1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
|
#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Alexander Hulpke.
##
## Copyright of GAP belongs to its developers, whose names are too numerous
## to list here. Please refer to the COPYRIGHT file for details.
##
## SPDX-License-Identifier: GPL-2.0-or-later
##
## This file contains the declarations for block matrices.
##
## <#GAPDoc Label="[1]{matblock}">
## Block matrices are a special representation of matrices which can save a
## lot of memory if large matrices have a block structure with lots of zero
## blocks. &GAP; uses the representation <C>IsBlockMatrixRep</C>
## to store block matrices.
## <Index Key="IsBlockMatrixRep">IsBlockMatrixRep</Index>
## <#/GAPDoc>
##
#############################################################################
##
#F BlockMatrix( <blocks>, <nrb>, <ncb>[, <rpb>, <cpb>, <zero>] )
##
## <#GAPDoc Label="BlockMatrix">
## <ManSection>
## <Func Name="BlockMatrix" Arg='blocks, nrb, ncb[, rpb, cpb, zero]'/>
##
## <Description>
## <Ref Func="BlockMatrix"/> returns an immutable matrix in the sparse
## representation <C>IsBlockMatrixRep</C>.
## The nonzero blocks are described by the list <A>blocks</A> of triples
## <M>[ <A>i</A>, <A>j</A>, M(i,j) ]</M> each consisting of a matrix
## <M>M(i,j)</M> and its block coordinates in the block matrix to be
## constructed.
## All matrices <M>M(i,j)</M> must have the same dimensions.
## As usual the first coordinate specifies the row and the second one
## the column.
## The resulting matrix has <A>nrb</A> row blocks and <A>ncb</A> column
## blocks.
## <P/>
## If <A>blocks</A> is empty (i.e., if the matrix is a zero matrix) then
## the dimensions of the blocks must be entered as <A>rpb</A> and
## <A>cpb</A>, and the zero element as <A>zero</A>.
## <P/>
## Note that all blocks must be ordinary matrices
## (see <Ref Filt="IsOrdinaryMatrix"/>),
## and also the block matrix is an ordinary matrix.
## <Example><![CDATA[
## gap> M := BlockMatrix([[1,1,[[1, 2],[ 3, 4]]],
## > [1,2,[[9,10],[11,12]]],
## > [2,2,[[5, 6],[ 7, 8]]]],2,2);
## <block matrix of dimensions (2*2)x(2*2)>
## gap> Display(M);
## [ [ 1, 2, 9, 10 ],
## [ 3, 4, 11, 12 ],
## [ 0, 0, 5, 6 ],
## [ 0, 0, 7, 8 ] ]
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareGlobalFunction( "BlockMatrix" );
#############################################################################
##
#A MatrixByBlockMatrix( <blockmat> ) . . . create matrix from (block) matrix
##
## <#GAPDoc Label="MatrixByBlockMatrix">
## <ManSection>
## <Attr Name="MatrixByBlockMatrix" Arg='blockmat'/>
##
## <Description>
## returns a plain ordinary matrix that is equal to the block matrix
## <A>blockmat</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "MatrixByBlockMatrix", IsMatrix );
#T ConvertToPlistRep?
#############################################################################
##
#F AsBlockMatrix( <m>, <nrb>, <ncb> ) . . . create block matrix from matrix
##
## <#GAPDoc Label="AsBlockMatrix">
## <ManSection>
## <Func Name="AsBlockMatrix" Arg='m, nrb, ncb'/>
##
## <Description>
## returns a block matrix with <A>nrb</A> row blocks and <A>ncb</A> column blocks
## which is equal to the ordinary matrix <A>m</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareGlobalFunction( "AsBlockMatrix" );
#T ConvertToBlockMatrixRep?
|
