DORGTR (3lapack)

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

SYNOPSIS

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

      CHARACTER      UPLO

      INTEGER        INFO, LDA, LWORK, N

      DOUBLE         PRECISION A( LDA, * ), TAU( * ), WORK( LWORK )

PURPOSE

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

  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
          DSYTRD; = 'L': Lower triangle of A contains elementary reflectors
          from DSYTRD.

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

  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the vectors which define the elementary reflectors, as
          returned by DSYTRD.  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 DSYTRD.

  WORK    (workspace/output) DOUBLE PRECISION 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