DLASQ1(l) ) DLASQ1(l)NAME
DLASQ1 - compute the singular values of a real N-by-N bidiagonal matrix
with diagonal D and off-diagonal E
SYNOPSIS
SUBROUTINE DLASQ1( N, D, E, WORK, INFO )
INTEGER INFO, N
DOUBLE PRECISION D( * ), E( * ), WORK( * )
PURPOSE
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 sin‐
gular 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 over‐
written.
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)
LAPACK version 3.0 15 June 2000 DLASQ1(l)
