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[project @ 2002-07-10 19:23:58 by jwe]
author jwe
date Wed, 10 Jul 2002 19:23:58 +0000
parents 63c75bc3db82
children aae05d51353c
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1 @c Copyright (C) 1996, 1997 John W. Eaton
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2 @c This is part of the Octave manual.
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3 @c For copying conditions, see the file gpl.texi.
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4
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5 @node Arithmetic, Linear Algebra, Matrix Manipulation, Top
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6 @chapter Arithmetic
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7
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8 Unless otherwise noted, all of the functions described in this chapter
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9 will work for real and complex scalar or matrix arguments.
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10
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11 @menu
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12 * Utility Functions::
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13 * Complex Arithmetic::
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14 * Trigonometry::
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15 * Sums and Products::
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16 * Special Functions::
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17 * Coordinate Transformations::
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18 * Mathematical Constants::
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19 @end menu
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20
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21 @node Utility Functions, Complex Arithmetic, Arithmetic, Arithmetic
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22 @section Utility Functions
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23
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24 The following functions are available for working with complex numbers.
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25 Each expects a single argument. They are called @dfn{mapping functions}
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26 because when given a matrix argument, they apply the given function to
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27 each element of the matrix.
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28
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29 @DOCSTRING(ceil)
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31 @DOCSTRING(exp)
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33 @DOCSTRING(fix)
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35 @DOCSTRING(floor)
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37 @DOCSTRING(gcd)
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39 @DOCSTRING(lcm)
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41 @DOCSTRING(log)
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43 @DOCSTRING(log10)
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45 @DOCSTRING(log2)
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47 @DOCSTRING(max)
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49 @DOCSTRING(min)
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50
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51 @DOCSTRING(mod)
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52
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53 @DOCSTRING(nextpow2)
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55 @DOCSTRING(pow2)
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57 @DOCSTRING(rem)
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59 @DOCSTRING(round)
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61 @DOCSTRING(sign)
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63 @DOCSTRING(sqrt)
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64
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65 @node Complex Arithmetic, Trigonometry, Utility Functions, Arithmetic
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66 @section Complex Arithmetic
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67
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68 The following functions are available for working with complex
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69 numbers. Each expects a single argument. Given a matrix they work on
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70 an element by element basis. In the descriptions of the following
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71 functions,
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72 @iftex
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73 @tex
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74 $z$ is the complex number $x + iy$, where $i$ is defined as
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75 $\sqrt{-1}$.
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76 @end tex
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77 @end iftex
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78 @ifinfo
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79 @var{z} is the complex number @var{x} + @var{i}@var{y}, where @var{i} is
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80 defined as @code{sqrt (-1)}.
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81 @end ifinfo
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82
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83 @DOCSTRING(abs)
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85 @DOCSTRING(arg)
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87 @DOCSTRING(conj)
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88
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89 @DOCSTRING(imag)
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90
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91 @DOCSTRING(real)
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92
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93 @node Trigonometry, Sums and Products, Complex Arithmetic, Arithmetic
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94 @section Trigonometry
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95
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96 Octave provides the following trigonometric functions. Angles are
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97 specified in radians. To convert from degrees to radians multipy by
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98 @iftex
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99 @tex
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100 $\pi/180$
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101 @end tex
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102 @end iftex
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103 @ifinfo
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104 @code{pi/180}
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105 @end ifinfo
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106 (e.g. @code{sin (30 * pi/180)} returns the sine of 30 degrees).
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107
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108 @DOCSTRING(sin)
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109 @DOCSTRING(cos)
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110 @DOCSTRING(tan)
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111 @DOCSTRING(sec)
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112 @DOCSTRING(csc)
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113 @DOCSTRING(cot)
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114
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115 @DOCSTRING(asin)
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116 @DOCSTRING(acos)
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117 @DOCSTRING(atan)
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118 @DOCSTRING(asec)
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119 @DOCSTRING(acsc)
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120 @DOCSTRING(acot)
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122 @DOCSTRING(sinh)
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123 @DOCSTRING(cosh)
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124 @DOCSTRING(tanh)
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125 @DOCSTRING(sech)
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126 @DOCSTRING(csch)
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127 @DOCSTRING(coth)
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129 @DOCSTRING(asinh)
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130 @DOCSTRING(acosh)
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131 @DOCSTRING(atanh)
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132 @DOCSTRING(asech)
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133 @DOCSTRING(acsch)
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134 @DOCSTRING(acoth)
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135
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136 Each of these functions expect a single argument. For matrix arguments,
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137 they work on an element by element basis. For example,
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138
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139 @example
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140 @group
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141 sin ([1, 2; 3, 4])
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142 @result{} 0.84147 0.90930
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143 0.14112 -0.75680
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144 @end group
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145 @end example
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146
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147 @DOCSTRING(atan2)
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148
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149
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150 @node Sums and Products, Special Functions, Trigonometry, Arithmetic
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151 @section Sums and Products
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152
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153 @DOCSTRING(sum)
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154
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155 @DOCSTRING(prod)
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156
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157 @DOCSTRING(cumsum)
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158
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159 @DOCSTRING(cumprod)
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160
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161 @DOCSTRING(sumsq)
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162
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163 @node Special Functions, Coordinate Transformations, Sums and Products, Arithmetic
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164 @section Special Functions
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165
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166 @DOCSTRING(besselj)
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167
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168 @DOCSTRING(airy)
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169
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170 @DOCSTRING(beta)
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171
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172 @DOCSTRING(betainc)
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173
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174 @DOCSTRING(bincoeff)
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175
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176 @DOCSTRING(erf)
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177
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178 @DOCSTRING(erfc)
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179
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180 @DOCSTRING(erfinv)
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181
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182 @DOCSTRING(gamma)
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183
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184 @DOCSTRING(gammainc)
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185
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186 @DOCSTRING(lgamma)
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187
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188 @DOCSTRING(cross)
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189
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190 @DOCSTRING(commutation_matrix)
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191
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192 @DOCSTRING(duplication_matrix)
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193
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194 @node Coordinate Transformations, Mathematical Constants, Special Functions, Arithmetic
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195 @section Coordinate Transformations
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196
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197 @DOCSTRING(cart2pol)
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198
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199 @DOCSTRING(pol2cart)
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200
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201 @DOCSTRING(cart2sph)
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202
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203 @DOCSTRING(sph2cart)
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204
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205 @node Mathematical Constants, , Coordinate Transformations, Arithmetic
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206 @section Mathematical Constants
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207
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208 @DOCSTRING(I)
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209
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210 @DOCSTRING(Inf)
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211
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212 @DOCSTRING(NaN)
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213
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214 @DOCSTRING(pi)
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215
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216 @DOCSTRING(e)
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217
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218 @DOCSTRING(eps)
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219
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220 @DOCSTRING(realmax)
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221
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222 @DOCSTRING(realmin)