annotate doc/interpreter/intro.txi @ 10828:322f43e0e170

Grammarcheck .txi documentation files.
author Rik <octave@nomad.inbox5.com>
date Wed, 28 Jul 2010 12:45:04 -0700
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1 @c Copyright (C) 1996, 1997, 2007, 2008, 2009 John W. Eaton
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2 @c
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3 @c This file is part of Octave.
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4 @c
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5 @c Octave is free software; you can redistribute it and/or modify it
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6 @c under the terms of the GNU General Public License as published by the
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7 @c Free Software Foundation; either version 3 of the License, or (at
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8 @c your option) any later version.
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9 @c
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10 @c Octave is distributed in the hope that it will be useful, but WITHOUT
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11 @c ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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12 @c FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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13 @c for more details.
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14 @c
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15 @c You should have received a copy of the GNU General Public License
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16 @c along with Octave; see the file COPYING. If not, see
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17 @c <http://www.gnu.org/licenses/>.
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18
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19 @node Introduction
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20 @chapter A Brief Introduction to Octave
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21 @cindex introduction
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22
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23 GNU Octave is a high-level language, primarily intended for numerical
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24 computations. It provides a convenient interactive command line
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25 interface for solving linear and nonlinear problems numerically, and
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26 for performing other numerical experiments. It may also be used as a
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27 batch-oriented language for data processing.
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28
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29 GNU Octave is freely redistributable software. You may redistribute
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30 it and/or modify it under the terms of the GNU General Public License
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31 as published by the Free Software Foundation. The GPL is included in
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32 this manual in @ref{Copying}.
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33
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34 This manual provides comprehensive documentation on how to install,
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35 run, use, and extend GNU Octave. Additional chapters describe how
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36 to report bugs and help contribute code.
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37
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38 This document corresponds to Octave version @value{VERSION}.
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39
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40 @menu
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41 * Running Octave::
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42 * Simple Examples::
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43 * Conventions::
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44 @end menu
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45
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46 @node Running Octave
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47 @section Running Octave
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48
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49 On most systems, Octave is started with the shell command
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50 @samp{octave}. Octave displays an initial message and then a prompt
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51 indicating it is ready to accept input. You can begin typing Octave
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52 commands immediately afterward.
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53
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54 If you get into trouble, you can usually interrupt Octave by typing
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55 @kbd{Control-C} (written @kbd{C-c} for short). @kbd{C-c} gets
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56 its name from the fact that you type it by holding down @key{CTRL} and
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57 then pressing @key{c}. Doing this will normally return you to Octave's
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58 prompt.
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59
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60 @cindex exiting octave
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61 @cindex quitting octave
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62 To exit Octave, type @kbd{quit}, or @kbd{exit} at the Octave prompt.
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63
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64 On systems that support job control, you can suspend Octave by sending
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65 it a @code{SIGTSTP} signal, usually by typing @kbd{C-z}.
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66
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67 @node Simple Examples
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68 @section Simple Examples
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69
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70 The following chapters describe all of Octave's features in detail, but
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71 before doing that, it might be helpful to give a sampling of some of its
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72 capabilities.
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73
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74 If you are new to Octave, I recommend that you try these examples to
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75 begin learning Octave by using it. Lines marked like so, @samp{octave:13>},
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76 are lines you type, ending each with a carriage return. Octave will
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77 respond with an answer, or by displaying a graph.
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78
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79 @subsection Elementary Calculations
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80
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81 Octave can easily be used for basic numerical calculations. Octave
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82 knows about arithmetic operations (+,-,*,/), exponentiation (^),
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83 natural logarithms/exponents (log, exp), and the trigonometric
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84 functions (sin, cos, @dots{}). Moreover, Octave calculations work
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85 on real or imaginary numbers (i,j). In addition, some mathematical
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86 constants such as the base of the natural logarithm (e) and the ratio
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87 of a circle's circumference to its diameter (pi) are pre-defined.
