32 ## over non-rectangular domains. |
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33 ## |
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34 ## @var{f} is a function handle, inline function, or string containing the name |
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35 ## of the function to evaluate. The function @var{f} must be of the form |
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36 ## @math{z = f(x,y)} where @var{x} is a vector and @var{y} is a scalar. It |
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37 ## should return a vector of the same length and orientation as @var{x}. |
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38 ## |
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39 ## Additional optional parameters can be specified using |
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40 ## @qcode{"@var{property}", @var{value}} pairs. Valid properties are: |
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41 ## |
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42 ## @table @code |
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43 ## @item AbsTol |
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44 ## Define the absolute error tolerance for the quadrature. The default |
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45 ## value is 1e-10 (1e-5 for single). |
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46 ## |
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47 ## @item RelTol |
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48 ## Define the relative error tolerance for the quadrature. The default |
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49 ## value is 1e-6 (1e-4 for single). |
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50 ## |
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51 ## @item MaxFunEvals |
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52 ## The maximum number of function calls to the vectorized function @var{f}. |
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53 ## The default value is 5000. |
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54 ## |
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55 ## @item Singular |
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56 ## Enable/disable transforms to weaken singularities on the edge of the |
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57 ## integration domain. The default value is @var{true}. |
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58 ## |
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59 ## @item Vectorized |
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60 ## Option to disable vectorized integration, forcing Octave to use only scalar |
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61 ## inputs when calling the integrand. The default value is @var{false}. |
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62 ## |
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63 ## @item FailurePlot |
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64 ## If @code{quad2d} fails to converge to the desired error tolerance before |
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65 ## MaxFunEvals is reached, a plot of the areas that still need refinement |
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66 ## is created. The default value is @var{false}. |
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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 ## The optional output @var{err} is an approximate bound on the error in the |
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85 ## integral @code{abs (@var{q} - @var{I})}, where @var{I} is the exact value |
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86 ## of the integral. The optional output @var{iter} is the number of vectorized |
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87 ## function calls to the function @var{f} that were used. |
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88 ## |
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89 ## Example 1 : integrate a rectangular region in x-y plane |
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90 ## |
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91 ## @example |
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92 ## @group |
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93 ## @var{f} = @@(@var{x},@var{y}) 2*ones (size (@var{x})); |
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94 ## @var{q} = quad2d (@var{f}, 0, 1, 0, 1) |
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95 ## @result{} @var{q} = 2 |
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96 ## @end group |
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97 ## @end example |
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98 ## |
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99 ## The result is a volume, which for this constant-value integrand, is just |
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100 ## @code{@var{Length} * @var{Width} * @var{Height}}. |
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101 ## |
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102 ## Example 2 : integrate a triangular region in x-y plane |
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103 ## |
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104 ## @example |
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105 ## @group |
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106 ## @var{f} = @@(@var{x},@var{y}) 2*ones (size (@var{x})); |
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107 ## @var{ymax} = @@(@var{x}) 1 - @var{x}; |
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108 ## @var{q} = quad2d (@var{f}, 0, 1, 0, @var{ymax}) |
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109 ## @result{} @var{q} = 1 |
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110 ## @end group |
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111 ## @end example |
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112 ## |
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113 ## The result is a volume, which for this constant-value integrand, is the |
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114 ## Triangle Area x Height or |
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115 ## @code{1/2 * @var{Base} * @var{Width} * @var{Height}}. |
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116 ## |
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117 ## Programming Notes: If there are singularities within the integration region |
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118 ## it is best to split the integral and place the singularities on the |
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119 ## boundary. |
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120 ## |
