---
name: "pttrf"
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/pttrf"
---

# pttrf(3)

pttrf: triangular factor

## NAME

pttrf - pttrf: triangular factor

## SYNOPSIS

### Functions

subroutine **cpttrf** (n, d, e, info)\
 **CPTTRF**  subroutine **dpttrf** (n, d, e, info)\
 **DPTTRF**  subroutine **spttrf** (n, d, e, info)\
 **SPTTRF**  subroutine **zpttrf** (n, d, e, info)\
 **ZPTTRF**

## Detailed Description

## Function Documentation

### subroutine cpttrf (integer n, real, dimension( \* ) d, complex, dimension( \* ) e, integer info)

**CPTTRF**

**Purpose:**

```
!>
!> CPTTRF computes the L*D*L**H factorization of a complex Hermitian
!> positive definite tridiagonal matrix A.  The factorization may also
!> be regarded as having the form A = U**H *D*U.
!>
```

**Parameters**

*N*

```
!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>
```

*D*

```
!>          D is REAL array, dimension (N)
!>          On entry, the n diagonal elements of the tridiagonal matrix
!>          A.  On exit, the n diagonal elements of the diagonal matrix
!>          D from the L*D*L**H factorization of A.
!>
```

*E*

```
!>          E is COMPLEX array, dimension (N-1)
!>          On entry, the (n-1) subdiagonal elements of the tridiagonal
!>          matrix A.  On exit, the (n-1) subdiagonal elements of the
!>          unit bidiagonal factor L from the L*D*L**H factorization of A.
!>          E can also be regarded as the superdiagonal of the unit
!>          bidiagonal factor U from the U**H *D*U factorization of A.
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -k, the k-th argument had an illegal value
!>          > 0: if INFO = k, the leading principal minor of order k
!>               is not positive; if k < N, the factorization could not
!>               be completed, while if k = N, the factorization was
!>               completed, but D(N) <= 0.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **91** of file **cpttrf.f**.

### subroutine dpttrf (integer n, double precision, dimension( \* ) d, double precision, dimension( \* ) e, integer info)

**DPTTRF**

**Purpose:**

```
!>
!> DPTTRF computes the L*D*L**T factorization of a real symmetric
!> positive definite tridiagonal matrix A.  The factorization may also
!> be regarded as having the form A = U**T*D*U.
!>
```

**Parameters**

*N*

```
!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>
```

*D*

```
!>          D is DOUBLE PRECISION array, dimension (N)
!>          On entry, the n diagonal elements of the tridiagonal matrix
!>          A.  On exit, the n diagonal elements of the diagonal matrix
!>          D from the L*D*L**T factorization of A.
!>
```

*E*

```
!>          E is DOUBLE PRECISION array, dimension (N-1)
!>          On entry, the (n-1) subdiagonal elements of the tridiagonal
!>          matrix A.  On exit, the (n-1) subdiagonal elements of the
!>          unit bidiagonal factor L from the L*D*L**T factorization of A.
!>          E can also be regarded as the superdiagonal of the unit
!>          bidiagonal factor U from the U**T*D*U factorization of A.
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -k, the k-th argument had an illegal value
!>          > 0: if INFO = k, the leading principal minor of order k
!>               is not positive; if k < N, the factorization could not
!>               be completed, while if k = N, the factorization was
!>               completed, but D(N) <= 0.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **90** of file **dpttrf.f**.

### subroutine spttrf (integer n, real, dimension( \* ) d, real, dimension( \* ) e, integer info)

**SPTTRF**

**Purpose:**

```
!>
!> SPTTRF computes the L*D*L**T factorization of a real symmetric
!> positive definite tridiagonal matrix A.  The factorization may also
!> be regarded as having the form A = U**T*D*U.
!>
```

**Parameters**

*N*

```
!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>
```

*D*

```
!>          D is REAL array, dimension (N)
!>          On entry, the n diagonal elements of the tridiagonal matrix
!>          A.  On exit, the n diagonal elements of the diagonal matrix
!>          D from the L*D*L**T factorization of A.
!>
```

*E*

```
!>          E is REAL array, dimension (N-1)
!>          On entry, the (n-1) subdiagonal elements of the tridiagonal
!>          matrix A.  On exit, the (n-1) subdiagonal elements of the
!>          unit bidiagonal factor L from the L*D*L**T factorization of A.
!>          E can also be regarded as the superdiagonal of the unit
!>          bidiagonal factor U from the U**T*D*U factorization of A.
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -k, the k-th argument had an illegal value
!>          > 0: if INFO = k, the leading principal minor of order k
!>               is not positive; if k < N, the factorization could not
!>               be completed, while if k = N, the factorization was
!>               completed, but D(N) <= 0.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **90** of file **spttrf.f**.

### subroutine zpttrf (integer n, double precision, dimension( \* ) d, complex\*16, dimension( \* ) e, integer info)

**ZPTTRF**

**Purpose:**

```
!>
!> ZPTTRF computes the L*D*L**H factorization of a complex Hermitian
!> positive definite tridiagonal matrix A.  The factorization may also
!> be regarded as having the form A = U**H *D*U.
!>
```

**Parameters**

*N*

```
!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>
```

*D*

```
!>          D is DOUBLE PRECISION array, dimension (N)
!>          On entry, the n diagonal elements of the tridiagonal matrix
!>          A.  On exit, the n diagonal elements of the diagonal matrix
!>          D from the L*D*L**H factorization of A.
!>
```

*E*

```
!>          E is COMPLEX*16 array, dimension (N-1)
!>          On entry, the (n-1) subdiagonal elements of the tridiagonal
!>          matrix A.  On exit, the (n-1) subdiagonal elements of the
!>          unit bidiagonal factor L from the L*D*L**H factorization of A.
!>          E can also be regarded as the superdiagonal of the unit
!>          bidiagonal factor U from the U**H *D*U factorization of A.
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -k, the k-th argument had an illegal value
!>          > 0: if INFO = k, the leading principal minor of order k
!>               is not positive; if k < N, the factorization could not
!>               be completed, while if k = N, the factorization was
!>               completed, but D(N) <= 0.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **91** of file **zpttrf.f**.

## Author

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