dlasq2(3F)

NAME
     DLASQ2 - DLASQ2 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 DLASQ2( M, Q, E, QQ, EE, EPS, TOL2, SMALL2, SUP, KEND, INFO )

         INTEGER        INFO, KEND, M

         DOUBLE         PRECISION EPS, SMALL2, SUP, TOL2

         DOUBLE         PRECISION E( * ), EE( * ), Q( * ), QQ( * )

PURPOSE
        DLASQ2 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) DOUBLE PRECISION array, dimension (M)
             On normal exit, contains the squared singular values.

     E       (workspace) DOUBLE PRECISION array, dimension (M)

     QQ      (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION
             Machine epsilon.

     TOL2    (input) DOUBLE PRECISION
             Desired relative accuracy of computed eigenvalues as defined in
             DLASQ1.

     SMALL2  (input) DOUBLE PRECISION
             A threshold value as defined in DLASQ1.
     SUP     (input/output) DOUBLE PRECISION
             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.