Provided by: liblapack-doc_3.3.1-1_all

#### NAME

```       LAPACK-3 - generates a real orthogonal matrix Q which is defined 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 defined 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 orthogonal 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 elementary
reflector H(i), as returned by DGEHRD.

WORK    (workspace/output) DOUBLE PRECISION 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

LAPACK routine (version 3.2)               April 2011                            DORGHR(3lapack)
```