cptcon(3S)

NAME
     CPTCON - 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 CPTTRF

SYNOPSIS
     SUBROUTINE CPTCON( N, D, E, ANORM, RCOND, RWORK, INFO )

         INTEGER        INFO, N

         REAL           ANORM, RCOND

         REAL           D( * ), RWORK( * )

         COMPLEX        E( * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     CPTCON 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 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 bidiagonal 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 routine.

     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, "Efficient Algorithms
     for Computing the Condition Number of a Tridiagonal Matrix", SIAM J. Sci.
     Stat. Comput., Vol. 7, No. 1, January 1986.


SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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