 DOPGTR(3) generates a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by DSPTRD using packed storage

## SYNOPSIS

SUBROUTINE DOPGTR(
UPLO, N, AP, TAU, Q, LDQ, WORK, INFO )

CHARACTER UPLO

INTEGER INFO, LDQ, N

DOUBLE PRECISION AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )

## PURPOSE

DOPGTR generates a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by DSPTRD using packed storage: 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 triangular packed storage used in previous call to DSPTRD; = 'L': Lower triangular packed storage used in previous call to DSPTRD.
N (input) INTEGER
The order of the matrix Q. N >= 0.
AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
The vectors which define the elementary reflectors, as returned by DSPTRD.
TAU (input) DOUBLE PRECISION array, dimension (N-1)
TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DSPTRD.
Q (output) DOUBLE PRECISION array, dimension (LDQ,N)
The N-by-N orthogonal matrix Q.
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= max(1,N).
WORK (workspace) DOUBLE PRECISION array, dimension (N-1)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value