Mercurial > hg > octave-nkf
annotate doc/interpreter/arith.txi @ 7638:2df457529cfa
implement expm1 and log1p functions
| author | Jaroslav Hajek <highegg@gmail.com> |
|---|---|
| date | Tue, 25 Mar 2008 19:47:21 -0400 |
| parents | fd42779a8428 |
| children | bbaa5d7d0143 |
| rev | line source |
|---|---|
| 7018 | 1 @c Copyright (C) 1996, 1997, 1999, 2000, 2001, 2002, 2007 John W. Eaton |
| 2 @c | |
| 3 @c This file is part of Octave. | |
| 4 @c | |
| 5 @c Octave is free software; you can redistribute it and/or modify it | |
| 6 @c under the terms of the GNU General Public License as published by the | |
| 7 @c Free Software Foundation; either version 3 of the License, or (at | |
| 8 @c your option) any later version. | |
| 9 @c | |
| 10 @c Octave is distributed in the hope that it will be useful, but WITHOUT | |
| 11 @c ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 12 @c FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 13 @c for more details. | |
| 14 @c | |
| 15 @c You should have received a copy of the GNU General Public License | |
| 16 @c along with Octave; see the file COPYING. If not, see | |
| 17 @c <http://www.gnu.org/licenses/>. | |
| 3294 | 18 |
| 4167 | 19 @node Arithmetic |
| 3294 | 20 @chapter Arithmetic |
| 21 | |
| 22 Unless otherwise noted, all of the functions described in this chapter | |
| 23 will work for real and complex scalar or matrix arguments. | |
| 24 | |
| 25 @menu | |
| 26 * Utility Functions:: | |
| 27 * Complex Arithmetic:: | |
| 28 * Trigonometry:: | |
| 29 * Sums and Products:: | |
| 30 * Special Functions:: | |
| 3803 | 31 * Coordinate Transformations:: |
| 3294 | 32 * Mathematical Constants:: |
| 33 @end menu | |
| 34 | |
| 4169 | 35 @node Utility Functions |
| 3294 | 36 @section Utility Functions |
| 37 | |
| 38 The following functions are available for working with complex numbers. | |
| 39 Each expects a single argument. They are called @dfn{mapping functions} | |
| 40 because when given a matrix argument, they apply the given function to | |
| 41 each element of the matrix. | |
| 42 | |
| 3321 | 43 @DOCSTRING(ceil) |
| 3294 | 44 |
| 6550 | 45 @DOCSTRING(cplxpair) |
| 46 | |
| 6788 | 47 @DOCSTRING(del2) |
| 48 | |
| 3321 | 49 @DOCSTRING(exp) |
| 3294 | 50 |
|
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implement expm1 and log1p functions
Jaroslav Hajek <highegg@gmail.com>
parents:
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changeset
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51 @DOCSTRING(expm1) |
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Jaroslav Hajek <highegg@gmail.com>
parents:
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52 |
| 6550 | 53 @DOCSTRING(factor) |
| 54 | |
| 55 @DOCSTRING(factorial) | |
| 56 | |
| 3321 | 57 @DOCSTRING(fix) |
| 3294 | 58 |
| 3321 | 59 @DOCSTRING(floor) |
| 3294 | 60 |
| 6550 | 61 @DOCSTRING(fmod) |
| 62 | |
| 3321 | 63 @DOCSTRING(gcd) |
| 3294 | 64 |
| 6551 | 65 @DOCSTRING(gradient) |
| 66 | |
|
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67 @DOCSTRING(hypot) |
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parents:
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68 |
| 3321 | 69 @DOCSTRING(lcm) |
| 3294 | 70 |
