# gttrs - Man Page

gttrs: triangular solve using factor

## Synopsis

### Functions

subroutine cgttrs (trans, n, nrhs, dl, d, du, du2, ipiv, b, ldb, info)
CGTTRS
subroutine dgttrs (trans, n, nrhs, dl, d, du, du2, ipiv, b, ldb, info)
DGTTRS
subroutine sgttrs (trans, n, nrhs, dl, d, du, du2, ipiv, b, ldb, info)
SGTTRS
subroutine zgttrs (trans, n, nrhs, dl, d, du, du2, ipiv, b, ldb, info)
ZGTTRS

## Function Documentation

### subroutine cgttrs (character trans, 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, integer info)

CGTTRS

Purpose:

``` CGTTRS 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

TRANS

```          TRANS is CHARACTER*1
Specifies the form of the system of equations.
= 'N':  A * X = B     (No transpose)
= 'T':  A**T * X = B  (Transpose)
= 'C':  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).```

INFO

```          INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -k, the k-th argument had an illegal value```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 136 of file cgttrs.f.

### subroutine dgttrs (character trans, 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, integer info)

DGTTRS

Purpose:

``` DGTTRS 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

TRANS

```          TRANS is CHARACTER*1
Specifies the form of the system of equations.
= 'N':  A * X = B  (No transpose)
= 'T':  A**T* X = B  (Transpose)
= 'C':  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).```

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

NAG Ltd.

Definition at line 136 of file dgttrs.f.

### subroutine sgttrs (character trans, 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, integer info)

SGTTRS

Purpose:

``` SGTTRS 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

TRANS

```          TRANS is CHARACTER*1
Specifies the form of the system of equations.
= 'N':  A * X = B  (No transpose)
= 'T':  A**T* X = B  (Transpose)
= 'C':  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).```

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

NAG Ltd.

Definition at line 136 of file sgttrs.f.

### subroutine zgttrs (character trans, 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, integer info)

ZGTTRS

Purpose:

``` ZGTTRS 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

TRANS

```          TRANS is CHARACTER*1
Specifies the form of the system of equations.
= 'N':  A * X = B     (No transpose)
= 'T':  A**T * X = B  (Transpose)
= 'C':  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).```

INFO

```          INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -k, the k-th argument had an illegal value```
Author

Univ. of Tennessee

Univ. of California Berkeley