carta
ptcon(3)

ptcon3

Ptcon: condition number estimate

Usage

Functions

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, , 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, , 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, , 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, , SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.
!>

Definition at line 118 of file zptcon.f.

History

  • Arch Linux 2026-11-01: the text shown here
  • Debian 13 (Trixie)

Author

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