The routine may be called by the names f08pnf, nagf_lapackeig_zgees or its LAPACK name zgees.
The Schur factorization of is given by
where , the matrix of Schur vectors, is unitary and is the Schur form. A complex matrix is in Schur form if it is upper triangular.
Optionally, f08pnf also orders the eigenvalues on the diagonal of the Schur form so that selected eigenvalues are at the top left. The leading columns of form an orthonormal basis for the invariant subspace corresponding to the selected eigenvalues.
Anderson E, Bai Z, Bischof C, Blackford S, Demmel J, Dongarra J J, Du Croz J J, Greenbaum A, Hammarling S, McKenney A and Sorensen D (1999) LAPACK Users' Guide (3rd Edition) SIAM, Philadelphia https://www.netlib.org/lapack/lug
Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore
1: – Character(1)Input
On entry: if , Schur vectors are not computed.
If , Schur vectors are computed.
2: – Character(1)Input
On entry: specifies whether or not to order the eigenvalues on the diagonal of the Schur form.
On entry: the first dimension of the array vs as declared in the (sub)program from which f08pnf is called.
if , ;
11: – Complex (Kind=nag_wp) arrayWorkspace
On exit: if , the real part of contains the minimum value of lwork required for optimal performance.
12: – IntegerInput
On entry: the dimension of the array work as declared in the (sub)program from which f08pnf is called.
If , a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued.
for optimal performance, lwork must generally be larger than the minimum, say , where is the optimal block size for f08nsf.
13: – Real (Kind=nag_wp) arrayWorkspace
Note: the dimension of the array rwork
must be at least
14: – Logical arrayWorkspace
Note: the dimension of the array bwork
must be at least
if , and at least otherwise.
Background information to multithreading can be found in the Multithreading documentation.
f08pnf is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
f08pnf makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.
The total number of floating-point operations is proportional to .