---
name: "hptrs"
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/hptrs"
---

# hptrs(3)

{hp,sp}trs: triangular solve using factor

## NAME

hptrs - {hp,sp}trs: triangular solve using factor

## SYNOPSIS

### Functions

subroutine **chptrs** (uplo, n, nrhs, ap, ipiv, b, ldb, info)\
 **CHPTRS**  subroutine **csptrs** (uplo, n, nrhs, ap, ipiv, b, ldb, info)\
 **CSPTRS**  subroutine **dsptrs** (uplo, n, nrhs, ap, ipiv, b, ldb, info)\
 **DSPTRS**  subroutine **ssptrs** (uplo, n, nrhs, ap, ipiv, b, ldb, info)\
 **SSPTRS**  subroutine **zhptrs** (uplo, n, nrhs, ap, ipiv, b, ldb, info)\
 **ZHPTRS**  subroutine **zsptrs** (uplo, n, nrhs, ap, ipiv, b, ldb, info)\
 **ZSPTRS**

## Detailed Description

## Function Documentation

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

**CHPTRS**

**Purpose:**

```
!>
!> CHPTRS solves a system of linear equations A*X = B with a complex
!> Hermitian matrix A stored in packed format using the factorization
!> A = U*D*U**H or A = L*D*L**H computed by CHPTRF.
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix.
!>          = 'U':  Upper triangular, form is A = U*D*U**H;
!>          = 'L':  Lower triangular, form is A = L*D*L**H.
!>
```

*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 block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by CHPTRF, stored as a
!>          packed triangular matrix.
!>
```

*IPIV*

```
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by CHPTRF.
!>
```

*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 **114** of file **chptrs.f**.

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

**CSPTRS**

**Purpose:**

```
!>
!> CSPTRS solves a system of linear equations A*X = B with a complex
!> symmetric matrix A stored in packed format using the factorization
!> A = U*D*U**T or A = L*D*L**T computed by CSPTRF.
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix.
!>          = 'U':  Upper triangular, form is A = U*D*U**T;
!>          = 'L':  Lower triangular, form is A = L*D*L**T.
!>
```

*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 block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by CSPTRF, stored as a
!>          packed triangular matrix.
!>
```

*IPIV*

```
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by CSPTRF.
!>
```

*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 **114** of file **csptrs.f**.

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

**DSPTRS**

**Purpose:**

```
!>
!> DSPTRS solves a system of linear equations A*X = B with a real
!> symmetric matrix A stored in packed format using the factorization
!> A = U*D*U**T or A = L*D*L**T computed by DSPTRF.
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix.
!>          = 'U':  Upper triangular, form is A = U*D*U**T;
!>          = 'L':  Lower triangular, form is A = L*D*L**T.
!>
```

*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 block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by DSPTRF, stored as a
!>          packed triangular matrix.
!>
```

*IPIV*

```
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by DSPTRF.
!>
```

*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 **114** of file **dsptrs.f**.

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

**SSPTRS**

**Purpose:**

```
!>
!> SSPTRS solves a system of linear equations A*X = B with a real
!> symmetric matrix A stored in packed format using the factorization
!> A = U*D*U**T or A = L*D*L**T computed by SSPTRF.
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix.
!>          = 'U':  Upper triangular, form is A = U*D*U**T;
!>          = 'L':  Lower triangular, form is A = L*D*L**T.
!>
```

*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 block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by SSPTRF, stored as a
!>          packed triangular matrix.
!>
```

*IPIV*

```
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by SSPTRF.
!>
```

*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 **114** of file **ssptrs.f**.

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

**ZHPTRS**

**Purpose:**

```
!>
!> ZHPTRS solves a system of linear equations A*X = B with a complex
!> Hermitian matrix A stored in packed format using the factorization
!> A = U*D*U**H or A = L*D*L**H computed by ZHPTRF.
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix.
!>          = 'U':  Upper triangular, form is A = U*D*U**H;
!>          = 'L':  Lower triangular, form is A = L*D*L**H.
!>
```

*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 block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by ZHPTRF, stored as a
!>          packed triangular matrix.
!>
```

*IPIV*

```
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by ZHPTRF.
!>
```

*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 **114** of file **zhptrs.f**.

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

**ZSPTRS**

**Purpose:**

```
!>
!> ZSPTRS solves a system of linear equations A*X = B with a complex
!> symmetric matrix A stored in packed format using the factorization
!> A = U*D*U**T or A = L*D*L**T computed by ZSPTRF.
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix.
!>          = 'U':  Upper triangular, form is A = U*D*U**T;
!>          = 'L':  Lower triangular, form is A = L*D*L**T.
!>
```

*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 block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by ZSPTRF, stored as a
!>          packed triangular matrix.
!>
```

*IPIV*

```
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by ZSPTRF.
!>
```

*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 **114** of file **zsptrs.f**.

## Author

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