slasq1()

subroutine slasq1	(	integer	n,
		real, dimension( * )	d,
		real, dimension( * )	e,
		real, dimension( * )	work,
		integer	info )

SLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr.

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Purpose:

!>
!> SLASQ1 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
!>
!>  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 , LAPACK Working Note.
!> 

Parameters

[in]	N	!> N is INTEGER !> The number of rows and columns in the matrix. N >= 0. !>
[in,out]	D	!> D is REAL 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. !>
[in,out]	E	!> E is REAL 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. !>
[out]	WORK	!> WORK is REAL array, dimension (4*N) !>
[out]	INFO	!> INFO is 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 100*N !> iterations (in inner while loop) On exit D and E !> represent a matrix with the same singular values !> which the calling subroutine could use to finish the !> computation, or even feed back into SLASQ1 !> = 3, termination criterion of outer while loop not met !> (program created more than N unreduced blocks) !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.