NAG Library Routine Document

F08QTF (ZTREXC)

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: N≥0.

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: LDT≥max1,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', LDQ≥max1,N;
if COMPQ='N', LDQ≥1.

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: 1≤IFST≤N and 1≤ILST≤N.

9: INFO – INTEGEROutput