Contents
sptcon - compute the reciprocal of the condition number (in
the 1-norm) of a real symmetric positive definite tridiago-
nal matrix using the factorization A = L*D*L**T or A =
U**T*D*U computed by SPTTRF
SUBROUTINE SPTCON(N, DIAG, OFFD, ANORM, RCOND, WORK, INFO)
INTEGER N, INFO
REAL ANORM, RCOND
REAL DIAG(*), OFFD(*), WORK(*)
SUBROUTINE SPTCON_64(N, DIAG, OFFD, ANORM, RCOND, WORK, INFO)
INTEGER*8 N, INFO
REAL ANORM, RCOND
REAL DIAG(*), OFFD(*), WORK(*)
F95 INTERFACE
SUBROUTINE PTCON([N], DIAG, OFFD, ANORM, RCOND, [WORK], [INFO])
INTEGER :: N, INFO
REAL :: ANORM, RCOND
REAL, DIMENSION(:) :: DIAG, OFFD, WORK
SUBROUTINE PTCON_64([N], DIAG, OFFD, ANORM, RCOND, [WORK], [INFO])
INTEGER(8) :: N, INFO
REAL :: ANORM, RCOND
REAL, DIMENSION(:) :: DIAG, OFFD, WORK
C INTERFACE
#include <sunperf.h>
void sptcon(int n, float *diag, float *offd, float anorm,
float *rcond, int *info);
void sptcon_64(long n, float *diag, float *offd, float
anorm, float *rcond, long *info);
sptcon computes the reciprocal of the condition number (in
the 1-norm) of a real symmetric positive definite tridiago-
nal matrix using the factorization 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))).
N (input) The order of the matrix A. N >= 0.
DIAG (input)
The n diagonal elements of the diagonal matrix
DIAG from the factorization of A, as computed by
SPTTRF.
OFFD (input)
The (n-1) off-diagonal elements of the unit bidi-
agonal 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, computed 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 ille-
gal value
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.