Mercurial > octave
view scripts/specfun/nthroot.m @ 31246:43a6be589387
doc: New documentation for memoization techniques (bug #60860)
vectorize.texi: New section on memoization
octave.texi: List new section
author | Arun Giridhar <arungiridhar@gmail.com> |
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date | Thu, 29 Sep 2022 20:31:52 -0400 |
parents | 5d3faba0342e |
children | 597f3ee61a48 |
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######################################################################## ## ## Copyright (C) 2004-2022 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or <https://octave.org/copyright/>. ## ## This file is part of Octave. ## ## Octave is free software: you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## <https://www.gnu.org/licenses/>. ## ######################################################################## ## ## Original version by Paul Kienzle distributed as free software in the ## public domain. ## -*- texinfo -*- ## @deftypefn {} {@var{y} =} nthroot (@var{x}, @var{n}) ## ## Compute the real (non-complex) @var{n}-th root of @var{x}. ## ## @var{x} must have all real entries and @var{n} must be a scalar. ## If @var{n} is an even integer and @var{x} has negative entries then ## @code{nthroot} aborts and issues an error. ## ## Example: ## ## @example ## @group ## nthroot (-1, 3) ## @result{} -1 ## (-1) ^ (1 / 3) ## @result{} 0.50000 - 0.86603i ## @end group ## @end example ## @seealso{realsqrt, sqrt, cbrt} ## @end deftypefn function y = nthroot (x, n) if (nargin != 2) print_usage (); endif if (iscomplex (x)) error ("nthroot: X must not contain complex values"); endif if (! isreal (n) || ! isscalar (n) || n == 0) error ("nthroot: N must be a real nonzero scalar"); endif if (n == 3) y = cbrt (x); elseif (n == -3) y = 1 ./ cbrt (x); elseif (n < 0) y = 1 ./ nthroot (x, -n); else ## Compute using power. integer_n = n == fix (n); if (integer_n && mod (n, 2) == 1) y = abs (x) .^ (1/n) .* sign (x); elseif (any (x(:) < 0)) error ("nthroot: N must be an odd integer if X contains negative values"); else y = x .^ (1/n); endif if (integer_n && n > 0 && isfinite (n)) if (isscalar (y) && y == 0) ## Don't apply correction which leads to division by zero (bug #43492) else ## FIXME: What is this correction for? y = ((n-1)*y + x ./ (y.^(n-1))) / n; y = merge (isfinite (y), y, x); endif endif endif endfunction %!assert (nthroot (-32, 5), -2) %!assert (nthroot (81, 4), 3) %!assert (nthroot (Inf, 4), Inf) %!assert (nthroot (-Inf, 7), -Inf) %!assert (nthroot (-Inf, -7), 0) ## This should not generate a division by zero warning %!test <*43492> %! warnmsg = lastwarn (); %! assert (nthroot (0, 2), 0); %! assert (lastwarn (), warnmsg); ## Test input validation %!error <Invalid call> nthroot () %!error <Invalid call> nthroot (1) %!error <X must not contain complex values> nthroot (1+j, 2) %!error <N must be a real nonzero scalar> nthroot (1, i) %!error <N must be a real nonzero scalar> nthroot (1, [1 2]) %!error <N must be a real nonzero scalar> nthroot (1, 0) %!error <N must be an odd integer> nthroot (-1, 2)