ZPTCON(3F) ZPTCON(3F)
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
SUBROUTINE ZPTCON( N, D, E, ANORM, RCOND, RWORK, INFO )
INTEGER INFO, N
DOUBLE PRECISION ANORM, RCOND
DOUBLE PRECISION D( * ), RWORK( * )
COMPLEX*16 E( * )
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))).
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
Page 1
ZPTCON(3F) ZPTCON(3F)
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.
ZPTCON(3F) ZPTCON(3F)
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
SUBROUTINE ZPTCON( N, D, E, ANORM, RCOND, RWORK, INFO )
INTEGER INFO, N
DOUBLE PRECISION ANORM, RCOND
DOUBLE PRECISION D( * ), RWORK( * )
COMPLEX*16 E( * )
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))).
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
Page 1
ZPTCON(3F) ZPTCON(3F)
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.
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