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| author | Rik <rdrider0-list@yahoo.com> |
|---|---|
| date | Sat, 28 Mar 2009 13:57:22 -0700 |
| parents | eb63fbe60fab |
| children | c1fff751b5a8 |
| rev | line source |
|---|---|
| 8920 | 1 @c Copyright (C) 1996, 1997, 1999, 2000, 2001, 2002, 2007, 2008, |
| 2 @c 2009 John W. Eaton | |
| 7018 | 3 @c |
| 4 @c This file is part of Octave. | |
| 5 @c | |
| 6 @c Octave is free software; you can redistribute it and/or modify it | |
| 7 @c under the terms of the GNU General Public License as published by the | |
| 8 @c Free Software Foundation; either version 3 of the License, or (at | |
| 9 @c your option) any later version. | |
| 10 @c | |
| 11 @c Octave is distributed in the hope that it will be useful, but WITHOUT | |
| 12 @c ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 13 @c FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 14 @c for more details. | |
| 15 @c | |
| 16 @c You should have received a copy of the GNU General Public License | |
| 17 @c along with Octave; see the file COPYING. If not, see | |
| 18 @c <http://www.gnu.org/licenses/>. | |
| 3294 | 19 |
| 4167 | 20 @node Arithmetic |
| 3294 | 21 @chapter Arithmetic |
| 22 | |
| 23 Unless otherwise noted, all of the functions described in this chapter | |
|
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24 will work for real and complex scalar or matrix arguments. Functions described as @dfn{mapping functions} apply the given operation to each element when given a matrix argument. |
| 3294 | 25 |
| 26 @menu | |
| 27 * Utility Functions:: | |
| 28 * Complex Arithmetic:: | |
| 29 * Trigonometry:: | |
| 30 * Sums and Products:: | |
| 31 * Special Functions:: | |
| 3803 | 32 * Coordinate Transformations:: |
| 3294 | 33 * Mathematical Constants:: |
| 34 @end menu | |
| 35 | |
| 4169 | 36 @node Utility Functions |
| 3294 | 37 @section Utility Functions |
| 38 | |
| 39 The following functions are available for working with complex numbers. | |
| 40 Each expects a single argument. They are called @dfn{mapping functions} | |
| 41 because when given a matrix argument, they apply the given function to | |
| 42 each element of the matrix. | |
| 43 | |
| 3321 | 44 @DOCSTRING(ceil) |
| 3294 | 45 |
| 6550 | 46 @DOCSTRING(cplxpair) |
| 47 | |
| 6788 | 48 @DOCSTRING(del2) |
| 49 | |
| 3321 | 50 @DOCSTRING(exp) |
| 3294 | 51 |
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52 @DOCSTRING(expm1) |
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53 |
| 6550 | 54 @DOCSTRING(factor) |
| 55 | |
| 56 @DOCSTRING(factorial) | |
| 57 | |
| 3321 | 58 @DOCSTRING(fix) |
| 3294 | 59 |
| 3321 | 60 @DOCSTRING(floor) |
| 3294 | 61 |
| 6550 | 62 @DOCSTRING(fmod) |
| 63 | |
| 3321 | 64 @DOCSTRING(gcd) |
| 3294 | 65 |
| 6551 | 66 @DOCSTRING(gradient) |
| 67 | |
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68 @DOCSTRING(hypot) |
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69 |
| 3321 | 70 @DOCSTRING(lcm) |
| 3294 | 71 |
| 3321 | 72 @DOCSTRING(log) |
| 3294 | 73 |
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74 @DOCSTRING(log1p) |
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75 |
| 3321 | 76 @DOCSTRING(log10) |
| 3294 | 77 |
| 3321 | 78 @DOCSTRING(log2) |
| 3294 | 79 |
| 3321 | 80 @DOCSTRING(max) |
