Man page - gtcon(3)

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Manual

gtcon

NAME
SYNOPSIS
Functions
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, realrcond, complex, dimension( * ) work, integer info)
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)
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)
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, doubleprecision anorm, double precision rcond, complex*16, dimension( * )work, integer info)
Author

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, realrcond, 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:
= ā€™1ā€™ or ā€™Oā€™: 1-norm;
= ā€™Iā€™: 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 = ā€™1ā€™ or ā€™Oā€™, the 1-norm of the original matrix A.
If NORM = ā€™Iā€™, 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.

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:
= ā€™1ā€™ or ā€™Oā€™: 1-norm;
= ā€™Iā€™: 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 = ā€™1ā€™ or ā€™Oā€™, the 1-norm of the original matrix A.
If NORM = ā€™Iā€™, 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.

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:
= ā€™1ā€™ or ā€™Oā€™: 1-norm;
= ā€™Iā€™: 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 = ā€™1ā€™ or ā€™Oā€™, the 1-norm of the original matrix A.
If NORM = ā€™Iā€™, 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.

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, doubleprecision 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:
= ā€™1ā€™ or ā€™Oā€™: 1-norm;
= ā€™Iā€™: 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 = ā€™1ā€™ or ā€™Oā€™, the 1-norm of the original matrix A.
If NORM = ā€™Iā€™, 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.

Author

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