Mercurial > octave
view libinterp/corefcn/mappers.cc @ 25413:39cf8145405f
Make "tolower" and "toupper" Unicode aware (bug #53873).
* ov-ch-mat.cc (map): Use UTF-8 aware functions for "tolower" and "toupper".
* mappers.cc: Add tests for "tolower" and "toupper".
* unicase-wrappers.[c/h]: Add wrappers for "u8_tolower" and "u8_toupper".
* module.mk: Add new files.
* bootstrap.conf: Add modules "unicase/u8-tolower" and "unicase/u8-toupper".
author | Markus Mützel <markus.muetzel@gmx.de> |
---|---|
date | Wed, 16 May 2018 21:36:27 +0200 |
parents | b9c62b62f9eb |
children | d4bc8590b5cf |
line wrap: on
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/* Copyright (C) 1993-2018 John W. Eaton Copyright (C) 2009-2010 VZLU Prague 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/>. */ #if defined (HAVE_CONFIG_H) # include "config.h" #endif #include <cctype> #include "lo-ieee.h" #include "lo-specfun.h" #include "lo-mappers.h" #include "defun.h" #include "error.h" #include "variables.h" DEFUN (abs, args, , doc: /* -*- texinfo -*- @deftypefn {} {} abs (@var{z}) Compute the magnitude of @var{z}. The magnitude is defined as @tex $|z| = \sqrt{x^2 + y^2}$. @end tex @ifnottex |@var{z}| = @code{sqrt (x^2 + y^2)}. @end ifnottex For example: @example @group abs (3 + 4i) @result{} 5 @end group @end example @seealso{arg} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).abs ()); } /* %!assert (abs (1), 1) %!assert (abs (-3.5), 3.5) %!assert (abs (3+4i), 5) %!assert (abs (3-4i), 5) %!assert (abs ([1.1, 3i; 3+4i, -3-4i]), [1.1, 3; 5, 5]) %!assert (abs (single (1)), single (1)) %!assert (abs (single (-3.5)), single (3.5)) %!assert (abs (single (3+4i)), single (5)) %!assert (abs (single (3-4i)), single (5)) %!assert (abs (single ([1.1, 3i; 3+4i, -3-4i])), single ([1.1, 3; 5, 5])) %!error abs () %!error abs (1, 2) */ DEFUN (acos, args, , doc: /* -*- texinfo -*- @deftypefn {} {} acos (@var{x}) Compute the inverse cosine in radians for each element of @var{x}. @seealso{cos, acosd} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).acos ()); } /* %!shared rt2, rt3 %! rt2 = sqrt (2); %! rt3 = sqrt (3); %!test %! x = [1, rt3/2, rt2/2, 1/2, 0, -1/2, -rt2/2, -rt3/2, -1]; %! v = [0, pi/6, pi/4, pi/3, pi/2, 2*pi/3, 3*pi/4, 5*pi/6, pi]; %! assert (acos (x), v, sqrt (eps)); %!test %! x = single ([1, rt3/2, rt2/2, 1/2, 0, -1/2, -rt2/2, -rt3/2, -1]); %! v = single ([0, pi/6, pi/4, pi/3, pi/2, 2*pi/3, 3*pi/4, 5*pi/6, pi]); %! assert (acos (x), v, sqrt (eps ("single"))); ## Test values on either side of branch cut %!test %! rval = 0; %! ival = 1.31695789692481671; %! obs = acos ([2, 2-i*eps, 2+i*eps]); %! exp = [rval + ival*i, rval + ival*i, rval - ival*i]; %! assert (obs, exp, 3*eps); %! rval = pi; %! obs = acos ([-2, -2-i*eps, -2+i*eps]); %! exp = [rval - ival*i, rval + ival*i, rval - ival*i]; %! assert (obs, exp, 5*eps); %! assert (acos ([2 0]), [ival*i, pi/2], 3*eps); %! assert (acos ([2 0i]), [ival*i, pi/2], 3*eps); ## Test large magnitude arguments (bug #45507) ## Test fails with older versions of libm, solution is to upgrade. %!testif ; ! ismac () && ! ispc () <*45507> %! x = [1, -1, i, -i] .* 1e150; %! v = [0, pi, pi/2, pi/2]; %! assert (real (acos (x)), v); %!xtest <52627> %! ## Same test code as above, but intended only for test statistics on Mac and %! ## Windows. Their trig/hyperbolic functions have huge tolerances. %! if (! ismac ()), return; endif %! x = [1, -1, i, -i] .* 1e150; %! v = [0, pi, pi/2, pi/2]; %! assert (real (acos (x)), v); %!error acos () %!error acos (1, 2) */ DEFUN (acosh, args, , doc: /* -*- texinfo -*- @deftypefn {} {} acosh (@var{x}) Compute the inverse hyperbolic cosine for each element of @var{x}. @seealso{cosh} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).acosh ()); } /* %!testif ; ! ismac () %! x = [1, 0, -1, 0]; %! v = [0, pi/2*i, pi*i, pi/2*i]; %! assert (acosh (x), v, sqrt (eps)); %!xtest <52627> %! ## Same test code as above, but intended only for test statistics on Mac. %! ## Mac trig/hyperbolic functions have huge tolerances. %! if (! ismac ()), return; endif %! x = [1, 0, -1, 0]; %! v = [0, pi/2*i, pi*i, pi/2*i]; %! assert (acosh (x), v, sqrt (eps)); ## FIXME: std::acosh on Windows platforms, returns a result that differs ## by 1 in the last significant digit. This is ~30*eps which is quite large. ## The decision now (9/15/2016) is to mark the test with a bug number so ## it is understood why it is failing, and wait for MinGw to improve their ## std library. %!test <49091> %! re = 2.99822295029797; %! im = pi/2; %! assert (acosh (-10i), re - i*im); %!testif ; ! ismac () %! x = single ([1, 0, -1, 0]); %! v = single ([0, pi/2*i, pi*i, pi/2*i]); %! assert (acosh (x), v, sqrt (eps ("single"))); %!xtest <52627> %! ## Same test code as above, but intended only for test statistics on Mac. %! ## Mac trig/hyperbolic functions have huge tolerances. %! if (! ismac ()), return; endif %! x = single ([1, 0, -1, 0]); %! v = single ([0, pi/2*i, pi*i, pi/2*i]); %! assert (acosh (x), v, sqrt (eps ("single"))); %!test <49091> %! re = single (2.99822295029797); %! im = single (pi/2); %! assert (acosh (single (10i)), re + i*im, 5*eps ("single")); %! assert (acosh (single (-10i)), re - i*im, 5*eps ("single")); ## Test large magnitude arguments (bug #45507) ## Test fails with older versions of libm, solution is to upgrade. %!testif ; ! ismac () && ! ispc () <*45507> %! x = [1, -1, i, -i] .* 1e150; %! v = [0, pi, pi/2, -pi/2]; %! assert (imag (acosh (x)), v); %!xtest <52627> %! ## Same test code as above, but intended only for test statistics on Mac and %! ## Windows. Their trig/hyperbolic functions have huge tolerances. %! if (! ismac ()), return; endif %! x = [1, -1, i, -i] .