| 3294 | 81 |
| 3321 | 82 @DOCSTRING(min) |
| 83 | |
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84 @DOCSTRING(cummax) |
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85 |
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86 @DOCSTRING(cummin) |
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87 |
| 3982 | 88 @DOCSTRING(mod) |
| 89 | |
| 3321 | 90 @DOCSTRING(nextpow2) |
| 3294 | 91 |
| 6550 | 92 @DOCSTRING(nthroot) |
| 93 | |
| 3321 | 94 @DOCSTRING(pow2) |
| 3294 | 95 |
| 6550 | 96 @DOCSTRING(primes) |
| 97 | |
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98 @DOCSTRING(reallog) |
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99 |
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100 @DOCSTRING(realpow) |
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101 |
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102 @DOCSTRING(realsqrt) |
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103 |
| 3321 | 104 @DOCSTRING(rem) |
| 3294 | 105 |
| 3321 | 106 @DOCSTRING(round) |
| 3294 | 107 |
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108 @DOCSTRING(roundb) |
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109 |
| 3321 | 110 @DOCSTRING(sign) |
| 3294 | 111 |
| 3321 | 112 @DOCSTRING(sqrt) |
| 3294 | 113 |
| 4169 | 114 @node Complex Arithmetic |
| 3294 | 115 @section Complex Arithmetic |
| 116 | |
| 117 The following functions are available for working with complex | |
| 118 numbers. Each expects a single argument. Given a matrix they work on | |
| 119 an element by element basis. In the descriptions of the following | |
| 120 functions, | |
| 121 @iftex | |
| 122 @tex | |
| 123 $z$ is the complex number $x + iy$, where $i$ is defined as | |
| 124 $\sqrt{-1}$. | |
| 125 @end tex | |
| 126 @end iftex | |
| 127 @ifinfo | |
| 128 @var{z} is the complex number @var{x} + @var{i}@var{y}, where @var{i} is | |
| 129 defined as @code{sqrt (-1)}. | |
| 130 @end ifinfo | |
| 131 | |
| 3321 | 132 @DOCSTRING(abs) |
| 3294 | 133 |
| 3321 | 134 @DOCSTRING(arg) |
| 3294 | 135 |
| 3321 | 136 @DOCSTRING(conj) |
| 3294 | 137 |
| 3321 | 138 @DOCSTRING(imag) |
| 3294 | 139 |
| 3321 | 140 @DOCSTRING(real) |
| 3294 | 141 |
| 4169 | 142 @node Trigonometry |
| 3294 | 143 @section Trigonometry |
| 144 | |
| 145 Octave provides the following trigonometric functions. Angles are | |
| 6939 | 146 specified in radians. To convert from degrees to radians multiply by |
| 3294 | 147 @iftex |
| 148 @tex | |
| 149 $\pi/180$ | |
| 150 @end tex | |
| 151 @end iftex | |
| 152 @ifinfo | |
| 153 @code{pi/180} | |
| 154 @end ifinfo | |
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9064
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Rik <rdrider0-list@yahoo.com>
parents:
8920
diff
changeset
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155 (e.g., @code{sin (30 * pi/180)} returns the sine of 30 degrees). |
| 3294 | 156 |
| 3321 | 157 @DOCSTRING(sin) |
| 158 @DOCSTRING(cos) | |
| 159 @DOCSTRING(tan) | |
| 160 @DOCSTRING(sec) | |
| 161 @DOCSTRING(csc) | |
| 162 @DOCSTRING(cot) | |
| 3294 | 163 |
| 3321 | 164 @DOCSTRING(asin) |
| 165 @DOCSTRING(acos) | |
| 166 @DOCSTRING(atan) | |
| 167 @DOCSTRING(asec) | |
| 168 @DOCSTRING(acsc) | |
| 169 @DOCSTRING(acot) | |
| 3294 | 170 |
| 3321 | 171 @DOCSTRING(sinh) |
