NAME

SLASQ2 - SLASQ2 computes the singular values of a real N-by-N unreduced  bidiagonal matrix with squared diagonal elements in Q and  squared off-diagonal elements in E

SYNOPSIS

SUBROUTINE SLASQ2(
M, Q, E, QQ, EE, EPS, TOL2, SMALL2, SUP, KEND, INFO )

INTEGER INFO, KEND, M

REAL EPS, SMALL2, SUP, TOL2

REAL E( ∗ ), EE( ∗ ), Q( ∗ ), QQ( ∗ )

PURPOSE

   SLASQ2 computes the singular values of a real N-by-N unreduced
   bidiagonal matrix with squared diagonal elements in Q and
   squared off-diagonal elements in E. The singular values are
   computed to relative accuracy TOL, barring over/underflow or
   denormalization.
 

ARGUMENTS

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

Q       (output) REAL array, dimension (M)
On normal exit, contains the squared singular values.

E       (workspace) REAL array, dimension (M)

QQ      (input/output) REAL array, dimension (M)
On entry, QQ contains the squared diagonal elements of the bidiagonal matrix whose SVD is desired. On exit, QQ is overwritten.

EE      (input/output) REAL array, dimension (M)
On entry, EE(1:N-1) contains the squared off-diagonal elements of the bidiagonal matrix whose SVD is desired. On exit, EE is overwritten.

EPS     (input) REAL
Machine epsilon.

TOL2    (input) REAL
Desired relative accuracy of computed eigenvalues as defined in SLASQ1.

SMALL2  (input) REAL
A threshold value as defined in SLASQ1.

SUP     (input/output) REAL
Upper bound for the smallest eigenvalue.

KEND    (input/output) INTEGER
Index where minimum d occurs.

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  if INFO = i, the algorithm did not converge;  i specifies how many superdiagonals did not converge.

  —  LAPACK version 2.0  —  08 October 1994