zptcon - 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, WORK, INFO) DOUBLE COMPLEX E(*) INTEGER N, INFO DOUBLE PRECISION ANORM, RCOND DOUBLE PRECISION D(*), WORK(*) SUBROUTINE ZPTCON_64(N, D, E, ANORM, RCOND, WORK, INFO) DOUBLE COMPLEX E(*) INTEGER*8 N, INFO DOUBLE PRECISION ANORM, RCOND DOUBLE PRECISION D(*), WORK(*) F95 INTERFACE SUBROUTINE PTCON(N, D, E, ANORM, RCOND, WORK, INFO) COMPLEX(8), DIMENSION(:) :: E INTEGER :: N, INFO REAL(8) :: ANORM, RCOND REAL(8), DIMENSION(:) :: D, WORK SUBROUTINE PTCON_64(N, D, E, ANORM, RCOND, WORK, INFO) COMPLEX(8), DIMENSION(:) :: E INTEGER(8) :: N, INFO REAL(8) :: ANORM, RCOND REAL(8), DIMENSION(:) :: D, WORK C INTERFACE #include <sunperf.h> void zptcon(int n, double *d, doublecomplex *e, double anorm, double *rcond, int *info); void zptcon_64(long n, double *d, doublecomplex *e, double anorm, dou- ble *rcond, long *info);
Oracle Solaris Studio Performance Library zptcon(3P) 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, WORK, INFO) DOUBLE COMPLEX E(*) INTEGER N, INFO DOUBLE PRECISION ANORM, RCOND DOUBLE PRECISION D(*), WORK(*) SUBROUTINE ZPTCON_64(N, D, E, ANORM, RCOND, WORK, INFO) DOUBLE COMPLEX E(*) INTEGER*8 N, INFO DOUBLE PRECISION ANORM, RCOND DOUBLE PRECISION D(*), WORK(*) F95 INTERFACE SUBROUTINE PTCON(N, D, E, ANORM, RCOND, WORK, INFO) COMPLEX(8), DIMENSION(:) :: E INTEGER :: N, INFO REAL(8) :: ANORM, RCOND REAL(8), DIMENSION(:) :: D, WORK SUBROUTINE PTCON_64(N, D, E, ANORM, RCOND, WORK, INFO) COMPLEX(8), DIMENSION(:) :: E INTEGER(8) :: N, INFO REAL(8) :: ANORM, RCOND REAL(8), DIMENSION(:) :: D, WORK C INTERFACE #include <sunperf.h> void zptcon(int n, double *d, doublecomplex *e, double anorm, double *rcond, int *info); void zptcon_64(long n, double *d, doublecomplex *e, double anorm, dou- ble *rcond, long *info); 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) The order of the matrix A. N >= 0. D (input) The n diagonal elements of the diagonal matrix D from the factorization of A, as computed by ZPTTRF. E (input) 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) The 1-norm of the original matrix A. RCOND (output) The reciprocal of the condition number of the matrix A, com- puted as RCOND = 1/(ANORM * AINVNM), where AINVNM is the 1-norm of inv(A) computed in this routine. WORK (workspace) INFO (output) = 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 Algo- rithms for Computing the Condition Number of a Tridiagonal Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986. 7 Nov 2015 zptcon(3P)