| 172 @DOCSTRING(cosh) | |
| 173 @DOCSTRING(tanh) | |
| 174 @DOCSTRING(sech) | |
| 3428 | 175 @DOCSTRING(csch) |
| 3321 | 176 @DOCSTRING(coth) |
| 3294 | 177 |
| 3321 | 178 @DOCSTRING(asinh) |
| 179 @DOCSTRING(acosh) | |
| 180 @DOCSTRING(atanh) | |
| 181 @DOCSTRING(asech) | |
| 182 @DOCSTRING(acsch) | |
| 183 @DOCSTRING(acoth) | |
| 3294 | 184 |
| 7001 | 185 Each of these functions expects a single argument. For matrix arguments, |
| 3294 | 186 they work on an element by element basis. For example, |
| 187 | |
| 188 @example | |
| 189 @group | |
| 190 sin ([1, 2; 3, 4]) | |
| 191 @result{} 0.84147 0.90930 | |
| 192 0.14112 -0.75680 | |
| 193 @end group | |
| 194 @end example | |
| 195 | |
| 3321 | 196 @DOCSTRING(atan2) |
| 197 | |
| 6502 | 198 In addition to the trigonometric functions that work with radians, |
| 199 Octave also provides the following functions which work with degrees. | |
| 200 | |
| 201 @DOCSTRING(sind) | |
| 202 @DOCSTRING(cosd) | |
| 203 @DOCSTRING(tand) | |
| 204 @DOCSTRING(secd) | |
| 205 @DOCSTRING(cscd) | |
| 206 @DOCSTRING(cotd) | |
| 207 | |
| 208 @DOCSTRING(asind) | |
| 209 @DOCSTRING(acosd) | |
| 210 @DOCSTRING(atand) | |
| 211 @DOCSTRING(asecd) | |
| 212 @DOCSTRING(acscd) | |
| 213 @DOCSTRING(acotd) | |
| 3294 | 214 |
| 4169 | 215 @node Sums and Products |
| 3294 | 216 @section Sums and Products |
| 217 | |
| 3321 | 218 @DOCSTRING(sum) |
| 3294 | 219 |
| 3321 | 220 @DOCSTRING(prod) |
| 3294 | 221 |
| 3321 | 222 @DOCSTRING(cumsum) |
| 3294 | 223 |
| 3321 | 224 @DOCSTRING(cumprod) |
| 3294 | 225 |
| 3321 | 226 @DOCSTRING(sumsq) |
| 3294 | 227 |
| 6770 | 228 @DOCSTRING(accumarray) |
| 229 | |
| 4169 | 230 @node Special Functions |
| 3294 | 231 @section Special Functions |
| 232 | |
| 3459 | 233 @DOCSTRING(besselj) |
| 234 | |
| 235 @DOCSTRING(airy) | |
| 3294 | 236 |
| 3321 | 237 @DOCSTRING(beta) |
| 3294 | 238 |
| 3444 | 239 @DOCSTRING(betainc) |
| 3294 | 240 |
| 6502 | 241 @DOCSTRING(betaln) |
| 242 | |
| 3321 | 243 @DOCSTRING(bincoeff) |
| 3294 | 244 |
| 3321 | 245 @DOCSTRING(erf) |
| 3294 | 246 |
| 3321 | 247 @DOCSTRING(erfc) |
| 3294 | 248 |
| 3321 | 249 @DOCSTRING(erfinv) |
| 3294 | 250 |
| 3321 | 251 @DOCSTRING(gamma) |
| 3294 | 252 |
| 3444 | 253 @DOCSTRING(gammainc) |
| 3294 | 254 |
| 6502 | 255 @DOCSTRING(legendre) |
| 256 | |
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257 @anchor{doc-gammaln} |
| 3321 | 258 @DOCSTRING(lgamma) |
| 259 | |
| 260 @DOCSTRING(cross) | |
| 3294 | 261 |
| 3321 | 262 @DOCSTRING(commutation_matrix) |
| 3294 | 263 |
| 3321 | 264 @DOCSTRING(duplication_matrix) |
| 3294 | 265 |
| 4169 | 266 @node Coordinate Transformations |
| 3803 | 267 @section Coordinate Transformations |
| 268 | |
| 269 @DOCSTRING(cart2pol) | |
| 270 | |
| 271 @DOCSTRING(pol2cart) | |
| 272 | |
| 273 @DOCSTRING(cart2sph) | |
| 274 | |
| 275 @DOCSTRING(sph2cart) | |
| 276 | |
| 4169 | 277 @node Mathematical Constants |
| 3294 | 278 @section Mathematical Constants |
| 279 | |
| 3321 | 280 @DOCSTRING(I) |
| 281 | |
| 282 @DOCSTRING(Inf) | |
| 3294 | 283 |
| 3321 | 284 @DOCSTRING(NaN) |
| 3294 | 285 |
| 3321 | 286 @DOCSTRING(pi) |
| 3294 | 287 |
| 3321 | 288 @DOCSTRING(e) |
| 289 | |
| 290 @DOCSTRING(eps) | |
| 3294 | 291 |
| 3321 | 292 @DOCSTRING(realmax) |
| 3294 | 293 |
| 3321 | 294 @DOCSTRING(realmin) |