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.\" Copyright (c) 2014 Stijn van Dongen
.TH "mcxmap" 1 "16 May 2014" "mcxmap 14-137" "USER COMMANDS "
.po 2m
.de ZI
.\" Zoem Indent/Itemize macro I.
.br
'in +\\$1
.nr xa 0
.nr xa -\\$1
.nr xb \\$1
.nr xb -\\w'\\$2'
\h'|\\n(xau'\\$2\h'\\n(xbu'\\
..
.de ZJ
.br
.\" Zoem Indent/Itemize macro II.
'in +\\$1
'in +\\$2
.nr xa 0
.nr xa -\\$2
.nr xa -\\w'\\$3'
.nr xb \\$2
\h'|\\n(xau'\\$3\h'\\n(xbu'\\
..
.if n .ll -2m
.am SH
.ie n .in 4m
.el .in 8m
..
.SH NAME
mcxmap \- permute or remap the indices of graphs and matrices\&.
.SH SYNOPSIS
\fBmcxmap\fP
\fB-imx\fP fname (\fIinput\fP)
\fB[-o\fP fname (\fIoutput\fP)\fB]\fP
\fB[-make-map\fP (\fIoutput map file name\fP)\fB]\fP
\fB[-make-mapc\fP (\fIoutput map file name\fP)\fB]\fP
\fB[-make-mapr\fP (\fIoutput map file name\fP)\fB]\fP
\fB[-cmul\fP a (\fIcoefficient\fP)\fB]\fP
\fB[-cshift\fP b (\fItranslate\fP)\fB]\fP
\fB[-rmul\fP c (\fIcoefficient\fP)\fB]\fP
\fB[-rshift\fP d (\fItranslate\fP)\fB]\fP
\fB[-mul\fP e (\fIcoefficient\fP)\fB]\fP
\fB[-shift\fP f (\fItranslate\fP)\fB]\fP
\fB[-map\fP fname (\fIrow/col map file\fP)\fB]\fP
\fB[-rmap\fP fname (\fIrow map file\fP)\fB]\fP
\fB[-cmap\fP fname (\fIcolumn map file\fP)\fB]\fP
\fB[-mapi\fP fname (\fIrow/col map file (use inverse)\fP)\fB]\fP
\fB[-rmapi\fP fname (\fIrow map file (use inverse)\fP)\fB]\fP
\fB[-cmapi\fP fname (\fIcolumn map file (use inverse)\fP)\fB]\fP
\fB[-tab\fP fname (\fIread (and map) tab file\fP)\fB]\fP
.SH DESCRIPTION
This utility relabels graphs or matrices\&. Its main use is in applying a
\fImap file\fP to a given matrix or graph\&. A map file contains a so called
\fImap matrix\fP in mcl format that has some special properties (given
further below)\&. The functionality of mcxmap can also be provided by \fBmcx\fP, as
a mapped matrix (i\&.e\&. the result of applying a map matrix to another matrix)
is simply the usual matrix product of a matrix and a map matrix\&. However,
\fBmcx\fP will construct a new matrix and leave the original matrix to be mapped
alone\&. When dealing with huge matrices, considerable gains in efficiency
memory-wise and time-wise can be achieved by doing the mapping in-place\&.
This is what mcxmap does\&. In the future, its functionality may be
embedded in \fBmcx\fP with new mcx operators\&.
The special properties of a map matrix are
.ZJ 1m 1m "\(bu"
The column domain and row domain are
of the same cardinality\&.
.in -2m
.ZJ 1m 1m "\(bu"
Each column has exactly one entry\&.
.in -2m
.ZJ 1m 1m "\(bu"
Each row domain index occurs in exactly one column\&.
.in -2m
These properties imply that the matrix can be used
as a map from the column domain onto the row domain\&.
An example map matrix is found in the \fBEXAMPLES\fP Section\&.
