cc_qz_zgees: QZ Decomposition for a Complex Matrix

In QZ: Generalized Eigenvalues and QZ Decomposition

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)

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.

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.

Author(s)

Wei-Chen Chen [e-mail]

References

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

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

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

See Also

qz.zgeev

Examples

library(QZ, quiet = TRUE)

### https://www.netlib.org/lapack/lug/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))

QZ documentation built on April 13, 2025, 9:07 a.m.