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88
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89 @noindent
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90 For example, to verify Euler's Identity,
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91 @tex
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92 $$e^{\imath\pi} = -1$$
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93 @end tex
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94 @ifnottex
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95 @display
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96
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97 i*pi
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98 e = -1
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99 @end display
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100 @end ifnottex
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101
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102 @noindent
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103 type the following which will evaluate to @code{-1} within the
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104 tolerance of the calculation.
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105
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106 @example
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107 octave:1> exp(i*pi)
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108 @end example
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109
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110 @subsection Creating a Matrix
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111
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112 Vectors and matrices are the basic building blocks for numerical analysis.
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113 To create a new matrix and store it in a variable so that you can
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114 refer to it later, type the command
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115
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116 @example
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117 octave:1> A = [ 1, 1, 2; 3, 5, 8; 13, 21, 34 ]
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118 @end example
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119
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120 @noindent
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121 Octave will respond by printing the matrix in neatly aligned columns.
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122 Octave uses a comma or space to separate entries in a row, and a
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123 semicolon or carriage return to separate one row from the next.
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124 Ending a command with a semicolon tells Octave not to print the result
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125 of the command. For example,
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126
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127 @example
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128 octave:2> B = rand (3, 2);
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129 @end example
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130
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131 @noindent
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132 will create a 3 row, 2 column matrix with each element set to a random
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133 value between zero and one.
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134
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135 To display the value of a variable, simply type the name of the
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136 variable at the prompt. For example, to display the value stored in the
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137 matrix @code{B}, type the command
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138
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139 @example
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140 octave:3> B
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141 @end example
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142
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143 @subsection Matrix Arithmetic
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144
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145 Octave has a convenient operator notation for performing matrix
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146 arithmetic. For example, to multiply the matrix @code{A} by a scalar
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147 value, type the command
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148
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149 @example
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150 octave:4> 2 * A
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151 @end example
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152
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153 @noindent
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154 To multiply the two matrices @code{A} and @code{B}, type the command
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155
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156 @example
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157 octave:5> A * B
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158 @end example
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159
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160 @noindent
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161 and to form the matrix product
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162 @tex
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163 $@code{A}^T@code{A}$,
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164 @end tex
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165 @ifnottex
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166 @code{transpose (A) * A},
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167 @end ifnottex
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168 type the command
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169
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170 @example
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171 octave:6> A' * A
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172 @end example
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173
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174 @subsection Solving Systems of Linear Equations
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175
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176 Systems of linear equations are ubiquitous in numerical analysis.
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177 To solve the set of linear equations @code{A@var{x} = b},
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178 use the left division operator, @samp{\}:
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179
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180 @example
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181 @var{x} = A \ b
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182 @end example
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183
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184 @noindent
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185 This is conceptually equivalent to
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186 @tex
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187 $@code{A}^{-1}@code{b}$,
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188 @end tex
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189 @ifnottex
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190 @code{inv (a) * b},
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191 @end ifnottex
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192 but avoids computing the inverse of a matrix directly.
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193
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194 If the coefficient matrix is singular, Octave will print a warning
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195 message and compute a minimum norm solution.
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196
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197 A simple example comes from chemistry and the need to obtain balanced
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198 chemical equations. Consider the burning of hydrogen and oxygen to
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199 produce water.
