# gtts2 - Man Page

gtts2: triangular solve using factor

## Synopsis

### Functions

subroutine cgtts2 (itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb)
CGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.
subroutine dgtts2 (itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb)
DGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.
subroutine sgtts2 (itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb)
SGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.
subroutine zgtts2 (itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb)
ZGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

## Function Documentation

### subroutine cgtts2 (integer itrans, integer n, integer nrhs, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du, complex, dimension( * ) du2, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb)

CGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

Purpose:

``` CGTTS2 solves one of the systems of equations
A * X = B,  A**T * X = B,  or  A**H * X = B,
with a tridiagonal matrix A using the LU factorization computed
by CGTTRF.```
Parameters

ITRANS

```          ITRANS is INTEGER
Specifies the form of the system of equations.
= 0:  A * X = B     (No transpose)
= 1:  A**T * X = B  (Transpose)
= 2:  A**H * X = B  (Conjugate transpose)```

N

```          N is INTEGER
The order of the matrix A.```

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)
The (n-1) multipliers that define the matrix L from the
LU factorization of A.```

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 super-diagonal of U.```

DU2

```          DU2 is COMPLEX array, dimension (N-2)
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.```

B

```          B is COMPLEX array, dimension (LDB,NRHS)
On entry, the matrix of right hand side vectors B.
On exit, B is overwritten by the solution vectors X.```

LDB

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

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 127 of file cgtts2.f.

### subroutine dgtts2 (integer itrans, integer n, integer nrhs, double precision, dimension( * ) dl, double precision, dimension( * ) d, double precision, dimension( * ) du, double precision, dimension( * ) du2, integer, dimension( * ) ipiv, double precision, dimension( ldb, * ) b, integer ldb)

DGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

Purpose:

``` DGTTS2 solves one of the systems of equations
A*X = B  or  A**T*X = B,
with a tridiagonal matrix A using the LU factorization computed
by DGTTRF.```
Parameters

ITRANS

```          ITRANS is INTEGER
Specifies the form of the system of equations.
= 0:  A * X = B  (No transpose)
= 1:  A**T* X = B  (Transpose)
= 2:  A**T* X = B  (Conjugate transpose = Transpose)```

N

```          N is INTEGER
The order of the matrix A.```

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)
The (n-1) multipliers that define the matrix L from the
LU factorization of A.```

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 super-diagonal of U.```

DU2

```          DU2 is DOUBLE PRECISION array, dimension (N-2)
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.```

B

```          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the matrix of right hand side vectors B.
On exit, B is overwritten by the solution vectors X.```

LDB

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

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 127 of file dgtts2.f.

### subroutine sgtts2 (integer itrans, integer n, integer nrhs, real, dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du, real, dimension( * ) du2, integer, dimension( * ) ipiv, real, dimension( ldb, * ) b, integer ldb)

SGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

Purpose:

``` SGTTS2 solves one of the systems of equations
A*X = B  or  A**T*X = B,
with a tridiagonal matrix A using the LU factorization computed
by SGTTRF.```
Parameters

ITRANS

```          ITRANS is INTEGER
Specifies the form of the system of equations.
= 0:  A * X = B  (No transpose)
= 1:  A**T* X = B  (Transpose)
= 2:  A**T* X = B  (Conjugate transpose = Transpose)```

N

```          N is INTEGER
The order of the matrix A.```

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)
The (n-1) multipliers that define the matrix L from the
LU factorization of A.```

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 super-diagonal of U.```

DU2

```          DU2 is REAL array, dimension (N-2)
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.```

B

```          B is REAL array, dimension (LDB,NRHS)
On entry, the matrix of right hand side vectors B.
On exit, B is overwritten by the solution vectors X.```

LDB

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

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 127 of file sgtts2.f.

### subroutine zgtts2 (integer itrans, integer n, integer nrhs, complex*16, dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension( * ) du, complex*16, dimension( * ) du2, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb)

ZGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

Purpose:

``` ZGTTS2 solves one of the systems of equations
A * X = B,  A**T * X = B,  or  A**H * X = B,
with a tridiagonal matrix A using the LU factorization computed
by ZGTTRF.```
Parameters

ITRANS

```          ITRANS is INTEGER
Specifies the form of the system of equations.
= 0:  A * X = B     (No transpose)
= 1:  A**T * X = B  (Transpose)
= 2:  A**H * X = B  (Conjugate transpose)```

N

```          N is INTEGER
The order of the matrix A.```

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)
The (n-1) multipliers that define the matrix L from the
LU factorization of A.```

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 super-diagonal of U.```

DU2

```          DU2 is COMPLEX*16 array, dimension (N-2)
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.```

B

```          B is COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the matrix of right hand side vectors B.
On exit, B is overwritten by the solution vectors X.```

LDB

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

Univ. of Tennessee

Univ. of California Berkeley