DPTCON(1) LAPACK routine (version 3.2) DPTCON(1)NAME
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
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 fac‐
torization 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 fac‐
torization 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, com‐
puted 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
FURTHER DETAILS
The method used is described in Nicholas J. Higham, "Efficient Algo‐
rithms for Computing the Condition Number of a Tridiagonal Matrix",
SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.
LAPACK routine (version 3.2) November 2008 DPTCON(1)