| 3321 | 71 @DOCSTRING(log) |
| 3294 | 72 |
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Jaroslav Hajek <highegg@gmail.com>
parents:
7018
diff
changeset
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73 @DOCSTRING(log1p) |
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2df457529cfa
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Jaroslav Hajek <highegg@gmail.com>
parents:
7018
diff
changeset
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74 |
| 3321 | 75 @DOCSTRING(log10) |
| 3294 | 76 |
| 3321 | 77 @DOCSTRING(log2) |
| 3294 | 78 |
| 3321 | 79 @DOCSTRING(max) |
| 3294 | 80 |
| 3321 | 81 @DOCSTRING(min) |
| 82 | |
| 3982 | 83 @DOCSTRING(mod) |
| 84 | |
| 3321 | 85 @DOCSTRING(nextpow2) |
| 3294 | 86 |
| 6550 | 87 @DOCSTRING(nthroot) |
| 88 | |
| 3321 | 89 @DOCSTRING(pow2) |
| 3294 | 90 |
| 6550 | 91 @DOCSTRING(primes) |
| 92 | |
| 3321 | 93 @DOCSTRING(rem) |
| 3294 | 94 |
| 3321 | 95 @DOCSTRING(round) |
| 3294 | 96 |
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Jaroslav Hajek <highegg@gmail.com>
parents:
7018
diff
changeset
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97 @DOCSTRING(roundb) |
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Jaroslav Hajek <highegg@gmail.com>
parents:
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diff
changeset
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98 |
| 3321 | 99 @DOCSTRING(sign) |
| 3294 | 100 |
| 3321 | 101 @DOCSTRING(sqrt) |
| 3294 | 102 |
| 4169 | 103 @node Complex Arithmetic |
| 3294 | 104 @section Complex Arithmetic |
| 105 | |
| 106 The following functions are available for working with complex | |
| 107 numbers. Each expects a single argument. Given a matrix they work on | |
| 108 an element by element basis. In the descriptions of the following | |
| 109 functions, | |
| 110 @iftex | |
| 111 @tex | |
| 112 $z$ is the complex number $x + iy$, where $i$ is defined as | |
| 113 $\sqrt{-1}$. | |
| 114 @end tex | |
| 115 @end iftex | |
| 116 @ifinfo | |
| 117 @var{z} is the complex number @var{x} + @var{i}@var{y}, where @var{i} is | |
| 118 defined as @code{sqrt (-1)}. | |
| 119 @end ifinfo | |
| 120 | |
| 3321 | 121 @DOCSTRING(abs) |
| 3294 | 122 |
| 3321 | 123 @DOCSTRING(arg) |
| 3294 | 124 |
| 3321 | 125 @DOCSTRING(conj) |
| 3294 | 126 |
| 3321 | 127 @DOCSTRING(imag) |
| 3294 | 128 |
| 3321 | 129 @DOCSTRING(real) |
| 3294 | 130 |
| 4169 | 131 @node Trigonometry |
| 3294 | 132 @section Trigonometry |
| 133 | |
| 134 Octave provides the following trigonometric functions. Angles are | |
| 6939 | 135 specified in radians. To convert from degrees to radians multiply by |
| 3294 | 136 @iftex |
| 137 @tex | |
| 138 $\pi/180$ | |
| 139 @end tex | |
| 140 @end iftex | |
| 141 @ifinfo | |
| 142 @code{pi/180} | |
| 143 @end ifinfo | |
| 144 (e.g. @code{sin (30 * pi/180)} returns the sine of 30 degrees). | |
| 145 | |
| 3321 | 146 @DOCSTRING(sin) |
| 147 @DOCSTRING(cos) | |
| 148 @DOCSTRING(tan) | |
| 149 @DOCSTRING(sec) | |
| 150 @DOCSTRING(csc) | |
| 151 @DOCSTRING(cot) | |
| 3294 | 152 |
| 3321 | 153 @DOCSTRING(asin) |
| 154 @DOCSTRING(acos) | |
| 155 @DOCSTRING(atan) | |
| 156 @DOCSTRING(asec) | |
| 157 @DOCSTRING(acsc) | |
| 158 @DOCSTRING(acot) | |
| 3294 | 159 |
| 3321 | 160 @DOCSTRING(sinh) |
