ptcon(3)

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.

Definition at line 118 of file cptcon.f.

  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.

Definition at line 117 of file dptcon.f.

  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.

Definition at line 117 of file sptcon.f.

  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.

Definition at line 118 of file zptcon.f.

Author

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