zunbdb2()

subroutine zunbdb2	(	integer	m,
		integer	p,
		integer	q,
		complex*16, dimension(ldx11,*)	x11,
		integer	ldx11,
		complex*16, dimension(ldx21,*)	x21,
		integer	ldx21,
		double precision, dimension(*)	theta,
		double precision, dimension(*)	phi,
		complex*16, dimension(*)	taup1,
		complex*16, dimension(*)	taup2,
		complex*16, dimension(*)	tauq1,
		complex*16, dimension(*)	work,
		integer	lwork,
		integer	info )

ZUNBDB2

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Purpose:

!>
!> ZUNBDB2 simultaneously bidiagonalizes the blocks of a tall and skinny
!> matrix X with orthonormal columns:
!>
!>                            [ B11 ]
!>      [ X11 ]   [ P1 |    ] [  0  ]
!>      [-----] = [---------] [-----] Q1**T .
!>      [ X21 ]   [    | P2 ] [ B21 ]
!>                            [  0  ]
!>
!> X11 is P-by-Q, and X21 is (M-P)-by-Q. P must be no larger than M-P,
!> Q, or M-Q. Routines ZUNBDB1, ZUNBDB3, and ZUNBDB4 handle cases in
!> which P is not the minimum dimension.
!>
!> The unitary matrices P1, P2, and Q1 are P-by-P, (M-P)-by-(M-P),
!> and (M-Q)-by-(M-Q), respectively. They are represented implicitly by
!> Householder vectors.
!>
!> B11 and B12 are P-by-P bidiagonal matrices represented implicitly by
!> angles THETA, PHI.
!>
!>

Parameters

[in]	M	!> M is INTEGER !> The number of rows X11 plus the number of rows in X21. !>
[in]	P	!> P is INTEGER !> The number of rows in X11. 0 <= P <= min(M-P,Q,M-Q). !>
[in]	Q	!> Q is INTEGER !> The number of columns in X11 and X21. 0 <= Q <= M. !>
[in,out]	X11	!> X11 is COMPLEX*16 array, dimension (LDX11,Q) !> On entry, the top block of the matrix X to be reduced. On !> exit, the columns of tril(X11) specify reflectors for P1 and !> the rows of triu(X11,1) specify reflectors for Q1. !>
[in]	LDX11	!> LDX11 is INTEGER !> The leading dimension of X11. LDX11 >= P. !>
[in,out]	X21	!> X21 is COMPLEX*16 array, dimension (LDX21,Q) !> On entry, the bottom block of the matrix X to be reduced. On !> exit, the columns of tril(X21) specify reflectors for P2. !>
[in]	LDX21	!> LDX21 is INTEGER !> The leading dimension of X21. LDX21 >= M-P. !>
[out]	THETA	!> THETA is DOUBLE PRECISION array, dimension (Q) !> The entries of the bidiagonal blocks B11, B21 are defined by !> THETA and PHI. See Further Details. !>
[out]	PHI	!> PHI is DOUBLE PRECISION array, dimension (Q-1) !> The entries of the bidiagonal blocks B11, B21 are defined by !> THETA and PHI. See Further Details. !>
[out]	TAUP1	!> TAUP1 is COMPLEX*16 array, dimension (P-1) !> The scalar factors of the elementary reflectors that define !> P1. !>
[out]	TAUP2	!> TAUP2 is COMPLEX*16 array, dimension (Q) !> The scalar factors of the elementary reflectors that define !> P2. !>
[out]	TAUQ1	!> TAUQ1 is COMPLEX*16 array, dimension (Q) !> The scalar factors of the elementary reflectors that define !> Q1. !>
[out]	WORK	!> WORK is COMPLEX*16 array, dimension (LWORK) !>
[in]	LWORK	!> LWORK is INTEGER !> The dimension of the array WORK. LWORK >= M-Q. !> !> 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.

Further Details:

!>
!>  The upper-bidiagonal blocks B11, B21 are represented implicitly by
!>  angles THETA(1), ..., THETA(Q) and PHI(1), ..., PHI(Q-1). Every entry
!>  in each bidiagonal band is a product of a sine or cosine of a THETA
!>  with a sine or cosine of a PHI. See [1] or ZUNCSD for details.
!>
!>  P1, P2, and Q1 are represented as products of elementary reflectors.
!>  See ZUNCSD2BY1 for details on generating P1, P2, and Q1 using ZUNGQR
!>  and ZUNGLQ.
!> 

References:

[1] Brian D. Sutton. Computing the complete CS decomposition. Numer. Algorithms, 50(1):33-65, 2009.