* 1e150; %! v = [0, pi, pi/2, -pi/2]; %! assert (imag (acosh (x)), v); %!error acosh () %!error acosh (1, 2) */ DEFUN (angle, args, , doc: /* -*- texinfo -*- @deftypefn {} {} angle (@var{z}) See @code{arg}. @seealso{arg} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).arg ()); } DEFUN (arg, args, , doc: /* -*- texinfo -*- @deftypefn {} {} arg (@var{z}) @deftypefnx {} {} angle (@var{z}) Compute the argument, i.e., angle of @var{z}. This is defined as, @tex $\theta = atan2 (y, x),$ @end tex @ifnottex @var{theta} = @code{atan2 (@var{y}, @var{x})}, @end ifnottex in radians. For example: @example @group arg (3 + 4i) @result{} 0.92730 @end group @end example @seealso{abs} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).arg ()); } /* %!assert (arg (1), 0) %!assert (arg (i), pi/2) %!assert (arg (-1), pi) %!assert (arg (-i), -pi/2) %!assert (arg ([1, i; -1, -i]), [0, pi/2; pi, -pi/2]) %!assert (arg (single (1)), single (0)) %!assert (arg (single (i)), single (pi/2)) %!test %! if (ismac ()) %! ## Avoid failing for a MacOS feature %! assert (arg (single (-1)), single (pi), 2*eps (single (1))); %! else %! assert (arg (single (-1)), single (pi)); %! endif %!assert (arg (single (-i)), single (-pi/2)) %!assert (arg (single ([1, i; -1, -i])), single ([0, pi/2; pi, -pi/2]), 2e1*eps ("single")) %!error arg () %!error arg (1, 2) */ DEFUN (asin, args, , doc: /* -*- texinfo -*- @deftypefn {} {} asin (@var{x}) Compute the inverse sine in radians for each element of @var{x}. @seealso{sin, asind} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).asin ()); } /* %!shared rt2, rt3 %! rt2 = sqrt (2); %! rt3 = sqrt (3); %!test %! x = [0, 1/2, rt2/2, rt3/2, 1, rt3/2, rt2/2, 1/2, 0]; %! v = [0, pi/6, pi/4, pi/3, pi/2, pi/3, pi/4, pi/6, 0]; %! assert (asin (x), v, sqrt (eps)); %!test %! x = single ([0, 1/2, rt2/2, rt3/2, 1, rt3/2, rt2/2, 1/2, 0]); %! v = single ([0, pi/6, pi/4, pi/3, pi/2, pi/3, pi/4, pi/6, 0]); %! assert (asin (x), v, sqrt (eps ("single"))); ## Test values on either side of branch cut %!test %! rval = pi/2; %! ival = 1.31695789692481635; %! obs = asin ([2, 2-i*eps, 2+i*eps]); %! exp = [rval - ival*i, rval - ival*i, rval + ival*i]; %! assert (obs, exp, 2*eps); %! obs = asin ([-2, -2-i*eps, -2+i*eps]); %! exp = [-rval + ival*i, -rval - ival*i, -rval + ival*i]; %! assert (obs, exp, 2*eps); %! assert (asin ([2 0]), [rval - ival*i, 0], 2*eps); %! assert (asin ([2 0i]), [rval - ival*i, 0], 2*eps); ## Test large magnitude arguments (bug #45507) ## Test fails with older versions of libm, solution is to upgrade. %!testif ; ! ismac () && ! ispc () <*45507> %! x = [1, -1, i, -i] .* 1e150; %! v = [pi/2, -pi/2, 0, -0]; %! assert (real (asin (x)), v); %!xtest <52627> %! ## Same test code as above, but intended only for test statistics on Mac and %! ## Windows. Their trig/hyperbolic functions have huge tolerances. %! if (! ismac ()), return; endif %! x = [1, -1, i, -i] .* 1e150; %! v = [pi/2, -pi/2, 0, -0]; %! assert (real (asin (x)), v); %!error asin () %!error asin (1, 2) */ DEFUN (asinh, args, , doc: /* -*- texinfo -*- @deftypefn {} {} asinh (@var{x}) Compute the inverse hyperbolic sine for each element of @var{x}. @seealso{sinh} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).asinh ()); } /* %!test %! v = [0, pi/2*i, 0, -pi/2*i]; %! x = [0, i, 0, -i]; %! assert (asinh (x), v, sqrt (eps)); %!test %! v = single ([0, pi/2*i, 0, -pi/2*i]); %! x = single ([0, i, 0, -i]); %! assert (asinh (x), v, sqrt (eps ("single"))); ## Test large magnitude arguments (bug #45507) ## Test fails with older versions of libm, solution is to upgrade. %!testif ; ! ismac () && ! ispc () <*45507> %! x = [1, -1, i, -i] .* 1e150; %! v = [0, 0, pi/2, -pi/2]; %! assert (imag (asinh (x)), v); %!xtest <52627> %! ## Same test code as above, but intended only for test statistics on Mac and %! ## Windows. Their trig/hyperbolic functions have huge tolerances. %! if (! ismac ()), return; endif %! x = [1, -1, i, -i] .* 1e150; %! v = [0, 0, pi/2, -pi/2]; %! assert (imag (asinh (x)), v); %!error asinh () %!error asinh (1, 2) */ DEFUN (atan, args, , doc: /* -*- texinfo -*- @deftypefn {} {} atan (@var{x}) Compute the inverse tangent in radians for each element of @var{x}. @seealso{tan, atand} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).atan ()); } /* %!shared rt2, rt3 %! rt2 = sqrt (2); %! rt3 = sqrt (3); %!test %! v = [0, pi/6, pi/4, pi/3, -pi/3, -pi/4, -pi/6, 0]; %! x = [0, rt3/3, 1, rt3, -rt3, -1, -rt3/3, 0]; %! assert (atan (x), v, sqrt (eps)); %!test %! v = single ([0, pi/6, pi/4, pi/3, -pi/3, -pi/4, -pi/6, 0]); %! x = single ([0, rt3/3, 1, rt3, -rt3, -1, -rt3/3, 0]); %! assert (atan (x), v, sqrt (eps ("single"))); ## Test large magnitude arguments (bug #44310, bug #45507) %!test <*44310> %! x = [1, -1, i, -i] .* 1e150; %! v = [pi/2, -pi/2, pi/2, -pi/2]; %! assert (real (atan (x)), v); %! assert (imag (atan (x)), [0, 0, 0, 0], eps); %!error atan () %!error atan (1, 2) */ DEFUN (atanh, args, , doc: /* -*- texinfo -*- @deftypefn {} {} atanh (@var{x}) Compute the inverse hyperbolic tangent for each element of @var{x}. @seealso{tanh} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).atanh ()); } /* %!test %! v = [0, 0]; %! x = [0, 0]; %! assert (atanh (x), v, sqrt (eps)); %!test %! v = single ([0, 0]); %! x = single ([0, 0]); %! assert (atanh (x), v, sqrt (eps ("single"))); ## Test large magnitude arguments (bug #44310, bug #45507) %!test <*44310> %! x = [1, -1, i, -i] .* 1e150; %! v = [pi/2, pi/2, pi/2, -pi/2]; %! assert (imag (atanh (x)), v); %! assert (real (atanh (x)), [0, 0, 0, 0], eps); %!error atanh () %!error atanh (1, 2) */ DEFUN (cbrt, args, , doc: /* -*- texinfo -*- @deftypefn {} {} cbrt (@var{x}) Compute the real cube root of each element of @var{x}. Unlike @code{@var{x}^(1/3)}, the result will be negative if @var{x} is negative. @seealso{nthroot} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).cbrt ()); } /* %!assert (cbrt (64), 4) %!assert (cbrt (-125), -5) %!assert (cbrt (0), 0) %!assert (cbrt (Inf), Inf) %!assert (cbrt (-Inf), -Inf) %!assert (cbrt (NaN), NaN) %!assert (cbrt (2^300), 2^100) %!assert (cbrt (125*2^300), 5*2^100) %!error cbrt () %!error cbrt (1, 2) */ DEFUN (ceil, args, , doc: /* -*- texinfo -*- @deftypefn {} {} ceil (@var{x}) Return the smallest integer not less than @var{x}. This is equivalent to rounding towards positive infinity. If @var{x} is complex, return @code{ceil (real (@var{x})) + ceil (imag (@var{x})) * I}. @example @group ceil ([-2.7, 2.7]) @result{} -2 3 @end group @end example @seealso{floor, round, fix} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).ceil ()); } /* ## double precision %!assert (ceil ([2, 1.1, -1.1, -1]), [2, 2, -1, -1]) ## complex double precison %!assert (ceil ([2+2i, 1.1+1.1i, -1.1-1.1i, -1-i]), [2+2i, 2+2i, -1-i, -1-i]) ## single precision %!assert (ceil (single ([2, 1.1, -1.1, -1])), single ([2, 2, -1, -1])) ## complex single