Man page - ptcon(3)

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Manual

ptcon

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cptcon (integer n, real, dimension( * ) d, complex, dimension( *) e, real anorm, real rcond, real, dimension( * ) rwork, integer info)
subroutine dptcon (integer n, double precision, dimension( * ) d, doubleprecision, dimension( * ) e, double precision anorm, double precisionrcond, double precision, dimension( * ) work, integer info)
subroutine sptcon (integer n, real, dimension( * ) d, real, dimension( * )e, real anorm, real rcond, real, dimension( * ) work, integer info)
subroutine zptcon (integer n, double precision, dimension( * ) d,complex*16, dimension( * ) e, double precision anorm, double precisionrcond, double precision, dimension( * ) rwork, integer info)
Author

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, doubleprecision, dimension( * ) e, double precision anorm, double precisionrcond, 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 precisionrcond, 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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