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annotate doc/interpreter/arith.txi @ 9165:8c71a86c4bf4
Update section 17.5 (Utility Functions) of arith.txi
author | Rik <rdrider0-list@yahoo.com> |
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date | Fri, 01 May 2009 10:06:16 -0700 |
parents | ad20b967e1c9 |
children | 1231b1762a9a |
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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, vector, or matrix arguments. Functions |
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25 described as @dfn{mapping functions} apply the given operation individually to |
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26 each element when given a matrix argument. For example, |
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27 |
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28 @example |
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29 @group |
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30 sin ([1, 2; 3, 4]) |
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31 @result{} 0.84147 0.90930 |
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32 0.14112 -0.75680 |
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33 @end group |
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34 @end example |
3294 | 35 |
36 @menu | |
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37 * Exponents and Logarithms:: |
3294 | 38 * Complex Arithmetic:: |
39 * Trigonometry:: | |
40 * Sums and Products:: | |
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41 * Utility Functions:: |
3294 | 42 * Special Functions:: |
3803 | 43 * Coordinate Transformations:: |
3294 | 44 * Mathematical Constants:: |
45 @end menu | |
46 | |
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47 @node Exponents and Logarithms |
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48 @section Exponents and Logarithms |
6788 | 49 |
3321 | 50 @DOCSTRING(exp) |
3294 | 51 |
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52 @DOCSTRING(expm1) |
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53 |
3321 | 54 @DOCSTRING(log) |
3294 | 55 |
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56 @DOCSTRING(log1p) |
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57 |
3321 | 58 @DOCSTRING(log10) |
3294 | 59 |
3321 | 60 @DOCSTRING(log2) |
3294 | 61 |
3321 | 62 @DOCSTRING(nextpow2) |
3294 | 63 |
6550 | 64 @DOCSTRING(nthroot) |
65 | |
3321 | 66 @DOCSTRING(pow2) |
3294 | 67 |
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68 @DOCSTRING(reallog) |
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69 |
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70 @DOCSTRING(realpow) |
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71 |
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72 @DOCSTRING(realsqrt) |
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73 |
3321 | 74 @DOCSTRING(sqrt) |
3294 | 75 |
4169 | 76 @node Complex Arithmetic |
3294 | 77 @section Complex Arithmetic |
78 | |
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79 In the descriptions of the following functions, |
3294 | 80 @iftex |
81 @tex | |
82 $z$ is the complex number $x + iy$, where $i$ is defined as | |
83 $\sqrt{-1}$. | |
84 @end tex | |
85 @end iftex | |
86 @ifinfo | |
87 @var{z} is the complex number @var{x} + @var{i}@var{y}, where @var{i} is | |
88 defined as @code{sqrt (-1)}. | |
89 @end ifinfo | |
90 | |
3321 | 91 @DOCSTRING(abs) |
3294 | 92 |
3321 | 93 @DOCSTRING(arg) |
3294 | 94 |
3321 | 95 @DOCSTRING(conj) |
3294 | 96 |
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97 @DOCSTRING(cplxpair) |
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98 |
3321 | 99 @DOCSTRING(imag) |
3294 | 100 |
3321 | 101 @DOCSTRING(real) |
3294 | 102 |
4169 | 103 @node Trigonometry |
3294 | 104 @section Trigonometry |
105 | |
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106 Octave provides the following trigonometric functions where angles are |
6939 | 107 specified in radians. To convert from degrees to radians multiply by |
3294 | 108 @iftex |
109 @tex | |
110 $\pi/180$ | |
111 @end tex | |
112 @end iftex | |
113 @ifinfo | |
114 @code{pi/180} | |
115 @end ifinfo | |
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116 (e.g., @code{sin (30 * pi/180)} returns the sine of 30 degrees). As |
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117 an alternative, Octave provides a number of trigonometric functions |
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118 which work directly on an argument specified in degrees. These functions |
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119 are named after the base trigonometric function with a @samp{d} suffix. For |
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120 example, @code{sin} expects an angle in radians while @code{sind} expects an |
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121 angle in degrees. |
3294 | 122 |
3321 | 123 @DOCSTRING(sin) |
124 @DOCSTRING(cos) | |
125 @DOCSTRING(tan) | |
126 @DOCSTRING(sec) | |
127 @DOCSTRING(csc) | |
128 @DOCSTRING(cot) | |
3294 | 129 |
3321 | 130 @DOCSTRING(asin) |
131 @DOCSTRING(acos) | |
132 @DOCSTRING(atan) | |
133 @DOCSTRING(asec) | |
134 @DOCSTRING(acsc) | |
135 @DOCSTRING(acot) | |
3294 | 136 |
3321 | 137 @DOCSTRING(sinh) |
138 @DOCSTRING(cosh) | |
139 @DOCSTRING(tanh) | |
140 @DOCSTRING(sech) | |
3428 | 141 @DOCSTRING(csch) |
3321 | 142 @DOCSTRING(coth) |
3294 | 143 |
3321 | 144 @DOCSTRING(asinh) |
145 @DOCSTRING(acosh) | |
146 @DOCSTRING(atanh) | |
147 @DOCSTRING(asech) | |
148 @DOCSTRING(acsch) | |
149 @DOCSTRING(acoth) | |
3294 | 150 |
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151 @DOCSTRING(atan2) |
3294 | 152 |
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153 Octave provides the following trigonometric functions where angles are |
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154 specified in degrees. These functions produce true zeros at the appropriate |
