---
name: "gttrs"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/gttrs"
---

# gttrs(3)

gttrs: triangular solve using factor

## NAME

gttrs - 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**

## Detailed Description

## 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

Univ. of Colorado Denver

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

Univ. of Colorado Denver

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

Univ. of Colorado Denver

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

Univ. of Colorado Denver

NAG Ltd.

Definition at line **136** of file **zgttrs.f**.

## Author

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