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LAPACK version 3.0
dlasq1(3)

PURPOSE
  DLASQ1 - compute the singular values of a real N-by-N bidiagonal matrix
  with diagonal D and off-diagonal E

SYNTAX
  SUBROUTINE DLASQ1( N, D, E, WORK, INFO )

      INTEGER	     INFO, N

      DOUBLE	     PRECISION D( * ), E( * ), WORK( * )

DESCRIPTION
  DLASQ1 computes the singular values of a real N-by-N bidiagonal matrix with
  diagonal D and off-diagonal E. The singular values are computed to high
  relative accuracy, in the absence of denormalization, underflow and
  overflow. The algorithm was first presented in

  "Accurate singular values and differential qd algorithms" by K. V.
  Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230, 1994,

  and the present implementation is described in "An implementation of the
  dqds Algorithm (Positive Case)", LAPACK Working Note.

ARGUMENTS
  N	(input) INTEGER
	The number of rows and columns in the matrix. N >= 0.

  D	(input/output) DOUBLE PRECISION array, dimension (N)
	On entry, D contains the diagonal elements of the bidiagonal matrix
	whose SVD is desired. On normal exit, D contains the singular values
	in decreasing order.

  E	(input/output) DOUBLE PRECISION array, dimension (N)
	On entry, elements E(1:N-1) contain the off-diagonal elements of the
	bidiagonal matrix whose SVD is desired.	 On exit, E is overwritten.

  WORK	(workspace) DOUBLE PRECISION 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 failed = 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)