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dorcsd2by1.f(3)			    LAPACK		       dorcsd2by1.f(3)

NAME
       dorcsd2by1.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dorcsd2by1 (JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, X21,
	   LDX21, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, WORK, LWORK, IWORK,
	   INFO)
	   DORCSD2BY1

Function/Subroutine Documentation
   subroutine dorcsd2by1 (characterJOBU1, characterJOBU2, characterJOBV1T,
       integerM, integerP, integerQ, double precision, dimension(ldx11,*)X11,
       integerLDX11, double precision, dimension(ldx21,*)X21, integerLDX21,
       double precision, dimension(*)THETA, double precision,
       dimension(ldu1,*)U1, integerLDU1, double precision,
       dimension(ldu2,*)U2, integerLDU2, double precision,
       dimension(ldv1t,*)V1T, integerLDV1T, double precision,
       dimension(*)WORK, integerLWORK, integer, dimension(*)IWORK,
       integerINFO)
       DORCSD2BY1 .SH "Purpose:"

	Purpose:
	========

	DORCSD2BY1 computes the CS decomposition of an M-by-Q matrix X with
	orthonormal columns that has been partitioned into a 2-by-1 block
	structure:

				       [  I  0	0 ]
				       [  0  C	0 ]
		 [ X11 ]   [ U1 |    ] [  0  0	0 ]
	     X = [-----] = [---------] [----------] V1**T .
		 [ X21 ]   [	| U2 ] [  0  0	0 ]
				       [  0  S	0 ]
				       [  0  0	I ]

	X11 is P-by-Q. The orthogonal matrices U1, U2, V1, and V2 are P-by-P,
	(M-P)-by-(M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. C and S are
	R-by-R nonnegative diagonal matrices satisfying C^2 + S^2 = I, in
	which R = MIN(P,M-P,Q,M-Q)..fi

       Parameters:
	   JOBU1

		     JOBU1 is CHARACTER
		      = 'Y':	  U1 is computed;
		      otherwise:  U1 is not computed.

	   JOBU2

		     JOBU2 is CHARACTER
		      = 'Y':	  U2 is computed;
		      otherwise:  U2 is not computed.

	   JOBV1T

		     JOBV1T is CHARACTER
		      = 'Y':	  V1T is computed;
		      otherwise:  V1T is not computed.

	   M

		     M is INTEGER
		      The number of rows and columns in X.

	   P

		     P is INTEGER
		      The number of rows in X11 and X12. 0 <= P <= M.

	   Q

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

	   X11

		     X11 is DOUBLE PRECISION array, dimension (LDX11,Q)
		      On entry, part of the orthogonal matrix whose CSD is
		      desired.

	   LDX11

		     LDX11 is INTEGER
		      The leading dimension of X11. LDX11 >= MAX(1,P).

	   X21

		     X21 is DOUBLE PRECISION array, dimension (LDX21,Q)
		      On entry, part of the orthogonal matrix whose CSD is
		      desired.

	   LDX21

		     LDX21 is INTEGER
		      The leading dimension of X21. LDX21 >= MAX(1,M-P).

	   THETA

		     THETA is DOUBLE PRECISION array, dimension (R), in which R =
		      MIN(P,M-P,Q,M-Q).
		      C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and
		      S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ).

	   U1

		     U1 is DOUBLE PRECISION array, dimension (P)
		      If JOBU1 = 'Y', U1 contains the P-by-P orthogonal matrix U1.

	   LDU1

		     LDU1 is INTEGER
		      The leading dimension of U1. If JOBU1 = 'Y', LDU1 >=
		      MAX(1,P).

	   U2

		     U2 is DOUBLE PRECISION array, dimension (M-P)
		      If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) orthogonal
		      matrix U2.

	   LDU2

		     LDU2 is INTEGER
		      The leading dimension of U2. If JOBU2 = 'Y', LDU2 >=
		      MAX(1,M-P).

	   V1T

		     V1T is DOUBLE PRECISION array, dimension (Q)
		      If JOBV1T = 'Y', V1T contains the Q-by-Q matrix orthogonal
		      matrix V1**T.

	   LDV1T

		     LDV1T is INTEGER
		      The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >=
		      MAX(1,Q).

	   WORK

		     WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
		      On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
		      If INFO > 0 on exit, WORK(2:R) contains the values PHI(1),
		      ..., PHI(R-1) that, together with THETA(1), ..., THETA(R),
		      define the matrix in intermediate bidiagonal-block form
		      remaining after nonconvergence. INFO specifies the number
		      of nonzero PHI's.

	   LWORK

		     LWORK is INTEGER
		      The dimension of the array WORK.

		 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.

	   IWORK

		     IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q))

	   INFO

		     INFO is INTEGER
		      = 0:  successful exit.
		      < 0:  if INFO = -i, the i-th argument had an illegal value.
		      > 0:  DBBCSD did not converge. See the description of WORK
			   above for details.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   July 2012

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

       Definition at line 236 of file dorcsd2by1.f.

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

Version 3.4.2			Sat Nov 16 2013		       dorcsd2by1.f(3)
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