sptcon - norm) of a real symmetric positive definite tridiagonal matrix using the fac- torization A = L*D*L**T or A = U**T*D*U computed by SPTTRF
SUBROUTINE SPTCON(N, D, E, ANORM, RCOND, WORK, INFO) INTEGER N, INFO REAL ANORM, RCOND REAL D(*), E(*), WORK(*) SUBROUTINE SPTCON_64(N, D, E, ANORM, RCOND, WORK, INFO) INTEGER*8 N, INFO REAL ANORM, RCOND REAL D(*), E(*), WORK(*) F95 INTERFACE SUBROUTINE PTCON(N, D, E, ANORM, RCOND, WORK, INFO) INTEGER :: N, INFO REAL :: ANORM, RCOND REAL, DIMENSION(:) :: D, E, WORK SUBROUTINE PTCON_64(N, D, E, ANORM, RCOND, WORK, INFO) INTEGER(8) :: N, INFO REAL :: ANORM, RCOND REAL, DIMENSION(:) :: D, E, WORK C INTERFACE #include <sunperf.h> void sptcon(int n, float *d, float *e, float anorm, float *rcond, int *info); void sptcon_64(long n, float *d, float *e, float anorm, float *rcond, long *info);
Oracle Solaris Studio Performance Library sptcon(3P) NAME sptcon - compute the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the fac- torization A = L*D*L**T or A = U**T*D*U computed by SPTTRF SYNOPSIS SUBROUTINE SPTCON(N, D, E, ANORM, RCOND, WORK, INFO) INTEGER N, INFO REAL ANORM, RCOND REAL D(*), E(*), WORK(*) SUBROUTINE SPTCON_64(N, D, E, ANORM, RCOND, WORK, INFO) INTEGER*8 N, INFO REAL ANORM, RCOND REAL D(*), E(*), WORK(*) F95 INTERFACE SUBROUTINE PTCON(N, D, E, ANORM, RCOND, WORK, INFO) INTEGER :: N, INFO REAL :: ANORM, RCOND REAL, DIMENSION(:) :: D, E, WORK SUBROUTINE PTCON_64(N, D, E, ANORM, RCOND, WORK, INFO) INTEGER(8) :: N, INFO REAL :: ANORM, RCOND REAL, DIMENSION(:) :: D, E, WORK C INTERFACE #include <sunperf.h> void sptcon(int n, float *d, float *e, float anorm, float *rcond, int *info); void sptcon_64(long n, float *d, float *e, float anorm, float *rcond, long *info); PURPOSE sptcon computes the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the fac- torization A = L*D*L**T or A = U**T*D*U computed by SPTTRF. 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 SPTTRF. E (input) The (n-1) off-diagonal elements of the unit bidiagonal factor U or L from the factorization of A, as computed by SPTTRF. 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) dimension(N) 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 sptcon(3P)