NAME¶

SLASQ1 - computes 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 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) 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.

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 criterion of outer while loop not met (program created more than N unreduced blocks)