uwedge {jointDiag}

Joint Approximate Diagonalization of a set of square, symmetric and real-valued matrices

Description

This function performs a Joint Approximate Diagonalization of a set of square, symmetric and real-valued matrices.

Usage

uwedge(M, W_est0 = NULL, eps = .Machine$double.eps, itermax = 200, 
		keepTrace = FALSE)

Arguments

M

DOUBLE ARRAY (KxKxN). Three-dimensional array with dimensions KxKxN representing the set of square, symmetric and real-valued matrices to be jointly diagonalized. N is the number of matrices. Matrices are KxK square matrices.

W_est0

DOUBLE MATRIX (KxK). The initial guess of a joint diagonalizer. If NULL, an initial guess is automatically generated by the algorithm.

eps

DOUBLE. The algorithm stops when the criterium difference between two iterations is less than eps.

itermax

INTEGER. Alternatively, the algorithm stops when itermax sweeps have been performed without reaching convergence. If the maximum number of iteration is performed, a warning appears.

keepTrace

BOOLEAN. Do we want to keep the successive estimations of the joint diagonalizer.

Details

Given a set C_i of N KxK symmetric and real-valued matrices, the algorithm is looking for a matrix B such that \forall i \in [1,N], B C_i B^T is as close as possible of a diagonal matrix.

Value

B

Estimation of the Joint Diagonalizer.

criter

Successive estimates of the cost function across sweeps.

B_trace

Array of the successive estimates of B across iterations.

Author(s)

Cedric Gouy-Pailler ([e-mail]), from the initial matlab code by P. Tichavsky.

References

Tichavsky, P. & Yeredor, A.; Fast Approximate Joint Diagonalization Incorporating Weight Matrices; IEEE Trans. Signal Process., 2009, 57, 878-891

Examples

# generating diagonal matrices
D <- replicate(30, diag(rchisq(df=1,n=10)), simplify=FALSE)
# Mixing and demixing matrices
B <- matrix(rnorm(100),10,10)
A <- solve(B)
C <- array(NA,dim=c(10,10,30))
for (i in 1:30) C[,,i] <- A %*% D[[i]] %*% t(A)
B_est <- uwedge(C)$B
# B_est should be an approximate of B=solve(A)
B_est %*% A
# close to a permutation matrix (with random scales)