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′ D_k V, where D_k is a diagonal matrix with entries randomly chosen 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.