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maint: update copyright notices for 2012
author John W. Eaton <jwe@octave.org>
date Mon, 02 Jan 2012 14:25:41 -0500
parents 951eacaf9381
children cb85e836d035
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14138
72c96de7a403 maint: update copyright notices for 2012
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1 @c Copyright (C) 1996-2012 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 Arithmetic
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20 @chapter Arithmetic
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21
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22 Unless otherwise noted, all of the functions described in this chapter
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23 will work for real and complex scalar, vector, or matrix arguments. Functions
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24 described as @dfn{mapping functions} apply the given operation individually to
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25 each element when given a matrix argument. For example:
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26
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27 @example
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28 @group
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29 sin ([1, 2; 3, 4])
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30 @result{} 0.84147 0.90930
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31 0.14112 -0.75680
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32 @end group
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33 @end example
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34
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35 @menu
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36 * Exponents and Logarithms::
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37 * Complex Arithmetic::
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38 * Trigonometry::
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39 * Sums and Products::
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40 * Utility Functions::
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41 * Special Functions::
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42 * Rational Approximations::
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43 * Coordinate Transformations::
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44 * Mathematical Constants::
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45 @end menu
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46
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47 @node Exponents and Logarithms
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48 @section Exponents and Logarithms
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49
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50 @DOCSTRING(exp)
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51
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52 @DOCSTRING(expm1)
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53
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54 @DOCSTRING(log)
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55
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56 @DOCSTRING(reallog)
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57
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58 @DOCSTRING(log1p)
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59
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60 @DOCSTRING(log10)
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61
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62 @DOCSTRING(log2)
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63
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64 @DOCSTRING(pow2)
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65
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66 @DOCSTRING(nextpow2)
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67
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68 @DOCSTRING(realpow)
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69
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70 @DOCSTRING(sqrt)
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71
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72 @DOCSTRING(realsqrt)
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73
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74 @DOCSTRING(cbrt)
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75
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76 @DOCSTRING(nthroot)
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77
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78 @node Complex Arithmetic
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79 @section Complex Arithmetic
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80
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81 In the descriptions of the following functions,
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82 @tex
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83 $z$ is the complex number $x + iy$, where $i$ is defined as
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84 $\sqrt{-1}$.
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85 @end tex
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86 @ifnottex
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87 @var{z} is the complex number @var{x} + @var{i}@var{y}, where @var{i} is
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88 defined as @code{sqrt (-1)}.
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89 @end ifnottex
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90
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91 @DOCSTRING(abs)
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92
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93 @DOCSTRING(arg)
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94
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95 @DOCSTRING(conj)
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96
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97 @DOCSTRING(cplxpair)
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98
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99 @DOCSTRING(imag)
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100
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101 @DOCSTRING(real)
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102
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103 @node Trigonometry
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104 @section Trigonometry
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105
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106 Octave provides the following trigonometric functions where angles are
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107 specified in radians. To convert from degrees to radians multiply by
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108 @tex
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109 $\pi/180$
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110 @end tex
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111 @ifnottex
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112 @code{pi/180}
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113 @end ifnottex
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114 (e.g., @code{sin (30 * pi/180)} returns the sine of 30 degrees). As
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115 an alternative, Octave provides a number of trigonometric functions
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116 which work directly on an argument specified in degrees. These functions
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117 are named after the base trigonometric function with a @samp{d} suffix. For
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118 example, @code{sin} expects an angle in radians while @code{sind} expects an
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119 angle in degrees.
