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DLASD0(1)	    LAPACK auxiliary routine (version 3.2)	     DLASD0(1)

NAME
       DLASD0  -  a  divide and conquer approach, DLASD0 computes the singular
       value decomposition (SVD) of a real upper bidiagonal  N-by-M  matrix  B
       with diagonal D and offdiagonal E, where M = N + SQRE

SYNOPSIS
       SUBROUTINE DLASD0( N,  SQRE,  D,	 E,  U,	 LDU, VT, LDVT, SMLSIZ, IWORK,
			  WORK, INFO )

	   INTEGER	  INFO, LDU, LDVT, N, SMLSIZ, SQRE

	   INTEGER	  IWORK( * )

	   DOUBLE	  PRECISION D( * ), E( * ), U( LDU, * ), VT(  LDVT,  *
			  ), WORK( * )

PURPOSE
       Using a divide and conquer approach, DLASD0 computes the singular value
       decomposition (SVD) of a real upper bidiagonal  N-by-M  matrix  B  with
       diagonal	 D  and offdiagonal E, where M = N + SQRE.  The algorithm com‐
       putes orthogonal matrices U and VT such that B = U * S * VT. The singu‐
       lar  values S are overwritten on D.  A related subroutine, DLASDA, com‐
       putes only the singular values, and optionally, the singular vectors in
       compact form.

ARGUMENTS
       N      (input) INTEGER
	      On  entry,  the  row  dimension  of the upper bidiagonal matrix.
	      This is also the dimension of the main diagonal array D.

       SQRE   (input) INTEGER
	      Specifies the column dimension of the bidiagonal matrix.	 =  0:
	      The bidiagonal matrix has column dimension M = N;
	      = 1: The bidiagonal matrix has column dimension M = N+1;

       D      (input/output) DOUBLE PRECISION array, dimension (N)
	      On  entry D contains the main diagonal of the bidiagonal matrix.
	      On exit D, if INFO = 0, contains its singular values.

       E      (input) DOUBLE PRECISION array, dimension (M-1)
	      Contains the subdiagonal entries of the bidiagonal  matrix.   On
	      exit, E has been destroyed.

       U      (output) DOUBLE PRECISION array, dimension at least (LDQ, N)
	      On exit, U contains the left singular vectors.

       LDU    (input) INTEGER
	      On entry, leading dimension of U.

       VT     (output) DOUBLE PRECISION array, dimension at least (LDVT, M)
	      On exit, VT' contains the right singular vectors.

       LDVT   (input) INTEGER
	      On  entry,  leading  dimension of VT.  SMLSIZ (input) INTEGER On
	      entry, maximum size of the subproblems at the bottom of the com‐
	      putation tree.

       IWORK  (workspace) INTEGER work array.
	      Dimension must be at least (8 * N)

       WORK   (workspace) DOUBLE PRECISION work array.
	      Dimension must be at least (3 * M**2 + 2 * M)

       INFO   (output) INTEGER
	      = 0:  successful exit.
	      < 0:  if INFO = -i, the i-th argument had an illegal value.
	      > 0:  if INFO = 1, an singular value did not converge

FURTHER DETAILS
       Based on contributions by
	  Ming Gu and Huan Ren, Computer Science Division, University of
	  California at Berkeley, USA

 LAPACK auxiliary routine (versioNovember 2008			     DLASD0(1)
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