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sbbcsd.f(3)				      LAPACK				      sbbcsd.f(3)

NAME
       sbbcsd.f -

SYNOPSIS
   Functions/Subroutines
       subroutine sbbcsd (JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, THETA, PHI, U1, LDU1, U2,
	   LDU2, V1T, LDV1T, V2T, LDV2T, B11D, B11E, B12D, B12E, B21D, B21E, B22D, B22E, WORK,
	   LWORK, INFO)
	   SBBCSD

Function/Subroutine Documentation
   subroutine sbbcsd (characterJOBU1, characterJOBU2, characterJOBV1T, characterJOBV2T,
       characterTRANS, integerM, integerP, integerQ, real, dimension( * )THETA, real, dimension(
       * )PHI, real, dimension( ldu1, * )U1, integerLDU1, real, dimension( ldu2, * )U2,
       integerLDU2, real, dimension( ldv1t, * )V1T, integerLDV1T, real, dimension( ldv2t, * )V2T,
       integerLDV2T, real, dimension( * )B11D, real, dimension( * )B11E, real, dimension( *
       )B12D, real, dimension( * )B12E, real, dimension( * )B21D, real, dimension( * )B21E, real,
       dimension( * )B22D, real, dimension( * )B22E, real, dimension( * )WORK, integerLWORK,
       integerINFO)
       SBBCSD

       Purpose:

	    SBBCSD computes the CS decomposition of an orthogonal matrix in
	    bidiagonal-block form,

		[ B11 | B12 0  0 ]
		[  0  |  0 -I  0 ]
	    X = [----------------]
		[ B21 | B22 0  0 ]
		[  0  |  0  0  I ]

					  [  C | -S  0	0 ]
			      [ U1 |	] [  0 |  0 -I	0 ] [ V1 |    ]**T
			    = [---------] [---------------] [---------]   .
			      [    | U2 ] [  S |  C  0	0 ] [	 | V2 ]
					  [  0 |  0  0	I ]

	    X is M-by-M, its top-left block is P-by-Q, and Q must be no larger
	    than P, M-P, or M-Q. (If Q is not the smallest index, then X must be
	    transposed and/or permuted. This can be done in constant time using
	    the TRANS and SIGNS options. See SORCSD for details.)

	    The bidiagonal matrices B11, B12, B21, and B22 are represented
	    implicitly by angles THETA(1:Q) and PHI(1:Q-1).

	    The orthogonal matrices U1, U2, V1T, and V2T are input/output.
	    The input matrices are pre- or post-multiplied by the appropriate
	    singular vector matrices.

       Parameters:
	   JOBU1

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

	   JOBU2

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

	   JOBV1T

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

	   JOBV2T

		     JOBV2T is CHARACTER
		     = 'Y':	 V2T is updated;
		     otherwise:  V2T is not updated.

	   TRANS

		     TRANS is CHARACTER
		     = 'T':	 X, U1, U2, V1T, and V2T are stored in row-major
				 order;
		     otherwise:  X, U1, U2, V1T, and V2T are stored in column-
				 major order.

	   M

		     M is INTEGER
		     The number of rows and columns in X, the orthogonal matrix in
		     bidiagonal-block form.

	   P

		     P is INTEGER
		     The number of rows in the top-left block of X. 0 <= P <= M.

	   Q

		     Q is INTEGER
		     The number of columns in the top-left block of X.
		     0 <= Q <= MIN(P,M-P,M-Q).

	   THETA

		     THETA is REAL array, dimension (Q)
		     On entry, the angles THETA(1),...,THETA(Q) that, along with
		     PHI(1), ...,PHI(Q-1), define the matrix in bidiagonal-block
		     form. On exit, the angles whose cosines and sines define the
		     diagonal blocks in the CS decomposition.

	   PHI

		     PHI is REAL array, dimension (Q-1)
		     The angles PHI(1),...,PHI(Q-1) that, along with THETA(1),...,
		     THETA(Q), define the matrix in bidiagonal-block form.

	   U1

		     U1 is REAL array, dimension (LDU1,P)
		     On entry, an LDU1-by-P matrix. On exit, U1 is postmultiplied
		     by the left singular vector matrix common to [ B11 ; 0 ] and
		     [ B12 0 0 ; 0 -I 0 0 ].

	   LDU1

		     LDU1 is INTEGER
		     The leading dimension of the array U1.

	   U2

		     U2 is REAL array, dimension (LDU2,M-P)
		     On entry, an LDU2-by-(M-P) matrix. On exit, U2 is
		     postmultiplied by the left singular vector matrix common to
		     [ B21 ; 0 ] and [ B22 0 0 ; 0 0 I ].

	   LDU2

		     LDU2 is INTEGER
		     The leading dimension of the array U2.

	   V1T

		     V1T is REAL array, dimension (LDV1T,Q)
		     On entry, a LDV1T-by-Q matrix. On exit, V1T is premultiplied
		     by the transpose of the right singular vector
		     matrix common to [ B11 ; 0 ] and [ B21 ; 0 ].

	   LDV1T

		     LDV1T is INTEGER
		     The leading dimension of the array V1T.

	   V2T

		     V2T is REAL array, dimenison (LDV2T,M-Q)
		     On entry, a LDV2T-by-(M-Q) matrix. On exit, V2T is
		     premultiplied by the transpose of the right
		     singular vector matrix common to [ B12 0 0 ; 0 -I 0 ] and
		     [ B22 0 0 ; 0 0 I ].

	   LDV2T

		     LDV2T is INTEGER
		     The leading dimension of the array V2T.

	   B11D

		     B11D is REAL array, dimension (Q)
		     When SBBCSD converges, B11D contains the cosines of THETA(1),
		     ..., THETA(Q). If SBBCSD fails to converge, then B11D
		     contains the diagonal of the partially reduced top-left
		     block.

	   B11E

		     B11E is REAL array, dimension (Q-1)
		     When SBBCSD converges, B11E contains zeros. If SBBCSD fails
		     to converge, then B11E contains the superdiagonal of the
		     partially reduced top-left block.

	   B12D

		     B12D is REAL array, dimension (Q)
		     When SBBCSD converges, B12D contains the negative sines of
		     THETA(1), ..., THETA(Q). If SBBCSD fails to converge, then
		     B12D contains the diagonal of the partially reduced top-right
		     block.

	   B12E

		     B12E is REAL array, dimension (Q-1)
		     When SBBCSD converges, B12E contains zeros. If SBBCSD fails
		     to converge, then B12E contains the subdiagonal of the
		     partially reduced top-right block.

	   B21D

		     B21D is REAL array, dimension (Q)
		     When CBBCSD converges, B21D contains the negative sines of
		     THETA(1), ..., THETA(Q). If CBBCSD fails to converge, then
		     B21D contains the diagonal of the partially reduced bottom-left
		     block.

	   B21E

		     B21E is REAL array, dimension (Q-1)
		     When CBBCSD converges, B21E contains zeros. If CBBCSD fails
		     to converge, then B21E contains the subdiagonal of the
		     partially reduced bottom-left block.

	   B22D

		     B22D is REAL array, dimension (Q)
		     When CBBCSD converges, B22D contains the negative sines of
		     THETA(1), ..., THETA(Q). If CBBCSD fails to converge, then
		     B22D contains the diagonal of the partially reduced bottom-right
		     block.

	   B22E

		     B22E is REAL array, dimension (Q-1)
		     When CBBCSD converges, B22E contains zeros. If CBBCSD fails
		     to converge, then B22E contains the subdiagonal of the
		     partially reduced bottom-right block.

	   WORK

		     WORK is REAL array, dimension (MAX(1,LWORK))
		     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

	   LWORK

		     LWORK is INTEGER
		     The dimension of the array WORK. LWORK >= MAX(1,8*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.
		     > 0:  if SBBCSD did not converge, INFO specifies the number
			   of nonzero entries in PHI, and B11D, B11E, etc.,
			   contain the partially reduced matrix.

       Internal Parameters:

	     TOLMUL  REAL, default = MAX(10,MIN(100,EPS**(-1/8)))
		     TOLMUL controls the convergence criterion of the QR loop.
		     Angles THETA(i), PHI(i) are rounded to 0 or PI/2 when they
		     are within TOLMUL*EPS of either bound.

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

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Definition at line 330 of file sbbcsd.f.

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

Version 3.4.2				 Tue Sep 25 2012			      sbbcsd.f(3)
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