Man page - gttrf(3)

Packages contains this manual

Manual

gttrf

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cgttrf (integer n, complex, dimension( * ) dl, complex,dimension( * ) d, complex, dimension( * ) du, complex, dimension( * )du2, integer, dimension( * ) ipiv, integer info)
subroutine dgttrf (integer n, double precision, dimension( * ) dl, doubleprecision, dimension( * ) d, double precision, dimension( * ) du,double precision, dimension( * ) du2, integer, dimension( * ) ipiv,integer info)
subroutine sgttrf (integer n, real, dimension( * ) dl, real, dimension( * )d, real, dimension( * ) du, real, dimension( * ) du2, integer,dimension( * ) ipiv, integer info)
subroutine zgttrf (integer n, complex*16, dimension( * ) dl, complex*16,dimension( * ) d, complex*16, dimension( * ) du, complex*16, dimension(* ) du2, integer, dimension( * ) ipiv, integer info)
Author

NAME

gttrf - gttrf: triangular factor

SYNOPSIS

Functions

subroutine cgttrf (n, dl, d, du, du2, ipiv, info)
CGTTRF
subroutine dgttrf (n, dl, d, du, du2, ipiv, info)
DGTTRF
subroutine sgttrf (n, dl, d, du, du2, ipiv, info)
SGTTRF
subroutine zgttrf (n, dl, d, du, du2, ipiv, info)
ZGTTRF

Detailed Description

Function Documentation

subroutine cgttrf (integer n, complex, dimension( * ) dl, complex,dimension( * ) d, complex, dimension( * ) du, complex, dimension( * )du2, integer, dimension( * ) ipiv, integer info)

CGTTRF

Purpose:

CGTTRF computes an LU factorization of a complex tridiagonal matrix A
using elimination with partial pivoting and row interchanges.

The factorization has the form
A = L * U
where L is a product of permutation and unit lower bidiagonal
matrices and U is upper triangular with nonzeros in only the main
diagonal and first two superdiagonals.

Parameters

N

N is INTEGER
The order of the matrix A.

DL

DL is COMPLEX array, dimension (N-1)
On entry, DL must contain the (n-1) sub-diagonal elements of
A.

On exit, DL is overwritten by the (n-1) multipliers that
define the matrix L from the LU factorization of A.

D

D is COMPLEX array, dimension (N)
On entry, D must contain the diagonal elements of A.

On exit, D is overwritten by the n diagonal elements of the
upper triangular matrix U from the LU factorization of A.

DU

DU is COMPLEX array, dimension (N-1)
On entry, DU must contain the (n-1) super-diagonal elements
of A.

On exit, DU is overwritten by the (n-1) elements of the first
super-diagonal of U.

DU2

DU2 is COMPLEX array, dimension (N-2)
On exit, DU2 is overwritten by the (n-2) elements of the
second super-diagonal 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.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -k, the k-th argument had an illegal value
> 0: if INFO = k, U(k,k) is exactly zero. The factorization
has been completed, but the factor U is exactly
singular, and division by zero will occur if it is used
to solve a system of equations.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dgttrf (integer n, double precision, dimension( * ) dl, doubleprecision, dimension( * ) d, double precision, dimension( * ) du,double precision, dimension( * ) du2, integer, dimension( * ) ipiv,integer info)

DGTTRF

Purpose:

DGTTRF computes an LU factorization of a real tridiagonal matrix A
using elimination with partial pivoting and row interchanges.

The factorization has the form
A = L * U
where L is a product of permutation and unit lower bidiagonal
matrices and U is upper triangular with nonzeros in only the main
diagonal and first two superdiagonals.

Parameters

N

N is INTEGER
The order of the matrix A.

DL

DL is DOUBLE PRECISION array, dimension (N-1)
On entry, DL must contain the (n-1) sub-diagonal elements of
A.

On exit, DL is overwritten by the (n-1) multipliers that
define the matrix L from the LU factorization of A.