precision %!assert (ceil (single ([2+2i, 1.1+1.1i, -1.1-1.1i, -1-i])), single ([2+2i, 2+2i, -1-i, -1-i])) %!error ceil () %!error ceil (1, 2) */ DEFUN (conj, args, , doc: /* -*- texinfo -*- @deftypefn {} {} conj (@var{z}) Return the complex conjugate of @var{z}. The complex conjugate is defined as @tex $\bar{z} = x - iy$. @end tex @ifnottex @code{conj (@var{z})} = @var{x} - @var{i}@var{y}. @end ifnottex @seealso{real, imag} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).conj ()); } /* %!assert (conj (1), 1) %!assert (conj (i), -i) %!assert (conj (1+i), 1-i) %!assert (conj (1-i), 1+i) %!assert (conj ([-1, -i; -1+i, -1-i]), [-1, i; -1-i, -1+i]) %!assert (conj (single (1)), single (1)) %!assert (conj (single (i)), single (-i)) %!assert (conj (single (1+i)), single (1-i)) %!assert (conj (single (1-i)), single (1+i)) %!assert (conj (single ([-1, -i; -1+i, -1-i])), single ([-1, i; -1-i, -1+i])) %!error conj () %!error conj (1, 2) */ DEFUN (cos, args, , doc: /* -*- texinfo -*- @deftypefn {} {} cos (@var{x}) Compute the cosine for each element of @var{x} in radians. @seealso{acos, cosd, cosh} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).cos ()); } /* %!shared rt2, rt3 %! rt2 = sqrt (2); %! rt3 = sqrt (3); %!test %! x = [0, pi/6, pi/4, pi/3, pi/2, 2*pi/3, 3*pi/4, 5*pi/6, pi]; %! v = [1, rt3/2, rt2/2, 1/2, 0, -1/2, -rt2/2, -rt3/2, -1]; %! assert (cos (x), v, sqrt (eps)); %!test %! rt2 = sqrt (2); %! rt3 = sqrt (3); %! x = single ([0, pi/6, pi/4, pi/3, pi/2, 2*pi/3, 3*pi/4, 5*pi/6, pi]); %! v = single ([1, rt3/2, rt2/2, 1/2, 0, -1/2, -rt2/2, -rt3/2, -1]); %! assert (cos (x), v, sqrt (eps ("single"))); %!error cos () %!error cos (1, 2) */ DEFUN (cosh, args, , doc: /* -*- texinfo -*- @deftypefn {} {} cosh (@var{x}) Compute the hyperbolic cosine for each element of @var{x}. @seealso{acosh, sinh, tanh} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).cosh ()); } /* %!test %! x = [0, pi/2*i, pi*i, 3*pi/2*i]; %! v = [1, 0, -1, 0]; %! assert (cosh (x), v, sqrt (eps)); %!test %! x = single ([0, pi/2*i, pi*i, 3*pi/2*i]); %! v = single ([1, 0, -1, 0]); %! assert (cosh (x), v, sqrt (eps ("single"))); %!error cosh () %!error cosh (1, 2) */ DEFUN (erf, args, , doc: /* -*- texinfo -*- @deftypefn {} {} erf (@var{z}) Compute the error function. The error function is defined as @tex $$ {\rm erf} (z) = {2 \over \sqrt{\pi}}\int_0^z e^{-t^2} dt $$ @end tex @ifnottex @example @group z 2 / erf (z) = --------- * | e^(-t^2) dt sqrt (pi) / t=0 @end group @end example @end ifnottex @seealso{erfc, erfcx, erfi, dawson, erfinv, erfcinv} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).erf ()); } /* %!test %! a = -1i*sqrt (-1/(6.4187*6.4187)); %! assert (erf (a), erf (real (a))); %!test %! x = [0,.5,1]; %! v = [0, .520499877813047, .842700792949715]; %! assert (erf (x), v, 1.e-10); %! assert (erf (-x), -v, 1.e-10); %! assert (erfc (x), 1-v, 1.e-10); %! assert (erfinv (v), x, 1.e-10); %!test %! a = -1i*sqrt (single (-1/(6.4187*6.4187))); %! assert (erf (a), erf (real (a))); %!test %! x = single ([0,.5,1]); %! v = single ([0, .520499877813047, .842700792949715]); %! assert (erf (x), v, 1.e-6); %! assert (erf (-x), -v, 1.e-6); %! assert (erfc (x), 1-v, 1.e-6); %! assert (erfinv (v), x, 1.e-6); %!test %! x = [1+2i,-1+2i,1e-6+2e-6i,0+2i]; %! v = [-0.53664356577857-5.04914370344703i, 0.536643565778565-5.04914370344703i, 0.112837916709965e-5+0.225675833419178e-5i, 18.5648024145755526i]; %! assert (erf (x), v, -1.e-10); %! assert (erf (-x), -v, -1.e-10); %! assert (erfc (x), 1-v, -1.e-10); %!error erf () %!error erf (1, 2) */ DEFUN (erfinv, args, , doc: /* -*- texinfo -*- @deftypefn {} {} erfinv (@var{x}) Compute the inverse error function. The inverse error function is defined such that @example erf (@var{y}) == @var{x} @end example @seealso{erf, erfc, erfcx, erfi, dawson, erfcinv} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).erfinv ()); } /* ## middle region %!assert (erf (erfinv ([-0.9 -0.3 0 0.4 0.8])), [-0.9 -0.3 0 0.4 0.8], eps) %!assert (erf (erfinv (single ([-0.9 -0.3 0 0.4 0.8]))), single ([-0.9 -0.3 0 0.4 0.8]), eps ("single")) ## tail region %!assert (erf (erfinv ([-0.999 -0.99 0.9999 0.99999])), [-0.999 -0.99 0.9999 0.99999], eps) %!assert (erf (erfinv (single ([-0.999 -0.99 0.9999 0.99999]))), single ([-0.999 -0.99 0.9999 0.99999]), eps ("single")) ## backward - loss of accuracy %!assert (erfinv (erf ([-3 -1 -0.4 0.7 1.3 2.8])), [-3 -1 -0.4 0.7 1.3 2.8], -1e-12) %!assert (erfinv (erf (single ([-3 -1 -0.4 0.7 1.3 2.8]))), single ([-3 -1 -0.4 0.7 1.3 2.8]), -1e-4) ## exceptional %!assert (erfinv ([-1, 1, 1.1, -2.1]), [-Inf, Inf, NaN, NaN]) %!error erfinv (1+2i) %!error erfinv () %!error erfinv (1, 2) */ DEFUN (erfcinv, args, , doc: /* -*- texinfo -*- @deftypefn {} {} erfcinv (@var{x}) Compute the inverse complementary error function. The inverse complementary error function is defined such that @example erfc (@var{y}) == @var{x} @end example @seealso{erfc, erf, erfcx, erfi, dawson, erfinv} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).erfcinv ()); } /* ## middle region %!assert (erfc (erfcinv ([1.9 1.3 1 0.6 0.2])), [1.9 1.3 1 0.6 0.2], eps) %!assert (erfc (erfcinv (single ([1.9 1.3 1 0.6 0.2]))), single ([1.9 1.3 1 0.6 0.2]), eps ("single")) ## tail region %!assert (erfc (erfcinv ([0.001 0.01 1.9999 1.99999])), [0.001 0.01 1.9999 1.99999], eps) %!assert (erfc (erfcinv (single ([0.001 0.01 1.9999 1.99999]))), single ([0.001 0.01 1.9999 1.99999]), eps ("single")) ## backward - loss of accuracy %!assert (erfcinv (erfc ([-3 -1 -0.4 0.7 1.3 2.8])), [-3 -1 -0.4 0.7 1.3 2.8], -1e-12) %!assert (erfcinv (erfc (single ([-3 -1 -0.4 0.7 1.3 2.8]))), single ([-3 -1 -0.4 0.7 1.3 2.8]), -1e-4) ## exceptional %!assert (erfcinv ([2, 0, -0.1, 2.1]), [-Inf, Inf, NaN, NaN]) %!error erfcinv (1+2i) %!error erfcinv () %!error erfcinv (1, 2) */ DEFUN (erfc, args, , doc: /* -*- texinfo -*- @deftypefn {} {} erfc (@var{z}) Compute the complementary error function. The complementary error function is defined as @tex $1 - {\rm erf} (z)$. @end tex @ifnottex @w{@code{1 - erf (@var{z})}}. @end ifnottex @seealso{erfcinv, erfcx, erfi, dawson, erf, erfinv} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).erfc ()); } /* %!test %! a = -1i*sqrt (-1/(6.4187*6.4187)); %! assert (erfc (a), erfc (real (a))); %!error erfc () %!error erfc (1, 2) */ DEFUN (erfcx, args, , doc: /* -*- texinfo -*- @deftypefn {} {} erfcx (@var{z}) Compute the scaled complementary error function. The scaled complementary error function is defined as @tex $$ e^{z^2} {\rm erfc} (z) \equiv e^{z^2} (1 - {\rm erf} (z)) $$ @end tex @ifnottex @example exp (z^2) * erfc (z) @end example @end ifnottex @seealso{erfc, erf, erfi, dawson, erfinv, erfcinv} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).erfcx ()); } /* %!test %! x = [1+2i,-1+2i,1e-6+2e-6i,0+2i]; %! assert (erfcx (x), exp (x.^2) .* erfc(x), -1.e-10); %!test %! x = [100, 100+20i]; %! v = [0.0056416137829894329, 0.0054246791754558-0.00108483153786434i]; %! assert (erfcx (x), v, -1.e-10); %!error erfcx () %!error erfcx (1, 2) */ DEFUN (erfi, args, , doc: /* -*- texinfo -*- @deftypefn {} {} erfi (@var{z}) Compute the imaginary error function. The imaginary error function is defined as @tex $$ -i {\rm erf} (iz) $$ @end tex @ifnottex @example -i * erf (i*z) @end example @end ifnottex @seealso{erfc, erf, erfcx, dawson, erfinv, erfcinv} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).erfi ()); } /* %!test %! x = [-0.1, 0.1, 1, 1+2i,-1+2i,1e-6+2e-6i,0+2i]; %! assert (erfi (x), -i * erf(i*x), -1.e-10); %!error erfi () %!error erfi (1, 2) */ DEFUN (dawson, args, , doc: /* -*- texinfo -*- @deftypefn {} {} dawson (@var{z}) Compute the Dawson (scaled imaginary error) function. The Dawson function is defined as @tex $$ {\sqrt{\pi} \over 2} e^{-z^2} {\rm erfi} (z) \equiv -i {\sqrt{\pi} \over 2} e^{-z^2} {\rm erf} (iz) $$ @end tex @ifnottex @example (sqrt (pi) / 2) * exp (-z^2) * erfi (z) @end example @end ifnottex @seealso{erfc, erf, erfcx, erfi, erfinv, erfcinv} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).dawson ()); } /* %!test %! x = [0.1, 1, 1+2i,-1+2i,1e-4+2e-4i,0+2i]; %! v = [0.099335992397852861, 0.53807950691, -13.38892731648-11.828715104i, 13.38892731648-11.828715104i, 0.0001000000073333+0.000200000001333i, 48.160012114291i]; %! assert (dawson (x), v, -1.e-10); %! assert (dawson (-x), -v, -1.e-10); %!error dawson () %!error dawson (1, 2) */ DEFUN (exp, args, , doc: /* -*- texinfo -*- @deftypefn {} {} exp (@var{x}) Compute @tex $e^{x}$ @end tex @ifnottex @code{e^x} @end ifnottex for each element of @var{x}. To compute the matrix exponential, see @ref{Linear Algebra}. @seealso{log} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).exp ()); } /* %!assert (exp ([0, 1, -1, -1000]), [1, e, 1/e, 0], sqrt (eps)) %!assert (exp (1+i), e * (cos (1) + sin (1) * i), sqrt (eps)) %!assert (exp (single ([0, 1, -1, -1000])), single ([1, e, 1/e, 0]), sqrt (eps ("single"))) %!assert (exp (single (1+i)), single (e * (cos (1) + sin (1) * i)), sqrt (eps ("single"))) %!assert (exp ([Inf, -Inf, NaN]), [Inf 0 NaN]) %!assert (exp (single ([Inf, -Inf, NaN])), single ([Inf 0 NaN])) %!error exp () %!error exp (1, 2) */ DEFUN (expm1, args, , doc: /* -*- texinfo -*- @deftypefn {} {} expm1 (@var{x}) Compute @tex $ e^{x} - 1 $ @end tex @ifnottex @code{exp (@var{x}) - 1} @end ifnottex accurately in the neighborhood of zero. @seealso{exp} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).expm1 ()); } /* %!assert (expm1 (2*eps), 2*eps, 1e-29) %!assert (expm1 ([Inf, -Inf, NaN]), [Inf -1 NaN]) %!assert (expm1 (single ([Inf, -Inf, NaN])), single ([Inf -1 NaN])) %!error expm1 () %!error expm1 (1, 2) */ DEFUN (isfinite, args, , doc: /* -*- texinfo -*- @deftypefn {} {} isfinite (@var{x}) Return a logical array which is true where the elements of @var{x} are finite values and false where they are not. For example: @example @group isfinite ([13, Inf, NA, NaN]) @result{} [ 1, 0, 0, 0 ] @end group @end example @seealso{isinf, isnan, isna} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).isfinite ()); } /* %!assert (! isfinite (Inf)) %!assert (! isfinite (NaN)) %!assert (isfinite (rand (1,10))) %!assert (! isfinite (single (Inf))) %!assert (! isfinite (single (NaN))) %!assert (isfinite (single (rand (1,10)))) %!error isfinite () %!error isfinite (1, 2) */ DEFUN (fix, args, , doc: /* -*- texinfo -*- @deftypefn {} {} fix (@var{x}) Truncate fractional portion of @var{x} and return the integer portion. This is equivalent to rounding towards zero. If @var{x} is complex, return @code{fix (real (@var{x})) + fix (imag (@var{x})) * I}. @example @group fix ([-2.7, 2.7]) @result{} -2 2 @end group @end example @seealso{ceil, floor, round} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).fix ()); } /* %!assert (fix ([1.1, 1, -1.1, -1]), [1, 1, -1, -1]) %!assert (fix ([1.1+1.1i, 1+i, -1.1-1.1i, -1-i]), [1+i, 1+i, -1-i, -1-i]) %!assert (fix (single ([1.1, 1, -1.1, -1])), single ([1, 1, -1, -1])) %!assert (fix (single ([1.1+1.1i, 1+i, -1.1-1.1i, -1-i])), single ([1+i, 1+i, -1-i, -1-i])) %!error fix () %!error fix (1, 2) */ DEFUN (floor, args, , doc: /* -*- texinfo -*- @deftypefn {} {} floor (@var{x}) Return the largest integer not greater than @var{x}. This is equivalent to rounding towards negative infinity. If @var{x} is complex, return @code{floor (real (@var{x})) + floor (imag (@var{x})) * I}. @example @group floor ([-2.7, 2.7]) @result{} -3 2 @end group @end example @seealso{ceil, round, fix} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).floor ()); } /* %!assert (floor ([2, 1.1, -1.1, -1]), [2, 1, -2, -1]) %!assert (floor ([2+2i, 1.1+1.1i, -1.1-1.1i, -1-i]), [2+2i, 1+i, -2-2i, -1-i]) %!assert (floor (single ([2, 1.1, -1.1, -1])), single ([2, 1, -2, -1])) %!assert (floor (single ([2+2i, 1.1+1.1i, -1.1-1.1i, -1-i])), single ([2+2i, 1+i, -2-2i, -1-i])) %!error floor () %!error floor (1, 2) */ DEFUN (gamma, args, , doc: /* -*- texinfo -*- @deftypefn {} {} gamma (@var{z}) Compute the Gamma function. The Gamma function is defined as @tex $$ \Gamma (z) = \int_0^\infty t^{z-1} e^{-t} dt. $$ @end tex @ifnottex @example @group infinity / gamma (z) = | t^(z-1) exp (-t) dt. / t=0 @end group @end example @end ifnottex Programming Note: The gamma function can grow quite large even for small input values. In many cases it may be preferable to use the natural logarithm of the gamma function (@code{gammaln}) in calculations to minimize loss of precision. The final result is then @code{exp (@var{result_using_gammaln}).} @seealso{gammainc, gammaln, factorial} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).gamma ()); } /* %!test %! a = -1i*sqrt (-1/(6.4187*6.4187)); %! assert (gamma (a), gamma (real (a))); %!test %! x = [.5, 1, 1.5, 2, 3, 4, 5]; %! v = [sqrt(pi), 1, .5*sqrt(pi), 1, 2, 6, 24]; %! assert (gamma (x), v, sqrt (eps)); %!test %! a = single (-1i*sqrt (-1/(6.4187*6.4187))); %! assert (gamma (a), gamma (real (a))); %!test %! x = single ([.5, 1, 1.5, 2, 3, 4, 5]); %! v = single ([sqrt(pi), 1, .5*sqrt(pi), 1, 2, 6, 24]); %! assert (gamma (x), v, sqrt (eps ("single"))); %!test %! ## Test exceptional values %! x = [-Inf, -1, -0, 0, 1, Inf, NaN]; %! v = [Inf, Inf, -Inf, Inf, 1, Inf, NaN]; %! assert (gamma (x), v); %! assert (gamma (single (x)), single (v)); %!error gamma () %!error gamma (1, 2) */ DEFUN (imag, args, , doc: /* -*- texinfo -*- @deftypefn {} {} imag (@var{z}) Return the imaginary part of @var{z} as a real number. @seealso{real, conj} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).imag ()); } /* %!assert (imag (1), 0) %!assert (imag (i), 1) %!assert (imag (1+i), 1) %!assert (imag ([i, 1; 1, i]), full (eye (2))) %!assert (imag (single (1)), single (0)) %!assert (imag (single (i)), single (1)) %!assert (imag (single (1+i)), single (1)) %!assert (imag (single ([i, 1; 1, i])), full (eye (2,"single"))) %!error imag () %!error imag (1, 2) */ DEFUNX ("isalnum", Fisalnum, args, , doc: /* -*- texinfo -*- @deftypefn {} {} isalnum (@var{s}) Return a logical array which is true where the elements of @var{s} are letters or digits and false where they are not. This is equivalent to (@code{isalpha (@var{s}) | isdigit (@var{s})}). @seealso{isalpha, isdigit, ispunct, isspace, iscntrl} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).xisalnum ()); } /* %!test %! charset = char (0:127); %! result = false (1, 128); %! result(double ("A":"Z") + 1) = true; %! result(double ("0":"9") + 1) = true; %! result(double ("a":"z") + 1) = true; %! assert (isalnum (charset), result); %!error isalnum () %!error isalnum (1, 2) */ DEFUNX ("isalpha", Fisalpha, args, , doc: /* -*- texinfo -*- @deftypefn {} {} isalpha (@var{s}) Return a logical array which is true where the elements of @var{s} are letters and false where they are not. This is equivalent to (@code{islower (@var{s}) | isupper (@var{s})}). @seealso{isdigit, ispunct, isspace, iscntrl, isalnum, islower, isupper} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).xisalpha ()); } /* %!test %! charset = char (0:127); %! result = false (1, 128); %! result(double ("A":"Z") + 1) = true; %! result(double ("a":"z") + 1) = true; %! assert (isalpha (charset), result); %!error isalpha () %!error isalpha (1, 2) */ DEFUNX ("isascii", Fisascii, args, , doc: /* -*- texinfo -*- @deftypefn {} {} isascii (@var{s}) Return a logical array which is true where the elements of @var{s} are ASCII characters (in the range 0 to 127 decimal) and false where they are not. @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).xisascii ()); } /* %!test %! charset = char (0:127); %! result = true (1, 128); %! assert (isascii (charset), result); %!error isascii () %!error isascii (1, 2) */ DEFUNX ("iscntrl", Fiscntrl, args, , doc: /* -*- texinfo -*- @deftypefn {} {} iscntrl (@var{s}) Return a logical array which is true where the elements of @var{s} are control characters and false where they are not. @seealso{ispunct, isspace, isalpha, isdigit} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).xiscntrl ()); } /* %!test %! charset = char (0:127); %! result = false (1, 128); %! result(1:32) = true; %! result(128) = true; %! assert (iscntrl (charset), result); %!error iscntrl () %!error iscntrl (1, 2) */ DEFUNX ("isdigit", Fisdigit, args, , doc: /* -*- texinfo -*- @deftypefn {} {} isdigit (@var{s}) Return a logical array which is true where the elements of @var{s} are decimal digits (0-9) and false where they are not. @seealso{isxdigit, isalpha, isletter, ispunct, isspace, iscntrl} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).xisdigit ()); } /* %!test %! charset = char (0:127); %! result = false (1, 128); %! result(double ("0":"9") + 1) = true; %! assert (isdigit (charset), result); %!error isdigit () %!error isdigit (1, 2) */ DEFUN (isinf, args, , doc: /* -*- texinfo -*- @deftypefn {} {} isinf (@var{x}) Return a logical array which is true where the elements of @var{x} are infinite and false where they are not. For example: @example @group isinf ([13, Inf, NA, NaN]) @result{} [ 0, 1, 0, 0 ] @end group @end example @seealso{isfinite, isnan, isna} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).isinf ()); } /* %!assert (isinf (Inf)) %!assert (! isinf (NaN)) %!assert (! isinf (NA)) %!assert (isinf (rand (1,10)), false (1,10)) %!assert (isinf ([NaN -Inf -1 0 1 Inf NA]), [false, true, false, false, false, true, false]) %!assert (isinf (single (Inf))) %!assert (! isinf (single (NaN))) %!assert (! isinf (single (NA))) %!assert (isinf (single (rand (1,10))), false (1,10)) %!assert (isinf (single ([NaN -Inf -1 0 1 Inf NA])), [false, true, false, false, false, true, false]) %!error isinf () %!error isinf (1, 2) */ DEFUNX ("isgraph", Fisgraph, args, , doc: /* -*- texinfo -*- @deftypefn {} {} isgraph (@var{s}) Return a logical array which is true where the elements of @var{s} are printable characters (but not the space character) and false where they are not. @seealso{isprint} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).xisgraph ()); } /* %!test %! charset = char (0:127); %! result = false (1, 128); %! result(34:127) = true; %! assert (isgraph (charset), result); %!error isgraph () %!error isgraph (1, 2) */ DEFUNX ("islower", Fislower, args, , doc: /* -*- texinfo -*- @deftypefn {} {} islower (@var{s}) Return a logical array which is true where the elements of @var{s} are lowercase letters and false where they are not. @seealso{isupper, isalpha, isletter, isalnum} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).xislower ()); } /* %!test %! charset = char (0:127); %! result = false (1, 128); %! result(double ("a":"z") + 1) = true; %! assert (islower (charset), result); %!error islower () %!error islower (1, 2) */ DEFUN (isna, args, , doc: /* -*- texinfo -*- @deftypefn {} {} isna (@var{x}) Return a logical array which is true where the elements of @var{x} are NA (missing) values and false where they are