DPTCON - Online Linux Manual Page

Section : 1
Updated : November 2008
Source : LAPACK routine (version 3.2)
Note : LAPACK routine (version 3.2)
NAMEDPTCON - 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
SYNOPSISSUBROUTINE DPTCON(  N, D, E, ANORM, RCOND, WORK, INFO )  INTEGER INFO, N  DOUBLE PRECISION ANORM, RCOND  DOUBLE PRECISION D( * ), E( * ), WORK( * )
PURPOSEDPTCON 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))).
ARGUMENTSN (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 DETAILSThe 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. 0
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