.SH OPTIONS
.ZI 2m "\fB-o\fP fname (\fIoutput file\fP)"
\&
.br
Output file\&.
.in -2m
.ZI 2m "\fB-imx\fP fname (\fIinput file\fP)"
\&
.br
Input file\&.
.in -2m
.ZI 2m "\fB-map\fP fname (\fIrow/col map file)\fP)"
\&
'in -2m
.ZI 2m "\fB-rmap\fP fname (\fIrow map file\fP)"
\&
'in -2m
.ZI 2m "\fB-cmap\fP fname (\fIcolumn map file\fP)"
\&
'in -2m
.ZI 2m "\fB-mapi\fP fname (\fIrow/col map file (use inverse)\fP)"
\&
'in -2m
.ZI 2m "\fB-rmapi\fP fname (\fIrow map fil (use inverse)\fP)"
\&
'in -2m
.ZI 2m "\fB-cmapi\fP fname (\fIcolumn map fil (use inverse)\fP)"
\&
'in -2m
'in +2m
\&
.br
Different ways to specify map files\&.
.in -2m
.ZI 2m "\fB-make-map\fP (\fIoutput map file name\fP)"
\&
'in -2m
.ZI 2m "\fB-make-mapc\fP (\fIoutput map file name\fP)"
\&
'in -2m
.ZI 2m "\fB-make-mapr\fP (\fIoutput map file name\fP)"
\&
'in -2m
'in +2m
\&
.br
Generate a map that maps the specified domain onto
the appropriate canonical domain and write the map
matrix to file\&.
.in -2m
.ZI 2m "\fB-cmul\fP a (\fIcoefficient\fP)"
\&
'in -2m
.ZI 2m "\fB-cshift\fP b (\fItranslate\fP)"
\&
'in -2m
'in +2m
\&
.br
These options have affect if neither a column map file nor column
canonification is specified\&. If any of the first two options is used,
column indices\ \&\fCi\fP are mapped to\ \&\fCa*i+b\fP\&.
.in -2m
.ZI 2m "\fB-rmul\fP c (\fIcoefficient\fP)"
\&
'in -2m
.ZI 2m "\fB-rshift\fP d (\fItranslate\fP)"
\&
'in -2m
'in +2m
\&
.br
These options have affect if neither a row map file nor row
canonification is specified\&. If any of the first two options is used,
indices\ \&\fCi\fP are mapped to\ \&\fCc*i+d\fP\&.
.in -2m
.ZI 2m "\fB-mul\fP e (\fIcoefficient\fP)"
\&
'in -2m
.ZI 2m "\fB-shift\fP f (\fItranslate\fP)"
\&
'in -2m
'in +2m
\&
.br
If a map file is specified for a given domain, neither a map file nor
canonification is specified\&. If any of the first two options is used, the
indices\ \&\fCi\fP will be mapped to\ \&\fCe*i+f\fP\&.
.in -2m
.ZI 2m "\fB-tab\fP fname (\fIread (and map) tab file\fP)"
\&
.br
This option requires the \fB-map\fP option\&. \fBmcxmap\fP will output the
mapped tab definition\&.
.in -2m
.SH EXAMPLES
The matrix below has two canonical domains which are identical\&.
It denotes a map of the canonical domain onto itself, in which
node 0 is relabeled to 8, node 1 is relabeled to 5, et cetera\&.
.nf \fC
(mclheader
mcltype matrix
dimensions 12x12
)
(mclmatrix
begin
0 8 $
1 5 $
2 3 $
3 2 $
4 4 $
5 6 $
6 7 $
7 9 $
8 1 $
9 10 $
10 11 $
11 0 $
)
.fi \fR
.SH AUTHOR
Stijn van Dongen\&.
.SH SEE ALSO
\fBmcxio(5)\fP,
\fBmcx(1)\fP,
\fBmcxsubs(1)\fP,
and \fBmclfamily(7)\fP for an overview of all the documentation
and the utilities in the mcl family\&.
|
