cjd {JADE}

Joint Diagonalization of Complex Matrices

Description

This is an R version of Cardoso's joint_diag matlab function for joint diagonalization of k complex-valued square matrices.

Usage

cjd(X, eps = 1e-06, maxiter = 100)

Arguments

X

A matrix of k stacked pxp complex matrices with dimension c(kp,p) or an array with dimension c(p,p,k).

eps

Convergence tolerance.

maxiter

Maximum number of iterations.

Value

V

An orthogonal matrix.

D

A stacked matrix with the diagonal matrices or an array with the diagonal matrices. The form of the output depends on the form of the input.

Author(s)

Jean-Francois Cardoso. Ported to R by Klaus Nordhausen.

References

Cardoso, J.-F. and Souloumiac, A., (1996), Jacobi angles for simultaneous diagonalization, SIAM J. Mat. Anal. Appl., 17, 161–164.

See Also

rjd, rjd.fortran

Examples

D1 <- diag(complex(real=runif(3,0,2), imaginary=runif(3)))
D2 <- diag(complex(real=runif(3,0,2), imaginary=runif(3)))
D3 <- diag(complex(real=runif(3,0,2), imaginary=runif(3)))
D4 <- diag(complex(real=runif(3,0,2), imaginary=runif(3)))

Z <- matrix(runif(9), ncol = 3)
V <- eigen(Z %*% t(Z))$vectors

M1 <- t(V)%*%D1%*%V
M2 <- t(V)%*%D2%*%V
M3 <- t(V)%*%D3%*%V
M4 <- t(V)%*%D4%*%V
MS <- rbind(M1,M2,M3,M4)
Ms <- array(0,dim=c(3,3,4))
Ms[,,1]<-M1
Ms[,,3]<-M3
Ms[,,2]<-M2
Ms[,,4]<-M4
res.array <- cjd(Ms)
res.mat <- cjd(MS)
Re(res.array$V)
V
round(V%*%Re(res.array$V),2)
round(V%*%Re(res.mat$V),2)