cptcon (l) - Linux Manuals

cptcon: 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 CPTTRF

NAME

CPTCON - 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 CPTTRF

SYNOPSIS

SUBROUTINE CPTCON(
N, D, E, ANORM, RCOND, RWORK, INFO )

    
INTEGER INFO, N

    
REAL ANORM, RCOND

    
REAL D( * ), RWORK( * )

    
COMPLEX E( * )

PURPOSE

CPTCON 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 CPTTRF. 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) REAL array, dimension (N)
The n diagonal elements of the diagonal matrix D from the factorization of A, as computed by CPTTRF.
E (input) COMPLEX 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 CPTTRF.
ANORM (input) REAL
The 1-norm of the original matrix A.
RCOND (output) REAL
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) REAL 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.

Pages related to cptcon

  • cptcon (3)
  • cpteqr (l) - computes all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using SPTTRF and then calling CBDSQR to compute the singular values of the bidiagonal factor
  • cptrfs (l) - improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution
  • cptsv (l) - computes the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices
  • cptsvx (l) - uses the factorization A = L*D*L**H to compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix and X and B are N-by-NRHS matrices
  • cpttrf (l) - computes the L*D*Laq factorization of a complex Hermitian positive definite tridiagonal matrix A
  • cpttrs (l) - solves a tridiagonal system of the form A * X = B using the factorization A = Uaq*D*U or A = L*D*Laq computed by CPTTRF
  • cptts2 (l) - solves a tridiagonal system of the form A * X = B using the factorization A = Uaq*D*U or A = L*D*Laq computed by CPTTRF