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200 @tex
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201 $$ {\rm H_{2}} + {\rm O_{2}} \rightarrow {\rm H_{2}O} $$
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202 @end tex
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203 @ifnottex
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204
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205 @example
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206 H2 + O2 --> H2O
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207 @end example
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208
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209 @end ifnottex
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210 @noindent
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211 The equation above is not accurate. The Law of Conservation of Mass requires
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212 that the number of molecules of each type balance on the left- and right-hand
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213 sides of the equation. Writing the variable overall reaction with
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214 individual equations for hydrogen and oxygen one finds:
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215 @tex
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216 \vbox{
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217 $$ x_{1}{\rm H_{2}} + x_{2}{\rm O_{2}} \rightarrow {\rm H_{2}O} $$
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218 $$ {\rm H:}\quad 2x_{1} + 0x_{2} \rightarrow 2 $$
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219 $$ {\rm O:}\quad 0x_{1} + 2x_{2} \rightarrow 1 $$
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220 }
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221 @end tex
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222 @ifnottex
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223
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224 @example
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225 @group
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226 x1*H2 + x2*O2 --> H2O
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227 H: 2*x1 + 0*x2 --> 2
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228 O: 0*x1 + 2*x2 --> 1
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229 @end group
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230 @end example
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231
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232 @end ifnottex
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233 @noindent
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234 The solution in Octave is found in just three steps.
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235
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236 @example
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237 @group
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238 octave:1> A = [ 2, 0; 0, 2 ];
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239 octave:2> b = [ 2; 1 ];
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240 octave:3> x = A \ b
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241 @end group
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242 @end example
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243
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244 @subsection Integrating Differential Equations
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245
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246 Octave has built-in functions for solving nonlinear differential
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247 equations of the form
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248 @tex
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249 $$
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250 {dx \over dt} = f(x,t), \qquad x(t=t_0) = x_0
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251 $$
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252 @end tex
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253 @ifnottex
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254
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255 @example
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256 @group
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257 dx
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258 -- = f (x, t)
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259 dt
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260 @end group
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261 @end example
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262
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263 @noindent
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264 with the initial condition
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265
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266 @example
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267 x(t = t0) = x0
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268 @end example
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269
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270 @end ifnottex
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271 @noindent
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272 For Octave to integrate equations of this form, you must first provide a
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273 definition of the function
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274 @tex
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275 $f (x, t)$.
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276 @end tex
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277 @ifnottex
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278 @code{f(x,t)}.
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279 @end ifnottex
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280 This is straightforward, and may be accomplished by entering the
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281 function body directly on the command line. For example, the following
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282 commands define the right-hand side function for an interesting pair of
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283 nonlinear differential equations. Note that while you are entering a
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284 function, Octave responds with a different prompt, to indicate that it
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285 is waiting for you to complete your input.
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286
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287 @example
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288 @group
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289 octave:1> function xdot = f (x, t)
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290 >
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291 > r = 0.25;
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292 > k = 1.4;
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293 > a = 1.5;
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294 > b = 0.16;
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295 > c = 0.9;
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296 > d = 0.8;
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297 >
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298 > xdot(1) = r*x(1)*(1 - x(1)/k) - a*x(1)*x(2)/(1 + b*x(1));
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299 > xdot(2) = c*a*x(1)*x(2)/(1 + b*x(1)) - d*x(2);
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300 >
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301 > endfunction
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302 @end group
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303 @end example
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304
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305 @noindent
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306 Given the initial condition
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307
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308 @example
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309 octave:2> x0 = [1; 2];
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310 @end example
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311
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312 @noindent
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313 and the set of output times as a column vector (note that the first
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314 output time corresponds to the initial condition given above)
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315
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316 @example
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317 octave:3> t = linspace (0, 50, 200)';
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318 @end example
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319
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320 @noindent
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321 it is easy to integrate the set of differential equations:
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322
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323 @example
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324 octave:4> x = lsode ("f", x0, t);
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325 @end example
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326
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327 @noindent
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328 The function @code{lsode} uses the Livermore Solver for Ordinary
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329 Differential Equations, described in A. C. Hindmarsh, @cite{ODEPACK, a
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330 Systematized Collection of ODE Solvers}, in: Scientific Computing, R. S.
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331 Stepleman et al. (Eds.), North-Holland, Amsterdam, 1983, pages 55--64.
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332
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333 @subsection Producing Graphical Output
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334
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335 To display the solution of the previous example graphically, use the
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336 command
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337
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338 @example
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339 octave:1> plot (t, x)
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340 @end example
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341
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342 @noindent
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343 If you are using a graphical user interface, Octave will automatically create
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344 a separate window to display the plot.