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121 ## Known @sc{matlab} incompatibility: If tolerances are left unspecified, and |
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122 ## any integration limits are of type @code{single}, then Octave's integral |
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123 ## functions automatically reduce the default absolute and relative error |
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124 ## tolerances as specified above. If tighter tolerances are desired they |
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125 ## must be specified. @sc{matlab} leaves the tighter tolerances appropriate |
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126 ## for @code{double} inputs in place regardless of the class of the |
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127 ## integration limits. |
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128 ## |
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129 ## Reference: @nospell{L.F. Shampine}, |
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130 ## @cite{@sc{matlab} program for quadrature in 2D}, Applied Mathematics and |
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131 ## Computation, pp.@: 266--274, Vol 1, 2008. |
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132 ## |
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133 ## @seealso{integral2, dblquad, integral, quad, quadgk, quadv, quadl, quadcc, |
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134 ## trapz, integral3, triplequad} |
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135 ## @end deftypefn |
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136 |
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137 function [q, err, iter] = quad2d (f, xa, xb, ya, yb, varargin) |
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138 |
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139 if (nargin < 5 || mod (nargin, 2) == 0) |
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140 print_usage (); |
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141 endif |
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142 |
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143 if (ischar (f)) |
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144 ## Convert function given as a string to a function handle |
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145 f = @(x) feval (f, x); |
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146 elseif (! is_function_handle (f)) |
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147 print_usage (); |
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148 endif |
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149 |
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150 if (! (isreal (xa) && isscalar (xa) && isreal (xb) && isscalar (xb))) |
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151 print_usage (); |
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152 endif |
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153 |
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154 ## Check for single or double limits to set appropriate default tolerance. |
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155 issingle = (isa ([xa, xb], "single") |
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156 || (! is_function_handle (ya) && isa (ya, "single")) |
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157 || (! is_function_handle (yb) && isa (yb, "single"))); |
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158 |
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159 ## Set defaults, update with any specified parameters. |
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160 if (issingle) |
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161 abstol = 1e-5; |
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162 reltol = 1e-4; |
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163 else |
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164 abstol = 1e-10; |
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165 reltol = 1e-6; |
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166 endif |
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167 |
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168 vectorized = true; |
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169 singular = true; |
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170 idx = 1; |
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171 maxiter = 5000; |
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172 failureplot = false; |
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173 |
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174 while (idx < nargin - 5) |
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175 prop = varargin{idx++}; |
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176 if (! ischar (prop)) |
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177 error ("quad2d: property PROP must be a string"); |
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178 endif |
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179 |
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180 switch (tolower (prop)) |
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181 case "abstol" |
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182 abstol = varargin{idx++}; |
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183 if (! (isnumeric (abstol) && isscalar (abstol) && abstol >= 0)) |
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184 error ("quad2d: AbsTol value must be a numeric scalar >= 0"); |
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185 endif |
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186 |
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187 case "reltol" |
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188 reltol = varargin{idx++}; |
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189 if (! (isnumeric (reltol) && isscalar (reltol) && reltol >= 0)) |
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190 error ("quad2d: RelTol value must be a numeric scalar >= 0"); |
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191 endif |
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192 |
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193 case "maxfunevals" |
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194 maxiter = varargin{idx++}; |
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195 if (! (isnumeric (maxiter) && isscalar (maxiter) |
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196 && fix (maxiter) == maxiter && maxiter >= 1)) |
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197 error ("quad2d: MaxFunEvals value must be a scalar integer >= 1"); |
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198 endif |
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Updated integral2.m and integral3.m and added quad2d (bug #52074).
