zungbr()

subroutine zungbr	(	character	vect,
		integer	m,
		integer	n,
		integer	k,
		complex*16, dimension( lda, * )	a,
		integer	lda,
		complex*16, dimension( * )	tau,
		complex*16, dimension( * )	work,
		integer	lwork,
		integer	info
	)

ZUNGBR

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Purpose:

 ZUNGBR generates one of the complex unitary matrices Q or P**H
 determined by ZGEBRD when reducing a complex matrix A to bidiagonal
 form: A = Q * B * P**H.  Q and P**H are defined as products of
 elementary reflectors H(i) or G(i) respectively.

 If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
 is of order M:
 if m >= k, Q = H(1) H(2) . . . H(k) and ZUNGBR returns the first n
 columns of Q, where m >= n >= k;
 if m < k, Q = H(1) H(2) . . . H(m-1) and ZUNGBR returns Q as an
 M-by-M matrix.

 If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**H
 is of order N:
 if k < n, P**H = G(k) . . . G(2) G(1) and ZUNGBR returns the first m
 rows of P**H, where n >= m >= k;
 if k >= n, P**H = G(n-1) . . . G(2) G(1) and ZUNGBR returns P**H as
 an N-by-N matrix.

Parameters

[in]	VECT	VECT is CHARACTER*1 Specifies whether the matrix Q or the matrix P**H is required, as defined in the transformation applied by ZGEBRD: = 'Q': generate Q; = 'P': generate P**H.
[in]	M	M is INTEGER The number of rows of the matrix Q or P**H to be returned. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix Q or P**H to be returned. N >= 0. If VECT = 'Q', M >= N >= min(M,K); if VECT = 'P', N >= M >= min(N,K).
[in]	K	K is INTEGER If VECT = 'Q', the number of columns in the original M-by-K matrix reduced by ZGEBRD. If VECT = 'P', the number of rows in the original K-by-N matrix reduced by ZGEBRD. K >= 0.
[in,out]	A	A is COMPLEX*16 array, dimension (LDA,N) On entry, the vectors which define the elementary reflectors, as returned by ZGEBRD. On exit, the M-by-N matrix Q or P**H.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= M.
[in]	TAU	TAU is COMPLEX*16 array, dimension (min(M,K)) if VECT = 'Q' (min(N,K)) if VECT = 'P' TAU(i) must contain the scalar factor of the elementary reflector H(i) or G(i), which determines Q or P**H, as returned by ZGEBRD in its array argument TAUQ or TAUP.
[out]	WORK	WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[in]	LWORK	LWORK is INTEGER The dimension of the array WORK. LWORK >= max(1,min(M,N)). For optimum performance LWORK >= min(M,N)*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
[out]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 156 of file zungbr.f.

*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          VECT
      INTEGER            INFO, K, LDA, LWORK, M, N
*     ..
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX*16         ZERO, ONE
      parameter( zero = ( 0.0d+0, 0.0d+0 ),
     $                   one = ( 1.0d+0, 0.0d+0 ) )
*     ..
*     .. Local Scalars ..
      LOGICAL            LQUERY, WANTQ
      INTEGER            I, IINFO, J, LWKOPT, MN
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla, zunglq, zungqr
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, min
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      info = 0
      wantq = lsame( vect, 'Q' )
      mn = min( m, n )
      lquery = ( lwork.EQ.-1 )
      IF( .NOT.wantq .AND. .NOT.lsame( vect, 'P' ) ) THEN
         info = -1
      ELSE IF( m.LT.0 ) THEN
         info = -2
      ELSE IF( n.LT.0 .OR. ( wantq .AND. ( n.GT.m .OR. n.LT.min( m,
     $         k ) ) ) .OR. ( .NOT.wantq .AND. ( m.GT.n .OR. m.LT.
     $         min( n, k ) ) ) ) THEN
         info = -3
      ELSE IF( k.LT.0 ) THEN
         info = -4
      ELSE IF( lda.LT.max( 1, m ) ) THEN
         info = -6
      ELSE IF( lwork.LT.max( 1, mn ) .AND. .NOT.lquery ) THEN
         info = -9
      END IF
*
      IF( info.EQ.0 ) THEN
         work( 1 ) = 1
         IF( wantq ) THEN
            IF( m.GE.k ) THEN
               CALL zungqr( m, n, k, a, lda, tau, work, -1, iinfo )
            ELSE
               IF( m.GT.1 ) THEN
                  CALL zungqr( m-1, m-1, m-1, a, lda, tau, work, -1,
     $                         iinfo )
               END IF
            END IF
         ELSE
            IF( k.LT.n ) THEN
               CALL zunglq( m, n, k, a, lda, tau, work, -1, iinfo )
            ELSE
               IF( n.GT.1 ) THEN
                  CALL zunglq( n-1, n-1, n-1, a, lda, tau, work, -1,
     $                         iinfo )
               END IF
            END IF
         END IF
         lwkopt = int( dble( work( 1 ) ) )
         lwkopt = max(lwkopt, mn)
      END IF
*
      IF( info.NE.0 ) THEN
         CALL xerbla( 'ZUNGBR', -info )
         RETURN
      ELSE IF( lquery ) THEN
         work( 1 ) = lwkopt
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( m.EQ.0 .OR. n.EQ.0 ) THEN
         work( 1 ) = 1
         RETURN
      END IF
*
      IF( wantq ) THEN
*
*        Form Q, determined by a call to ZGEBRD to reduce an m-by-k
*        matrix
*
         IF( m.GE.k ) THEN
*
*           If m >= k, assume m >= n >= k
*
            CALL zungqr( m, n, k, a, lda, tau, work, lwork, iinfo )
*
         ELSE
*
*           If m < k, assume m = n
*
*           Shift the vectors which define the elementary reflectors one
*           column to the right, and set the first row and column of Q
*           to those of the unit matrix
*
            DO 20 j = m, 2, -1
               a( 1, j ) = zero
               DO 10 i = j + 1, m
                  a( i, j ) = a( i, j-1 )
   10          CONTINUE
   20       CONTINUE
            a( 1, 1 ) = one
            DO 30 i = 2, m
               a( i, 1 ) = zero
   30       CONTINUE
            IF( m.GT.1 ) THEN
*
*              Form Q(2:m,2:m)
*
               CALL zungqr( m-1, m-1, m-1, a( 2, 2 ), lda, tau, work,
     $                      lwork, iinfo )
            END IF
         END IF
      ELSE
*
*        Form P**H, determined by a call to ZGEBRD to reduce a k-by-n
*        matrix
*
         IF( k.LT.n ) THEN
*
*           If k < n, assume k <= m <= n
*
            CALL zunglq( m, n, k, a, lda, tau, work, lwork, iinfo )
*
         ELSE
*
*           If k >= n, assume m = n
*
*           Shift the vectors which define the elementary reflectors one
*           row downward, and set the first row and column of P**H to
*           those of the unit matrix
*
            a( 1, 1 ) = one
            DO 40 i = 2, n
               a( i, 1 ) = zero
   40       CONTINUE
            DO 60 j = 2, n
               DO 50 i = j - 1, 2, -1
                  a( i, j ) = a( i-1, j )
   50          CONTINUE
               a( 1, j ) = zero
   60       CONTINUE
            IF( n.GT.1 ) THEN
*
*              Form P**H(2:n,2:n)
*
               CALL zunglq( n-1, n-1, n-1, a( 2, 2 ), lda, tau, work,
     $                      lwork, iinfo )
            END IF
         END IF
      END IF
      work( 1 ) = lwkopt
      RETURN
*
*     End of ZUNGBR
*

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