| 161 @DOCSTRING(cosh) | |
| 162 @DOCSTRING(tanh) | |
| 163 @DOCSTRING(sech) | |
| 3428 | 164 @DOCSTRING(csch) |
| 3321 | 165 @DOCSTRING(coth) |
| 3294 | 166 |
| 3321 | 167 @DOCSTRING(asinh) |
| 168 @DOCSTRING(acosh) | |
| 169 @DOCSTRING(atanh) | |
| 170 @DOCSTRING(asech) | |
| 171 @DOCSTRING(acsch) | |
| 172 @DOCSTRING(acoth) | |
| 3294 | 173 |
| 7001 | 174 Each of these functions expects a single argument. For matrix arguments, |
| 3294 | 175 they work on an element by element basis. For example, |
| 176 | |
| 177 @example | |
| 178 @group | |
| 179 sin ([1, 2; 3, 4]) | |
| 180 @result{} 0.84147 0.90930 | |
| 181 0.14112 -0.75680 | |
| 182 @end group | |
| 183 @end example | |
| 184 | |
| 3321 | 185 @DOCSTRING(atan2) |
| 186 | |
| 6502 | 187 In addition to the trigonometric functions that work with radians, |
| 188 Octave also provides the following functions which work with degrees. | |
| 189 | |
| 190 @DOCSTRING(sind) | |
| 191 @DOCSTRING(cosd) | |
| 192 @DOCSTRING(tand) | |
| 193 @DOCSTRING(secd) | |
| 194 @DOCSTRING(cscd) | |
| 195 @DOCSTRING(cotd) | |
| 196 | |
| 197 @DOCSTRING(asind) | |
| 198 @DOCSTRING(acosd) | |
| 199 @DOCSTRING(atand) | |
| 200 @DOCSTRING(asecd) | |
| 201 @DOCSTRING(acscd) | |
| 202 @DOCSTRING(acotd) | |
| 3294 | 203 |
| 4169 | 204 @node Sums and Products |
| 3294 | 205 @section Sums and Products |
| 206 | |
| 3321 | 207 @DOCSTRING(sum) |
| 3294 | 208 |
| 3321 | 209 @DOCSTRING(prod) |
| 3294 | 210 |
| 3321 | 211 @DOCSTRING(cumsum) |
| 3294 | 212 |
| 3321 | 213 @DOCSTRING(cumprod) |
| 3294 | 214 |
| 3321 | 215 @DOCSTRING(sumsq) |
| 3294 | 216 |
| 6770 | 217 @DOCSTRING(accumarray) |
| 218 | |
| 4169 | 219 @node Special Functions |
| 3294 | 220 @section Special Functions |
| 221 | |
| 3459 | 222 @DOCSTRING(besselj) |
| 223 | |
| 224 @DOCSTRING(airy) | |
| 3294 | 225 |
| 3321 | 226 @DOCSTRING(beta) |
| 3294 | 227 |
| 3444 | 228 @DOCSTRING(betainc) |
| 3294 | 229 |
| 6502 | 230 @DOCSTRING(betaln) |
| 231 | |
| 3321 | 232 @DOCSTRING(bincoeff) |
| 3294 | 233 |
| 3321 | 234 @DOCSTRING(erf) |
| 3294 | 235 |
| 3321 | 236 @DOCSTRING(erfc) |
| 3294 | 237 |
| 3321 | 238 @DOCSTRING(erfinv) |
| 3294 | 239 |
| 3321 | 240 @DOCSTRING(gamma) |
| 3294 | 241 |
| 3444 | 242 @DOCSTRING(gammainc) |
| 3294 | 243 |
| 6502 | 244 @DOCSTRING(legendre) |
| 245 | |
| 3321 | 246 @DOCSTRING(lgamma) |
| 247 | |
| 248 @DOCSTRING(cross) | |
| 3294 | 249 |
| 3321 | 250 @DOCSTRING(commutation_matrix) |
| 3294 | 251 |
| 3321 | 252 @DOCSTRING(duplication_matrix) |
| 3294 | 253 |
| 4169 | 254 @node Coordinate Transformations |
| 3803 | 255 @section Coordinate Transformations |
| 256 | |
| 257 @DOCSTRING(cart2pol) | |
| 258 | |
| 259 @DOCSTRING(pol2cart) | |
| 260 | |
| 261 @DOCSTRING(cart2sph) | |
| 262 | |
| 263 @DOCSTRING(sph2cart) | |
| 264 | |
| 4169 | 265 @node Mathematical Constants |
| 3294 | 266 @section Mathematical Constants |
| 267 | |
| 3321 | 268 @DOCSTRING(I) |
| 269 | |
| 270 @DOCSTRING(Inf) | |
| 3294 | 271 |
| 3321 | 272 @DOCSTRING(NaN) |
| 3294 | 273 |
| 3321 | 274 @DOCSTRING(pi) |
| 3294 | 275 |
| 3321 | 276 @DOCSTRING(e) |
| 277 | |
| 278 @DOCSTRING(eps) | |
| 3294 | 279 |
| 3321 | 280 @DOCSTRING(realmax) |
| 3294 | 281 |
| 3321 | 282 @DOCSTRING(realmin) |