Previous: cpptrs Up: ../lapack-c.html Next: cpteqr

NAME CPTCON - compute the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridi- agonal matrix using the factorization A = L*D*L**T or A = U**T*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 tridi- agonal matrix using the factorization A = L*D*L**T or A = U**T*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 bidiago- nal 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 rou- tine. 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, "Effi- cient Algorithms for Computing the Condition Number of a Tridiagonal Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.