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parents:
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changeset
|
199 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
200 case "singular" |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
201 singular = varargin{idx++}; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
202 if (! (isscalar (singular) && isreal (singular))) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
203 error ("quad2d: Singular must be a logical value"); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
204 endif |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
205 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
206 case "vectorized" |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
207 vectorized = varargin{idx++}; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
208 if (! (isscalar (vectorized) && isreal (vectorized))) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
209 error ("quad2d: 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:
diff
changeset
|
210 endif |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
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|
211 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
212 case "failureplot" |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
213 failureplot = varargin{idx++}; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
214 if (! (isscalar (failureplot) && isreal (failureplot))) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
215 error ("quad2d: FailurePlot must be a logical value"); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
216 endif |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
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|
217 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
218 otherwise |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
219 error ("quad2d: unknown property '%s'", prop); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
220 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
221 endswitch |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
222 endwhile |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
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|
223 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
224 if (! vectorized) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
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|
225 f = @(x, y) arrayfun (f, x, y); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
226 endif |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
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|
227 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
228 ## 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:
diff
changeset
|
229 if (! is_function_handle (ya)) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
230 if (! (isreal (ya) && isscalar (ya))) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
231 error ("quad2d: 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:
diff
changeset
|
232 endif |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
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|
233 ya = @(x) ya * ones(rows (x), columns (x)); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
234 endif |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
235 if (! is_function_handle (yb)) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
236 if (! (isreal (yb) && isscalar (yb))) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
237 error ("quad2d: 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:
diff
changeset
|
238 endif |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
239 yb = @(x) yb * ones(rows (x), columns (x)); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
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|
240 endif |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
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|
241 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
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|
242 iter = 0; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
243 qaccept = 0; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
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changeset
|
244 qerraccept = 0; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
245 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
246 if (singular) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
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|
247 ## Shampine suggests using the singularity weakening transform |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
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|
248 ## suggested by Havie. |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
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|
249 ## \int_a^b f(x) dx = \int_0^pi f (g(t)) (dx / dt) dt |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
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|
250 ## where |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
251 ## g(t) = ((a - b) * cos(t) + (a + b)) / 2 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
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|
252 ## dx = - (a - b) * sin(t) / 2 dt |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
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|
253 ## Now our integral is |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
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parents:
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|
254 ## \int_a^b \int_0^1 f(x,y) dydx |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
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|
255 ## as we already subsitute for "y", so |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
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|
256 ## gx(tx) = ((a - b) * cos(tx) + (a + b)) / 2 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
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parents:
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changeset
|
257 ## gy(ty) = (1 - cos(ty)) / 2 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
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|
258 ## dydx = (b - a) * sin(tx) * sin(ty) / 4 dtydtx |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
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parents:
diff
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|
259 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
260 xtrans = @(tx) ((xa - xb) .* cos (tx) + (xa + xb)) ./ 2; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
261 ytrans = @(ty) (1 - cos (ty)) ./ 2; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
262 ztrans = @(tx, ty) (xb - xa) .* sin(tx) .* sin(ty) ./ 4; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
263 area = pi ^ 2; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