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155 intervals rather than the small roundoff error that occurs when using |
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156 radians. For example: |
3294 | 157 @example |
158 @group | |
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159 cosd (90) |
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160 @result{} 0 |
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161 cos (pi/2) |
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162 @result{} 6.1230e-17 |
3294 | 163 @end group |
164 @end example | |
165 | |
6502 | 166 @DOCSTRING(sind) |
167 @DOCSTRING(cosd) | |
168 @DOCSTRING(tand) | |
169 @DOCSTRING(secd) | |
170 @DOCSTRING(cscd) | |
171 @DOCSTRING(cotd) | |
172 | |
173 @DOCSTRING(asind) | |
174 @DOCSTRING(acosd) | |
175 @DOCSTRING(atand) | |
176 @DOCSTRING(asecd) | |
177 @DOCSTRING(acscd) | |
178 @DOCSTRING(acotd) | |
3294 | 179 |
4169 | 180 @node Sums and Products |
3294 | 181 @section Sums and Products |
182 | |
3321 | 183 @DOCSTRING(sum) |
3294 | 184 |
3321 | 185 @DOCSTRING(prod) |
3294 | 186 |
3321 | 187 @DOCSTRING(cumsum) |
3294 | 188 |
3321 | 189 @DOCSTRING(cumprod) |
3294 | 190 |
3321 | 191 @DOCSTRING(sumsq) |
3294 | 192 |
6770 | 193 @DOCSTRING(accumarray) |
194 | |
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195 @node Utility Functions |
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196 @section Utility Functions |
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197 |
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198 @DOCSTRING(ceil) |
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199 |
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200 @DOCSTRING(cross) |
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201 |
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202 @DOCSTRING(del2) |
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203 |
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204 @DOCSTRING(factor) |
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205 |
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206 @DOCSTRING(factorial) |
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207 |
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208 @DOCSTRING(fix) |
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209 |
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210 @DOCSTRING(floor) |
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211 |
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212 @DOCSTRING(fmod) |
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213 |
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214 @DOCSTRING(gcd) |
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215 |
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216 @DOCSTRING(gradient) |
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217 |
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218 @DOCSTRING(hypot) |
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219 |
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220 @DOCSTRING(lcm) |
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221 |
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222 @DOCSTRING(list_primes) |
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224 @DOCSTRING(max) |
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226 @DOCSTRING(min) |
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228 @DOCSTRING(cummax) |
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230 @DOCSTRING(cummin) |
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232 @DOCSTRING(mod) |
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234 @DOCSTRING(primes) |
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236 @DOCSTRING(rem) |
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238 @DOCSTRING(round) |
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240 @DOCSTRING(roundb) |
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241 |
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242 @DOCSTRING(sign) |
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243 |
4169 | 244 @node Special Functions |
3294 | 245 @section Special Functions |
246 | |
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247 @DOCSTRING(airy) |
3459 | 248 |
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249 @DOCSTRING(besselj) |
3294 | 250 |
3321 | 251 @DOCSTRING(beta) |
3294 | 252 |
3444 | 253 @DOCSTRING(betainc) |
3294 | 254 |
6502 | 255 @DOCSTRING(betaln) |
256 | |
3321 | 257 @DOCSTRING(bincoeff) |
3294 | 258 |
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259 @DOCSTRING(commutation_matrix) |
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260 |
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261 @DOCSTRING(duplication_matrix) |
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262 |
3321 | 263 @DOCSTRING(erf) |
3294 | 264 |
3321 | 265 @DOCSTRING(erfc) |
3294 | 266 |
3321 | 267 @DOCSTRING(erfinv) |
3294 | 268 |
3321 | 269 @DOCSTRING(gamma) |
3294 | 270 |
3444 | 271 @DOCSTRING(gammainc) |
3294 | 272 |
6502 | 273 @DOCSTRING(legendre) |
274 | |
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275 @anchor{doc-gammaln} |
3321 | 276 @DOCSTRING(lgamma) |
277 | |
4169 | 278 @node Coordinate Transformations |
3803 | 279 @section Coordinate Transformations |
280 | |
281 @DOCSTRING(cart2pol) | |
282 | |
283 @DOCSTRING(pol2cart) | |
284 | |
285 @DOCSTRING(cart2sph) | |
286 | |
287 @DOCSTRING(sph2cart) | |
288 | |
4169 | 289 @node Mathematical Constants |
3294 | 290 @section Mathematical Constants |
291 | |
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292 @DOCSTRING(e) |
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293 |
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294 @DOCSTRING(pi) |
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295 |
3321 | 296 @DOCSTRING(I) |
297 | |
298 @DOCSTRING(Inf) | |
3294 | 299 |
3321 | 300 @DOCSTRING(NaN) |
3294 | 301 |
3321 | 302 @DOCSTRING(eps) |
3294 | 303 |
3321 | 304 @DOCSTRING(realmax) |
3294 | 305 |
3321 | 306 @DOCSTRING(realmin) |