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+## Copyright (C) 2012 Rik Wehbring
+## Copyright (C) 1995-2012 Kurt Hornik
+##
+## 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
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn  {Function File} {} cauchy_pdf (@var{x})
+## @deftypefnx {Function File} {} cauchy_pdf (@var{x}, @var{location}, @var{scale})
+## For each element of @var{x}, compute the probability density function
+## (PDF) at @var{x} of the Cauchy distribution with location parameter
+## @var{location} and scale parameter @var{scale} > 0.  Default values are
+## @var{location} = 0, @var{scale} = 1.
+## @end deftypefn
+
+## Author: KH <Kurt.Hornik@wu-wien.ac.at>
+## Description: PDF of the Cauchy distribution
+
+function pdf = cauchy_pdf (x, location = 0, scale = 1)
+
+  if (nargin != 1 && nargin != 3)
+    print_usage ();
+  endif
+
+  if (!isscalar (location) || !isscalar (scale))
+    [retval, x, location, scale] = common_size (x, location, scale);
+    if (retval > 0)
+      error ("cauchy_pdf: X, LOCATION, and SCALE must be of common size or scalars");
+    endif
+  endif
+
+  if (iscomplex (x) || iscomplex (location) || iscomplex (scale))
+    error ("cauchy_pdf: X, LOCATION, and SCALE must not be complex");
+  endif
+
+  if (isa (x, "single") || isa (location, "single") || isa (scale, "single"))
+    pdf = NaN (size (x), "single");
+  else
+    pdf = NaN (size (x));
+  endif
+
+  k = !isinf (location) & (scale > 0) & (scale < Inf);
+  if (isscalar (location) && isscalar (scale))
+    pdf = ((1 ./ (1 + ((x - location) / scale) .^ 2))
+              / pi / scale);
+  else
+    pdf(k) = ((1 ./ (1 + ((x(k) - location(k)) ./ scale(k)) .^ 2))
+              / pi ./ scale(k));
+  endif
+
+endfunction
+
+
+%!shared x,y
+%! x = [-1 0 0.5 1 2];
+%! y = 1/pi * ( 2 ./ ((x-1).^2 + 2^2) );
+%!assert(cauchy_pdf (x, ones(1,5), 2*ones(1,5)), y);
+%!assert(cauchy_pdf (x, 1, 2*ones(1,5)), y);
+%!assert(cauchy_pdf (x, ones(1,5), 2), y);
+%!assert(cauchy_pdf (x, [-Inf 1 NaN 1 Inf], 2), [NaN y(2) NaN y(4) NaN]);
+%!assert(cauchy_pdf (x, 1, 2*[0 1 NaN 1 Inf]), [NaN y(2) NaN y(4) NaN]);
+%!assert(cauchy_pdf ([x, NaN], 1, 2), [y, NaN]);
+
+%% Test class of input preserved
+%!assert(cauchy_pdf (single([x, NaN]), 1, 2), single([y, NaN]), eps("single"));
+%!assert(cauchy_pdf ([x, NaN], single(1), 2), single([y, NaN]), eps("single"));
+%!assert(cauchy_pdf ([x, NaN], 1, single(2)), single([y, NaN]), eps("single"));
+
+%% Cauchy (0,1) == Student's T distribution with 1 DOF
+%!test
+%! x = rand (10, 1);
+%! assert(cauchy_pdf (x, 0, 1), tpdf (x, 1), eps);
+
+%% Test input validation
+%!error cauchy_pdf ()
+%!error cauchy_pdf (1,2)
+%!error cauchy_pdf (1,2,3,4)
+%!error cauchy_pdf (ones(3),ones(2),ones(2))
+%!error cauchy_pdf (ones(2),ones(3),ones(2))
+%!error cauchy_pdf (ones(2),ones(2),ones(3))
+%!error cauchy_pdf (i, 2, 2)
+%!error cauchy_pdf (2, i, 2)
+%!error cauchy_pdf (2, 2, i)
+