# gtsv - Man Page

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

## 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

NAG Ltd.

Definition at line 123 of file cgtsv.f.

### 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, integer info)

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

NAG Ltd.

Definition at line 126 of file dgtsv.f.

### 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

NAG Ltd.

Definition at line 126 of file sgtsv.f.

### 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