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# sorgtr

```
NAME
SORGTR - generate a real orthogonal matrix Q which is
defined as the product of n-1 elementary reflectors of order
N, as returned by SSYTRD

SYNOPSIS
SUBROUTINE SORGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )

CHARACTER      UPLO

INTEGER        INFO, LDA, LWORK, N

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

PURPOSE
SORGTR generates a real orthogonal matrix Q which is defined
as the product of n-1 elementary reflectors of order N, as
returned by SSYTRD:

if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),

if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).

ARGUMENTS
UPLO    (input) CHARACTER*1
= 'U': Upper triangle of A contains elementary
reflectors from SSYTRD; = 'L': Lower triangle of A
contains elementary reflectors from SSYTRD.

N       (input) INTEGER
The order of the matrix Q. N >= 0.

A       (input/output) REAL array, dimension (LDA,N)
On entry, the vectors which define the elementary
reflectors, as returned by SSYTRD.  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 elemen-
tary reflector H(i), as returned by SSYTRD.

WORK    (workspace) REAL array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal
LWORK.

LWORK   (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,N-

1).  For optimum performance LWORK >= (N-1)*NB,
where NB is the optimal blocksize.

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal
value
```