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## Copyright (C) 2000-2013 Paul Kienzle
##
## 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} {[@var{b}, @var{c}] =} spdiags (@var{A})
## @deftypefnx {Function File} {@var{b} =} spdiags (@var{A}, @var{c})
## @deftypefnx {Function File} {@var{b} =} spdiags (@var{v}, @var{c}, @var{A})
## @deftypefnx {Function File} {@var{b} =} spdiags (@var{v}, @var{c}, @var{m}, @var{n})
## A generalization of the function @code{diag}. Called with a single
## input argument, the non-zero diagonals @var{c} of @var{A} are extracted.
## With two arguments the diagonals to extract are given by the vector
## @var{c}.
##
## The other two forms of @code{spdiags} modify the input matrix by
## replacing the diagonals. They use the columns of @var{v} to replace
## the columns represented by the vector @var{c}. If the sparse matrix
## @var{A} is defined then the diagonals of this matrix are replaced.
## Otherwise a matrix of @var{m} by @var{n} is created with the
## diagonals given by @var{v}.
##
## Negative values of @var{c} represent diagonals below the main
## diagonal, and positive values of @var{c} diagonals above the main
## diagonal.
##
## For example:
##
## @example
## @group
## spdiags (reshape (1:12, 4, 3), [-1 0 1], 5, 4)
## @result{} 5 10 0 0
## 1 6 11 0
## 0 2 7 12
## 0 0 3 8
## 0 0 0 4
## @end group
## @end example
##
## @end deftypefn
function [A, c] = spdiags (v, c, m, n)
if (nargin == 1 || nargin == 2)
## extract nonzero diagonals of v into A,c
[nr, nc] = size (v);
[i, j, v] = find (v);
if (nargin == 1)
## c contains the active diagonals
c = unique (j-i);
endif
## FIXME: we can do this without a loop if we are clever
offset = max (min (c, nc-nr), 0);
A = zeros (min (nr, nc), length (c));
for k = 1:length (c)
idx = find (j-i == c(k));
A(j(idx)-offset(k),k) = v(idx);
endfor
elseif (nargin == 3)
## Replace specific diagonals c of m with v,c
[nr, nc] = size (m);
B = spdiags (m, c);
A = m - spdiags (B, c, nr, nc) + spdiags (v, c, nr, nc);
else
## Create new matrix of size mxn using v,c
[j, i, v] = find (v);
offset = max (min (c(:), n-m), 0);
j = j(:) + offset(i(:));
i = j - c(:)(i(:));
idx = i > 0 & i <= m & j > 0 & j <= n;
A = sparse (i(idx), j(idx), v(idx), m, n);
endif
endfunction
%!assert (spdiags (zeros (1,0),1,1,1), sparse (0))
%!assert (spdiags (zeros (0,1),1,1,1), sparse (0))
%!assert (spdiags ([0.5 -1 0.5], 0:2, 1, 1), sparse(0.5))
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