cungbr()

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

CUNGBR

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Purpose:

 CUNGBR generates one of the complex unitary matrices Q or P**H
 determined by CGEBRD 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 CUNGBR returns the first n
 columns of Q, where m >= n >= k;
 if m < k, Q = H(1) H(2) . . . H(m-1) and CUNGBR 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 CUNGBR 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 CUNGBR 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 CGEBRD: = '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 CGEBRD. If VECT = 'P', the number of rows in the original K-by-N matrix reduced by CGEBRD. K >= 0.
[in,out]	A	A is COMPLEX array, dimension (LDA,N) On entry, the vectors which define the elementary reflectors, as returned by CGEBRD. 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 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 CGEBRD in its array argument TAUQ or TAUP.
[out]	WORK	WORK is COMPLEX 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 cungbr.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            A( LDA, * ), TAU( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX            ZERO, ONE
      parameter( zero = ( 0.0e+0, 0.0e+0 ),
     $                   one = ( 1.0e+0, 0.0e+0 ) )
*     ..
*     .. Local Scalars ..
      LOGICAL            LQUERY, WANTQ
      INTEGER            I, IINFO, J, LWKOPT, MN
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      REAL               SROUNDUP_LWORK
      EXTERNAL           lsame, sroundup_lwork
*     ..
*     .. External Subroutines ..
      EXTERNAL           cunglq, cungqr, xerbla
*     ..
*     .. 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 cungqr( m, n, k, a, lda, tau, work, -1, iinfo )
            ELSE
               IF( m.GT.1 ) THEN
                  CALL cungqr( m-1, m-1, m-1, a, lda, tau, work, -1,
     $                         iinfo )
               END IF
            END IF
         ELSE
            IF( k.LT.n ) THEN
               CALL cunglq( m, n, k, a, lda, tau, work, -1, iinfo )
            ELSE
               IF( n.GT.1 ) THEN
                  CALL cunglq( n-1, n-1, n-1, a, lda, tau, work, -1,
     $                         iinfo )
               END IF
            END IF
         END IF
         lwkopt = int( work( 1 ) )
         lwkopt = max(lwkopt, mn)
      END IF
*
      IF( info.NE.0 ) THEN
         CALL xerbla( 'CUNGBR', -info )
         RETURN
      ELSE IF( lquery ) THEN
         work( 1 ) = sroundup_lwork(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 CGEBRD to reduce an m-by-k
*        matrix
*
         IF( m.GE.k ) THEN
*
*           If m >= k, assume m >= n >= k
*
            CALL cungqr( 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 cungqr( 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 CGEBRD to reduce a k-by-n
*        matrix
*
         IF( k.LT.n ) THEN
*
*           If k < n, assume k <= m <= n
*
            CALL cunglq( 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 cunglq( n-1, n-1, n-1, a( 2, 2 ), lda, tau, work,
     $                      lwork, iinfo )
            END IF
         END IF
      END IF
      work( 1 ) = sroundup_lwork(lwkopt)
      RETURN
*
*     End of CUNGBR
*

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