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345
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346 To save a plot once it has been displayed on the screen, use the print
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347 command. For example,
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348
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349 @example
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350 print -deps foo.eps
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351 @end example
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352
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353 @noindent
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354 will create a file called @file{foo.eps} that contains a rendering of
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355 the current plot in Encapsulated PostScript format. The command
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356
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357 @example
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358 help print
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359 @end example
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360
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361 @noindent
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362 explains more options for the @code{print} command and provides a list
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363 of additional output file formats.
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364
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365 @subsection Editing What You Have Typed
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366
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367 At the Octave prompt, you can recall, edit, and reissue previous
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368 commands using Emacs- or vi-style editing commands. The default
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369 keybindings use Emacs-style commands. For example, to recall the
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370 previous command, press @kbd{Control-p} (written @kbd{C-p} for
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371 short). Doing this will normally bring back the previous line of input.
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372 @kbd{C-n} will bring up the next line of input, @kbd{C-b} will move
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373 the cursor backward on the line, @kbd{C-f} will move the cursor forward
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374 on the line, etc.
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375
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376 A complete description of the command line editing capability is given
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377 in this manual in @ref{Command Line Editing}.
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378
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379 @subsection Help and Documentation
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380
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381 Octave has an extensive help facility. The same documentation that is
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382 available in printed form is also available from the Octave prompt,
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383 because both forms of the documentation are created from the same input
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384 file.
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385
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386 In order to get good help you first need to know the name of the command
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387 that you want to use. This name of the function may not always be
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388 obvious, but a good place to start is to just type @code{help}.
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389 This will show you all the operators, reserved words, functions,
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390 built-in variables, and function files. An alternative is to search the
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391 documentation using the @code{lookfor} function. This function is
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392 described in @ref{Getting Help}.
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393
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394 Once you know the name of the function you wish to use, you can get more
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395 help on the function by simply including the name as an argument to help.
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396 For example,
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397
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398 @example
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399 help plot
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400 @end example
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401
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402 @noindent
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403 will display the help text for the @code{plot} function.
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404
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405 Octave sends output that is too long to fit on one screen through a
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406 pager like @code{less} or @code{more}. Type a @key{RET} to advance one
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407 line, a @key{SPC} to advance one page, and @key{q} to exit the pager.
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408
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409 The part of Octave's help facility that allows you to read the complete
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410 text of the printed manual from within Octave normally uses a separate
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411 program called Info. When you invoke Info you will be put into a menu
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412 driven program that contains the entire Octave manual. Help for using
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413 Info is provided in this manual in @ref{Getting Help}.
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414
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415 @node Conventions
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416 @section Conventions
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417
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418 This section explains the notational conventions that are used in this
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419 manual. You may want to skip this section and refer back to it later.
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420
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421 @menu
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422 * Fonts::
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423 * Evaluation Notation::
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424 * Printing Notation::
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425 * Error Messages::
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426 * Format of Descriptions::
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427 @end menu
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428
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429 @node Fonts
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430 @subsection Fonts
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431 @cindex documentation fonts
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432
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433 Examples of Octave code appear in this font or form: @code{svd (a)}.
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434 Names that represent variables or function arguments appear
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435 in this font or form: @var{first-number}. Commands that you type at the
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436 shell prompt appear in this font or form: @samp{octave --no-init-file}.
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437 Commands that you type at the Octave prompt sometimes appear in this font
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438 or form: @kbd{foo --bar --baz}. Specific keys on your keyboard appear
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439 in this font or form: @key{ANY}.
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440
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441 @node Evaluation Notation
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442 @subsection Evaluation Notation
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443 @cindex evaluation notation
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444 @cindex documentation notation
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445
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446 In the examples in this manual, results from expressions that you
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447 evaluate are indicated with @samp{@result{}}. For example:
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448
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449 @example
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450 @group
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451 sqrt (2)
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452 @result{} 1.4142
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453 @end group
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454 @end example
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455
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456 @noindent
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457 You can read this as ``@code{sqrt (2)} evaluates to 1.4142''.
