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SBDSQR(l)					)					SBDSQR(l)

       SBDSQR  - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower)
       bidiagonal matrix B




	   REAL 	  C( LDC, * ), D( * ), E( * ), U( LDU, * ), VT( LDVT, * ), WORK( * )

       SBDSQR computes the singular value decomposition (SVD) of a real N-by-N (upper  or  lower)
       bidiagonal matrix B: B = Q * S * P' (P' denotes the transpose of P), where S is a diagonal
       matrix with non-negative diagonal elements (the singular values of B), and  Q  and  P  are
       orthogonal matrices.

       The  routine computes S, and optionally computes U * Q, P' * VT, or Q' * C, for given real
       input matrices U, VT, and 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.

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

       N       (input) INTEGER
	       The order of the matrix B.  N >= 0.

       NCVT    (input) INTEGER
	       The number of columns of the matrix VT. NCVT >= 0.

       NRU     (input) INTEGER
	       The number of rows of the matrix U. NRU >= 0.

       NCC     (input) INTEGER
	       The number of columns of the matrix C. NCC >= 0.

       D       (input/output) REAL 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       (input/output) REAL array, dimension (N)
	       On  entry,  the	elements  of E contain the offdiagonal elements of the bidiagonal
	       matrix whose SVD is desired. On normal exit (INFO = 0), E is  destroyed.   If  the
	       algorithm  does	not  converge  (INFO  > 0), D and E will contain the diagonal and
	       superdiagonal elements of a bidiagonal matrix orthogonally equivalent to  the  one
	       given as input. E(N) is used for workspace.

       VT      (input/output) REAL array, dimension (LDVT, NCVT)
	       On  entry,  an N-by-NCVT matrix VT.  On exit, VT is overwritten by P' * VT.  VT is
	       not referenced if NCVT = 0.

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

       U       (input/output) REAL array, dimension (LDU, N)
	       On  entry,  an  NRU-by-N  matrix U.  On exit, U is overwritten by U * Q.  U is not
	       referenced if NRU = 0.

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

       C       (input/output) REAL array, dimension (LDC, NCC)
	       On entry, an N-by-NCC matrix C.	On exit, C is overwritten by Q' * C.   C  is  not
	       referenced if NCC = 0.

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

       WORK    (workspace) REAL array, dimension (4*N)

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  If INFO = -i, the i-th argument had an illegal value
	       > 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 ele-
	       ments of E have not converged to zero.

       TOLMUL  REAL, default = max(10,min(100,EPS**(-1/8)))
	       TOLMUL controls the convergence criterion of the QR loop.  If it is positive, TOL-
	       MUL*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.

LAPACK version 3.0			   15 June 2000 				SBDSQR(l)
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