zptcon(l) [redhat man page]
ZPTCON(l) ) ZPTCON(l) NAME
ZPTCON - compute the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A = U**H*D*U computed by ZPTTRF SYNOPSIS
SUBROUTINE ZPTCON( N, D, E, ANORM, RCOND, RWORK, INFO ) INTEGER INFO, N DOUBLE PRECISION ANORM, RCOND DOUBLE PRECISION D( * ), RWORK( * ) COMPLEX*16 E( * ) PURPOSE
ZPTCON computes the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A = U**H*D*U computed by ZPTTRF. 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 ZPTTRF. E (input) COMPLEX*16 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 ZPTTRF. 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. RWORK (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 version 3.0 15 June 2000 ZPTCON(l)
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DPTCON(l) ) DPTCON(l) NAME
DPTCON - compute 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 con- dition 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 version 3.0 15 June 2000 DPTCON(l)