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[project @ 1996-12-14 16:28:46 by jwe]
author jwe
date Sat, 14 Dec 1996 16:28:46 +0000
parents 140fd45c1b84
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24 other numerical experiments. It may also be used as a batch-oriented 24 other numerical experiments. It may also be used as a batch-oriented
25 language. 25 language.
26 </p> 26 </p>
27 27
28 <h2><a name="Language Features">Language Features</a></h2> 28 <h2><a name="Language Features">Language Features</a></h2>
29 <p>
30 The best way to introduce Octave's language is probably to show a few
31 simple examples.
32 </p>
33
34 <p>
35 If you are new to Octave, I recommend that you try these examples to
36 begin learning Octave by using it. Lines marked with
37 <tt>octave:13></tt> are lines you type, ending each with a carriage
38 return. Octave will respond with an answer, or by displaying a graph.
39 </p>
40
41 <h3>Creating a Matrix</h3>
42
43 <p>
44 To create a new matrix and store it in a variable so that it you can
45 refer to it later, type the command
46
47 <pre>
48 octave:1> a = [ 1, 1, 2; 3, 5, 8; 13, 21, 34 ]
49 </pre>
50
51 Octave will respond by printing the matrix in neatly aligned columns.
52 Ending a command with a semicolon tells Octave to not print the result
53 of a command. For example
54
55 <pre>
56 octave:2> b = rand (3, 2);
57 </pre>
58
59 will create a 3 row, 2 column matrix with each element set to a random
60 value between zero and one.
61 </p>
62
63 <p>
64 To display the value of any variable, simply type the name of the
65 variable. For example, to display the value stored in the matrix
66 <tt>b</tt>, type the command
67
68 <pre>
69 octave:3> b
70 </pre>
71
72 <h3>Matrix Arithmetic</h3>
73
74 <p>
75 Octave has a convenient operator notation for performing matrix
76 arithmetic. For example, to multiply the matrix <tt>a</tt> by a
77 scalar value, type the command
78
79 <pre>
80 octave:4> 2 * a
81 </pre>
82
83 <p>
84 To multiply the two matrices <tt>a</tt> and <tt>b</tt>, type the
85 command
86
87 <pre>
88 octave:5> a * b
89 </pre>
90
91 <p>
92 To form the matrix product <tt>transpose (a) * a</tt>, type the command
93
94 <pre>
95 octave:6> a' * a
96 </pre>
97 </p>
98
99 <h3>Solving Linear Equations</h3>
100
101 <p>
102 To solve the set of linear equations <tt>Ax = b</tt> use the left
103 division operator, <tt>\</tt>:
104
105 <pre>
106 octave:7> a \ b
107 </pre>
108
109 This is conceptually equivalent to <tt>inv (A) * b</tt>, but avoids
110 computing the inverse of a matrix directly.
111 </p>
112
113 <p>
114 If the coefficient matrix is singular, Octave will print a warning
115 message and compute a minimum norm solution.
116 </p>
117
118 <h3>Integrating Differential Equations</h3>
119
120 <p>
121 Octave has built-in functions for solving nonlinear differential
122 equations of the form
123
124 <pre>
125 dx
126 -- = f (x, t)
127 dt
128 </pre>
129
130 with the initial condition
131
132 <pre>
133 x(t = t0) = x0
134 </pre>
135 </p>
136
137 <p>
138 For Octave to integrate equations of this form, you must first provide a
139 definition of the function <tt> f (x, t)</tt>. This is
140 straightforward, and may be accomplished by entering the function body
141 directly on the command line. For example, the following commands
142 define the right hand side function for an interesting pair of
143 nonlinear differential equations. Note that while you are entering a
144 function, Octave responds with a different prompt, to indicate that it
145 is waiting for you to complete your input.
