Man page - gtsv(3)

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Manual

gtsv

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cgtsv (integer n, integer nrhs, complex, dimension( * ) dl,complex, dimension( * ) d, complex, dimension( * ) du, complex,dimension( ldb, * ) b, integer ldb, integer info)
subroutine dgtsv (integer n, integer nrhs, double precision, dimension( * )dl, double precision, dimension( * ) d, double precision, dimension( *) du, double precision, dimension( ldb, * ) b, integer ldb, integerinfo)
subroutine sgtsv (integer n, integer nrhs, real, dimension( * ) dl, real,dimension( * ) d, real, dimension( * ) du, real, dimension( ldb, * ) b,integer ldb, integer info)
subroutine zgtsv (integer n, integer nrhs, complex*16, dimension( * ) dl,complex*16, dimension( * ) d, complex*16, dimension( * ) du,complex*16, dimension( ldb, * ) b, integer ldb, integer info)
Author

NAME

gtsv - gtsv: factor and solve

SYNOPSIS

Functions

subroutine cgtsv (n, nrhs, dl, d, du, b, ldb, info)
CGTSV computes the solution to system of linear equations A * X = B for GT matrices
subroutine dgtsv (n, nrhs, dl, d, du, b, ldb, info)
DGTSV computes the solution to system of linear equations A * X = B for GT matrices
subroutine sgtsv (n, nrhs, dl, d, du, b, ldb, info)
SGTSV computes the solution to system of linear equations A * X = B for GT matrices
subroutine zgtsv (n, nrhs, dl, d, du, b, ldb, info)
ZGTSV computes the solution to system of linear equations A * X = B for GT matrices

Detailed Description

Function Documentation

subroutine cgtsv (integer n, integer nrhs, complex, dimension( * ) dl,complex, dimension( * ) d, complex, dimension( * ) du, complex,dimension( ldb, * ) b, integer ldb, integer info)

CGTSV computes the solution to system of linear equations A * X = B for GT matrices

Purpose:

CGTSV solves the equation

A*X = B,

where A is an N-by-N tridiagonal matrix, by Gaussian elimination with
partial pivoting.

Note that the equation A**T *X = B may be solved by interchanging the
order of the arguments DU and DL.

Parameters

N

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

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.

DL

DL is COMPLEX array, dimension (N-1)
On entry, DL must contain the (n-1) subdiagonal elements of
A.
On exit, DL is overwritten by the (n-2) elements of the
second superdiagonal of the upper triangular matrix U from
the LU factorization of A, in DL(1), ..., DL(n-2).

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 U.

DU

DU is COMPLEX array, dimension (N-1)
On entry, DU must contain the (n-1) superdiagonal elements
of A.
On exit, DU is overwritten by the (n-1) elements of the first
superdiagonal of U.

B

B is COMPLEX array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution matrix X.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, U(i,i) is exactly zero, and the solution
has not been computed. The factorization has not been
completed unless i = N.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dgtsv (integer n, integer nrhs, double precision, dimension( * )dl, double precision, dimension( * ) d, double precision, dimension( *) du, double precision, dimension( ldb, * ) b, integer ldb, integerinfo)

DGTSV computes the solution to system of linear equations A * X = B for GT matrices

Purpose:

DGTSV solves the equation

A*X = B,

where A is an n by n tridiagonal matrix, by Gaussian elimination with
partial pivoting.

Note that the equation A**T*X = B may be solved by interchanging the
order of the arguments DU and DL.

Parameters

N

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

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.

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-2) elements of the
second super-diagonal of the upper triangular matrix U from
the LU factorization of A, in DL(1), ..., DL(n-2).

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 U.

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.

B

B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the N by NRHS matrix of right hand side matrix B.
On exit, if INFO = 0, the N by NRHS solution matrix X.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, U(i,i) is exactly zero, and the solution
has not been computed. The factorization has not been
completed unless i = N.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine sgtsv (integer n, integer nrhs, real, dimension( * ) dl, real,dimension( * ) d, real, dimension( * ) du, real, dimension( ldb, * ) b,integer ldb, integer info)

SGTSV computes the solution to system of linear equations A * X = B for GT matrices

Purpose:

SGTSV solves the equation

A*X = B,

where A is an n by n tridiagonal matrix, by Gaussian elimination with
partial pivoting.

Note that the equation A**T*X = B may be solved by interchanging the
order of the arguments DU and DL.

Parameters

N

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

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.

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-2) elements of the
second super-diagonal of the upper triangular matrix U from
the LU factorization of A, in DL(1), ..., DL(n-2).

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 U.

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.

B

B is REAL array, dimension (LDB,NRHS)
On entry, the N by NRHS matrix of right hand side matrix B.
On exit, if INFO = 0, the N by NRHS solution matrix X.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, U(i,i) is exactly zero, and the solution
has not been computed. The factorization has not been
completed unless i = N.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zgtsv (integer n, integer nrhs, complex*16, dimension( * ) dl,complex*16, dimension( * ) d, complex*16, dimension( * ) du,complex*16, dimension( ldb, * ) b, integer ldb, integer info)

ZGTSV computes the solution to system of linear equations A * X = B for GT matrices

Purpose:

ZGTSV solves the equation

A*X = B,

where A is an N-by-N tridiagonal matrix, by Gaussian elimination with
partial pivoting.

Note that the equation A**T *X = B may be solved by interchanging the
order of the arguments DU and DL.

Parameters

N

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

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.

DL

DL is COMPLEX*16 array, dimension (N-1)
On entry, DL must contain the (n-1) subdiagonal elements of
A.
On exit, DL is overwritten by the (n-2) elements of the
second superdiagonal of the upper triangular matrix U from
the LU factorization of A, in DL(1), ..., DL(n-2).

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 U.

DU

DU is COMPLEX*16 array, dimension (N-1)
On entry, DU must contain the (n-1) superdiagonal elements
of A.
On exit, DU is overwritten by the (n-1) elements of the first
superdiagonal of U.

B

B is COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution matrix X.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, U(i,i) is exactly zero, and the solution
has not been computed. The factorization has not been
completed unless i = N.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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