D

D is DOUBLE PRECISION array, dimension (N)
On entry, D must contain the diagonal elements of A.

On exit, D is overwritten by 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)
On entry, DU must contain the (n-1) super-diagonal elements
of A.

On exit, DU is overwritten by the (n-1) elements of the first
super-diagonal of U.

DU2

DU2 is DOUBLE PRECISION array, dimension (N-2)
On exit, DU2 is overwritten by the (n-2) elements of the
second super-diagonal 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.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -k, the k-th argument had an illegal value
> 0: if INFO = k, U(k,k) is exactly zero. The factorization
has been completed, but the factor U is exactly
singular, and division by zero will occur if it is used
to solve a system of equations.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine sgttrf (integer n, real, dimension( * ) dl, real, dimension( * )d, real, dimension( * ) du, real, dimension( * ) du2, integer,dimension( * ) ipiv, integer info)

SGTTRF

Purpose:

SGTTRF computes an LU factorization of a real tridiagonal matrix A
using elimination with partial pivoting and row interchanges.

The factorization has the form
A = L * U
where L is a product of permutation and unit lower bidiagonal
matrices and U is upper triangular with nonzeros in only the main
diagonal and first two superdiagonals.

Parameters

N

N is INTEGER
The order of the matrix A.

DL

DL is REAL array, dimension (N-1)
On entry, DL must contain the (n-1) sub-diagonal elements of
A.

On exit, DL is overwritten by the (n-1) multipliers that
define the matrix L from the LU factorization of A.

D

D is REAL array, dimension (N)
On entry, D must contain the diagonal elements of A.

On exit, D is overwritten by the n diagonal elements of the
upper triangular matrix U from the LU factorization of A.

DU

DU is REAL array, dimension (N-1)
On entry, DU must contain the (n-1) super-diagonal elements
of A.

On exit, DU is overwritten by the (n-1) elements of the first
super-diagonal of U.

DU2

DU2 is REAL array, dimension (N-2)
On exit, DU2 is overwritten by the (n-2) elements of the
second super-diagonal 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.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -k, the k-th argument had an illegal value
> 0: if INFO = k, U(k,k) is exactly zero. The factorization
has been completed, but the factor U is exactly
singular, and division by zero will occur if it is used
to solve a system of equations.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zgttrf (integer n, complex*16, dimension( * ) dl, complex*16,dimension( * ) d, complex*16, dimension( * ) du, complex*16, dimension(* ) du2, integer, dimension( * ) ipiv, integer info)

ZGTTRF

Purpose:

ZGTTRF computes an LU factorization of a complex tridiagonal matrix A
using elimination with partial pivoting and row interchanges.

The factorization has the form
A = L * U
where L is a product of permutation and unit lower bidiagonal
matrices and U is upper triangular with nonzeros in only the main
diagonal and first two superdiagonals.

Parameters

N

N is INTEGER
The order of the matrix A.

DL

DL is COMPLEX*16 array, dimension (N-1)
On entry, DL must contain the (n-1) sub-diagonal elements of
A.

On exit, DL is overwritten by the (n-1) multipliers that
define the matrix L from the LU factorization of A.

D

D is COMPLEX*16 array, dimension (N)
On entry, D must contain the diagonal elements of A.

On exit, D is overwritten by 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)
On entry, DU must contain the (n-1) super-diagonal elements
of A.

On exit, DU is overwritten by the (n-1) elements of the first
super-diagonal of U.

DU2

DU2 is COMPLEX*16 array, dimension (N-2)
On exit, DU2 is overwritten by the (n-2) elements of the
second super-diagonal 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.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -k, the k-th argument had an illegal value
> 0: if INFO = k, U(k,k) is exactly zero. The factorization
has been completed, but the factor U is exactly
singular, and division by zero will occur if it is used
to solve a system of equations.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

Generated automatically by Doxygen for LAPACK from the source code.