zupgtr.f

          SUBROUTINE ZUPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          UPLO
          INTEGER            INFO, LDQ, N
    *     ..
    *     .. Array Arguments ..
          COMPLEX*16         AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  ZUPGTR generates a complex unitary matrix Q which is defined as the
    *  product of n-1 elementary reflectors H(i) of order n, as returned by
    *  ZHPTRD 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 ZHPTRD;
    *          = 'L': Lower triangular packed storage used in previous
    *                 call to ZHPTRD.
    *
    *  N       (input) INTEGER
    *          The order of the matrix Q. N >= 0.
    *
    *  AP      (input) COMPLEX*16 array, dimension (N*(N+1)/2)
    *          The vectors which define the elementary reflectors, as
    *          returned by ZHPTRD.
    *
    *  TAU     (input) COMPLEX*16 array, dimension (N-1)
    *          TAU(i) must contain the scalar factor of the elementary
    *          reflector H(i), as returned by ZHPTRD.
    *
    *  Q       (output) COMPLEX*16 array, dimension (LDQ,N)
    *          The N-by-N unitary matrix Q.
    *
    *  LDQ     (input) INTEGER
    *          The leading dimension of the array Q. LDQ >= max(1,N).
    *
    *  WORK    (workspace) COMPLEX*16 array, dimension (N-1)
    *
    *  INFO    (output) INTEGER
    *          = 0:  successful exit
    *          < 0:  if INFO = -i, the i-th argument had an illegal value
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          COMPLEX*16         CZERO, CONE
          PARAMETER          ( CZERO = ( 0.0D+0, 0.0D+0 ),
         $                   CONE = ( 1.0D+0, 0.0D+0 ) )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            UPPER
          INTEGER            I, IINFO, IJ, J
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           XERBLA, ZUNG2L, ZUNG2R
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input arguments
    *
          INFO = 0
          UPPER = LSAME( UPLO, 'U' )
          IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
             INFO = -1
          ELSE IF( N.LT.0 ) THEN
             INFO = -2
          ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN
             INFO = -6
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'ZUPGTR', -INFO )
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( N.EQ.0 )
         $   RETURN
    *
          IF( UPPER ) THEN
    *
    *        Q was determined by a call to ZHPTRD with UPLO = 'U'
    *
    *        Unpack the vectors which define the elementary reflectors and
    *        set the last row and column of Q equal to those of the unit
    *        matrix
    *
             IJ = 2
             DO 20 J = 1, N - 1
                DO 10 I = 1, J - 1
                   Q( I, J ) = AP( IJ )
                   IJ = IJ + 1
       10       CONTINUE
                IJ = IJ + 2
                Q( N, J ) = CZERO
       20    CONTINUE
             DO 30 I = 1, N - 1
                Q( I, N ) = CZERO
       30    CONTINUE
             Q( N, N ) = CONE
    *
    *        Generate Q(1:n-1,1:n-1)
    *
             CALL ZUNG2L( N-1, N-1, N-1, Q, LDQ, TAU, WORK, IINFO )
    *
          ELSE
    *
    *        Q was determined by a call to ZHPTRD with UPLO = 'L'.
    *
    *        Unpack the vectors which define the elementary reflectors and
    *        set the first row and column of Q equal to those of the unit
    *        matrix
    *
             Q( 1, 1 ) = CONE
             DO 40 I = 2, N
                Q( I, 1 ) = CZERO
       40    CONTINUE
             IJ = 3
             DO 60 J = 2, N
                Q( 1, J ) = CZERO
                DO 50 I = J + 1, N
                   Q( I, J ) = AP( IJ )
                   IJ = IJ + 1
       50       CONTINUE
                IJ = IJ + 2
       60    CONTINUE
             IF( N.GT.1 ) THEN
    *
    *           Generate Q(2:n,2:n)
    *
                CALL ZUNG2R( N-1, N-1, N-1, Q( 2, 2 ), LDQ, TAU, WORK,
         $                   IINFO )
             END IF
          END IF
          RETURN
    *
    *     End of ZUPGTR
    *
          END