DOPGTR (3lapack)

generate 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