146
147 <pre>
148 octave:8> function xdot = f (x, t)
149 >
150 > r = 0.25;
151 > k = 1.4;
152 > a = 1.5;
153 > b = 0.16;
154 > c = 0.9;
155 > d = 0.8;
156 >
157 > xdot(1) = r*x(1)*(1 - x(1)/k) - a*x(1)*x(2)/(1 + b*x(1));
158 > xdot(2) = c*a*x(1)*x(2)/(1 + b*x(1)) - d*x(2);
159 >
160 > endfunction
161 </pre>
162 </p>
163
164 <p>
165 Given the initial condition
166
167 <pre>
168 x0 = [1; 2];
169 </pre>
170
171 and the set of output times as a column vector (note that the first
172 output time corresponds to the initial condition given above)
173
174 <pre>
175 t = linspace (0, 50, 200)';
176 </pre>
177
178 it is easy to integrate the set of differential equations:
179
180 <pre>
181 x = lsode ("f", x0, t);
182 </pre>
183
184 <p>
185 The function <tt>lsode</tt> uses the Livermore Solver for Ordinary
186 Differential Equations, described in A. C. Hindmarsh, <em>ODEPACK, a
187 Systematized Collection of ODE Solvers</em>, in: Scientific Computing,
188 R. S. Stepleman et al. (Eds.), North-Holland, Amsterdam, 1983, pages
189 55-64.
190 </p>
191
192 <h3>Producing Graphical Output</h3>
193
194 <p>
195 To display the solution of the previous example graphically, use the
196 command
197
198 <pre>
199 plot (t, x)
200 </pre>
201 </p>
202
203 <p>
204 If you are using the X Window System, Octave will automatically create
205 a separate window to display the plot. If you are using a terminal that
206 supports some other graphics commands, you will need to tell Octave what
207 kind of terminal you have. Type the command
208 </p>
209
210 <pre>
211 gset term
212 </pre>
213
214 to see a list of the supported terminal types. Octave uses
215 <tt>gnuplot</tt> to display graphics, and can display graphics on any
216 terminal that is supported by <tt>gnuplot</tt>.
217
218 <p>
219 To capture the output of the plot command in a file rather than sending
220 the output directly to your terminal, you can use a set of commands like
221 this
222
223 <pre>
224 gset term postscript
225 gset output "foo.ps"
226 replot
227 </pre>
228
229 This will work for other types of output devices as well. Octave's
230 <tt>gset</tt> command is really just piped to the <tt>gnuplot</tt>
231 subprocess, so that once you have a plot on the screen that you like,
232 you should be able to do something like this to create an output file
233 suitable for your graphics printer.
234 </p>
235
236 <p>
237 Or, you can eliminate the intermediate file by using commands like this
238
239 <pre>
240 gset term postscript
241 gset output "|lpr -Pname_of_your_graphics_printer"
242 replot
243 </pre>
244
245 <h3>Editing What You Have Typed</h3>
246
247 <p>
248 At the Octave prompt, you can recall, edit, and reissue previous
249 commands using Emacs- or vi-style editing commands. The default
250 keybindings use Emacs-style commands.
251 </p>
252
253 <h3>Getting Help</h3>
254
255 <p>
256 Octave has an extensive help facility. The same documentation that is
257 available in printed form is also available from the Octave prompt,
258 because both forms of the documentation are created from the same input
259 file.
260 </p>
261
262 <p>
263 In order to get good help you first need to know the name of the command
264 that you want to use. This name of the function may not always be
265 obvious, but a good place to start is to just type <tt>help</tt>.
266 This will show you all the operators, reserved words, functions,
267 built-in variables, and function files. You can then get more
268 help on anything that is listed by simply including the name as an
269 argument to help. For example,
270
271 <pre>
272 help plot
273 </pre>
274
275 will display the help text for the <tt>plot</tt> function.
276 </p>
277
278 <p>
279 The complete text of the manual is availabe from Octave's command line
280 using the command <tt>help -i</tt>. Because it is written in Texinfo,
281 it is also possible to put
282 <a href="http://www.che.wisc.edu/cgi-bin/info2www?(octave)">the manual
283 on the WWW</a>.
284 </p>
29 285
30 <h2><a name="Distribution Terms">Distribution Terms</a></h2> 286 <h2><a name="Distribution Terms">Distribution Terms</a></h2>
31 <p> 287 <p>
32 Octave is free software; you can redistribute it and/or modify it 288 Octave is free software; you can redistribute it and/or modify it
33 under the terms of the 289 under the terms of the