 SORGHR(3) generates a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by SGEHRD

## SYNOPSIS

SUBROUTINE SORGHR(
N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )

INTEGER IHI, ILO, INFO, LDA, LWORK, N

REAL A( LDA, * ), TAU( * ), WORK( * )

## PURPOSE

SORGHR generates a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by SGEHRD: 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 SGEHRD. 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) REAL array, dimension (LDA,N)
On entry, the vectors which define the elementary reflectors, as returned by SGEHRD. On exit, the N-by-N orthogonal matrix Q.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
TAU (input) REAL array, dimension (N-1)
TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGEHRD.
WORK (workspace/output) REAL array, dimension (MAX(1,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 illegal value