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.

SunSoft, Inc.  —  Last change: 27 Jun 1995