gtcon - Man Page

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

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

DL

          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

          D is COMPLEX array, dimension (N)
          The n diagonal elements of the upper triangular matrix U from
          the LU factorization of A.

DU

          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

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

DL

          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

          D is DOUBLE PRECISION array, dimension (N)
          The n diagonal elements of the upper triangular matrix U from
          the LU factorization of A.

DU

          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

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

DL

          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

          D is REAL array, dimension (N)
          The n diagonal elements of the upper triangular matrix U from
          the LU factorization of A.

DU

          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, complex*16, dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension( * ) du, complex*16, dimension( * ) du2, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, complex*16, 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

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

DL

          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

          D is COMPLEX*16 array, dimension (N)
          The n diagonal elements of the upper triangular matrix U from
          the LU factorization of A.

DU

          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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Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK