ons, 03 03 2010 kl. 18:28 +0000, skrev Neil Lawrence:
> The implementation of erfcx in the octave-specfun package is simply
>
>
> exp(x^2)*erfc(x)
Could you try the attached implementation instead? It seems to behave
like the Matlab implementation, but as I don't have a real example to
work on, I have just tried some arbitrary numbers as my test set.
If it works for you, I'll commit it to the 'specfun' package.
Thanks,
Søren
## Copyright (C) 2010 Soren Hauberg
##
## This program 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.
##
## This program 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 this program; see the file COPYING. If not, see
## <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} erfcx (@var{x})
## Compute the scaled complementary error function.
##
## The scaled complementary error function is defined as
##
## @example
## erfcx (@var{x}) = exp (@var{x}^2) * erfc (@var{x})
## @end example
##
## although it is not evaluated as such.
##
## @seealso{erf, erfc, erfinv}
## @end deftypefn
function result = erfcx (arg)
## Check input
if (nargin == 0)
print_usage ();
endif
if (!isreal (arg))
error ("erfcx: input must be real");
endif
## Get precision dependent thresholds
if (isa (arg, "double"))
xneg = -26.628;
xmax = 2.53e+307;
elseif (isa (arg, "single"))
xneg = -9.382;
xmax = 4.79e+37;
else
error ("erfcx: unsupported numeric class '%s'", class (arg));
endif
## Allocate output
result = zeros (size (arg), class (arg));
## Find values where erfcx can be evaluated
idx_neg = (arg < xneg);
idx_max = (arg > xmax);
idx = !(idx_neg | idx_max);
arg = arg (idx);
## Perform the actual computation
t = 3.97886080735226 ./ (abs (arg) + 3.97886080735226);
u = t - 0.5;
y = (((((((((u .* 0.00127109764952614092 + 1.19314022838340944e-4) .* u ...
- 0.003963850973605135) .* u - 8.70779635317295828e-4) .* u + ...
0.00773672528313526668) .* u + 0.00383335126264887303) .* u - ...
0.0127223813782122755) .* u - 0.0133823644533460069) .* u + ...
0.0161315329733252248) .* u + 0.0390976845588484035) .* u + ...
0.00249367200053503304;
y = ((((((((((((y .* u - 0.0838864557023001992) .* u - ...
0.119463959964325415) .* u + 0.0166207924969367356) .* u + ...
0.357524274449531043) .* u + 0.805276408752910567) .* u + ...
1.18902982909273333) .* u + 1.37040217682338167) .* u + ...
1.31314653831023098) .* u + 1.07925515155856677) .* u + ...
0.774368199119538609) .* u + 0.490165080585318424) .* u + ...
0.275374741597376782) .* t;
y (arg < 0) = 2 .* exp (arg (arg < 0).^2) - y (arg < 0);
## Put the results back into something with the same size is the original input
result (idx) = y;
result (idx_neg) = Inf;
## result (idx_max) = 0; # not needed as we initialise with zeros
endfunction
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