F08QTF (ZTREXC) (PDF version)
F08 Chapter Contents
F08 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F08QTF (ZTREXC)

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

F08QTF (ZTREXC) reorders the Schur factorization of a complex general matrix.

2  Specification

SUBROUTINE F08QTF ( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, INFO)
INTEGER  N, LDT, LDQ, IFST, ILST, INFO
COMPLEX (KIND=nag_wp)  T(LDT,*), Q(LDQ,*)
CHARACTER(1)  COMPQ
The routine may be called by its LAPACK name ztrexc.

3  Description

F08QTF (ZTREXC) reorders the Schur factorization of a complex general matrix A=QTQH, so that the diagonal element of T with row index IFST is moved to row ILST.
The reordered Schur form T~ is computed by a unitary similarity transformation: T~=ZHTZ. Optionally the updated matrix Q~ of Schur vectors is computed as Q~=QZ, giving A=Q~T~Q~H.

4  References

Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore

5  Parameters

1:     COMPQ – CHARACTER(1)Input
On entry: indicates whether the matrix Q of Schur vectors is to be updated.
COMPQ='V'
The matrix Q of Schur vectors is updated.
COMPQ='N'
No Schur vectors are updated.
Constraint: COMPQ='V' or 'N'.
2:     N – INTEGERInput
On entry: n, the order of the matrix T.
Constraint: N0.
3:     T(LDT,*) – COMPLEX (KIND=nag_wp) arrayInput/Output
Note: the second dimension of the array T must be at least max1,N.
On entry: the n by n upper triangular matrix T, as returned by F08PSF (ZHSEQR).
On exit: T is overwritten by the updated matrix T~.
4:     LDT – INTEGERInput
On entry: the first dimension of the array T as declared in the (sub)program from which F08QTF (ZTREXC) is called.
Constraint: LDTmax1,N.
5:     Q(LDQ,*) – COMPLEX (KIND=nag_wp) arrayInput/Output
Note: the second dimension of the array Q must be at least max1,N if COMPQ='V' and at least 1 if COMPQ='N'.
On entry: if COMPQ='V', Q must contain the n by n unitary matrix Q of Schur vectors.
On exit: if COMPQ='V', Q contains the updated matrix of Schur vectors.
If COMPQ='N', Q is not referenced.
6:     LDQ – INTEGERInput
On entry: the first dimension of the array Q as declared in the (sub)program from which F08QTF (ZTREXC) is called.
Constraints:
  • if COMPQ='V', LDQmax1,N;
  • if COMPQ='N', LDQ1.
7:     IFST – INTEGERInput
8:     ILST – INTEGERInput
On entry: IFST and ILST must specify the reordering of the diagonal elements of T. The element with row index IFST is moved to row ILST by a sequence of exchanges between adjacent elements.
Constraint: 1IFSTN and 1ILSTN.
9:     INFO – INTEGEROutput

6  Error Indicators and Warnings

INFO<0
If INFO=-i, argument i had an illegal value. An explanatory message is output, and execution of the program is terminated.

7  Accuracy

The computed matrix T~ is exactly similar to a matrix T+E, where
E2 = Oε T2 ,
and ε is the machine precision.
The values of the eigenvalues are never changed by the reordering.

8  Further Comments

The total number of real floating point operations is approximately 20nr if COMPQ='N', and 40nr if COMPQ='V', where r=IFST-ILST.
The real analogue of this routine is F08QFF (DTREXC).

9  Example

This example reorders the Schur factorization of the matrix T so that element t11 is moved to t44, where
T = -6.00-7.00i 0.36-0.36i -0.19+0.48i 0.88-0.25i 0.00+0.00i -5.00+2.00i -0.03-0.72i -0.23+0.13i 0.00+0.00i 0.00+0.00i 8.00-1.00i 0.94+0.53i 0.00+0.00i 0.00+0.00i 0.00+0.00i 3.00-4.00i .

9.1  Program Text

Program Text (f08qtfe.f90)

9.2  Program Data

Program Data (f08qtfe.d)

9.3  Program Results

Program Results (f08qtfe.r)


F08QTF (ZTREXC) (PDF version)
F08 Chapter Contents
F08 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2011