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458
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459 In some cases, matrix values that are returned by expressions are
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460 displayed like this
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461
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462 @example
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463 @group
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464 [1, 2; 3, 4] == [1, 3; 2, 4]
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465 @result{} [ 1, 0; 0, 1 ]
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466 @end group
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467 @end example
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468
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469 @noindent
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470 and in other cases, they are displayed like this
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471
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472 @example
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473 @group
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474 eye (3)
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475 @result{} 1 0 0
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476 0 1 0
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477 0 0 1
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478 @end group
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479 @end example
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480
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481 @noindent
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482 in order to clearly show the structure of the result.
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483
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484 Sometimes to help describe one expression, another expression is
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485 shown that produces identical results. The exact equivalence of
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486 expressions is indicated with @samp{@equiv{}}. For example:
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487
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488 @example
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489 @group
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490 rot90 ([1, 2; 3, 4], -1)
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491 @equiv{}
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492 rot90 ([1, 2; 3, 4], 3)
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493 @equiv{}
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494 rot90 ([1, 2; 3, 4], 7)
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495 @end group
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496 @end example
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497
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498 @node Printing Notation
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499 @subsection Printing Notation
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500 @cindex printing notation
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501
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502 Many of the examples in this manual print text when they are
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503 evaluated. In this manual the printed text resulting from an example
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504 is indicated by @samp{@print{}}. The value that is returned by
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505 evaluating the expression is displayed with @samp{@result{}}
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506 (@code{1} in the next example) and follows on a separate line.
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507
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508 @example
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509 @group
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510 printf ("foo %s\n", "bar")
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511 @print{} foo bar
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512 @result{} 1
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513 @end group
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514 @end example
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515
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516 @node Error Messages
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517 @subsection Error Messages
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518 @cindex error message notation
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519
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520 Some examples signal errors. This normally displays an error message
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521 on your terminal. Error messages are shown on a line beginning with
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522 @code{error:}.
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523
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524 @example
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525 @group
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526 fieldnames ([1, 2; 3, 4])
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527 error: fieldnames: wrong type argument `matrix'
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528 @end group
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529 @end example
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530
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531 @node Format of Descriptions
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532 @subsection Format of Descriptions
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533 @cindex description format
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534
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535 Functions, commands, and variables are described in this manual in a
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536 uniform format. The first line of a description contains the name of
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537 the item followed by its arguments, if any.
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538 @ifnottex
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539 The category---function, variable, or whatever---appears at the
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540 beginning of the line.
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541 @end ifnottex
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542 @iftex
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543 The category---function, variable, or whatever---is printed next to the
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544 right margin.
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545 @end iftex
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546 The description follows on succeeding lines, sometimes with examples.
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547
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548 @menu
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549 * A Sample Function Description::
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550 * A Sample Command Description::
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551 * A Sample Variable Description::
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552 @end menu
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553
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554 @node A Sample Function Description
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555 @subsubsection A Sample Function Description
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556 @cindex function descriptions
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557
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558 In a function description, the name of the function being described
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559 appears first. It is followed on the same line by a list of parameters.
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560 The names used for the parameters are also used in the body of the
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561 description.
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562
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563 Here is a description of an imaginary function @code{foo}:
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564
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565 @deftypefn {Function} {} foo (@var{x}, @var{y}, @dots{})
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diff changeset
566 The function @code{foo} subtracts @var{x} from @var{y}, then adds the
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567 remaining arguments to the result. If @var{y} is not supplied, then the
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568 number 19 is used by default.
