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sopgtr

 NAME
      SOPGTR - generate a real orthogonal matrix Q which is
      defined as the product of n-1 elementary reflectors 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 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 pre-
              vious 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 elemen-
              tary 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