slasq1(3)

NAME

SLASQ1 - compute the singular values of a real N-by-N

bidiagonal matrix with diagonal D and off-diagonal E

SYNOPSIS

SUBROUTINE SLASQ1( N, D, E, WORK, INFO )
    INTEGER        INFO, N
    REAL           D( * ), E( * ), WORK( * )

PURPOSE

SLASQ1 computes the singular values of a real N-by-N bidi

agonal 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 imple

mentation 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) REAL array, dimension (N)

On entry, D contains the diagonal elements of the

bidiagonal matrix whose SVD is desired. On normal exit, D con

tains the singular values in decreasing order.

E (input/output) 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.

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 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 cri

terion of outer while loop not met (program created more than N

unreduced blocks)

LAPACK version 3.0 15 June 2000

SLASQ1(3)