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dptcon (3)
  • >> dptcon (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         dptcon - 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 DPTTRF
    
    SYNOPSIS
         SUBROUTINE DPTCON( N, D, E, ANORM, RCOND, WORK, INFO )
    
         INTEGER INFO, N
    
         DOUBLE PRECISION ANORM, RCOND
    
         DOUBLE PRECISION D( * ), E( * ), WORK( * )
    
    
    
         #include <sunperf.h>
    
         void dptcon(int n, double *d, double *e, double anorm,  dou-
                   ble *drcond, int *info) ;
    
    PURPOSE
         DPTCON 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 DPTTRF.
    
         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) DOUBLE PRECISION array, dimension (N)
                   The n diagonal elements of the diagonal  matrix  D
                   from  the  factorization  of  A,  as  computed  by
                   DPTTRF.
    
         E         (input) DOUBLE PRECISION array, dimension (N-1)
                   The (n-1) off-diagonal elements of the unit  bidi-
                   agonal  factor U or L from the factorization of A,
                   as computed by DPTTRF.
    
         ANORM     (input) DOUBLE PRECISION
                   The 1-norm of the original matrix A.
    
         RCOND     (output) DOUBLE PRECISION
                   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) DOUBLE PRECISION array, dimension (N)
    
         INFO      (output) INTEGER
                   = 0:  successful exit
                   < 0:  if INFO = -i, the i-th argument had an ille-
                   gal 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.
    
    
    
    


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