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dbdsdc.f(3)				      LAPACK				      dbdsdc.f(3)

NAME
       dbdsdc.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dbdsdc (UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q, IQ, WORK, IWORK, INFO)
	   DBDSDC

Function/Subroutine Documentation
   subroutine dbdsdc (characterUPLO, characterCOMPQ, integerN, double precision, dimension( * )D,
       double precision, dimension( * )E, double precision, dimension( ldu, * )U, integerLDU,
       double precision, dimension( ldvt, * )VT, integerLDVT, double precision, dimension( * )Q,
       integer, dimension( * )IQ, double precision, dimension( * )WORK, integer, dimension( *
       )IWORK, integerINFO)
       DBDSDC

       Purpose:

	    DBDSDC computes the singular value decomposition (SVD) of a real
	    N-by-N (upper or lower) bidiagonal matrix B:  B = U * S * VT,
	    using a divide and conquer method, where S is a diagonal matrix
	    with non-negative diagonal elements (the singular values of B), and
	    U and VT are orthogonal matrices of left and right singular vectors,
	    respectively. DBDSDC can be used to compute all singular values,
	    and optionally, singular vectors or singular vectors in compact form.

	    This code makes very mild assumptions about floating point
	    arithmetic. It will work on machines with a guard digit in
	    add/subtract, or on those binary machines without guard digits
	    which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
	    It could conceivably fail on hexadecimal or decimal machines
	    without guard digits, but we know of none.	See DLASD3 for details.

	    The code currently calls DLASDQ if singular values only are desired.
	    However, it can be slightly modified to compute singular values
	    using the divide and conquer method.

       Parameters:
	   UPLO

		     UPLO is CHARACTER*1
		     = 'U':  B is upper bidiagonal.
		     = 'L':  B is lower bidiagonal.

	   COMPQ

		     COMPQ is CHARACTER*1
		     Specifies whether singular vectors are to be computed
		     as follows:
		     = 'N':  Compute singular values only;
		     = 'P':  Compute singular values and compute singular
			     vectors in compact form;
		     = 'I':  Compute singular values and singular vectors.

	   N

		     N is INTEGER
		     The order of the matrix B.  N >= 0.

	   D

		     D is DOUBLE PRECISION array, dimension (N)
		     On entry, the n diagonal elements of the bidiagonal matrix B.
		     On exit, if INFO=0, the singular values of B.

	   E

		     E is DOUBLE PRECISION array, dimension (N-1)
		     On entry, the elements of E contain the offdiagonal
		     elements of the bidiagonal matrix whose SVD is desired.
		     On exit, E has been destroyed.

	   U

		     U is DOUBLE PRECISION array, dimension (LDU,N)
		     If  COMPQ = 'I', then:
			On exit, if INFO = 0, U contains the left singular vectors
			of the bidiagonal matrix.
		     For other values of COMPQ, U is not referenced.

	   LDU

		     LDU is INTEGER
		     The leading dimension of the array U.  LDU >= 1.
		     If singular vectors are desired, then LDU >= max( 1, N ).

	   VT

		     VT is DOUBLE PRECISION array, dimension (LDVT,N)
		     If  COMPQ = 'I', then:
			On exit, if INFO = 0, VT**T contains the right singular
			vectors of the bidiagonal matrix.
		     For other values of COMPQ, VT is not referenced.

	   LDVT

		     LDVT is INTEGER
		     The leading dimension of the array VT.  LDVT >= 1.
		     If singular vectors are desired, then LDVT >= max( 1, N ).

	   Q

		     Q is DOUBLE PRECISION array, dimension (LDQ)
		     If  COMPQ = 'P', then:
			On exit, if INFO = 0, Q and IQ contain the left
			and right singular vectors in a compact form,
			requiring O(N log N) space instead of 2*N**2.
			In particular, Q contains all the DOUBLE PRECISION data in
			LDQ >= N*(11 + 2*SMLSIZ + 8*INT(LOG_2(N/(SMLSIZ+1))))
			words of memory, where SMLSIZ is returned by ILAENV and
			is equal to the maximum size of the subproblems at the
			bottom of the computation tree (usually about 25).
		     For other values of COMPQ, Q is not referenced.

	   IQ

		     IQ is INTEGER array, dimension (LDIQ)
		     If  COMPQ = 'P', then:
			On exit, if INFO = 0, Q and IQ contain the left
			and right singular vectors in a compact form,
			requiring O(N log N) space instead of 2*N**2.
			In particular, IQ contains all INTEGER data in
			LDIQ >= N*(3 + 3*INT(LOG_2(N/(SMLSIZ+1))))
			words of memory, where SMLSIZ is returned by ILAENV and
			is equal to the maximum size of the subproblems at the
			bottom of the computation tree (usually about 25).
		     For other values of COMPQ, IQ is not referenced.

	   WORK

		     WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
		     If COMPQ = 'N' then LWORK >= (4 * N).
		     If COMPQ = 'P' then LWORK >= (6 * N).
		     If COMPQ = 'I' then LWORK >= (3 * N**2 + 4 * N).

	   IWORK

		     IWORK is INTEGER array, dimension (8*N)

	   INFO

		     INFO is INTEGER
		     = 0:  successful exit.
		     < 0:  if INFO = -i, the i-th argument had an illegal value.
		     > 0:  The algorithm failed to compute a singular value.
			   The update process of divide and conquer failed.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Contributors:
	   Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley,
	   USA

       Definition at line 205 of file dbdsdc.f.

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

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