not. For example: @example @group isna ([13, Inf, NA, NaN]) @result{} [ 0, 0, 1, 0 ] @end group @end example @seealso{isnan, isinf, isfinite} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).isna ()); } /* %!assert (! isna (Inf)) %!assert (! isna (NaN)) %!assert (isna (NA)) %!assert (isna (rand (1,10)), false (1,10)) %!assert (isna ([NaN -Inf -1 0 1 Inf NA]), [false, false, false, false, false, false, true]) %!assert (! isna (single (Inf))) %!assert (! isna (single (NaN))) %!assert (isna (single (NA))) %!assert (isna (single (rand (1,10))), false (1,10)) %!assert (isna (single ([NaN -Inf -1 0 1 Inf NA])), [false, false, false, false, false, false, true]) %!error isna () %!error isna (1, 2) */ DEFUN (isnan, args, , doc: /* -*- texinfo -*- @deftypefn {} {} isnan (@var{x}) Return a logical array which is true where the elements of @var{x} are NaN values and false where they are not. NA values are also considered NaN values. For example: @example @group isnan ([13, Inf, NA, NaN]) @result{} [ 0, 0, 1, 1 ] @end group @end example @seealso{isna, isinf, isfinite} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).isnan ()); } /* %!assert (! isnan (Inf)) %!assert (isnan (NaN)) %!assert (isnan (NA)) %!assert (isnan (rand (1,10)), false (1,10)) %!assert (isnan ([NaN -Inf -1 0 1 Inf NA]), [true, false, false, false, false, false, true]) %!assert (! isnan (single (Inf))) %!assert (isnan (single (NaN))) %!assert (isnan (single (NA))) %!assert (isnan (single (rand (1,10))), false (1,10)) %!assert (isnan (single ([NaN -Inf -1 0 1 Inf NA])), [true, false, false, false, false, false, true]) %!error isnan () %!error isnan (1, 2) */ DEFUNX ("isprint", Fisprint, args, , doc: /* -*- texinfo -*- @deftypefn {} {} isprint (@var{s}) Return a logical array which is true where the elements of @var{s} are printable characters (including the space character) and false where they are not. @seealso{isgraph} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).xisprint ()); } /* %!test %! charset = char (0:127); %! result = false (1, 128); %! result(33:127) = true; %! assert (isprint (charset), result); %!error isprint () %!error isprint (1, 2) */ DEFUNX ("ispunct", Fispunct, args, , doc: /* -*- texinfo -*- @deftypefn {} {} ispunct (@var{s}) Return a logical array which is true where the elements of @var{s} are punctuation characters and false where they are not. @seealso{isalpha, isdigit, isspace, iscntrl} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).xispunct ()); } /* %!test %! charset = char (0:127); %! result = false (1, 128); %! result(34:48) = true; %! result(59:65) = true; %! result(92:97) = true; %! result(124:127) = true; %! assert (ispunct (charset), result); %!error ispunct () %!error ispunct (1, 2) */ DEFUNX ("isspace", Fisspace, args, , doc: /* -*- texinfo -*- @deftypefn {} {} isspace (@var{s}) Return a logical array which is true where the elements of @var{s} are whitespace characters (space, formfeed, newline, carriage return, tab, and vertical tab) and false where they are not. @seealso{iscntrl, ispunct, isalpha, isdigit} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).xisspace ()); } /* %!test %! charset = char (0:127); %! result = false (1, 128); %! result(double (" \f\n\r\t\v") + 1) = true; %! assert (isspace (charset), result); %!error isspace () %!error isspace (1, 2) */ DEFUNX ("isupper", Fisupper, args, , doc: /* -*- texinfo -*- @deftypefn {} {} isupper (@var{s}) Return a logical array which is true where the elements of @var{s} are uppercase letters and false where they are not. @seealso{islower, isalpha, isletter, isalnum} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).xisupper ()); } /* %!test %! charset = char (0:127); %! result = false (1, 128); %! result(double ("A":"Z") + 1) = true; %! assert (isupper (charset), result); %!error isupper () %!error isupper (1, 2) */ DEFUNX ("isxdigit", Fisxdigit, args, , doc: /* -*- texinfo -*- @deftypefn {} {} isxdigit (@var{s}) Return a logical array which is true where the elements of @var{s} are hexadecimal digits (0-9 and @nospell{a-fA-F}). @seealso{isdigit} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).xisxdigit ()); } /* %!test %! charset = char (0:127); %! result = false (1, 128); %! result(double ("A":"F") + 1) = true; %! result(double ("0":"9") + 1) = true; %! result(double ("a":"f") + 1) = true; %! assert (isxdigit (charset), result); %!error isxdigit () %!error isxdigit (1, 2) */ DEFUN (lgamma, args, , doc: /* -*- texinfo -*- @deftypefn {} {} gammaln (@var{x}) @deftypefnx {} {} lgamma (@var{x}) Return the natural logarithm of the gamma function of @var{x}. @seealso{gamma, gammainc} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).lgamma ()); } /* %!test %! a = -1i*sqrt (-1/(6.4187*6.4187)); %! assert (gammaln (a), gammaln (real (a))); %!test %! x = [.5, 1, 1.5, 2, 3, 4, 5]; %! v = [sqrt(pi), 1, .5*sqrt(pi), 1, 2, 6, 24]; %! assert (gammaln (x), log (v), sqrt (eps)); %!test %! a = single (-1i*sqrt (-1/(6.4187*6.4187))); %! assert (gammaln (a), gammaln (real (a))); %!test %! x = single ([.5, 1, 1.5, 2, 3, 4, 5]); %! v = single ([sqrt(pi), 1, .5*sqrt(pi), 1, 2, 6, 24]); %! assert (gammaln (x), log (v), sqrt (eps ("single"))); %!test %! x = [-1, 0, 1, Inf]; %! v = [Inf, Inf, 0, Inf]; %! assert (gammaln (x), v); %! assert (gammaln (single (x)), single (v)); %!error gammaln () %!error gammaln (1,2) */ DEFUN (log, args, , doc: /* -*- texinfo -*- @deftypefn {} {} log (@var{x}) Compute the natural logarithm, @tex $\ln{(x)},$ @end tex @ifnottex @code{ln (@var{x})}, @end ifnottex for each element of @var{x}. To compute the matrix logarithm, see @ref{Linear Algebra}. @seealso{exp, log1p, log2, log10, logspace} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).log ()); } /* %!assert (log ([1, e, e^2]), [0, 1, 2], sqrt (eps)) %!assert (log ([-0.5, -1.5, -2.5]), log ([0.5, 1.5, 2.5]) + pi*1i, sqrt (eps)) %!assert (log (single ([1, e, e^2])), single ([0, 1, 2]), sqrt (eps ("single"))) %!assert (log (single ([-0.5, -1.5, -2.5])), single (log ([0.5, 1.5, 2.5]) + pi*1i), 4*eps ("single")) %!error log () %!error log (1, 2) */ DEFUN (log10, args, , doc: /* -*- texinfo -*- @deftypefn {} {} log10 (@var{x}) Compute the base-10 logarithm of each element of @var{x}. @seealso{log, log2, logspace, exp} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).log10 ()); } /* %!assert (log10 ([0.01, 0.1, 1, 10, 100]), [-2, -1, 0, 1, 2], sqrt (eps)) %!assert (log10 (single ([0.01, 0.1, 1, 10, 100])), single ([-2, -1, 0, 1, 2]), sqrt (eps ("single"))) %!error log10 () %!error log10 (1, 2) */ DEFUN (log1p, args, , doc: /* -*- texinfo -*- @deftypefn {} {} log1p (@var{x}) Compute @tex $\ln{(1 + x)}$ @end tex @ifnottex @code{log (1 + @var{x})} @end ifnottex accurately in the neighborhood of zero. @seealso{log, exp, expm1} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).log1p ()); } /* %!assert (log1p ([0, 2*eps, -2*eps]), [0, 2*eps, -2*eps], 1e-29) %!assert (log1p (single ([0, 2*eps, -2*eps])), single ([0, 2*eps, -2*eps]), 1e-29) %!error log1p () %!error log1p (1, 2) */ DEFUN (real, args, , doc: /* -*- texinfo -*- @deftypefn {} {} real (@var{z}) Return the real part of @var{z}. @seealso{imag, conj} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).real ()); } /* %!assert (real (1), 1) %!assert (real (i), 0) %!assert (real (1+i), 1) %!assert (real ([1, i; i, 1]), full (eye (2))) %!assert (real (single (1)), single (1)) %!assert (real (single (i)), single (0)) %!assert (real (single (1+i)), single (1)) %!assert (real (single ([1, i; i, 1])), full (eye (2, "single"))) %!error real () %!error real (1, 2) */ DEFUN (round, args, , doc: /* -*- texinfo -*- @deftypefn {} {} round (@var{x}) Return the integer nearest to @var{x}. If @var{x} is complex, return @code{round (real (@var{x})) + round (imag (@var{x})) * I}. If there are two nearest integers, return the one further away from zero. @example @group round ([-2.7, 2.7]) @result{} -3 3 @end group @end example @seealso{ceil, floor, fix, roundb} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).round ()); } /* %!assert (round (1), 1) %!assert (round (1.1), 1) %!assert (round (5.5), 6) %!assert (round (i), i) %!assert (round (2.5+3.5i), 3+4i) %!assert (round (-2.6), -3) %!assert (round ([1.1, -2.4; -3.7, 7.1]), [1, -2; -4, 7]) %!assert (round (single (1)), single (1)) %!assert (round (single (1.1)), single (1)) %!assert (round (single (5.5)), single (6)) %!assert (round (single (i)), single (i)) %!assert (round (single (2.5+3.5i)), single (3+4i)) %!assert (round (single (-2.6)), single (-3)) %!assert (round (single ([1.1, -2.4; -3.7, 7.1])), single ([1, -2; -4, 7])) %!error round () %!error round (1, 2) */ DEFUN (roundb, args, , doc: /* -*- texinfo -*- @deftypefn {} {} roundb (@var{x}) Return the integer nearest to @var{x}. If there are two nearest integers, return the even one (banker's rounding). If @var{x} is complex, return @code{roundb (real (@var{x})) + roundb (imag (@var{x})) * I}. @seealso{round} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).roundb ()); } /* %!assert (roundb (1), 1) %!assert (roundb (1.1), 1) %!assert (roundb (1.5), 2) %!assert (roundb (4.5), 4) %!assert (roundb (i), i) %!assert (roundb (2.5+3.5i), 2+4i) %!assert (roundb (-2.6), -3) %!assert (roundb ([1.1, -2.4; -3.7, 7.1]), [1, -2; -4, 7]) %!assert (roundb (single (1)), single (1)) %!assert (roundb (single (1.1)), single (1)) %!assert (roundb (single (1.5)), single (2)) %!assert (roundb (single (4.5)), single (4)) %!assert (roundb (single (i)), single (i)) %!assert (roundb (single (2.5+3.5i)), single (2+4i)) %!assert (roundb (single (-2.6)), single (-3)) %!assert (roundb (single ([1.1, -2.4; -3.7, 7.1])), single ([1, -2; -4, 7])) %!error roundb () %!error roundb (1, 2) */ DEFUN (sign, args, , doc: /* -*- texinfo -*- @deftypefn {} {} sign (@var{x}) Compute the @dfn{signum} function. This is defined as @tex $$ {\rm sign} (@var{x}) = \cases{1,&$x>0$;\cr 0,&$x=0$;\cr -1,&$x<0$.\cr} $$ @end tex @ifnottex @example @group -1, x < 0; sign (x) = 0, x = 0; 1, x > 0. @end group @end example @end ifnottex For complex arguments, @code{sign} returns @code{x ./ abs (@var{x})}. Note that @code{sign (-0.0)} is 0. Although IEEE 754 floating point allows zero to be signed, 0.0 and -0.0 compare equal. If you must test whether zero is signed, use the @code{signbit} function. @seealso{signbit} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).signum ()); } /* %!assert (sign (-2) , -1) %!assert (sign (0), 0) %!assert (sign (3), 1) %!assert (sign ([1, -pi; e, 0]), [1, -1; 1, 0]) %!assert (sign (single (-2)) , single (-1)) %!assert (sign (single (0)), single (0)) %!assert (sign (single (3)), single (1)) %!assert (sign (single ([1, -pi; e, 0])), single ([1, -1; 1, 0])) %!error sign () %!error sign (1, 2) */ DEFUNX ("signbit", Fsignbit, args, , doc: /* -*- texinfo -*- @deftypefn {} {} signbit (@var{x}) Return logical true if the value of @var{x} has its sign bit set and false otherwise. This behavior is consistent with the other logical functions. See @ref{Logical Values}. The behavior differs from the C language function which returns nonzero if the sign bit is set. This is not the same as @code{x < 0.0}, because IEEE 754 floating point allows zero to be signed. The comparison @code{-0.0 < 0.0} is false, but @code{signbit (-0.0)} will return a nonzero value. @seealso{sign} @end deftypefn */) { if (args.length () != 1) print_usage (); octave_value tmp = args(0).xsignbit (); return ovl (tmp != 0); } /* %!assert (signbit (1) == 0) %!assert (signbit (-2) != 0) %!assert (signbit (0) == 0) %!assert (signbit (-0) != 0) %!assert (signbit (single (1)) == 0) %!assert (signbit (single (-2)) != 0) %!assert (signbit (single (0)) == 0) %!assert (signbit (single (-0)) != 0) %!error sign () %!error sign (1, 2) */ DEFUN (sin, args, , doc: /* -*- texinfo -*- @deftypefn {} {} sin (@var{x}) Compute the sine for each element of @var{x} in radians. @seealso{asin, sind, sinh} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).sin ()); } /* %!shared rt2, rt3 %! rt2 = sqrt (2); %! rt3 = sqrt (3); %!test %! x = [0, pi/6, pi/4, pi/3, pi/2, 2*pi/3, 3*pi/4, 5*pi/6, pi]; %! v = [0, 1/2, rt2/2, rt3/2, 1, rt3/2, rt2/2, 1/2, 0]; %! assert (sin (x), v, sqrt (eps)); %!test %! x = single ([0, pi/6, pi/4, pi/3, pi/2, 2*pi/3, 3*pi/4, 5*pi/6, pi]); %! v = single ([0, 1/2, rt2/2, rt3/2, 1, rt3/2, rt2/2, 1/2, 0]); %! assert (sin (x), v, sqrt (eps ("single"))); %!error sin () %!error sin (1, 2) */ DEFUN (sinh, args, , doc: /* -*- texinfo -*- @deftypefn {} {} sinh (@var{x}) Compute the hyperbolic sine for each element