264 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
265 ## Initialize tile list |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
266 tilelist(1) = struct ("xa", 0, "xb", pi, "ya", 0, "yb", pi, ... |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
267 "q", 0, "qerr", Inf); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
268 else |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
269 xtrans = @(tx) tx; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
270 ytrans = @(ty) ty; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
271 ztrans = @(tx, ty) 1; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
272 area = (xb - xa); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
273 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
274 ## Initialize tile list |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
275 tilelist(1) = struct ("xa", xa, "xb", xb, "ya", 0, "yb", 1, ... |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
276 "q", 0, "qerr", Inf); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
277 endif |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
278 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
279 while (length (tilelist) > 0 && iter < maxiter) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
280 ## Get tile with the largest error |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
281 [~, idx] = max ([tilelist.qerr]); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
282 tile = tilelist(idx); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
283 tilelist(idx) = []; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
284 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
285 ## Subdivide the tile into 4 subtiles |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
286 iter += 4; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
287 tiles(4) = struct ("xa", tile.xa, "xb", tile.xa + (tile.xb - tile.xa) / 2, |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
288 "ya", tile.ya, "yb", tile.ya + (tile.yb - tile.ya) / 2, |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
289 "q", 0, "qerr", 0); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
290 tiles(3) = struct ("xa", tile.xa, "xb", tile.xa + (tile.xb - tile.xa) / 2, |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
291 "ya", tile.ya + (tile.yb - tile.ya) / 2, "yb", tile.yb, |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
292 "q", 0, "qerr", 0); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
293 tiles(2) = struct ("xa", tile.xa + (tile.xb - tile.xa) / 2, "xb", tile.xb, |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
294 "ya", tile.ya, "yb", tile.ya + (tile.yb - tile.ya) / 2, |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
295 "q", 0, "qerr", 0); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
296 tiles(1) = struct ("xa", tile.xa + (tile.xb - tile.xa) / 2, "xb", tile.xb, |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
297 "ya", tile.ya + (tile.yb - tile.ya) / 2, "yb", tile.yb, |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
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|
298 "q", 0, "qerr", 0); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
299 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
300 ## Perform the quadrature of 4 subtiles |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
301 for i = 1:4 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
302 [tiles(i).q, tiles(i).qerr] = ... |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
303 tensorproduct (f, ya, yb, tiles(i), xtrans, ytrans, ztrans, singular); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
304 endfor |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
305 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
306 q = qaccept + sum ([[tilelist.q], tiles.q]); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
307 err = qerraccept + sum ([[tilelist.qerr], tiles.qerr]); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
308 tol = max (abstol, reltol .* abs (q)); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
309 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
310 ## Shampine suggests taking a margin of a factor of 8 for |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
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|
311 ## the local tolerance. That, and the fact that we are subdividing |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
312 ## into 4 tiles, means we divide by 32 at this point. |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
313 localtol = tol * ([tile.xb] - [tile.xa]) * ([tile.yb] - [tile.ya]) ... |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
314 / area / 32; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
315 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
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|
316 ## If global tolerance is met, return. |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
317 if (err < tol) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
318 break; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
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|
319 endif |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
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|
320 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
321 ## Accept the tiles meeting the tolerance, and add the others back to |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
322 ## the list of tiles to treat. |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
323 idx = find ([tiles.qerr] < localtol); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
324 qaccept += sum ([tiles(idx).q]); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
325 qerraccept += sum ([tiles(idx).qerr]); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
326 tiles(idx) = []; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
327 tilelist = [tilelist, tiles]; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
328 endwhile |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
329 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
330 ## Verify convergence |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
331 if (iter >= maxiter) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
332 if (err > max (abstol, reltol .* abs (q))) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
333 warning (["quad2d: " ... |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
334 "Maximum number of sub-tiles reached without convergence"]); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
335 else |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
336 warning (["quad2d: " ... |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
337 "Maximum number of sub-tiles reached, accuracy may be low"]); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
338 endif |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
