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

mcxmap [-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)] [--invert (invert map file(s))] [--invertc (invert column map file)] [--invertr (invert row map file)] [-digits n (digits width)] [-o fname (output)] -imx fname (input)

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.

Output file.

Input file.

Number of digits output for values.

If the map file is specified, column indices will be mapped according to this file. Otherwise, if any of the first two options is used, column indices i are mapped to a*i+b.

Specifies to use the inverse of the map file(s) given.

If the map file is specified, row indices will be mapped according to this file. Otherwise, if any of the first two options is used, row indices i are mapped to c*i+d.

If the map file is specified, both column and row indices will be mapped according to it. Otherwise, if any of the two first options is specified, both column and row indices i will be mapped to e*i+f.

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  $
)

Stijn van Dongen.

mcxio(5), mcx(1), mcxsubs(1), and mclfamily(7) for an overview of all the documentation and the utilities in the mcl family.