---
name: "pptrs"
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/pptrs"
---

# pptrs(3)

pptrs: triangular solve using factor

## NAME

pptrs - pptrs: triangular solve using factor

## SYNOPSIS

### Functions

subroutine **cpptrs** (uplo, n, nrhs, ap, b, ldb, info)\
 **CPPTRS**  subroutine **dpptrs** (uplo, n, nrhs, ap, b, ldb, info)\
 **DPPTRS**  subroutine **spptrs** (uplo, n, nrhs, ap, b, ldb, info)\
 **SPPTRS**  subroutine **zpptrs** (uplo, n, nrhs, ap, b, ldb, info)\
 **ZPPTRS**

## Detailed Description

## Function Documentation

### subroutine cpptrs (character uplo, integer n, integer nrhs, complex, dimension( \* ) ap, complex, dimension( ldb, \* ) b, integer ldb, integer info)

**CPPTRS**

**Purpose:**

```
!>
!> CPPTRS solves a system of linear equations A*X = B with a Hermitian
!> positive definite matrix A in packed storage using the Cholesky
!> factorization A = U**H*U or A = L*L**H computed by CPPTRF.
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>
```

*N*

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

*NRHS*

```
!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!>
```

*AP*

```
!>          AP is COMPLEX array, dimension (N*(N+1)/2)
!>          The triangular factor U or L from the Cholesky factorization
!>          A = U**H*U or A = L*L**H, packed columnwise in a linear
!>          array.  The j-th column of U or L is stored in the array AP
!>          as follows:
!>          if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
!>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
!>
```

*B*

```
!>          B is COMPLEX array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B.
!>          On exit, the solution matrix 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 **107** of file **cpptrs.f**.

### subroutine dpptrs (character uplo, integer n, integer nrhs, double precision, dimension( \* ) ap, double precision, dimension( ldb, \* ) b, integer ldb, integer info)

**DPPTRS**

**Purpose:**

```
!>
!> DPPTRS solves a system of linear equations A*X = B with a symmetric
!> positive definite matrix A in packed storage using the Cholesky
!> factorization A = U**T*U or A = L*L**T computed by DPPTRF.
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>
```

*N*

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

*NRHS*

```
!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!>
```

*AP*

```
!>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
!>          The triangular factor U or L from the Cholesky factorization
!>          A = U**T*U or A = L*L**T, packed columnwise in a linear
!>          array.  The j-th column of U or L is stored in the array AP
!>          as follows:
!>          if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
!>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
!>
```

*B*

```
!>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B.
!>          On exit, the solution matrix 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 **107** of file **dpptrs.f**.

### subroutine spptrs (character uplo, integer n, integer nrhs, real, dimension( \* ) ap, real, dimension( ldb, \* ) b, integer ldb, integer info)

**SPPTRS**

**Purpose:**

```
!>
!> SPPTRS solves a system of linear equations A*X = B with a symmetric
!> positive definite matrix A in packed storage using the Cholesky
!> factorization A = U**T*U or A = L*L**T computed by SPPTRF.
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>
```

*N*

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

*NRHS*

```
!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!>
```

*AP*

```
!>          AP is REAL array, dimension (N*(N+1)/2)
!>          The triangular factor U or L from the Cholesky factorization
!>          A = U**T*U or A = L*L**T, packed columnwise in a linear
!>          array.  The j-th column of U or L is stored in the array AP
!>          as follows:
!>          if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
!>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
!>
```

*B*

```
!>          B is REAL array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B.
!>          On exit, the solution matrix 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 **107** of file **spptrs.f**.

### subroutine zpptrs (character uplo, integer n, integer nrhs, complex\*16, dimension( \* ) ap, complex\*16, dimension( ldb, \* ) b, integer ldb, integer info)

**ZPPTRS**

**Purpose:**

```
!>
!> ZPPTRS solves a system of linear equations A*X = B with a Hermitian
!> positive definite matrix A in packed storage using the Cholesky
!> factorization A = U**H * U or A = L * L**H computed by ZPPTRF.
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>
```

*N*

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

*NRHS*

```
!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!>
```

*AP*

```
!>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
!>          The triangular factor U or L from the Cholesky factorization
!>          A = U**H * U or A = L * L**H, packed columnwise in a linear
!>          array.  The j-th column of U or L is stored in the array AP
!>          as follows:
!>          if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
!>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
!>
```

*B*

```
!>          B is COMPLEX*16 array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B.
!>          On exit, the solution matrix 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 **107** of file **zpptrs.f**.

## Author

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