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cunbdb3.f(3)			    LAPACK			  cunbdb3.f(3)

NAME
       cunbdb3.f -

SYNOPSIS
   Functions/Subroutines
       subroutine cunbdb3 (M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1,
	   TAUP2, TAUQ1, WORK, LWORK, INFO)
	   CUNBDB3

Function/Subroutine Documentation
   subroutine cunbdb3 (integerM, integerP, integerQ, complex,
       dimension(ldx11,*)X11, integerLDX11, complex, dimension(ldx21,*)X21,
       integerLDX21, real, dimension(*)THETA, real, dimension(*)PHI, complex,
       dimension(*)TAUP1, complex, dimension(*)TAUP2, complex,
       dimension(*)TAUQ1, complex, dimension(*)WORK, integerLWORK,
       integerINFO)
       CUNBDB3 .SH "Purpose:"

	CUNBDB3 simultaneously bidiagonalizes the blocks of a tall and skinny
	matrix X with orthonomal columns:

				   [ B11 ]
	     [ X11 ]   [ P1 |	 ] [  0	 ]
	     [-----] = [---------] [-----] Q1**T .
	     [ X21 ]   [    | P2 ] [ B21 ]
				   [  0	 ]

	X11 is P-by-Q, and X21 is (M-P)-by-Q. M-P must be no larger than P,
	Q, or M-Q. Routines CUNBDB1, CUNBDB2, and CUNBDB4 handle cases in
	which M-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 (M-P)-by-(M-P) bidiagonal matrices represented
	implicitly by angles THETA, PHI..fi

       Parameters:
	   M

		     M is INTEGER
		      The number of rows X11 plus the number of rows in X21.

	   P

		     P is INTEGER
		      The number of rows in X11. 0 <= P <= M. M-P <= min(P,Q,M-Q).

	   Q

		     Q is INTEGER
		      The number of columns in X11 and X21. 0 <= Q <= M.

	   X11

		     X11 is COMPLEX 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.

	   LDX11

		     LDX11 is INTEGER
		      The leading dimension of X11. LDX11 >= P.

	   X21

		     X21 is COMPLEX 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.

	   LDX21

		     LDX21 is INTEGER
		      The leading dimension of X21. LDX21 >= M-P.

	   THETA

		     THETA is REAL array, dimension (Q)
		      The entries of the bidiagonal blocks B11, B21 are defined by
		      THETA and PHI. See Further Details.

	   PHI

		     PHI is REAL array, dimension (Q-1)
		      The entries of the bidiagonal blocks B11, B21 are defined by
		      THETA and PHI. See Further Details.

	   TAUP1

		     TAUP1 is COMPLEX array, dimension (P)
		      The scalar factors of the elementary reflectors that define
		      P1.

	   TAUP2

		     TAUP2 is COMPLEX array, dimension (M-P)
		      The scalar factors of the elementary reflectors that define
		      P2.

	   TAUQ1

		     TAUQ1 is COMPLEX array, dimension (Q)
		      The scalar factors of the elementary reflectors that define
		      Q1.

	   WORK

		     WORK is COMPLEX array, dimension (LWORK)

	   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.

	   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.

       Date:
	   July 2012

       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 CUNCSD for details.

       P1, P2, and Q1 are represented as products of elementary reflectors.
       See CUNCSD2BY1 for details on generating P1, P2, and Q1 using CUNGQR
       and CUNGLQ.

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

       Definition at line 202 of file cunbdb3.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2			Sat Nov 16 2013			  cunbdb3.f(3)
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