339 if (failureplot) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
340 newplot (); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
341 title ("quad2d : Areas needing refinement"); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
342 for tile = tilelist |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
343 xaa = xtrans(tile.xa); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
344 xbb = xtrans(tile.xb); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
345 y1 = ya(xaa) + ytrans(tile.ya) * (yb(xaa) - ya(xaa)); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
346 y2 = ya(xaa) + ytrans(tile.yb) * (yb(xaa) - ya(xaa)); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
347 y3 = ya(xbb) + ytrans(tile.yb) * (yb(xbb) - ya(xbb)); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
348 y4 = ya(xbb) + ytrans(tile.ya) * (yb(xbb) - ya(xbb)); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
349 patch ([xaa, xaa, xbb, xbb, xaa], [y1, y2, y3, y4, y1], "b"); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
350 endfor |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
351 endif |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
352 endif |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
353 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
354 endfunction |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
355 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
356 function [q, qerr] = tensorproduct (f, ya, yb, tile, xtrans, ytrans, ztrans, singular) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
357 ## The Shampine TwoD paper proposes using a G3,K7 rule in a tensor product. |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
358 ## I couldn't find a tabulated abscissas and weights of a G3,K7 rule publicly |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
359 ## available, so use a G7,K15 rule from Octave's implementation of quadgk. |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
360 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
361 persistent abscissa = [-0.9914553711208126e+00, -0.9491079123427585e+00, ... |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
362 -0.8648644233597691e+00, -0.7415311855993944e+00, ... |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
363 -0.5860872354676911e+00, -0.4058451513773972e+00, ... |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
364 -0.2077849550078985e+00, 0.0000000000000000e+00, ... |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
365 0.2077849550078985e+00, 0.4058451513773972e+00, ... |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
366 0.5860872354676911e+00, 0.7415311855993944e+00, ... |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
367 0.8648644233597691e+00, 0.9491079123427585e+00, ... |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
368 0.9914553711208126e+00]; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
369 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
370 persistent weights15 = [0.2293532201052922e-01, 0.6309209262997855e-01, ... |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
371 0.1047900103222502e+00, 0.1406532597155259e+00, ... |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
372 0.1690047266392679e+00, 0.1903505780647854e+00, ... |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
373 0.2044329400752989e+00, 0.2094821410847278e+00, ... |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
374 0.2044329400752989e+00, 0.1903505780647854e+00, ... |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
375 0.1690047266392679e+00, 0.1406532597155259e+00, ... |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
376 0.1047900103222502e+00, 0.6309209262997855e-01, ... |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
377 0.2293532201052922e-01]; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
378 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
379 persistent weights7 = [0.0, ... |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
380 0.1294849661688697e+00, 0.0, ... |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
381 0.2797053914892767e+00, 0.0, ... |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
382 0.3818300505051889e+00, 0.0, ... |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
383 0.4179591836734694e+00, 0.0, ... |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
384 0.3818300505051889e+00, 0.0, ... |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
385 0.2797053914892767e+00, 0.0, ... |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
386 0.1294849661688697e+00, 0.0]; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
387 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
388 xaa = tile.xa; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
389 xbb = tile.xb; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
390 yaa = tile.ya; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
391 ybb = tile.yb; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
392 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
393 tx = ((xbb - xaa) * abscissa + xaa + xbb) / 2; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
394 x = xtrans(tx); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
395 ty = (abscissa' * (ybb - yaa) + yaa + ybb) / 2; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
396 y = ones (15, 1) * ya(x) + ytrans(ty) * (yb(x) - ya(x)); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
397 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
398 xhalfwidth = (xbb - xaa ) / 2; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
399 yhalfwidth = ones (15, 1) * (yb(x) - ya(x)) .* (ybb - yaa) ./ 2; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
400 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
401 x = ones (15, 1) * x; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
402 tx = ones (15,1) * tx; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
403 ty = ty * ones (1, 15); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
404 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
405 z = yhalfwidth .* f (x, y) .* ztrans(tx, ty) .* xhalfwidth; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
406 q = weights15 * (weights15 * z)'; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
407 qerr = abs (weights7 * (weights7 * z)' - q); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
408 endfunction |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
409 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
410 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
411 %!shared f |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
412 %! f = @(x, y) x .* y; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
413 %!assert (quad2d (f, 0, 1, 0, 1), 0.25, 1e-10) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
414 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
