NAME

gtcon - gtcon: condition number estimate

SYNOPSIS

Functions

subroutine cgtcon (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work, info)
CGTCON subroutine dgtcon (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work, iwork, info)
DGTCON subroutine sgtcon (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work, iwork, info)
SGTCON subroutine zgtcon (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work, info)
ZGTCON

Detailed Description

Function Documentation

subroutine cgtcon (character norm, integer n, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du, complex, dimension( * ) du2, integer, dimension( * ) ipiv, real anorm, real rcond, complex, dimension( * ) work, integer info)

CGTCON

Purpose:



 CGTCON estimates the reciprocal of the condition number of a complex


 tridiagonal matrix A using the LU factorization as computed by


 CGTTRF.


 An estimate is obtained for norm(inv(A)), and the reciprocal of the


 condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

Parameters

NORM



          NORM is CHARACTER*1


          Specifies whether the 1-norm condition number or the


          infinity-norm condition number is required:


          = '1' or 'O':  1-norm;


          = 'I':         Infinity-norm.



          N is INTEGER


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



          DL is COMPLEX array, dimension (N-1)


          The (n-1) multipliers that define the matrix L from the


          LU factorization of A as computed by CGTTRF.



          D is COMPLEX array, dimension (N)


          The n diagonal elements of the upper triangular matrix U from


          the LU factorization of A.



          DU is COMPLEX array, dimension (N-1)


          The (n-1) elements of the first superdiagonal of U.

DU2



          DU2 is COMPLEX array, dimension (N-2)


          The (n-2) elements of the second superdiagonal of U.

IPIV



          IPIV is INTEGER array, dimension (N)


          The pivot indices; for 1 <= i <= n, row i of the matrix was


          interchanged with row IPIV(i).  IPIV(i) will always be either


          i or i+1; IPIV(i) = i indicates a row interchange was not


          required.

ANORM



          ANORM is REAL


          If NORM = '1' or 'O', the 1-norm of the original matrix A.


          If NORM = 'I', the infinity-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 an


          estimate of the 1-norm of inv(A) computed in this routine.

WORK



          WORK is COMPLEX array, dimension (2*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.

Definition at line 139 of file cgtcon.f.

subroutine dgtcon (character norm, integer n, double precision, dimension( * ) dl, double precision, dimension( * ) d, double precision, dimension( * ) du, double precision, dimension( * ) du2, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)

DGTCON

Purpose:



 DGTCON estimates the reciprocal of the condition number of a real


 tridiagonal matrix A using the LU factorization as computed by


 DGTTRF.


 An estimate is obtained for norm(inv(A)), and the reciprocal of the


 condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

Parameters

NORM



          NORM is CHARACTER*1


          Specifies whether the 1-norm condition number or the


          infinity-norm condition number is required:


          = '1' or 'O':  1-norm;


          = 'I':         Infinity-norm.



          N is INTEGER


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



          DL is DOUBLE PRECISION array, dimension (N-1)


          The (n-1) multipliers that define the matrix L from the


          LU factorization of A as computed by DGTTRF.



          D is DOUBLE PRECISION array, dimension (N)


          The n diagonal elements of the upper triangular matrix U from


          the LU factorization of A.



          DU is DOUBLE PRECISION array, dimension (N-1)


          The (n-1) elements of the first superdiagonal of U.

DU2



          DU2 is DOUBLE PRECISION array, dimension (N-2)


          The (n-2) elements of the second superdiagonal of U.

IPIV



          IPIV is INTEGER array, dimension (N)


          The pivot indices; for 1 <= i <= n, row i of the matrix was


          interchanged with row IPIV(i).  IPIV(i) will always be either


          i or i+1; IPIV(i) = i indicates a row interchange was not


          required.

ANORM



          ANORM is DOUBLE PRECISION


          If NORM = '1' or 'O', the 1-norm of the original matrix A.


          If NORM = 'I', the infinity-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 an


          estimate of the 1-norm of inv(A) computed in this routine.

