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dbdsqr.f(3)				      LAPACK				      dbdsqr.f(3)

NAME
       dbdsqr.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dbdsqr (UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C, LDC, WORK, INFO)
	   DBDSQR

Function/Subroutine Documentation
   subroutine dbdsqr (characterUPLO, integerN, integerNCVT, integerNRU, integerNCC, double
       precision, dimension( * )D, double precision, dimension( * )E, double precision,
       dimension( ldvt, * )VT, integerLDVT, double precision, dimension( ldu, * )U, integerLDU,
       double precision, dimension( ldc, * )C, integerLDC, double precision, dimension( * )WORK,
       integerINFO)
       DBDSQR

       Purpose:

	    DBDSQR computes the singular values and, optionally, the right and/or
	    left singular vectors from the singular value decomposition (SVD) of
	    a real N-by-N (upper or lower) bidiagonal matrix B using the implicit
	    zero-shift QR algorithm.  The SVD of B has the form

	       B = Q * S * P**T

	    where S is the diagonal matrix of singular values, Q is an orthogonal
	    matrix of left singular vectors, and P is an orthogonal matrix of
	    right singular vectors.  If left singular vectors are requested, this
	    subroutine actually returns U*Q instead of Q, and, if right singular
	    vectors are requested, this subroutine returns P**T*VT instead of
	    P**T, for given real input matrices U and VT.  When U and VT are the
	    orthogonal matrices that reduce a general matrix A to bidiagonal
	    form:  A = U*B*VT, as computed by DGEBRD, then

	       A = (U*Q) * S * (P**T*VT)

	    is the SVD of A.  Optionally, the subroutine may also compute Q**T*C
	    for a given real input matrix C.

	    See "Computing  Small Singular Values of Bidiagonal Matrices With
	    Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan,
	    LAPACK Working Note #3 (or SIAM J. Sci. Statist. Comput. vol. 11,
	    no. 5, pp. 873-912, Sept 1990) and
	    "Accurate singular values and differential qd algorithms," by
	    B. Parlett and V. Fernando, Technical Report CPAM-554, Mathematics
	    Department, University of California at Berkeley, July 1992
	    for a detailed description of the algorithm.

       Parameters:
	   UPLO

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

	   N

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

	   NCVT

		     NCVT is INTEGER
		     The number of columns of the matrix VT. NCVT >= 0.

	   NRU

		     NRU is INTEGER
		     The number of rows of the matrix U. NRU >= 0.

	   NCC

		     NCC is INTEGER
		     The number of columns of the matrix C. NCC >= 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 in decreasing
		     order.

	   E

		     E is DOUBLE PRECISION array, dimension (N-1)
		     On entry, the N-1 offdiagonal elements of the bidiagonal
		     matrix B.
		     On exit, if INFO = 0, E is destroyed; if INFO > 0, D and E
		     will contain the diagonal and superdiagonal elements of a
		     bidiagonal matrix orthogonally equivalent to the one given
		     as input.

	   VT

		     VT is DOUBLE PRECISION array, dimension (LDVT, NCVT)
		     On entry, an N-by-NCVT matrix VT.
		     On exit, VT is overwritten by P**T * VT.
		     Not referenced if NCVT = 0.

	   LDVT

		     LDVT is INTEGER
		     The leading dimension of the array VT.
		     LDVT >= max(1,N) if NCVT > 0; LDVT >= 1 if NCVT = 0.

	   U

		     U is DOUBLE PRECISION array, dimension (LDU, N)
		     On entry, an NRU-by-N matrix U.
		     On exit, U is overwritten by U * Q.
		     Not referenced if NRU = 0.

	   LDU

		     LDU is INTEGER
		     The leading dimension of the array U.  LDU >= max(1,NRU).

	   C

		     C is DOUBLE PRECISION array, dimension (LDC, NCC)
		     On entry, an N-by-NCC matrix C.
		     On exit, C is overwritten by Q**T * C.
		     Not referenced if NCC = 0.

	   LDC

		     LDC is INTEGER
		     The leading dimension of the array C.
		     LDC >= max(1,N) if NCC > 0; LDC >=1 if NCC = 0.

	   WORK

		     WORK is DOUBLE PRECISION array, dimension (4*N)

	   INFO

		     INFO is INTEGER
		     = 0:  successful exit
		     < 0:  If INFO = -i, the i-th argument had an illegal value
		     > 0:
			if NCVT = NRU = NCC = 0,
			   = 1, a split was marked by a positive value in E
			   = 2, current block of Z not diagonalized after 30*N
				iterations (in inner while loop)
			   = 3, termination criterion of outer while loop not met
				(program created more than N unreduced blocks)
			else NCVT = NRU = NCC = 0,
			      the algorithm did not converge; D and E contain the
			      elements of a bidiagonal matrix which is orthogonally
			      similar to the input matrix B;  if INFO = i, i
			      elements of E have not converged to zero.

       Internal Parameters:

	     TOLMUL  DOUBLE PRECISION, default = max(10,min(100,EPS**(-1/8)))
		     TOLMUL controls the convergence criterion of the QR loop.
		     If it is positive, TOLMUL*EPS is the desired relative
			precision in the computed singular values.
		     If it is negative, abs(TOLMUL*EPS*sigma_max) is the
			desired absolute accuracy in the computed singular
			values (corresponds to relative accuracy
			abs(TOLMUL*EPS) in the largest singular value.
		     abs(TOLMUL) should be between 1 and 1/EPS, and preferably
			between 10 (for fast convergence) and .1/EPS
			(for there to be some accuracy in the results).
		     Default is to lose at either one eighth or 2 of the
			available decimal digits in each computed singular value
			(whichever is smaller).

	     MAXITR  INTEGER, default = 6
		     MAXITR controls the maximum number of passes of the
		     algorithm through its inner loop. The algorithms stops
		     (and so fails to converge) if the number of passes
		     through the inner loop exceeds MAXITR*N**2.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Definition at line 230 of file dbdsqr.f.

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

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