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comparison doc/interpreter/quad.txi @ 19630:0e1f5a750d00

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maint: Periodic merge of gui-release to default.
author John W. Eaton <jwe@octave.org>
date Tue, 20 Jan 2015 10:24:46 -0500
parents 0850b5212619 446c46af4b42
children 4197fc428c7d
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19626:37d37297acf8 19630:0e1f5a750d00
4 @c 4 @c
5 @c Octave is free software; you can redistribute it and/or modify it 5 @c Octave is free software; you can redistribute it and/or modify it
6 @c under the terms of the GNU General Public License as published by the 6 @c under the terms of the GNU General Public License as published by the
7 @c Free Software Foundation; either version 3 of the License, or (at 7 @c Free Software Foundation; either version 3 of the License, or (at
8 @c your option) any later version. 8 @c your option) any later version.
9 @c 9 @c
10 @c Octave is distributed in the hope that it will be useful, but WITHOUT 10 @c Octave is distributed in the hope that it will be useful, but WITHOUT
11 @c ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or 11 @c ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
12 @c FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 12 @c FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
13 @c for more details. 13 @c for more details.
14 @c 14 @c
15 @c You should have received a copy of the GNU General Public License 15 @c You should have received a copy of the GNU General Public License
16 @c along with Octave; see the file COPYING. If not, see 16 @c along with Octave; see the file COPYING. If not, see
17 @c <http://www.gnu.org/licenses/>. 17 @c <http://www.gnu.org/licenses/>.
18 18
19 @node Numerical Integration 19 @node Numerical Integration
167 167
168 Sometimes one does not have the function, but only the raw (x, y) points from 168 Sometimes one does not have the function, but only the raw (x, y) points from
169 which to perform an integration. This can occur when collecting data in an 169 which to perform an integration. This can occur when collecting data in an
170 experiment. The @code{trapz} function can integrate these values as shown in 170 experiment. The @code{trapz} function can integrate these values as shown in
171 the following example where "data" has been collected on the cosine function 171 the following example where "data" has been collected on the cosine function
172 over the range [0, pi/2). 172 over the range [0, pi/2).
173 173
174 @example 174 @example
175 @group 175 @group
176 x = 0:0.1:pi/2; # Uniformly spaced points 176 x = 0:0.1:pi/2; # Uniformly spaced points
177 y = cos (x); 177 y = cos (x);
179 @result{} 0.99666 179 @result{} 0.99666
180 @end group 180 @end group
181 @end example 181 @end example
182 182
183 The answer is reasonably close to the exact value of 1. Ordinary quadrature 183 The answer is reasonably close to the exact value of 1. Ordinary quadrature
184 is sensitive to the characteristics of the integrand. Empirical integration 184 is sensitive to the characteristics of the integrand. Empirical integration
185 depends not just on the integrand, but also on the particular points chosen to 185 depends not just on the integrand, but also on the particular points chosen to
186 represent the function. Repeating the example above with the sine function 186 represent the function. Repeating the example above with the sine function
187 over the range [0, pi/2) produces far inferior results. 187 over the range [0, pi/2) produces far inferior results.
188 188
189 @example 189 @example