---
name: "hptri"
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/hptri"
---

# hptri(3)

{hp,sp}tri: triangular inverse

## NAME

hptri - {hp,sp}tri: triangular inverse

## SYNOPSIS

### Functions

subroutine **chptri** (uplo, n, ap, ipiv, work, info)\
 **CHPTRI**  subroutine **csptri** (uplo, n, ap, ipiv, work, info)\
 **CSPTRI**  subroutine **dsptri** (uplo, n, ap, ipiv, work, info)\
 **DSPTRI**  subroutine **ssptri** (uplo, n, ap, ipiv, work, info)\
 **SSPTRI**  subroutine **zhptri** (uplo, n, ap, ipiv, work, info)\
 **ZHPTRI**  subroutine **zsptri** (uplo, n, ap, ipiv, work, info)\
 **ZSPTRI**

## Detailed Description

## Function Documentation

### subroutine chptri (character uplo, integer n, complex, dimension( \* ) ap, integer, dimension( \* ) ipiv, complex, dimension( \* ) work, integer info)

**CHPTRI**

**Purpose:**

```
!>
!> CHPTRI computes the inverse of a complex Hermitian indefinite matrix
!> A in packed storage 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.
!>
```

*AP*

```
!>          AP is COMPLEX array, dimension (N*(N+1)/2)
!>          On entry, 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.
!>
!>          On exit, if INFO = 0, the (Hermitian) inverse of the original
!>          matrix, stored as a packed triangular matrix. The j-th column
!>          of inv(A) is stored in the array AP as follows:
!>          if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
!>          if UPLO = 'L',
!>             AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.
!>
```

*IPIV*

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

*WORK*

```
!>          WORK is COMPLEX array, dimension (N)
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -i, the i-th argument had an illegal value
!>          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
!>               inverse could not be computed.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **108** of file **chptri.f**.

### subroutine csptri (character uplo, integer n, complex, dimension( \* ) ap, integer, dimension( \* ) ipiv, complex, dimension( \* ) work, integer info)

**CSPTRI**

**Purpose:**

```
!>
!> CSPTRI computes the inverse of a complex symmetric indefinite matrix
!> A in packed storage 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.
!>
```

*AP*

```
!>          AP is COMPLEX array, dimension (N*(N+1)/2)
!>          On entry, 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.
!>
!>          On exit, if INFO = 0, the (symmetric) inverse of the original
!>          matrix, stored as a packed triangular matrix. The j-th column
!>          of inv(A) is stored in the array AP as follows:
!>          if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
!>          if UPLO = 'L',
!>             AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.
!>
```

*IPIV*

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

*WORK*

```
!>          WORK is COMPLEX array, dimension (N)
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -i, the i-th argument had an illegal value
!>          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
!>               inverse could not be computed.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **108** of file **csptri.f**.

### subroutine dsptri (character uplo, integer n, double precision, dimension( \* ) ap, integer, dimension( \* ) ipiv, double precision, dimension( \* ) work, integer info)

**DSPTRI**

**Purpose:**

```
!>
!> DSPTRI computes the inverse of a real symmetric indefinite matrix
!> A in packed storage 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.
!>
```

*AP*

```
!>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
!>          On entry, 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.
!>
!>          On exit, if INFO = 0, the (symmetric) inverse of the original
!>          matrix, stored as a packed triangular matrix. The j-th column
!>          of inv(A) is stored in the array AP as follows:
!>          if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
!>          if UPLO = 'L',
!>             AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.
!>
```

*IPIV*

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

*WORK*

```
!>          WORK is DOUBLE PRECISION array, dimension (N)
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -i, the i-th argument had an illegal value
!>          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
!>               inverse could not be computed.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **108** of file **dsptri.f**.

### subroutine ssptri (character uplo, integer n, real, dimension( \* ) ap, integer, dimension( \* ) ipiv, real, dimension( \* ) work, integer info)

**SSPTRI**

**Purpose:**

```
!>
!> SSPTRI computes the inverse of a real symmetric indefinite matrix
!> A in packed storage 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.
!>
```

*AP*

```
!>          AP is REAL array, dimension (N*(N+1)/2)
!>          On entry, 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.
!>
!>          On exit, if INFO = 0, the (symmetric) inverse of the original
!>          matrix, stored as a packed triangular matrix. The j-th column
!>          of inv(A) is stored in the array AP as follows:
!>          if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
!>          if UPLO = 'L',
!>             AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.
!>
```

*IPIV*

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

*WORK*

```
!>          WORK is REAL array, dimension (N)
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -i, the i-th argument had an illegal value
!>          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
!>               inverse could not be computed.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **108** of file **ssptri.f**.

### subroutine zhptri (character uplo, integer n, complex\*16, dimension( \* ) ap, integer, dimension( \* ) ipiv, complex\*16, dimension( \* ) work, integer info)

**ZHPTRI**

**Purpose:**

```
!>
!> ZHPTRI computes the inverse of a complex Hermitian indefinite matrix
!> A in packed storage 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.
!>
```

*AP*

```
!>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
!>          On entry, 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.
!>
!>          On exit, if INFO = 0, the (Hermitian) inverse of the original
!>          matrix, stored as a packed triangular matrix. The j-th column
!>          of inv(A) is stored in the array AP as follows:
!>          if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
!>          if UPLO = 'L',
!>             AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.
!>
```

*IPIV*

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

*WORK*

```
!>          WORK is COMPLEX*16 array, dimension (N)
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -i, the i-th argument had an illegal value
!>          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
!>               inverse could not be computed.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **108** of file **zhptri.f**.

### subroutine zsptri (character uplo, integer n, complex\*16, dimension( \* ) ap, integer, dimension( \* ) ipiv, complex\*16, dimension( \* ) work, integer info)

**ZSPTRI**

**Purpose:**

```
!>
!> ZSPTRI computes the inverse of a complex symmetric indefinite matrix
!> A in packed storage 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.
!>
```

*AP*

```
!>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
!>          On entry, 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.
!>
!>          On exit, if INFO = 0, the (symmetric) inverse of the original
!>          matrix, stored as a packed triangular matrix. The j-th column
!>          of inv(A) is stored in the array AP as follows:
!>          if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
!>          if UPLO = 'L',
!>             AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.
!>
```

*IPIV*

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

*WORK*

```
!>          WORK is COMPLEX*16 array, dimension (N)
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -i, the i-th argument had an illegal value
!>          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
!>               inverse could not be computed.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **108** of file **zsptri.f**.

## Author

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