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

**FURTHER** **DETAILS**

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)