NAME

       ptcon - ptcon: condition number estimate

SYNOPSIS

   Functions
       subroutine cptcon (n, d, e, anorm, rcond, rwork, info)
           CPTCON
       subroutine dptcon (n, d, e, anorm, rcond, work, info)
           DPTCON
       subroutine sptcon (n, d, e, anorm, rcond, work, info)
           SPTCON
       subroutine zptcon (n, d, e, anorm, rcond, rwork, info)
           ZPTCON

Detailed Description

Function Documentation

   subroutine cptcon (integer n, real, dimension( * ) d, complex, dimension( * ) e, real anorm,
       real rcond, real, dimension( * ) rwork, integer info)
       CPTCON

       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))).

       Parameters
           N

                     N is INTEGER
                     The order of the matrix A.  N >= 0.

           D

                     D is REAL array, dimension (N)
                     The n diagonal elements of the diagonal matrix D from the
                     factorization of A, as computed by CPTTRF.

           E

                     E is 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

                     ANORM is REAL
                     The 1-norm of the original matrix A.

           RCOND

                     RCOND is 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

                     RWORK is REAL array, dimension (N)

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       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.

   subroutine dptcon (integer n, double precision, dimension( * ) d, double precision, dimension(
       * ) e, double precision anorm, double precision rcond, double precision, dimension( * )
       work, integer info)
       DPTCON

       Purpose:

            DPTCON computes the reciprocal of the condition number (in the
            1-norm) of a real symmetric positive definite tridiagonal 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))).

       Parameters
           N

                     N is INTEGER
                     The order of the matrix A.  N >= 0.

           D

                     D is DOUBLE PRECISION array, dimension (N)
                     The n diagonal elements of the diagonal matrix D from the
                     factorization of A, as computed by DPTTRF.

           E

                     E is DOUBLE PRECISION 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 DPTTRF.

           ANORM

                     ANORM is DOUBLE PRECISION
                     The 1-norm of the original matrix A.

           RCOND

                     RCOND is 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

                     WORK is DOUBLE PRECISION array, dimension (N)

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       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.

   subroutine sptcon (integer n, real, dimension( * ) d, real, dimension( * ) e, real anorm, real
       rcond, real, dimension( * ) work, integer info)
       SPTCON

       Purpose:

            SPTCON computes the reciprocal of the condition number (in the
            1-norm) of a real symmetric positive definite tridiagonal 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))).

       Parameters
           N

                     N is INTEGER
                     The order of the matrix A.  N >= 0.

           D

                     D is REAL array, dimension (N)
                     The n diagonal elements of the diagonal matrix D from the
                     factorization of A, as computed by SPTTRF.

           E

                     E is REAL 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 SPTTRF.

           ANORM

                     ANORM is REAL
                     The 1-norm of the original matrix A.

           RCOND

                     RCOND is 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.

           WORK

                     WORK is REAL array, dimension (N)

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       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.

   subroutine zptcon (integer n, double precision, dimension( * ) d, complex*16, dimension( * )
       e, double precision anorm, double precision rcond, double precision, dimension( * ) rwork,
       integer info)
       ZPTCON

       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))).

       Parameters
           N

                     N is INTEGER
                     The order of the matrix A.  N >= 0.

           D

                     D is DOUBLE PRECISION array, dimension (N)
                     The n diagonal elements of the diagonal matrix D from the
                     factorization of A, as computed by ZPTTRF.

           E

                     E is COMPLEX*16 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 ZPTTRF.

           ANORM

                     ANORM is DOUBLE PRECISION
                     The 1-norm of the original matrix A.

           RCOND

                     RCOND is 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.

           RWORK

                     RWORK is DOUBLE PRECISION array, dimension (N)

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       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.

Author

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