NAME¶

SOPGTR - 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 SSPTRD using packed storage

SYNOPSIS¶

SUBROUTINE SOPGTR(

UPLO, N, AP, TAU, Q, LDQ, WORK, INFO )

CHARACTER UPLO INTEGER INFO, LDQ, N REAL AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )

PURPOSE¶

SOPGTR 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 SSPTRD 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 SSPTRD; = 'L': Lower triangular packed storage used in previous call to SSPTRD.

N (input) INTEGER

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

AP (input) REAL array, dimension (N*(N+1)/2)

The vectors which define the elementary reflectors, as returned by SSPTRD.

TAU (input) REAL array, dimension (N-1)

TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SSPTRD.

Q (output) REAL 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) REAL array, dimension (N-1)

INFO (output) INTEGER

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