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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 * Mathematical Constants:: |
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18 @end menu |
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19 |
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20 @node Utility Functions, Complex Arithmetic, Arithmetic, Arithmetic |
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21 @section Utility Functions |
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22 |
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23 The following functions are available for working with complex numbers. |
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24 Each expects a single argument. They are called @dfn{mapping functions} |
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25 because when given a matrix argument, they apply the given function to |
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26 each element of the matrix. |
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27 |
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28 @DOCSTRING(ceil) |
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29 |
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30 @DOCSTRING(exp) |
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31 |
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32 @DOCSTRING(fix) |
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33 |
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34 @DOCSTRING(floor) |
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35 |
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36 @DOCSTRING(gcd) |
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37 |
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38 @DOCSTRING(lcm) |
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39 |
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40 @DOCSTRING(log) |
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41 |
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42 @DOCSTRING(log10) |
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43 |
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44 @DOCSTRING(log2) |
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45 |
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46 @DOCSTRING(max) |
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47 |
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48 @DOCSTRING(min) |
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49 |
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50 @DOCSTRING(nextpow2) |
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51 |
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52 @DOCSTRING(pow2) |
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53 |
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54 @DOCSTRING(rem) |
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55 |
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56 @DOCSTRING(round) |
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57 |
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58 @DOCSTRING(sign) |
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59 |
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60 @DOCSTRING(sqrt) |
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61 |
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62 @node Complex Arithmetic, Trigonometry, Utility Functions, Arithmetic |
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63 @section Complex Arithmetic |
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64 |
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65 The following functions are available for working with complex |
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66 numbers. Each expects a single argument. Given a matrix they work on |
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67 an element by element basis. In the descriptions of the following |
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68 functions, |
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69 @iftex |
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70 @tex |
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71 $z$ is the complex number $x + iy$, where $i$ is defined as |
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72 $\sqrt{-1}$. |
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73 @end tex |
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74 @end iftex |
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75 @ifinfo |
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76 @var{z} is the complex number @var{x} + @var{i}@var{y}, where @var{i} is |
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77 defined as @code{sqrt (-1)}. |
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78 @end ifinfo |
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79 |
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80 @DOCSTRING(abs) |
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81 |
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82 @DOCSTRING(arg) |
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83 |
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84 @DOCSTRING(conj) |
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85 |
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86 @DOCSTRING(imag) |
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87 |
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88 @DOCSTRING(real) |
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89 |
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90 @node Trigonometry, Sums and Products, Complex Arithmetic, Arithmetic |
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91 @section Trigonometry |
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92 |
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93 Octave provides the following trigonometric functions. Angles are |
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94 specified in radians. To convert from degrees to radians multipy by |
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95 @iftex |
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96 @tex |
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97 $\pi/180$ |
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98 @end tex |
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99 @end iftex |
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100 @ifinfo |
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101 @code{pi/180} |
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102 @end ifinfo |
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103 (e.g. @code{sin (30 * pi/180)} returns the sine of 30 degrees). |
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104 |
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105 @DOCSTRING(sin) |
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106 @DOCSTRING(cos) |
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107 @DOCSTRING(tan) |
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108 @DOCSTRING(sec) |
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109 @DOCSTRING(csc) |
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110 @DOCSTRING(cot) |
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111 |
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112 @DOCSTRING(asin) |
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113 @DOCSTRING(acos) |
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114 @DOCSTRING(atan) |
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115 @DOCSTRING(asec) |
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116 @DOCSTRING(acsc) |
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117 @DOCSTRING(acot) |
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118 |
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119 @DOCSTRING(sinh) |
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120 @DOCSTRING(cosh) |
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121 @DOCSTRING(tanh) |
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122 @DOCSTRING(sech) |
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123 @DOCSTRING(csch) |
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124 @DOCSTRING(coth) |
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125 |
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126 @DOCSTRING(asinh) |
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127 @DOCSTRING(acosh) |
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128 @DOCSTRING(atanh) |
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129 @DOCSTRING(asech) |
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130 @DOCSTRING(acsch) |
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131 @DOCSTRING(acoth) |
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132 |
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133 Each of these functions expect a single argument. For matrix arguments, |
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134 they work on an element by element basis. For example, |
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135 |
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136 @example |
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137 @group |
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138 sin ([1, 2; 3, 4]) |
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139 @result{} 0.84147 0.90930 |
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140 0.14112 -0.75680 |
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141 @end group |
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142 @end example |
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143 |
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144 @DOCSTRING(atan2) |
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145 |
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146 |
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147 @node Sums and Products, Special Functions, Trigonometry, Arithmetic |
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148 @section Sums and Products |
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149 |
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150 @DOCSTRING(sum) |
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151 |
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152 @DOCSTRING(prod) |
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153 |
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154 @DOCSTRING(cumsum) |
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155 |
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156 @DOCSTRING(cumprod) |
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157 |
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158 @DOCSTRING(sumsq) |
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159 |
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160 @node Special Functions, Mathematical Constants, Sums and Products, Arithmetic |
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161 @section Special Functions |
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162 |
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163 @DOCSTRING(bessel) |
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164 |
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165 @DOCSTRING(beta) |
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166 |
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167 @DOCSTRING(betai) |
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168 |
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169 @DOCSTRING(bincoeff) |
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170 |
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171 @DOCSTRING(erf) |
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172 |
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173 @DOCSTRING(erfc) |
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174 |
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175 @DOCSTRING(erfinv) |
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176 |
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177 @DOCSTRING(gamma) |
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178 |
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179 @DOCSTRING(gammai) |
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180 |
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181 @DOCSTRING(lgamma) |
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182 |
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183 @DOCSTRING(cross) |
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184 |
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185 @DOCSTRING(commutation_matrix) |
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186 |
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187 @DOCSTRING(duplication_matrix) |
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188 |
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189 @node Mathematical Constants, , Special Functions, Arithmetic |
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190 @section Mathematical Constants |
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191 |
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192 @DOCSTRING(I) |
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193 |
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194 @DOCSTRING(Inf) |
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195 |
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196 @DOCSTRING(NaN) |
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197 |
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198 @DOCSTRING(pi) |
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199 |
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200 @DOCSTRING(e) |
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201 |
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202 @DOCSTRING(eps) |
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203 |
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204 @DOCSTRING(realmax) |
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205 |
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206 @DOCSTRING(realmin) |
