QZ (version 0.1-7)

qz.zgees: QZ Decomposition for a Complex Matrix

Description

This function call 'zgees' in Fortran to decompose a 'complex' matrix A.

Usage

qz.zgees(A, vs = TRUE, LWORK = NULL)

Arguments

A

a 'complex' matrix, dim = c(N, N).

vs

if compute 'complex' Schur vectors. (Q)

LWORK

optional, dimension of array WORK for workspace. (>= 2N)

Value

Return a list contains next:

'T'

A's generalized Schur form.

'W'

generalized eigenvalues.

'VS'

original returns from 'zgees.f'.

'WORK'

optimal LWORK (for zgees.f only)

'INFO'

= 0: successful. < 0: if INFO = -i, the i-th argument had an illegal value. =1,...,N: QZ iteration failed. =N+1: reordering problem. =N+2: reordering failed.

Extra returns in the list:

'Q'

the Schur vectors.

Warning(s)

The results may not be consistent on 32 bits and 64 bits Windows systems, but may be valid on both systems.

Details

See 'zgees.f' for all details.

ZGEES computes for an N-by-N complex non-symmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Q. This gives the Schur factorization A = Q*T*(Q**H).

Optionally, it also orders the eigenvalues on the diagonal of the Schur form so that selected eigenvalues are at the top left. The leading columns of Q then form an orthonormal basis for the invariant subspace corresponding to the selected eigenvalues.

A complex matrix is in Schur form if it is upper triangular.

References

Anderson, E., et al. (1999) LAPACK User's Guide, 3rd edition, SIAM, Philadelphia.

http://www.netlib.org/lapack/complex16/zgees.f

http://en.wikipedia.org/wiki/Schur_decomposition

See Also

qz.zgeev

Examples

# NOT RUN {
<!-- % \dontrun{ -->
# }
# NOT RUN {
library(QZ, quiet = TRUE)

### http://www.nag.com/lapack-ex/node94.html
A <- exA1$A
ret <- qz.zgees(A)

# Verify 1
A.new <- ret$Q %*% ret$T %*% H(ret$Q)
round(A - A.new)

# verify 2
round(ret$Q %*% H(ret$Q))
# }
# NOT RUN {
<!-- % } -->
# }