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function L = laplacian (A, type, check)
%GRB.LAPLACIAN Laplacian matrix
% L = laplacian (A) is the graph Laplacian of the matrix A. spones(A)
% must be symmetric. The diagonal of A is ignored. The diagonal of L is
% the degree of the nodes. That is, L(j,j) = sum (spones (A (:,j))),
% assuming A has no diagonal entries.. For off-diagonal entries, L(i,j) =
% L(j,i) = -1 if the edge (i,j) exists in A.
%
% The type of L defaults to double. With a second argument, the type of L
% can be specified, as L = laplacian (A,type); type may be 'double',
% 'single', 'int8', 'int16', 'int32', 'int64', 'single complex', or
% 'double complex'. Be aware that integer overflow may occur with the
% smaller integer types, if the degree of any nodes exceeds the largest
% integer value.
%
% spones(A) must be symmetric on input, but this condition is not checked
% by default. If it is not symmetric, the results are undefined. To
% check this condition, use GrB.laplacian (A, 'double', 'check') ;
%
% L is returned as symmetric GraphBLAS matrix.
%
% Example:
%
% A = bucky ;
% L = GrB.laplacian (A)
%
% See also graph/laplacian.
% SuiteSparse:GraphBLAS, Timothy A. Davis, (c) 2017-2022, All Rights Reserved.
% SPDX-License-Identifier: Apache-2.0
if (isobject (A))
A = A.opaque ;
end
[m, n] = gbsize (A) ;
if (m ~= n)
error ('GrB:error', 'A must be square and symmetric') ;
end
% get the type
if (nargin < 2)
type = 'double' ;
elseif (~gb_issigned (type))
% type must be signed
error ('GrB:error', 'type cannot be logical or unsigned integer') ;
end
% S = spones (A)
S = gbapply (['1.' type], A) ;
% check the input matrix, if requested
if (nargin > 2 && isequal (check, 'check'))
% make sure spones (S) is symmetric
if (~gb_issymmetric (S, 'nonskew', false))
error ('GrB:error', 'spones(A) must be symmetric') ;
end
end
% D = diagonal matrix with d(i,i) = row/column degree of node i
fmt = gbformat (S) ;
if (isequal (fmt, 'by row'))
D = gbdegree (S, 'row') ;
else
D = gbdegree (S, 'col') ;
end
D = gbmdiag (D, 0) ;
if (~isequal (type, gbtype (D)))
% gbdegree returns its result as int64; typecast to desired type
D = gbnew (D, type) ;
end
% construct the Laplacian
% L = D-S
L = GrB (gbeadd (D, '+', gbapply ('-', S))) ;
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