NAG Library Routine Document

F08NFF (DORGHR)

F08NFF (DORGHR) is intended to be used following a call to F08NEF (DGEHRD), which reduces a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation: A=QHQT. F08NEF (DGEHRD) represents the matrix Q as a product of ihi-ilo elementary reflectors. Here ilo and ihi are values determined by F08NHF (DGEBAL) when balancing the matrix; if the matrix has not been balanced, ilo=1 and ihi=n.

This routine may be used to generate Q explicitly as a square matrix. Q has the structure:

Q = I 0 0 0 Q22 0 0 0 I

where Q22 occupies rows and columns ilo to ihi.

4 References

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

5 Parameters

1: N – INTEGERInput

On entry: n, the order of the matrix Q.

Constraint: N≥0.

2: ILO – INTEGERInput

3: IHI – INTEGERInput

On entry: these must be the same parameters ILO and IHI, respectively, as supplied to F08NEF (DGEHRD).

Constraints:

if N>0, 1≤ILO≤IHI≤N;
if N=0, ILO=1 and IHI=0.

4: A(LDA,*) – REAL (KIND=nag_wp) arrayInput/Output

Note: the second dimension of the array A must be at least max1,N.

On entry: details of the vectors which define the elementary reflectors, as returned by F08NEF (DGEHRD).

On exit: the n by n orthogonal matrix Q.

5: LDA – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F08NFF (DORGHR) is called.

Constraint: LDA≥max1,N.

6: TAU(*) – REAL (KIND=nag_wp) arrayInput

Note: the dimension of the array TAU must be at least max1,N-1.

On entry: further details of the elementary reflectors, as returned by F08NEF (DGEHRD).

7: WORK(max1,LWORK) – REAL (KIND=nag_wp) arrayWorkspace

On exit: if INFO=0, WORK1 contains the minimum value of LWORK required for optimal performance.

8: LWORK – INTEGERInput

On entry: the dimension of the array WORK as declared in the (sub)program from which F08NFF (DORGHR) is called, unless LWORK=-1, in which case a workspace query is assumed and the routine only calculates the optimal dimension of WORK (using the formula given below).

Suggested value: for optimal performance LWORK should be at least IHI-ILO×nb, where nb is the block size.