update packages

[CreaPhase.git] / octave_packages / m / special-matrix / pascal.m

diff --git a/octave_packages/m/special-matrix/pascal.m b/octave_packages/m/special-matrix/pascal.m
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+## Copyright (C) 1999-2012 Peter Ekberg
+## Copyright (C) 2009 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
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn  {Function File} {} pascal (@var{n})
+## @deftypefnx {Function File} {} pascal (@var{n}, @var{t})
+## Return the Pascal matrix of order @var{n} if @code{@var{t} = 0}.  @var{t}
+## defaults to 0.  Return the pseudo-lower triangular Cholesky@tie{}factor of
+## the Pascal matrix if @code{@var{t} = 1} (The sign of some columns may be
+## negative).  This matrix is its own inverse, that is @code{pascal (@var{n},
+## 1) ^ 2 == eye (@var{n})}.  If @code{@var{t} = -1}, return the true
+## Cholesky@tie{}factor with strictly positive values on the diagonal.  If
+## @code{@var{t} = 2}, return a transposed and permuted version of @code{pascal
+## (@var{n}, 1)}, which is the cube root of the identity matrix.  That is,
+## @code{pascal (@var{n}, 2) ^ 3 == eye (@var{n})}.
+##
+## @seealso{chol}
+## @end deftypefn
+
+## Author: Peter Ekberg
+##         (peda)
+
+function retval = pascal (n, t = 0)
+
+  if (nargin < 1 || nargin > 2)
+    print_usage ();
+  elseif (! (isscalar (n) && isscalar (t)))
+    error ("pascal: N and T must be scalars");
+  elseif (! any (t == [-1, 0, 1, 2]))
+    error ("pascal: expecting T to be -1, 0, 1, or 2, found %d", t);
+  endif
+
+  retval = zeros (n);
+  if (n > 0)
+    retval(:,1) = 1;
+  endif
+
+  if (t == -1)
+    for j = 2:n
+      retval(j:n,j) = cumsum (retval(j-1:n-1,j-1));
+    endfor
+  else
+    for j = 2:n
+      retval(j:n,j) = -cumsum (retval(j-1:n-1,j-1));
+    endfor
+  endif
+
+  if (t == 0)
+    retval = retval*retval';
+  elseif (t == 2)
+    retval = rot90 (retval, 3);
+    if (rem (n,2) != 1)
+      retval *= -1;
+    endif
+  endif
+
+endfunction
+
+
+%!assert (pascal (3,-1), [1,0,0;1,1,0;1,2,1])
+%!assert (pascal (3,0), [1,1,1;1,2,3;1,3,6])
+%!assert (pascal (3,0), pascal (3))
+%!assert (pascal (3,1), [1,0,0;1,-1,0;1,-2,1])
+%!assert (pascal (3,2), [1,1,1;-2,-1,0;1,0,0])
+%!assert (pascal (0,2), [])
+
+%% Test input validation
+%!error pascal ()
+%!error pascal (1,2,3)
+%!error <N and T must be scalars> pascal ([1 2])
+%!error <N and T must be scalars> pascal (1, [1 2])
+%!error <expecting T to be> pascal (3,-2)
+%!error <expecting T to be> pascal (3,4)
+