Mercurial > octave-dspies
view doc/interpreter/arith.txi @ 19010:3fb030666878 draft default tip dspies
Added special-case logical-indexing function
* logical-index.h (New file) : Logical-indexing function. May be called on
octave_value types via call_bool_index
* nz-iterators.h : Add base-class nz_iterator for iterator types. Array has
template bool for whether to internally store row-col or compute on the fly
Add skip_ahead method which skips forward to the next nonzero after its
argument
Add flat_index for computing octave_idx_type index of current position (with
assertion failure in the case of overflow)
Move is_zero to separate file
* ov-base-diag.cc, ov-base-mat.cc, ov-base-sparse.cc, ov-perm.cc
(do_index_op): Add call to call_bool_index in logical-index.h
* Array.h : Move forward-declaration for array_iterator to separate header file
* dim-vector.cc (dim_max): Refers to idx-bounds.h (max_idx)
* array-iter-decl.h (New file): Header file for forward declaration of
array-iterator
* direction.h : Add constants fdirc and bdirc to avoid having to reconstruct
them
* dv-utils.h, dv-utils.cc (New files) :
Utility functions for querying and constructing dim-vectors
* idx-bounds.h (New file) :
Utility constants and functions for determining whether things will overflow
the maximum allowed bounds
* interp-idx.h (New function : to_flat_idx) : Converts row-col pair to linear
index of octave_idx_type
* is-zero.h (New file) : Function for determining whether an element is zero
* logical-index.tst : Add tests for correct return-value dimensions and large
sparse matrix behavior
author | David Spies <dnspies@gmail.com> |
---|---|
date | Fri, 25 Jul 2014 13:39:31 -0600 |
parents | d63878346099 |
children |
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@c Copyright (C) 1996-2013 John W. Eaton @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 the @c Free Software Foundation; either version 3 of the License, or (at @c your option) any later version. @c @c Octave is distributed in the hope that it will be useful, but WITHOUT @c ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or @c FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License @c 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 <http://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 (e.g., @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. For 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(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) @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(chop) @DOCSTRING(rem) @DOCSTRING(mod) @DOCSTRING(primes) @DOCSTRING(list_primes) @DOCSTRING(sign) @DOCSTRING(signbit) @node Special Functions @section Special Functions @DOCSTRING(airy) @DOCSTRING(besselj) @DOCSTRING(beta) @DOCSTRING(betainc) @DOCSTRING(betaincinv) @DOCSTRING(betaln) @DOCSTRING(bincoeff) @DOCSTRING(commutation_matrix) @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(legendre) @anchor{XREFgammaln} @DOCSTRING(lgamma) @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)