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function result = spsym (A, quick) %#ok
%SPSYM determine if a sparse matrix is symmetric, Hermitian, or skew-symmetric.
% If so, also determine if its diagonal has all positive real entries.
% A must be sparse.
%
% Example:
% result = spsym (A) ;
% result = spsym (A,quick) ;
%
% If quick = 0, or is not present, then this routine returns:
%
% 1: if A is rectangular
% 2: if A is unsymmetric
% 3: if A is symmetric, but with one or more A(j,j) <= 0
% 4: if A is Hermitian, but with one or more A(j,j) <= 0 or with
% nonzero imaginary part
% 5: if A is skew symmetric (and thus the diagonal is all zero as well)
% 6: if A is symmetric with real positive diagonal
% 7: if A is Hermitian with real positive diagonal
%
% If quick is nonzero, then the function can return more quickly, as soon as
% it finds a diagonal entry that is <= 0 or with a nonzero imaginary part.
% In this case, it returns 2 for a square matrix, even if the matrix might
% otherwise be symmetric or Hermitian.
%
% Regardless of the value of "quick", this function returns 6 or 7 if A is
% a candidate for sparse Cholesky.
%
% For an MATLAB M-file function that computes the same thing as this
% mexFunction (but much slower), see the get_symmetry function by typing
% "type spsym".
%
% This spsym function does not compute the transpose of A, nor does it need
% to examine the entire matrix if it is unsymmetric. It uses very little
% memory as well (just size-n workspace, where n = size (A,1)).
%
% Examples:
% load west0479
% A = west0479 ;
% spsym (A)
% spsym (A+A')
% spsym (A-A')
% spsym (A+A'+3*speye(size(A,1)))
%
% See also mldivide.
% function result = get_symmetry (A,quick)
% %GET_SYMMETRY: does the same thing as the spsym mexFunction.
% % It's just a lot slower and uses much more memory. This function
% % is meant for testing and documentation only.
% [m n] = size (A) ;
% if (m ~= n)
% result = 1 ; % rectangular
% return
% end
% if (nargin < 2)
% quick = 0 ;
% end
% d = diag (A) ;
% posdiag = all (real (d) > 0) & all (imag (d) == 0) ;
% if (quick & ~posdiag)
% result = 2 ; % Not a candidate for sparse Cholesky.
% elseif (~isreal (A) & nnz (A-A') == 0)
% if (posdiag)
% result = 7 ; % complex Hermitian, with positive diagonal
% else
% result = 4 ; % complex Hermitian, nonpositive diagonal
% end
% elseif (nnz (A-A.') == 0)
% if (posdiag)
% result = 6 ; % symmetric with positive diagonal
% else
% result = 3 ; % symmetric, nonpositive diagonal
% end
% elseif (nnz (A+A.') == 0)
% result = 5 ; % skew symmetric
% else
% result = 2 ; % unsymmetric
% end
% With additional outputs, spsym computes the following for square matrices:
% (in this case "quick" is ignored, and set to zero):
%
% [result xmatched pmatched nzoffdiag nnzdiag] = spsym(A)
%
% xmatched is the number of nonzero entries for which A(i,j) = conj(A(j,i)).
% pmatched is the number of entries (i,j) for which A(i,j) and A(j,i) are
% both in the pattern of A (the value doesn't matter). nzoffdiag is the
% total number of off-diagonal entries in the pattern. nzdiag is the number
% of diagonal entries in the pattern. If the matrix is rectangular,
% xmatched, pmatched, nzoffdiag, and nzdiag are not computed (all of them are
% returned as zero). Note that a matched pair, A(i,j) and A(j,i) for i != j,
% is counted twice (once per entry).
% Copyright 2006-2007, Timothy A. Davis, http://www.suitesparse.com
error ('spsym mexFunction not found') ;
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