16 May 2014 mcxmap 14-137

1.
NAME
2.
SYNOPSIS
3.
DESCRIPTION
4.
OPTIONS
5.
EXAMPLES
6.
AUTHOR
7.
SEE ALSO

## NAME

mcxmap — permute or remap the indices of graphs and matrices.

## SYNOPSIS

mcxmap -imx fname (input)

[-o fname (output)] [-make-map (output map file name)] [-make-mapc (output map file name)] [-make-mapr (output map file name)] [-cmul a (coefficient)] [-cshift b (translate)] [-rmul c (coefficient)] [-rshift d (translate)] [-mul e (coefficient)] [-shift f (translate)] [-map fname (row/col map file)] [-rmap fname (row map file)] [-cmap fname (column map file)] [-mapi fname (row/col map file (use inverse))] [-rmapi fname (row map file (use inverse))] [-cmapi fname (column map file (use inverse))] [-tab fname (read (and map) tab file)]

## DESCRIPTION

This utility relabels graphs or matrices. Its main use is in applying a map file to a given matrix or graph. A map file contains a so called map matrix in mcl format that has some special properties (given further below). The functionality of mcxmap can also be provided by mcx, 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, mcx 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 mcx with new mcx operators.

The special properties of a map matrix are

•

The column domain and row domain are of the same cardinality.

•

Each column has exactly one entry.

•

Each row domain index occurs in exactly one column.

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 EXAMPLES Section.

## OPTIONS

-o fname (output file)

Output file.

-imx fname (input file)

Input file.

-map fname (row/col map file))
-rmap fname (row map file)
-cmap fname (column map file)
-mapi fname (row/col map file (use inverse))
-rmapi fname (row map fil (use inverse))
-cmapi fname (column map fil (use inverse))

Different ways to specify map files.

-make-map (output map file name)
-make-mapc (output map file name)
-make-mapr (output map file name)

Generate a map that maps the specified domain onto the appropriate canonical domain and write the map matrix to file.

-cmul a (coefficient)
-cshift b (translate)

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 `i` are mapped to `a*i+b`.

-rmul c (coefficient)
-rshift d (translate)

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 `i` are mapped to `c*i+d`.

-mul e (coefficient)
-shift f (translate)

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 `i` will be mapped to `e*i+f`.

-tab fname (read (and map) tab file)

This option requires the -map option. mcxmap will output the mapped tab definition.

## 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.

(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 $ )

## AUTHOR

Stijn van Dongen.

## SEE ALSO

mcxio, mcx, mcxsubs, and mclfamily for an overview of all the documentation and the utilities in the mcl family.