PERMUTATION MATRIX MANUAL
PERMUTATION MATRIX FULL

The function symrcm(A) actually operates on the nonzero structure of the symmetric matrix A + A', but the result is also useful for asymmetric matrices. It is not guaranteed to find the smallest possible bandwidth, but it usually does. The reverse Cuthill-McKee ordering is intended to reduce the profile or bandwidth of the matrix. The second output argument from sort is the permutation that sorts this vector. sort sorts the values in ascending order.

PERMUTATION MATRIX FULL

full converts this vector to full storage format.

The sum function sums down the columns of the matrix, producing a vector that contains the count of nonzeros in each column.

The inner call to spones creates a sparse matrix with ones at the location of every nonzero element in S.

The colperm M-file has only a single line.

The function p = colperm(S) computes this column-count permutation. This is sometimes a good reordering for matrices with very irregular structures, especially if there is great variation in the nonzero counts of rows or columns.

The simplest such reordering is to sort the columns by nonzero count. Reordering the rows and columns can often make its Cholesky, factors sparser. Reordering the columns of a matrix can often make its LU or QR factors sparser.

You can compute the inverse of p with r(p) = 1:n. To convert between the two representations, let I = speye(n) be an identity matrix of the appropriate size. The vector representation is slightly more compact and efficient, so the various sparse matrix permutation routines all return full row vectors with the exception of the pivoting permutation in LU (triangular) factorization, which returns a matrix compatible with earlier versions of MATLAB. If P is a sparse matrix, then both representations use storage proportional to n and you can apply either to S in time proportional to nnz(S). For example, the statements S(p,:) and P*S produce You can now try some permutations using the permutation vector p and the permutation matrix P.

A permutation vector p, which is a full vector containing a permutation of 1:n, acts on the rows of S as S(p,:), or on the columns as S(:,p).

A permutation matrix P acts on the rows of S as P*S or on the columns as S*P'.

18, NO.Sparse Matrices (Mathematics) MathematicsĪ permutation of the rows and columns of a sparse matrix S can be represented in two ways: Ref: Comparing Clusterings Using Bertin’s Idea Alexander Pilhofer, Alexander Gribov, and Antony Unwin IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. Box 607, FIN-33014 University of Tampere, Finland īelow is given some implementations that shows the limitations of the method. The most optimal mapping is for 'true' or 'false' variables, where a matrix cell is 'white' for 'false' and 'black' for 'true' (or vice versa).Įach of the identifiers are then placed into a matrix that is sorted and/or grouped into categories of cells with visual likeness, which effectively groups data that has corresponding ranges.īelow is given some examples of good implementations of the method: Ref: Reordering the Reorderable Matrix as an Algorithmic Problem, Erkki M¨akinen and Harri Siirtola Department of Computer and Information Sciences P.O. The method of using permutation matrices consist of converting raw numerical data into appropriate ranges and then associating each of these ranges to corresponding identifying shapes, sizes and/or colour mappings for example numerical data is mapped to different different sizes of circles or squares and hues of colour. Suitable data sets included variables that do not rely on order i.e. (see here) Jacques Bertin's physical permutation matrix ( ) Use of a permutation matrix ( ) Photographs of the results were then used in scientific publications.

PERMUTATION MATRIX MANUAL

The matrix was then assembled and reordered with a laborious manual method to reveal patterns and groups. The re-orderable matrices were made through collecting data and encoding it for different ranges, firstly on paper, then on wood. Before modern computers existed, Bertin constructed physical wooden matrices (called 'Dominos') to explore data. Jacques Bertin knew that interaction is at the heart of exploring hidden relationships in data. Permutation matrices are sortable charts used to explore patterns and correlations in multi-dimensional re-orderable data.

Permutation matrix