Mercurial > octave
annotate scripts/general/quad2d.m @ 27918:b442ec6dda5c
use centralized file for copyright info for individual contributors
* COPYRIGHT.md: New file.
* In most other files, use "Copyright (C) YYYY-YYYY The Octave Project
Developers" instead of tracking individual names in separate source
files. The motivation is to reduce the effort required to update the
notices each year.
Until now, the Octave source files contained copyright notices that
list individual contributors. I adopted these file-scope copyright
notices because that is what everyone was doing 30 years ago in the
days before distributed version control systems. But now, with many
contributors and modern version control systems, having these
file-scope copyright notices causes trouble when we update copyright
years or refactor code.
Over time, the file-scope copyright notices may become outdated as new
contributions are made or code is moved from one file to
another. Sometimes people contribute significant patches but do not
add a line claiming copyright. Other times, people add a copyright
notice for their contribution but then a later refactoring moves part
or all of their contribution to another file and the notice is not
moved with the code. As a practical matter, moving such notices is
difficult -- determining what parts are due to a particular
contributor requires a time-consuming search through the project
history. Even managing the yearly update of copyright years is
problematic. We have some contributors who are no longer
living. Should we update the copyright dates for their contributions
when we release new versions? Probably not, but we do still want to
claim copyright for the project as a whole.
To minimize the difficulty of maintaining the copyright notices, I
would like to change Octave's sources to use what is described here:
https://softwarefreedom.org/resources/2012/ManagingCopyrightInformation.html
in the section "Maintaining centralized copyright notices":
The centralized notice approach consolidates all copyright
notices in a single location, usually a top-level file.
This file should contain all of the copyright notices
provided project contributors, unless the contribution was
clearly insignificant. It may also credit -- without a copyright
notice -- anyone who helped with the project but did not
contribute code or other copyrighted material.
This approach captures less information about contributions
within individual files, recognizing that the DVCS is better
equipped to record those details. As we mentioned before, it
does have one disadvantage as compared to the file-scope
approach: if a single file is separated from the distribution,
the recipient won't see the contributors' copyright notices.
But this can be easily remedied by including a single
copyright notice in each file's header, pointing to the
top-level file:
Copyright YYYY-YYYY The Octave Project Developers
See the COPYRIGHT file at the top-level directory
of this distribution or at https://octave.org/COPYRIGHT.html.
followed by the usual GPL copyright statement.
For more background, see the discussion here:
https://lists.gnu.org/archive/html/octave-maintainers/2020-01/msg00009.html
Most files in the following directories have been skipped intentinally
in this changeset:
doc
libgui/qterminal
liboctave/external
m4
author | John W. Eaton <jwe@octave.org> |
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date | Mon, 06 Jan 2020 15:38:17 -0500 |
parents | 5a6a19a4e3da |
children | 1891570abac8 |
rev | line source |
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1 ## Copyright (C) 2017-2019 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)) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
190 error ("quad2d: RelTol value must be a numeric scalar >= 0"); |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
191 endif |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
192 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
193 case "maxfunevals" |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
194 maxiter = varargin{idx++}; |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
195 if (! (isnumeric (maxiter) && isscalar (maxiter) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
196 && fix (maxiter) == maxiter && maxiter >= 1)) |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
197 error ("quad2d: 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
|
198 endif |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
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
changeset
|
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
changeset
|
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
changeset
|
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
changeset
|
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
changeset
|
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:
diff
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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
changeset
|
240 endif |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
241 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
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:
diff
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:
diff
changeset
|
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:
diff
changeset
|
248 ## suggested by Havie. |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
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
changeset
|
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:
diff
changeset
|
252 ## dx = - (a - b) * sin(t) / 2 dt |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
253 ## Now our integral is |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
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:
diff
changeset
|
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
changeset
|
256 ## gx(tx) = ((a - b) * cos(tx) + (a + b)) / 2 |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
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
changeset
|
258 ## dydx = (b - a) * sin(tx) * sin(ty) / 4 dtydtx |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
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
changeset
|
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
changeset
|
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
changeset
|
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
changeset
|
319 endif |
2e64bed0bb3a
Updated integral2.m and integral3.m and added quad2d (bug #52074).
Nicholas R. Jankowski <jankowskin@asme.org>
parents:
diff
changeset
|
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); |