CrossCorrelationTableList: Create test set...

Create a collection of CrossCorrelationTables that are all derived from different diagonal matrices by the same transformation matrix.

Settings

Matrix dimension
determines the size of the square matrix with cross-correlations.
Number of matrices
determines the number of matrices that have to be generated.
First is positive-definite
guarantees that the first matrix of the series is positive definite.
Sigma
the standard deviation of the noise that is added to each transformation matrix element. A value of zero makes all the cross-correlation matrices jointly diagonalizable. A value greater than zero makes each transformation matrix a little different and the collection not jointly diagonalizable anymore.

Algorithm

All the CrossCorrelationTable matrices are generated as V′·Dk· V, where Dk is a diagonal matrix with entries randomly choosen from the [-1,1] interval. The matrix V is a "random" orthogonal matrix obtained from the singular value decomposition of a matrix M = U·D·V′, where the cells of the matrix M are random Gaussian numbers with mean 0 and standard deviation 1.

If the first matrix has to be positive definite, the numbers on the diagonal of D1 are randomly chosen from the [0.1,1] interval.


© djmw, February 12, 2011