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120
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121 @DOCSTRING(sin)
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122 @DOCSTRING(cos)
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123 @DOCSTRING(tan)
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124 @DOCSTRING(sec)
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125 @DOCSTRING(csc)
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126 @DOCSTRING(cot)
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127
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128 @DOCSTRING(asin)
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129 @DOCSTRING(acos)
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130 @DOCSTRING(atan)
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131 @DOCSTRING(asec)
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132 @DOCSTRING(acsc)
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133 @DOCSTRING(acot)
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134
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135 @DOCSTRING(sinh)
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136 @DOCSTRING(cosh)
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137 @DOCSTRING(tanh)
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138 @DOCSTRING(sech)
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139 @DOCSTRING(csch)
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140 @DOCSTRING(coth)
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141
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142 @DOCSTRING(asinh)
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143 @DOCSTRING(acosh)
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144 @DOCSTRING(atanh)
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145 @DOCSTRING(asech)
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146 @DOCSTRING(acsch)
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147 @DOCSTRING(acoth)
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148
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149 @DOCSTRING(atan2)
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150
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151 Octave provides the following trigonometric functions where angles are
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152 specified in degrees. These functions produce true zeros at the appropriate
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153 intervals rather than the small round-off error that occurs when using
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154 radians. For example:
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155
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156 @example
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157 @group
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158 cosd (90)
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159 @result{} 0
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160 cos (pi/2)
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161 @result{} 6.1230e-17
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162 @end group
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163 @end example
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164
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165 @DOCSTRING(sind)
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166 @DOCSTRING(cosd)
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167 @DOCSTRING(tand)
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168 @DOCSTRING(secd)
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169 @DOCSTRING(cscd)
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170 @DOCSTRING(cotd)
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171
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172 @DOCSTRING(asind)
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173 @DOCSTRING(acosd)
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174 @DOCSTRING(atand)
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175 @DOCSTRING(asecd)
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176 @DOCSTRING(acscd)
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177 @DOCSTRING(acotd)
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178
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179 @node Sums and Products
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180 @section Sums and Products
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181
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182 @DOCSTRING(sum)
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183
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184 @DOCSTRING(prod)
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185
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186 @DOCSTRING(cumsum)
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187
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188 @DOCSTRING(cumprod)
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189
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190 @DOCSTRING(sumsq)
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191
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192 @node Utility Functions
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193 @section Utility Functions
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194
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195 @DOCSTRING(ceil)
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196
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197 @DOCSTRING(fix)
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198
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199 @DOCSTRING(floor)
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200
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201 @DOCSTRING(round)
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202
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203 @DOCSTRING(roundb)
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204
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205 @DOCSTRING(max)
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206
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207 @DOCSTRING(min)
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208
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209 @DOCSTRING(cummax)
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210
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211 @DOCSTRING(cummin)
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212
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213 @DOCSTRING(hypot)
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214
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215 @DOCSTRING(gradient)
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216
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217 @DOCSTRING(dot)
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218
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219 @DOCSTRING(cross)
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220
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221 @DOCSTRING(divergence)
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222
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223 @DOCSTRING(curl)
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224
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225 @DOCSTRING(del2)
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226
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227 @DOCSTRING(factorial)
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228
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229 @DOCSTRING(factor)
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230
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231 @DOCSTRING(gcd)
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232
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233 @DOCSTRING(lcm)
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234
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235 @DOCSTRING(chop)
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236
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237 @DOCSTRING(rem)
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238
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239 @DOCSTRING(mod)
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240
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241 @DOCSTRING(primes)
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242
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243 @DOCSTRING(list_primes)
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244
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245 @DOCSTRING(sign)
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246
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247 @node Special Functions
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248 @section Special Functions
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249
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250 @DOCSTRING(airy)
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251
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252 @DOCSTRING(besselj)
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253
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254 @DOCSTRING(beta)
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255
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256 @DOCSTRING(betainc)
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257
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258 @DOCSTRING(betaln)
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259
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260 @DOCSTRING(bincoeff)
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261
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262 @DOCSTRING(commutation_matrix)
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263
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264 @DOCSTRING(duplication_matrix)
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265
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266 @DOCSTRING(erf)
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267
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268 @DOCSTRING(erfc)
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269
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270 @DOCSTRING(erfcx)
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271
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272 @DOCSTRING(erfinv)
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273
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274 @DOCSTRING(gamma)
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275
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276 @DOCSTRING(gammainc)
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277
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278 @DOCSTRING(legendre)
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279
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280 @anchor{doc-gammaln}
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281 @DOCSTRING(lgamma)
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282
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283 @node Rational Approximations
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284 @section Rational Approximations
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285
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286 @DOCSTRING(rat)
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287
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288 @DOCSTRING(rats)
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289
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290 @node Coordinate Transformations
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291 @section Coordinate Transformations
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292
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293 @DOCSTRING(cart2pol)
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294
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295 @DOCSTRING(pol2cart)
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296
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297 @DOCSTRING(cart2sph)
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298
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299 @DOCSTRING(sph2cart)
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300
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301 @node Mathematical Constants
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302 @section Mathematical Constants
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304 @DOCSTRING(e)
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305
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306 @DOCSTRING(pi)
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307
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308 @DOCSTRING(I)
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309
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310 @DOCSTRING(Inf)
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311
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312 @DOCSTRING(NaN)
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313
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314 @DOCSTRING(eps)
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315
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316 @DOCSTRING(realmax)
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317
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318 @DOCSTRING(realmin)