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diff changeset
569
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570 @example
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571 @group
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572 foo (1, [3, 5], 3, 9)
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573 @result{} [ 14, 16 ]
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diff changeset
574 foo (5)
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diff changeset
575 @result{} 14
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576 @end group
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577 @end example
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578
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diff changeset
579 More generally,
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580
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diff changeset
581 @example
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diff changeset
582 @group
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diff changeset
583 foo (@var{w}, @var{x}, @var{y}, @dots{})
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diff changeset
584 @equiv{}
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diff changeset
585 @var{x} - @var{w} + @var{y} + @dots{}
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diff changeset
586 @end group
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587 @end example
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588 @end deftypefn
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589
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diff changeset
590 Any parameter whose name contains the name of a type (e.g.,
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591 @var{integer} or @var{matrix}) is expected to be of that
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592 type. Parameters named @var{object} may be of any type. Parameters
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593 with other sorts of names (e.g., @var{new_file}) are discussed
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diff changeset
594 specifically in the description of the function. In some sections,
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diff changeset
595 features common to parameters of several functions are described at the
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diff changeset
596 beginning.
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597
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598 Functions in Octave may be defined in several different ways. The
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599 category name for functions may include another name that indicates the
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600 way that the function is defined. These additional tags include
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diff changeset
601
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diff changeset
602 @table @asis
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diff changeset
603 @item Function File
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diff changeset
604 @cindex function file
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diff changeset
605 The function described is defined using Octave commands stored in a text
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606 file. @xref{Function Files}.
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diff changeset
607
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608 @item Built-in Function
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diff changeset
609 @cindex built-in function
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diff changeset
610 The function described is written in a language like C++, C, or Fortran,
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diff changeset
611 and is part of the compiled Octave binary.
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diff changeset
612
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diff changeset
613 @item Loadable Function
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diff changeset
614 @cindex loadable function
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diff changeset
615 The function described is written in a language like C++, C, or Fortran.
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diff changeset
616 On systems that support dynamic linking of user-supplied functions, it
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diff changeset
617 may be automatically linked while Octave is running, but only if it is
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diff changeset
618 needed. @xref{Dynamically Linked Functions}.
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diff changeset
619
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620 @item Mapping Function
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diff changeset
621 @cindex mapping function
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diff changeset
622 The function described works element-by-element for matrix and vector
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diff changeset
623 arguments.
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624 @end table
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625
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626 @node A Sample Command Description
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627 @subsubsection A Sample Command Description
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diff changeset
628 @cindex command descriptions
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diff changeset
629
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630 Command descriptions have a format similar to function descriptions,
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diff changeset
631 except that the word `Function' is replaced by `Command'. Commands are
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632 functions that may be called without surrounding their arguments in
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633 parentheses. For example, here is the description for Octave's
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634 @code{cd} command:
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635
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636 @deffn {Command} cd dir
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637 @deffnx {Command} chdir dir
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638 Change the current working directory to @var{dir}. For example,
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639 @kbd{cd ~/octave} changes the current working directory to
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640 @file{~/octave}. If the directory does not exist, an error message is
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641 printed and the working directory is not changed.
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642 @end deffn
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643
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644 @node A Sample Variable Description
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645 @subsubsection A Sample Variable Description
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646 @cindex variable descriptions
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647
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648 A @dfn{variable} is a name that can hold a value. Although any variable
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649 can be set by the user, @dfn{built-in variables} typically exist
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650 specifically so that users can change them to alter the way Octave
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651 behaves (built-in variables are also sometimes called @dfn{user
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652 options}). Ordinary variables and built-in variables are described
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653 using a format like that for functions except that there are no
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654 arguments.
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655
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656 Here is a description of the imaginary variable
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657 @code{do_what_i_mean_not_what_i_say}.
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658
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659 @defvr {Built-in Variable} do_what_i_mean_not_what_i_say
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660 If the value of this variable is nonzero, Octave will do what you
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661 actually wanted, even if you have typed a completely different and
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662 meaningless list of commands.
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663 @end defvr
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664
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665 Other variable descriptions have the same format, but `Built-in
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666 Variable' is replaced by `Variable', for ordinary variables, or
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667 `Constant' for symbolic constants whose values cannot be changed.