dorghr(3)

NAME

DORGHR - generate a real orthogonal matrix Q which is de

fined as the product of IHI-ILO elementary reflectors of order N,

as returned by DGEHRD

SYNOPSIS

SUBROUTINE DORGHR( N, ILO, IHI, A, LDA, TAU, WORK,  LWORK,
INFO )
    INTEGER        IHI, ILO, INFO, LDA, LWORK, N
    DOUBLE          PRECISION A( LDA, * ), TAU( * ), WORK(
* )

PURPOSE

DORGHR generates a real orthogonal matrix Q which is de

fined as the product of IHI-ILO elementary reflectors of order N,

as returned by DGEHRD: Q = H(ilo) H(ilo+1) . . . H(ihi-1).

ARGUMENTS

N (input) INTEGER

The order of the matrix Q. N >= 0.

ILO (input) INTEGER

IHI (input) INTEGER ILO and IHI must have the

same values as in the previous call of DGEHRD. Q is equal to the

unit matrix except in the submatrix Q(ilo+1:ihi,ilo+1:ihi). 1 <=

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

A (input/output) DOUBLE PRECISION array, dimension

(LDA,N)

On entry, the vectors which define the elementary

reflectors, as returned by DGEHRD. On exit, the N-by-N orthogo

nal matrix Q.

LDA (input) INTEGER

The leading dimension of the array A. LDA >=

max(1,N).

TAU (input) DOUBLE PRECISION array, dimension (N-1)

TAU(i) must contain the scalar factor of the ele

mentary reflector H(i), as returned by DGEHRD.

WORK (workspace/output) DOUBLE PRECISION array, dimen

sion (LWORK)

On exit, if INFO = 0, WORK(1) returns the optimal

LWORK.

LWORK (input) INTEGER

The dimension of the array WORK. LWORK >= IHI-ILO.

For optimum performance LWORK >= (IHI-ILO)*NB, where NB is the

optimal blocksize.

If LWORK = -1, then 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 by XERBLA.

INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille

gal value

LAPACK version 3.0 15 June 2000

DORGHR(3)