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.