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function C = incidence (A, varargin)
%GRB.INCIDENCE graph incidence matrix.
% C = GrB.incidence (A) is the graph incidence matrix of the square
% matrix A. C is GraphBLAS matrix of size n-by-e, if A is n-by-n with e
% entries (not including diagonal entries). The jth column of C has 2
% entries: C(s,j) = -1 and C(t,j) = 1, where A(s,t) is an entry A.
% Diagonal entries in A are ignored.
%
% C = GrB.incidence (A, ..., 'directed') constructs a matrix C of size
% n-by-e where e = GrB.entries (GrB.offdiag (A)). Any entry in the
% upper or lower trianglar part of A results in a unique column of
% C. The diagonal is ignored. This is the default.
%
% C = GrB.incidence (A, ..., 'unsymmetric') is the same as 'directed'.
%
% C = GrB.incidence (A, ..., 'undirected') assumes A is symmetric, and
% only creates columns of C based on entries in tril (A,-1). The
% diagonal and upper triangular part of A are ignored.
%
% C = GrB.incidence (A, ..., 'symmetric') is the same as 'undirected'.
%
% C = GrB.incidence (A, ..., 'lower') is the same as 'undirected'.
%
% C = GrB.incidence (A, ..., 'upper') is the same as 'undirected',
% except that only entries in triu (A,1) are used.
%
% C = GrB.incidence (A, ..., type) constructs C with the type 'double',
% 'single', 'int8', 'int16', 'int32', or 'int64'. The default is
% 'double'. The type cannot be 'logical' or 'uint*' since C
% must contain -1's.
%
% Examples:
%
% A = sprand (5, 5, 0.5)
% C = GrB.incidence (A)
%
% See also graph/incidence, digraph/incidence.
% 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') ;
end
% get the string options
kind = 'directed' ;
type = 'double' ;
for k = 1:nargin-1
arg = lower (varargin {k}) ;
switch arg
case { 'directed', 'undirected', 'symmetric', 'unsymmetric', ...
'lower', 'upper' }
kind = arg ;
case { 'double', 'single', 'int8', 'int16', 'int32', 'int64' }
type = arg ;
case { 'uint8', 'uint16', 'uint32', 'uint64', 'logical' }
error ('GrB:error', 'type must be signed') ;
otherwise
error ('GrB:error', 'unknown option') ;
end
end
switch (kind)
case { 'directed', 'unsymmetric' }
% create the incidence matrix of a directed graph, using all of A;
% except that diagonal entries are ignored.
A = gbselect ('offdiag', A, 0) ;
case { 'upper' }
% create the incidence matrix of an undirected graph, using only
% entries in the strictly upper triangular part of A.
A = gbselect ('triu', A, 1) ;
otherwise % 'undirected', 'symmetric', or 'lower'
% create the incidence matrix of an undirected graph, using only
% entries in the strictly lower triangular part of A.
A = gbselect ('tril', A, -1) ;
end
% build the incidence matrix
desc.base = 'zero-based' ;
[I, J] = gbextracttuples (A, desc) ;
e = length (I) ;
I = [I ; J] ;
J = (int64 (0) : int64 (e-1))' ;
J = [J ; J] ;
X = ones (e, 1, type) ;
X = [-X ; X] ;
C = GrB (gbbuild (I, J, X, n, e, desc)) ;
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