Mercurial > octave
view doc/interpreter/arith.txi @ 30564:796f54d4ddbf stable
update Octave Project Developers copyright for the new year
In files that have the "Octave Project Developers" copyright notice,
update for 2021.
In all .txi and .texi files except gpl.txi and gpl.texi in the
doc/liboctave and doc/interpreter directories, change the copyright
to "Octave Project Developers", the same as used for other source
files. Update copyright notices for 2022 (not done since 2019). For
gpl.txi and gpl.texi, change the copyright notice to be "Free Software
Foundation, Inc." and leave the date at 2007 only because this file
only contains the text of the GPL, not anything created by the Octave
Project Developers.
Add Paul Thomas to contributors.in.
author | John W. Eaton <jwe@octave.org> |
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date | Tue, 28 Dec 2021 18:22:40 -0500 |
parents | b58e3a04fab3 |
children | 597f3ee61a48 |
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@c Copyright (C) 1996-2022 The Octave Project Developers @c @c This file is part of Octave. @c @c Octave is free software: you can redistribute it and/or modify it @c under the terms of the GNU General Public License as published by @c the Free Software Foundation, either version 3 of the License, or @c (at your option) any later version. @c @c Octave is distributed in the hope that it will be useful, but @c WITHOUT ANY WARRANTY; without even the implied warranty of @c MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the @c GNU General Public License for more details. @c @c You should have received a copy of the GNU General Public License @c along with Octave; see the file COPYING. If not, see @c <https://www.gnu.org/licenses/>. @node Arithmetic @chapter Arithmetic Unless otherwise noted, all of the functions described in this chapter will work for real and complex scalar, vector, or matrix arguments. Functions described as @dfn{mapping functions} apply the given operation individually to each element when given a matrix argument. For example: @example @group sin ([1, 2; 3, 4]) @result{} 0.84147 0.90930 0.14112 -0.75680 @end group @end example @menu * Exponents and Logarithms:: * Complex Arithmetic:: * Trigonometry:: * Sums and Products:: * Utility Functions:: * Special Functions:: * Rational Approximations:: * Coordinate Transformations:: * Mathematical Constants:: @end menu @node Exponents and Logarithms @section Exponents and Logarithms @DOCSTRING(exp) @DOCSTRING(expm1) @DOCSTRING(log) @DOCSTRING(reallog) @DOCSTRING(log1p) @DOCSTRING(log10) @DOCSTRING(log2) @DOCSTRING(pow2) @DOCSTRING(nextpow2) @DOCSTRING(realpow) @DOCSTRING(sqrt) @DOCSTRING(realsqrt) @DOCSTRING(cbrt) @DOCSTRING(nthroot) @node Complex Arithmetic @section Complex Arithmetic In the descriptions of the following functions, @tex $z$ is the complex number $x + iy$, where $i$ is defined as $\sqrt{-1}$. @end tex @ifnottex @var{z} is the complex number @var{x} + @var{i}@var{y}, where @var{i} is defined as @code{sqrt (-1)}. @end ifnottex @DOCSTRING(abs) @DOCSTRING(arg) @DOCSTRING(conj) @DOCSTRING(cplxpair) @DOCSTRING(imag) @DOCSTRING(real) @node Trigonometry @section Trigonometry Octave provides the following trigonometric functions where angles are specified in radians. To convert from degrees to radians multiply by @tex $\pi/180$ @end tex @ifnottex @code{pi/180} @end ifnottex or use the @code{deg2rad} function. For example, @code{sin (30 * pi/180)} returns the sine of 30 degrees. As an alternative, Octave provides a number of trigonometric functions which work directly on an argument specified in degrees. These functions are named after the base trigonometric function with a @samp{d} suffix. As an example, @code{sin} expects an angle in radians while @code{sind} expects