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## Copyright (C) 1995, 1996, 1997 Kurt Hornik
##
## 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 2, 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 file. If not, write to the Free Software Foundation,
## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
## usage: cauchy_inv (x [, lambda, sigma])
##
## For each element of x, compute the quantile (the inverse of the CDF)
## at x of the Cauchy distribution with location parameter lambda and
## scale parameter sigma. Default values are lambda = 0, sigma = 1.
## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
## Description: Quantile function of the Cauchy distribution
function inv = cauchy_inv (x, location, scale)
if !(nargin == 1 || nargin == 3)
usage ("cauchy_inv (x [, lambda, sigma])");
endif
if (nargin == 1)
location = 0;
scale = 1;
endif
[retval, x, location, scale] = common_size (x, location, scale);
if (retval > 0)
error (["cauchy_inv: ", ...
"x, lambda and sigma must be of common size or scalar"]);
endif
[r, c] = size (x);
s = r * c;
x = reshape (x, 1, s);
location = reshape (location, 1, s);
scale = reshape (scale, 1, s);
inv = NaN * ones (1, s);
ok = ((location > -Inf) & (location < Inf) &
(scale > 0) & (scale < Inf));
k = find ((x == 0) & ok);
if any (k)
inv(k) = -Inf * ones (1, length (k));
endif
k = find ((x > 0) & (x < 1) & ok);
if any (k)
inv(k) = location(k) - scale(k) .* cot (pi * x(k));
endif
k = find ((x == 1) & ok);
if any (k)
inv(k) = Inf * ones (1, length (k));
endif
inv = reshape (inv, r, c);
endfunction
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