Provided by: liblapack-doc_3.3.1-1_all NAME

LAPACK-3  -  computes  the  reciprocal  of  the condition number (in the 1-norm) of a real
symmetric positive definite tridiagonal matrix using the factorization A = L*D*L**T or A =
U**T*D*U computed by DPTTRF

SYNOPSIS

SUBROUTINE DPTCON( N, D, E, ANORM, RCOND, WORK, INFO )

INTEGER        INFO, N

DOUBLE         PRECISION ANORM, RCOND

DOUBLE         PRECISION D( * ), E( * ), WORK( * )

PURPOSE

DPTCON computes the reciprocal of the condition number (in the 1-norm) of a real symmetric
positive definite tridiagonal matrix using the factorization A = L*D*L**T or A =  U**T*D*U
computed by DPTTRF.
Norm(inv(A)) is computed by a direct method, and the reciprocal of
the condition number is computed as
RCOND = 1 / (ANORM * norm(inv(A))).

ARGUMENTS

N       (input) INTEGER
The order of the matrix A.  N >= 0.

D       (input) DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the diagonal matrix D from the
factorization of A, as computed by DPTTRF.

E       (input) DOUBLE PRECISION array, dimension (N-1)
The (n-1) off-diagonal elements of the unit bidiagonal factor
U or L from the factorization of A,  as computed by DPTTRF.

ANORM   (input) DOUBLE PRECISION
The 1-norm of the original matrix A.

RCOND   (output) DOUBLE PRECISION
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is the
1-norm of inv(A) computed in this routine.

WORK    (workspace) DOUBLE PRECISION array, dimension (N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

FURTHERDETAILS

The method used is described in Nicholas J. Higham, "Efficient
Algorithms for Computing the Condition Number of a Tridiagonal
Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.

LAPACK routine (version 3.3.1)             April 2011                            DPTCON(3lapack)