an angle in degrees. Octave uses the C library trigonometric functions. It is expected that these functions are defined by the ISO/IEC 9899 Standard. This Standard is available at: @url{http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1124.pdf}. Section F.9.1 deals with the trigonometric functions. The behavior of most of the functions is relatively straightforward. However, there are some exceptions to the standard behavior. Many of the exceptions involve the behavior for -0. The most complex case is atan2. Octave exactly implements the behavior given in the Standard. Including @tex $atan2(\pm0, -0)$ returns $\pm \pi$. @end tex @ifnottex @code{atan2(+- 0, 0)} returns @code{+- pi}. @end ifnottex It should be noted that @sc{matlab} uses different definitions which apparently do not distinguish -0. @DOCSTRING(deg2rad) @DOCSTRING(rad2deg) @DOCSTRING(sin) @DOCSTRING(cos) @DOCSTRING(tan) @DOCSTRING(sec) @DOCSTRING(csc) @DOCSTRING(cot) @DOCSTRING(asin) @DOCSTRING(acos) @DOCSTRING(atan) @DOCSTRING(asec) @DOCSTRING(acsc) @DOCSTRING(acot) @DOCSTRING(sinh) @DOCSTRING(cosh) @DOCSTRING(tanh) @DOCSTRING(sech) @DOCSTRING(csch) @DOCSTRING(coth) @DOCSTRING(asinh) @DOCSTRING(acosh) @DOCSTRING(atanh) @DOCSTRING(asech) @DOCSTRING(acsch) @DOCSTRING(acoth) @DOCSTRING(atan2) Octave provides the following trigonometric functions where angles are specified in degrees. These functions produce true zeros at the appropriate intervals rather than the small round-off error that occurs when using radians. For example: @example @group cosd (90) @result{} 0 cos (pi/2) @result{} 6.1230e-17 @end group @end example @DOCSTRING(sind) @DOCSTRING(cosd) @DOCSTRING(tand) @DOCSTRING(secd) @DOCSTRING(cscd) @DOCSTRING(cotd) @DOCSTRING(asind) @DOCSTRING(acosd) @DOCSTRING(atand) @DOCSTRING(atan2d) @DOCSTRING(asecd) @DOCSTRING(acscd) @DOCSTRING(acotd) Finally, there are two trigonometric functions that calculate special arguments with increased accuracy. @DOCSTRING(sinpi) @DOCSTRING(cospi) @node Sums and Products @section Sums and Products @DOCSTRING(sum) @DOCSTRING(prod) @DOCSTRING(cumsum) @DOCSTRING(cumprod) @DOCSTRING(sumsq) @node Utility Functions @section Utility Functions @DOCSTRING(ceil) @DOCSTRING(fix) @DOCSTRING(floor) @DOCSTRING(round) @DOCSTRING(roundb) @DOCSTRING(max) @DOCSTRING(min) @DOCSTRING(cummax) @DOCSTRING(cummin) @DOCSTRING(hypot) @DOCSTRING(gradient) @DOCSTRING(dot) @DOCSTRING(cross) @DOCSTRING(divergence) @DOCSTRING(curl) @DOCSTRING(del2) @DOCSTRING(factorial) @DOCSTRING(factor) @DOCSTRING(gcd) @DOCSTRING(lcm) @DOCSTRING(rem) @DOCSTRING(mod) @DOCSTRING(primes) @DOCSTRING(list_primes) @DOCSTRING(sign) @DOCSTRING(signbit) @node Special Functions @section Special Functions @DOCSTRING(airy) @DOCSTRING(besselj) @DOCSTRING(bessely) @DOCSTRING(besseli) @DOCSTRING(besselk) @DOCSTRING(besselh) @DOCSTRING(beta) @DOCSTRING(betainc) @DOCSTRING(betaincinv) @DOCSTRING(betaln) @DOCSTRING(bincoeff) @DOCSTRING(commutation_matrix) @DOCSTRING(cosint) @DOCSTRING(duplication_matrix) @DOCSTRING(dawson) @DOCSTRING(ellipj) @DOCSTRING(ellipke) @DOCSTRING(erf) @DOCSTRING(erfc) @DOCSTRING(erfcx) @DOCSTRING(erfi) @DOCSTRING(erfinv) @DOCSTRING(erfcinv) @DOCSTRING(expint) @DOCSTRING(gamma) @DOCSTRING(gammainc) @DOCSTRING(gammaincinv) @DOCSTRING(legendre) @anchor{XREFgammaln} @DOCSTRING(lgamma) @DOCSTRING(psi) @DOCSTRING(sinint) @node Rational Approximations @section Rational Approximations @DOCSTRING(rat) @DOCSTRING(rats) @node Coordinate Transformations @section Coordinate Transformations @DOCSTRING(cart2pol) @DOCSTRING(pol2cart) @DOCSTRING(cart2sph) @DOCSTRING(sph2cart) @node Mathematical Constants @section Mathematical Constants @DOCSTRING(e) @DOCSTRING(pi) @DOCSTRING(I) @DOCSTRING(Inf) @DOCSTRING(NaN) @DOCSTRING(eps) @DOCSTRING(realmax) @DOCSTRING(realmin)