---
name: "gttrf"
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/gttrf"
---

# gttrf(3)

gttrf: triangular factor

## NAME

gttrf - gttrf: triangular factor

## SYNOPSIS

### Functions

subroutine **cgttrf** (n, dl, d, du, du2, ipiv, info)\
 **CGTTRF**  subroutine **dgttrf** (n, dl, d, du, du2, ipiv, info)\
 **DGTTRF**  subroutine **sgttrf** (n, dl, d, du, du2, ipiv, info)\
 **SGTTRF**  subroutine **zgttrf** (n, dl, d, du, du2, ipiv, info)\
 **ZGTTRF**

## Detailed Description

## Function Documentation

### subroutine cgttrf (integer n, complex, dimension( \* ) dl, complex, dimension( \* ) d, complex, dimension( \* ) du, complex, dimension( \* ) du2, integer, dimension( \* ) ipiv, integer info)

**CGTTRF**

**Purpose:**

```
!>
!> CGTTRF computes an LU factorization of a complex tridiagonal matrix A
!> using elimination with partial pivoting and row interchanges.
!>
!> The factorization has the form
!>    A = L * U
!> where L is a product of permutation and unit lower bidiagonal
!> matrices and U is upper triangular with nonzeros in only the main
!> diagonal and first two superdiagonals.
!>
```

**Parameters**

*N*

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

*DL*

```
!>          DL is COMPLEX 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-1) multipliers that
!>          define the matrix L from the LU factorization of A.
!>
```

*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 the
!>          upper triangular matrix U from the LU factorization of A.
!>
```

*DU*

```
!>          DU is COMPLEX 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.
!>
```

*DU2*

```
!>          DU2 is COMPLEX array, dimension (N-2)
!>          On exit, DU2 is overwritten by 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.
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -k, the k-th argument had an illegal value
!>          > 0:  if INFO = k, U(k,k) is exactly zero. The factorization
!>                has been completed, but the factor U is exactly
!>                singular, and division by zero will occur if it is used
!>                to solve a system of equations.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **123** of file **cgttrf.f**.

### subroutine dgttrf (integer n, double precision, dimension( \* ) dl, double precision, dimension( \* ) d, double precision, dimension( \* ) du, double precision, dimension( \* ) du2, integer, dimension( \* ) ipiv, integer info)

**DGTTRF**

**Purpose:**

```
!>
!> DGTTRF computes an LU factorization of a real tridiagonal matrix A
!> using elimination with partial pivoting and row interchanges.
!>
!> The factorization has the form
!>    A = L * U
!> where L is a product of permutation and unit lower bidiagonal
!> matrices and U is upper triangular with nonzeros in only the main
!> diagonal and first two superdiagonals.
!>
```

**Parameters**

*N*

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

*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-1) multipliers that
!>          define the matrix L from the LU factorization of A.
!>
```

*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 the
!>          upper triangular matrix U from the LU factorization of A.
!>
```

*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.
!>
```

*DU2*

```
!>          DU2 is DOUBLE PRECISION array, dimension (N-2)
!>          On exit, DU2 is overwritten by 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.
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -k, the k-th argument had an illegal value
!>          > 0:  if INFO = k, U(k,k) is exactly zero. The factorization
!>                has been completed, but the factor U is exactly
!>                singular, and division by zero will occur if it is used
!>                to solve a system of equations.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **123** of file **dgttrf.f**.

### subroutine sgttrf (integer n, real, dimension( \* ) dl, real, dimension( \* ) d, real, dimension( \* ) du, real, dimension( \* ) du2, integer, dimension( \* ) ipiv, integer info)

**SGTTRF**

**Purpose:**

```
!>
!> SGTTRF computes an LU factorization of a real tridiagonal matrix A
!> using elimination with partial pivoting and row interchanges.
!>
!> The factorization has the form
!>    A = L * U
!> where L is a product of permutation and unit lower bidiagonal
!> matrices and U is upper triangular with nonzeros in only the main
!> diagonal and first two superdiagonals.
!>
```

**Parameters**

*N*

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

*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-1) multipliers that
!>          define the matrix L from the LU factorization of A.
!>
```

*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 the
!>          upper triangular matrix U from the LU factorization of A.
!>
```

*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.
!>
```

*DU2*

```
!>          DU2 is REAL array, dimension (N-2)
!>          On exit, DU2 is overwritten by 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.
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -k, the k-th argument had an illegal value
!>          > 0:  if INFO = k, U(k,k) is exactly zero. The factorization
!>                has been completed, but the factor U is exactly
!>                singular, and division by zero will occur if it is used
!>                to solve a system of equations.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **123** of file **sgttrf.f**.

### subroutine zgttrf (integer n, complex\*16, dimension( \* ) dl, complex\*16, dimension( \* ) d, complex\*16, dimension( \* ) du, complex\*16, dimension( \* ) du2, integer, dimension( \* ) ipiv, integer info)

**ZGTTRF**

**Purpose:**

```
!>
!> ZGTTRF computes an LU factorization of a complex tridiagonal matrix A
!> using elimination with partial pivoting and row interchanges.
!>
!> The factorization has the form
!>    A = L * U
!> where L is a product of permutation and unit lower bidiagonal
!> matrices and U is upper triangular with nonzeros in only the main
!> diagonal and first two superdiagonals.
!>
```

**Parameters**

*N*

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

*DL*

```
!>          DL is COMPLEX*16 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-1) multipliers that
!>          define the matrix L from the LU factorization of A.
!>
```

*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 the
!>          upper triangular matrix U from the LU factorization of A.
!>
```

*DU*

```
!>          DU is COMPLEX*16 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.
!>
```

*DU2*

```
!>          DU2 is COMPLEX*16 array, dimension (N-2)
!>          On exit, DU2 is overwritten by 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.
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -k, the k-th argument had an illegal value
!>          > 0:  if INFO = k, U(k,k) is exactly zero. The factorization
!>                has been completed, but the factor U is exactly
!>                singular, and division by zero will occur if it is used
!>                to solve a system of equations.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **123** of file **zgttrf.f**.

## Author

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