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 is INTEGER


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



          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 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 is INTEGER


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



          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 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 is INTEGER


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



          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 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, complex16, 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 is INTEGER


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



          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 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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