of @var{x}. @seealso{asinh, cosh, tanh} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).sinh ()); } /* %!test %! x = [0, pi/2*i, pi*i, 3*pi/2*i]; %! v = [0, i, 0, -i]; %! assert (sinh (x), v, sqrt (eps)); %!test %! x = single ([0, pi/2*i, pi*i, 3*pi/2*i]); %! v = single ([0, i, 0, -i]); %! assert (sinh (x), v, sqrt (eps ("single"))); %!error sinh () %!error sinh (1, 2) */ DEFUN (sqrt, args, , doc: /* -*- texinfo -*- @deftypefn {} {} sqrt (@var{x}) Compute the square root of each element of @var{x}. If @var{x} is negative, a complex result is returned. To compute the matrix square root, see @ref{Linear Algebra}. @seealso{realsqrt, nthroot} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).sqrt ()); } /* %!assert (sqrt (4), 2) %!assert (sqrt (-1), i) %!assert (sqrt (1+i), exp (0.5 * log (1+i)), sqrt (eps)) %!assert (sqrt ([4, -4; i, 1-i]), [2, 2i; exp(0.5 * log (i)), exp(0.5 * log (1-i))], sqrt (eps)) %!assert (sqrt (single (4)), single (2)) %!assert (sqrt (single (-1)), single (i)) %!assert (sqrt (single (1+i)), single (exp (0.5 * log (1+i))), sqrt (eps ("single"))) %!assert (sqrt (single ([4, -4; i, 1-i])), single ([2, 2i; exp(0.5 * log (i)), exp(0.5 * log (1-i))]), sqrt (eps ("single"))) %!error sqrt () %!error sqrt (1, 2) */ DEFUN (tan, args, , doc: /* -*- texinfo -*- @deftypefn {} {} tan (@var{z}) Compute the tangent for each element of @var{x} in radians. @seealso{atan, tand, tanh} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).tan ()); } /* %!shared rt2, rt3 %! rt2 = sqrt (2); %! rt3 = sqrt (3); %!test %! x = [0, pi/6, pi/4, pi/3, 2*pi/3, 3*pi/4, 5*pi/6, pi]; %! v = [0, rt3/3, 1, rt3, -rt3, -1, -rt3/3, 0]; %! assert (tan (x), v, sqrt (eps)); %!test %! x = single ([0, pi/6, pi/4, pi/3, 2*pi/3, 3*pi/4, 5*pi/6, pi]); %! v = single ([0, rt3/3, 1, rt3, -rt3, -1, -rt3/3, 0]); %! assert (tan (x), v, sqrt (eps ("single"))); %!error tan () %!error tan (1, 2) */ DEFUN (tanh, args, , doc: /* -*- texinfo -*- @deftypefn {} {} tanh (@var{x}) Compute hyperbolic tangent for each element of @var{x}. @seealso{atanh, sinh, cosh} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).tanh ()); } /* %!test %! x = [0, pi*i]; %! v = [0, 0]; %! assert (tanh (x), v, sqrt (eps)); %!test %! x = single ([0, pi*i]); %! v = single ([0, 0]); %! assert (tanh (x), v, sqrt (eps ("single"))); %!error tanh () %!error tanh (1, 2) */ DEFUNX ("tolower", Ftolower, args, , doc: /* -*- texinfo -*- @deftypefn {} {} tolower (@var{s}) @deftypefnx {} {} lower (@var{s}) Return a copy of the string or cell string @var{s}, with each uppercase character replaced by the corresponding lowercase one; non-alphabetic characters are left unchanged. For example: @example @group tolower ("MiXeD cAsE 123") @result{} "mixed case 123" @end group @end example @seealso{toupper} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).xtolower ()); } DEFALIAS (lower, tolower); /* %!assert (tolower ("OCTAVE"), "octave") %!assert (tolower ("123OCTave! _&"), "123octave! _&") %!assert (tolower ({"ABC", "DEF", {"GHI", {"JKL"}}}), {"abc", "def", {"ghi", {"jkl"}}}) %!assert (tolower (["ABC"; "DEF"]), ["abc"; "def"]) %!assert (tolower ({["ABC"; "DEF"]}), {["abc";"def"]}) %!assert (tolower (["ABCÄÖÜSS"; "abcäöüß"]), ["abcäöüss"; "abcäöüß"]) %!assert (tolower (repmat ("ÄÖÜ", 2, 1, 3)), repmat ("äöü", 2, 1, 3)) %!assert (tolower (68), 68) %!assert (tolower ({[68, 68; 68, 68]}), {[68, 68; 68, 68]}) %!assert (tolower (68i), 68i) %!assert (tolower ({[68i, 68; 68, 68i]}), {[68i, 68; 68, 68i]}) %!assert (tolower (single (68i)), single (68i)) %!assert (tolower ({single([68i, 68; 68, 68i])}), {single([68i, 68; 68, 68i])}) %!test %! classes = {@char, @double, @single, ... %! @int8, @int16, @int32, @int64, ... %! @uint8, @uint16, @uint32, @uint64}; %! for i = 1:numel (classes) %! cls = classes{i}; %! assert (class (tolower (cls (97))), class (cls (97))); %! assert (class (tolower (cls ([98, 99]))), class (cls ([98, 99]))); %! endfor %!test %! a(3,3,3,3) = "D"; %! assert (tolower (a)(3,3,3,3), "d"); %!test %! charset = char (0:127); %! result = charset; %! result (double ("A":"Z") + 1) = result (double ("a":"z") + 1); %! assert (tolower (charset), result); %!error <Invalid call to tolower> lower () %!error <Invalid call to tolower> tolower () %!error tolower (1, 2) */ DEFUNX ("toupper", Ftoupper, args, , doc: /* -*- texinfo -*- @deftypefn {} {} toupper (@var{s}) @deftypefnx {} {} upper (@var{s}) Return a copy of the string or cell string @var{s}, with each lowercase character replaced by the corresponding uppercase one; non-alphabetic characters are left unchanged. For example: @example @group toupper ("MiXeD cAsE 123") @result{} "MIXED CASE 123" @end group @end example @seealso{tolower} @end deftypefn */) { if (args.length () != 1) print_usage (); return ovl (args(0).xtoupper ()); } DEFALIAS (upper, toupper); /* %!assert (toupper ("octave"), "OCTAVE") %!assert (toupper ("123OCTave! _&"), "123OCTAVE! _&") %!assert (toupper ({"abc", "def", {"ghi", {"jkl"}}}), {"ABC", "DEF", {"GHI", {"JKL"}}}) %!assert (toupper (["abc"; "def"]), ["ABC"; "DEF"]) %!assert (toupper ({["abc"; "def"]}), {["ABC";"DEF"]}) %!assert (toupper (["ABCÄÖÜSS"; "abcäöüß"]), ["ABCÄÖÜSS"; "ABCÄÖÜSS"]) %!assert (toupper (repmat ("äöü", 2, 1, 3)), repmat ("ÄÖÜ", 2, 1, 3)) %!assert (toupper (100), 100) %!assert (toupper ({[100, 100; 100, 100]}), {[100, 100; 100, 100]}) %!assert (toupper (100i), 100i) %!assert (toupper ({[100i, 100; 100, 100i]}), {[100i, 100; 100, 100i]}) %!assert (toupper (single (100i)), single (100i)) %!assert (toupper ({single([100i, 100; 100, 100i])}), %! {single([100i, 100; 100, 100i])}) %!test %! classes = {@char, @double, @single, ... %! @int8, @int16, @int32, @int64, ... %! @uint8, @uint16, @uint32, @uint64}; %! for i = 1:numel (classes) %! cls = classes{i}; %! assert (class (toupper (cls (97))), class (cls (97))); %! assert (class (toupper (cls ([98, 99]))), class (cls ([98, 99]))); %! endfor %!test %! a(3,3,3,3) = "d"; %! assert (toupper (a)(3,3,3,3), "D"); %!test %! charset = char (0:127); %! result = charset; %! result (double ("a":"z") + 1) = result (double ("A":"Z") + 1); %! assert (toupper (charset), result); %!error <Invalid call to toupper> toupper () %!error <Invalid call to toupper> upper () %!error toupper (1, 2) */ DEFALIAS (gammaln, lgamma);