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dorbdb4.f(3)			    LAPACK			  dorbdb4.f(3)

NAME
       dorbdb4.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dorbdb4 (M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1,
	   TAUP2, TAUQ1, PHANTOM, WORK, LWORK, INFO)
	   DORBDB4

Function/Subroutine Documentation
   subroutine dorbdb4 (integerM, integerP, integerQ, double precision,
       dimension(ldx11,*)X11, integerLDX11, double precision,
       dimension(ldx21,*)X21, integerLDX21, double precision,
       dimension(*)THETA, double precision, dimension(*)PHI, double precision,
       dimension(*)TAUP1, double precision, dimension(*)TAUP2, double
       precision, dimension(*)TAUQ1, double precision, dimension(*)PHANTOM,
       double precision, dimension(*)WORK, integerLWORK, integerINFO)
       DORBDB4 .SH "Purpose:"

	DORBDB4 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-Q must be no larger than P,
	M-P, or Q. Routines DORBDB1, DORBDB2, and DORBDB3 handle cases in
	which M-Q is not the minimum dimension.

	The orthogonal 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-Q)-by-(M-Q) 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.

	   Q

		     Q is INTEGER
		      The number of columns in X11 and X21. 0 <= Q <= M and
		      M-Q <= min(P,M-P,Q).

	   X11

		     X11 is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (Q)
		      The entries of the bidiagonal blocks B11, B21 are defined by
		      THETA and PHI. See Further Details.

	   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.

	   TAUP1

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

	   TAUP2

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

	   TAUQ1

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

	   PHANTOM

		     PHANTOM is DOUBLE PRECISION array, dimension (M)
		      The routine computes an M-by-1 column vector Y that is
		      orthogonal to the columns of [ X11; X21 ]. PHANTOM(1:P) and
		      PHANTOM(P+1:M) contain Householder vectors for Y(1:P) and
		      Y(P+1:M), respectively.

	   WORK

		     WORK is DOUBLE PRECISION 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 DORCSD for details.

	     P1, P2, and Q1 are represented as products of elementary reflectors.
	     See DORCSD2BY1 for details on generating P1, P2, and Q1 using DORGQR
	     and DORGLQ.

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

       Definition at line 212 of file dorbdb4.f.

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

Version 3.4.2			Sat Nov 16 2013			  dorbdb4.f(3)
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