WORK



          WORK is DOUBLE PRECISION array, dimension (2*N)

IWORK



          IWORK is INTEGER 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.

Definition at line 144 of file dgtcon.f.

subroutine sgtcon (character norm, integer n, real, dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du, real, dimension( * ) du2, integer, dimension( * ) ipiv, real anorm, real rcond, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)

SGTCON

Purpose:



 SGTCON estimates the reciprocal of the condition number of a real


 tridiagonal matrix A using the LU factorization as computed by


 SGTTRF.


 An estimate is obtained for norm(inv(A)), and the reciprocal of the


 condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

Parameters

NORM



          NORM is CHARACTER*1


          Specifies whether the 1-norm condition number or the


          infinity-norm condition number is required:


          = '1' or 'O':  1-norm;


          = 'I':         Infinity-norm.



          N is INTEGER


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



          DL is REAL array, dimension (N-1)


          The (n-1) multipliers that define the matrix L from the


          LU factorization of A as computed by SGTTRF.



          D is REAL array, dimension (N)


          The n diagonal elements of the upper triangular matrix U from


          the LU factorization of A.



          DU is REAL array, dimension (N-1)


          The (n-1) elements of the first superdiagonal of U.

DU2



          DU2 is REAL array, dimension (N-2)


          The (n-2) elements of the second superdiagonal of U.

IPIV



          IPIV is INTEGER array, dimension (N)


          The pivot indices; for 1 <= i <= n, row i of the matrix was


          interchanged with row IPIV(i).  IPIV(i) will always be either


          i or i+1; IPIV(i) = i indicates a row interchange was not


          required.

ANORM



          ANORM is REAL


          If NORM = '1' or 'O', the 1-norm of the original matrix A.


          If NORM = 'I', the infinity-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 an


          estimate of the 1-norm of inv(A) computed in this routine.

WORK



          WORK is REAL array, dimension (2*N)

IWORK



          IWORK is INTEGER 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.

Definition at line 144 of file sgtcon.f.

subroutine zgtcon (character norm, integer n, complex16, dimension( ) dl, complex16, dimension( ) d, complex16, dimension( ) du, complex16, dimension( ) du2, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, complex16, dimension( ) work, integer info)

ZGTCON

Purpose:



 ZGTCON estimates the reciprocal of the condition number of a complex


 tridiagonal matrix A using the LU factorization as computed by


 ZGTTRF.


 An estimate is obtained for norm(inv(A)), and the reciprocal of the


 condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

Parameters

NORM



          NORM is CHARACTER*1


          Specifies whether the 1-norm condition number or the


          infinity-norm condition number is required:


          = '1' or 'O':  1-norm;


          = 'I':         Infinity-norm.



          N is INTEGER


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



          DL is COMPLEX*16 array, dimension (N-1)


          The (n-1) multipliers that define the matrix L from the


          LU factorization of A as computed by ZGTTRF.



          D is COMPLEX*16 array, dimension (N)


          The n diagonal elements of the upper triangular matrix U from


          the LU factorization of A.



          DU is COMPLEX*16 array, dimension (N-1)


          The (n-1) elements of the first superdiagonal of U.

DU2



          DU2 is COMPLEX*16 array, dimension (N-2)


          The (n-2) elements of the second superdiagonal of U.

IPIV



          IPIV is INTEGER array, dimension (N)


          The pivot indices; for 1 <= i <= n, row i of the matrix was


          interchanged with row IPIV(i).  IPIV(i) will always be either


          i or i+1; IPIV(i) = i indicates a row interchange was not


          required.

ANORM



          ANORM is DOUBLE PRECISION


          If NORM = '1' or 'O', the 1-norm of the original matrix A.


          If NORM = 'I', the infinity-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 an


          estimate of the 1-norm of inv(A) computed in this routine.

WORK



          WORK is COMPLEX*16 array, dimension (2*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.

Definition at line 139 of file zgtcon.f.

Author

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