1function C = lt (A, B)
2%A < B less than.
3% C = (A < B) is an element-by-element comparison of A and B.  One or
4% both may be scalars.  Otherwise, A and B must have the same size.
5%
6% See also GrB/le, GrB/gt, GrB/ge, GrB/ne, GrB/eq.
7
8% FUTURE: lt(A,B) for two matrices A and B is slower than it could be.
9% See comments in gb_union_op.
10
11% The pattern of C depends on the type of inputs:
12% A scalar, B scalar:  C is scalar.
13% A scalar, B matrix:  C is full if A<0, otherwise C is a subset of B.
14% B scalar, A matrix:  C is full if B>0, otherwise C is a subset of A.
15% A matrix, B matrix:  C has the pattern of the set union, A+B.
16
17% SuiteSparse:GraphBLAS, Timothy A. Davis, (c) 2017-2021, All Rights Reserved.
18% SPDX-License-Identifier: GPL-3.0-or-later
19
20if (isobject (A))
21    A = A.opaque ;
22end
23
24if (isobject (B))
25    B = B.opaque ;
26end
27
28[am, an, atype] = gbsize (A) ;
29[bm, bn, btype] = gbsize (B) ;
30a_is_scalar = (am == 1) && (an == 1) ;
31b_is_scalar = (bm == 1) && (bn == 1) ;
32ctype = gboptype (atype, btype) ;
33
34if (a_is_scalar)
35    if (b_is_scalar)
36        % both A and B are scalars
37        C = GrB (gb_union_op ('<', A, B)) ;
38    else
39        % A is a scalar, B is a matrix
40        if (gb_scalar (A) < 0)
41            if (~gb_issigned (btype))
42                % a < 0, and B has an unsigned type.  C is all true.
43                C = GrB (gb_scalar_to_full (bm, bn, 'logical', ...
44                    gb_fmt (B), true)) ;
45            else
46                % since a < 0, entries not present in B result in a true
47                % value, so the result is full.  Expand A to full.
48                A = gb_scalar_to_full (bm, bn, ctype, gb_fmt (B), A) ;
49                C = GrB (gbemult (A, '<', gbfull (B, ctype))) ;
50            end
51        else
52            % since a >= 0, entries not present in B result in a false
53            % value, so the result is a sparse subset of B.  select all
54            % entries in B > a, then convert to true.
55            C = GrB (gbapply ('1.logical', gbselect (B, '>', A))) ;
56        end
57    end
58else
59    if (b_is_scalar)
60        % A is a matrix, B is a scalar
61        b = gb_scalar (B) ;
62        if (b < 0 && ~gb_issigned (atype))
63            % b is negative, and A has an unsigned type.  C is all false.
64            C = GrB (gbnew (am, an, 'logical')) ;
65        elseif (b > 0)
66            % since b > 0, entries not present in A result in a true
67            % value, so the result is full.  Expand B to a full matrix.
68            B = gb_scalar_to_full (am, an, ctype, gb_fmt (A), B) ;
69            C = GrB (gbemult (gbfull (A, ctype), '<', B)) ;
70        else
71            % since b <= 0, entries not present in A result in a false
72            % value, so the result is a sparse subset of A.  Select all
73            % entries in A < b, then convert to true.
74            C = GrB (gbapply ('1.logical', gbselect (A, '<', B))) ;
75        end
76    else
77        % both A and B are matrices.  C is the set union of A and B.
78        C = GrB (gb_union_op ('<', A, B)) ;
79    end
80end
81
82