## Copyright (C) 2004-2011 David Bateman and Andy Adler
##
## 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.
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## 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} {} sprandsym (@var{n}, @var{d})
## @deftypefnx {Function File} {} sprandsym (@var{s})
## Generate a symmetric random sparse matrix.  The size of the matrix will be
## @var{n} by @var{n}, with a density of values given by @var{d}.
## @var{d} should be between 0 and 1. Values will be normally
## distributed with mean of zero and variance 1.
##
## Note: sometimes the actual density may be a bit smaller than @var{d}.
## This is unlikely to happen for large really sparse matrices.
##
## If called with a single matrix argument, a random sparse matrix is
## generated wherever the matrix @var{S} is non-zero in its lower
## triangular part.
## @seealso{sprand, sprandn}
## @end deftypefn

function S = sprandsym (n, d)

  if (nargin != 1 && nargin != 2)
    print_usage ();
  endif

  if (nargin == 1)
    [i, j] = find (tril (n));
    [nr, nc] = size (n);
    S = sparse (i, j, randn (size (i)), nr, nc);
    S = S + tril (S, -1)';
    return;
  endif

  if (!(isscalar (n) && n == fix (n) && n > 0))
    error ("sprand: N must be an integer greater than 0");
  endif

  if (d < 0 || d > 1)
    error ("sprand: density D must be between 0 and 1");
  endif

  m1 = floor (n/2);
  n1 = m1 + rem (n, 2);
  mn1 = m1*n1;
  k1 = round (d*mn1);
  idx1 = unique (fix (rand (min (k1*1.01, k1+10), 1) * mn1)) + 1;
  ## idx contains random numbers in [1,mn] generate 1% or 10 more
  ## random values than necessary in order to reduce the probability
  ## that there are less than k distinct values; maybe a better
  ## strategy could be used but I don't think it's worth the price.

  ## Actual number of entries in S.
  k1 = min (length (idx1), k1);
  j1 = floor ((idx1(1:k1)-1)/m1);
  i1 = idx1(1:k1) - j1*m1;

  n2 = ceil (n/2);
  nn2 = n2*n2;
  k2 = round (d*nn2);
  idx2 = unique (fix (rand (min (k2*1.01, k1+10), 1) * nn2)) + 1;
  k2 = min (length (idx2), k2);
  j2 = floor ((idx2(1:k2)-1)/n2);
  i2 = idx2(1:k2) - j2*n2;

  if (isempty (i1) && isempty (i2))
    S = sparse (n, n);
  else
    S1 = sparse (i1, j1+1, randn (k1, 1), m1, n1);
    S = [tril(S1), sparse(m1,m1); ...
         sparse(i2,j2+1,randn(k2,1),n2,n2), triu(S1,1)'];
    S = S + tril (S, -1)';
  endif

endfunction


## FIXME: Test for density can't happen until code of sprandsym is improved
%!test
%! s = sprandsym (10, 0.1);
%! assert (issparse (s));
%! assert (issymmetric (s));
%! assert (size (s), [10, 10]);
##%! assert (nnz (s) / numel (s), 0.1, .01);

%% Test 1-input calling form
%!test
%! s = sprandsym (sparse ([1 2 3], [3 2 3], [2 2 2]));
%! [i, j] = find (s);
%! assert (sort (i), [2 3]');
%! assert (sort (j), [2 3]');

%% Test input validation
%!error sprandsym ()
%!error sprandsym (1, 2, 3)
%!error sprandsym (ones(3), 0.5)
%!error sprandsym (3.5, 0.5)
%!error sprandsym (0, 0.5)
%!error sprandsym (3, -1)
%!error sprandsym (3, 2)