415 %!test |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
416 %! f = @(x, y) 9 * x.^2 + 15 * y.^2; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
417 %!assert (quad2d (f, 0, 5, -5, 0, "AbsTol", 1e-9), 5000, 1e-9) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
418 %!assert (quad2d (f, 0, 5, -5, 0, "RelTol", 1e-6), 5000, -1e-6) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
419 %!assert (quad2d (f, 0, 5, -5, 0, "RelTol", 1e-6, "AbsTol", 1e-9), 5000, 1e-9) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
420 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
421 ## tests from dblquad |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
422 %!test |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
423 %! f = @(x, y) 1 ./ (x+y); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
424 %!assert (quad2d (f, 0, 1, 0, 1, "AbsTol", 1e-7), 2*log (2), 1e-7) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
425 %!assert (quad2d (f, 0, 1, 0, 1, "RelTol", 1e-5), 2*log (2), -1e-5) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
426 %!assert (quad2d (f, 0, 1, 0, 1, "AbsTol", 1e-8, "RelTol", 1e-6), |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
427 %! 2*log (2), -1e-6) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
428 %!assert (quad2d (f, 0, 1, 0, @(x) 1 - x), 1, -1e-6) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
429 %!assert (quad2d (f, 0, 1, 0, @(x) 1 - x, "Singular", true), 1, -1e-6) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
430 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
431 %!assert (quad2d (@(x, y) exp (-x.^2 - y.^2) , -1, 1, -1, 1), |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
432 %! pi * erf (1).^2, 1e-10) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
433 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
434 %!assert (quad2d (@plus, 1, 2, 3, 4), 5, 1e-10) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
435 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
436 ## Test input validation |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
437 %!error quad2d () |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
438 %!error quad2d (@plus) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
439 %!error quad2d (@plus, 1) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
440 %!error quad2d (@plus, 1, 2) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
441 %!error quad2d (@plus, 1, 2, 3) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
442 %!error quad2d (@plus, 1, 2, 3, 4, "foo") |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
443 %!error quad2d (0, 1, 2, 3, 4) # f must be function handle |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
444 %!error quad2d (@plus, 1i, 2, 3, 4) # real limits |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
445 %!error quad2d (@plus, 1, 2i, 3, 4) # real limits |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
446 %!error quad2d (@plus, [1 1], 2, 3, 4) # scalar limits |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
447 %!error quad2d (@plus, 1, [2 2], 3, 4) # scalar limits |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
448 %!error <property PROP must be a string> quad2d (@plus, 1, 2, 3, 4, 99, "bar") |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
449 %!error <AbsTol value must be a numeric> quad2d (@plus, 1, 2, 3, 4, "AbsTol", "foo") |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
450 %!error <AbsTol value must be a .* scalar> quad2d (@plus, 1, 2, 3, 4, "AbsTol", [1, 2]) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
451 %!error <AbsTol value must be.* .= 0> quad2d (@plus, 1, 2, 3, 4, "AbsTol", -1) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
452 %!error <RelTol value must be a numeric> quad2d (@plus, 1, 2, 3, 4, "RelTol", "foo") |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
453 %!error <RelTol value must be a .* scalar> quad2d (@plus, 1, 2, 3, 4, "RelTol", [1, 2]) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
454 %!error <RelTol value must be.* .= 0> quad2d (@plus, 1, 2, 3, 4, "RelTol", -1) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
455 %!error <MaxFunEvals value must be a scalar integer> |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
456 %! quad2d (@plus,1,2,3,4, "MaxFunEvals", {1}); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
457 %!error <MaxFunEvals value must be a scalar integer> |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
458 %! quad2d (@plus,1,2,3,4, "MaxFunEvals", [1 1]); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
459 %!error <MaxFunEvals value must be a scalar integer> |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
460 %! quad2d (@plus,1,2,3,4, "MaxFunEvals", 1.5); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
461 %!error <MaxFunEvals value must be a scalar integer .= 1> |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
462 %! quad2d (@plus,1,2,3,4, "MaxFunEvals", -1); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
463 %!error <Singular must be a logical value> |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
464 %! quad2d (@plus,1,2,3,4, "Singular", [0 1]); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
465 %!error <Singular must be a logical value> |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
466 %! quad2d (@plus,1,2,3,4, "Singular", {true}); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
467 %!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:
diff
changeset
|
468 %! quad2d (@plus,1,2,3,4, "Vectorized", [0 1]); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
469 %!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:
diff
changeset
|
470 %! quad2d (@plus,1,2,3,4, "Vectorized", {true}); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
471 %!error <FailurePlot must be a logical value> |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
472 %! quad2d (@plus,1,2,3,4, "FailurePlot", [0 1]); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
473 %!error <FailurePlot must be a logical value> |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
474 %! quad2d (@plus,1,2,3,4, "FailurePlot", {true}); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
475 %!error <unknown property 'foo'> quad2d (@plus, 1, 2, 3, 4, "foo", "bar") |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
476 %!error <YA must be a real scalar> quad2d (@plus, 1, 2, 3i, 4) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
477 %!error <YA must be a real scalar> quad2d (@plus, 1, 2, [3 3], 4) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
478 %!error <YB must be a real scalar> quad2d (@plus, 1, 2, 3, 4i) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
479 %!error <YB must be a real scalar> quad2d (@plus, 1, 2, 3, [4 4]) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
480 %!warning <Maximum number of> quad2d (@plus, 1, 2, 3, 4, "MaxFunEvals", 1); |