---
name: "hpr2"
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/hpr2"
---

# hpr2(3)

{hp,sp}r2: Hermitian/symmetric rank-2 update

## NAME

hpr2 - {hp,sp}r2: Hermitian/symmetric rank-2 update

## SYNOPSIS

### Functions

subroutine **chpr2** (uplo, n, alpha, x, incx, y, incy, ap)\
 **CHPR2**  subroutine **dspr2** (uplo, n, alpha, x, incx, y, incy, ap)\
 **DSPR2**  subroutine **sspr2** (uplo, n, alpha, x, incx, y, incy, ap)\
 **SSPR2**  subroutine **zhpr2** (uplo, n, alpha, x, incx, y, incy, ap)\
 **ZHPR2**

## Detailed Description

## Function Documentation

### subroutine chpr2 (character uplo, integer n, complex alpha, complex, dimension(\*) x, integer incx, complex, dimension(\*) y, integer incy, complex, dimension(\*) ap)

**CHPR2**

**Purpose:**

```
!>
!> CHPR2  performs the hermitian rank 2 operation
!>
!>    A := alpha*x*y**H + conjg( alpha )*y*x**H + A,
!>
!> where alpha is a scalar, x and y are n element vectors and A is an
!> n by n hermitian matrix, supplied in packed form.
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>           On entry, UPLO specifies whether the upper or lower
!>           triangular part of the matrix A is supplied in the packed
!>           array AP as follows:
!>
!>              UPLO = 'U' or 'u'   The upper triangular part of A is
!>                                  supplied in AP.
!>
!>              UPLO = 'L' or 'l'   The lower triangular part of A is
!>                                  supplied in AP.
!>
```

*N*

```
!>          N is INTEGER
!>           On entry, N specifies the order of the matrix A.
!>           N must be at least zero.
!>
```

*ALPHA*

```
!>          ALPHA is COMPLEX
!>           On entry, ALPHA specifies the scalar alpha.
!>
```

*X*

```
!>          X is COMPLEX array, dimension at least
!>           ( 1 + ( n - 1 )*abs( INCX ) ).
!>           Before entry, the incremented array X must contain the n
!>           element vector x.
!>
```

*INCX*

```
!>          INCX is INTEGER
!>           On entry, INCX specifies the increment for the elements of
!>           X. INCX must not be zero.
!>
```

*Y*

```
!>          Y is COMPLEX array, dimension at least
!>           ( 1 + ( n - 1 )*abs( INCY ) ).
!>           Before entry, the incremented array Y must contain the n
!>           element vector y.
!>
```

*INCY*

```
!>          INCY is INTEGER
!>           On entry, INCY specifies the increment for the elements of
!>           Y. INCY must not be zero.
!>
```

*AP*

```
!>          AP is COMPLEX array, dimension at least
!>           ( ( n*( n + 1 ) )/2 ).
!>           Before entry with  UPLO = 'U' or 'u', the array AP must
!>           contain the upper triangular part of the hermitian matrix
!>           packed sequentially, column by column, so that AP( 1 )
!>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
!>           and a( 2, 2 ) respectively, and so on. On exit, the array
!>           AP is overwritten by the upper triangular part of the
!>           updated matrix.
!>           Before entry with UPLO = 'L' or 'l', the array AP must
!>           contain the lower triangular part of the hermitian matrix
!>           packed sequentially, column by column, so that AP( 1 )
!>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
!>           and a( 3, 1 ) respectively, and so on. On exit, the array
!>           AP is overwritten by the lower triangular part of the
!>           updated matrix.
!>           Note that the imaginary parts of the diagonal elements need
!>           not be set, they are assumed to be zero, and on exit they
!>           are set to zero.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

```
!>
!>  Level 2 Blas routine.
!>
!>  -- Written on 22-October-1986.
!>     Jack Dongarra, Argonne National Lab.
!>     Jeremy Du Croz, Nag Central Office.
!>     Sven Hammarling, Nag Central Office.
!>     Richard Hanson, Sandia National Labs.
!>
```

Definition at line **144** of file **chpr2.f**.

### subroutine dspr2 (character uplo, integer n, double precision alpha, double precision, dimension(\*) x, integer incx, double precision, dimension(\*) y, integer incy, double precision, dimension(\*) ap)

**DSPR2**

**Purpose:**

```
!>
!> DSPR2  performs the symmetric rank 2 operation
!>
!>    A := alpha*x*y**T + alpha*y*x**T + A,
!>
!> where alpha is a scalar, x and y are n element vectors and A is an
!> n by n symmetric matrix, supplied in packed form.
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>           On entry, UPLO specifies whether the upper or lower
!>           triangular part of the matrix A is supplied in the packed
!>           array AP as follows:
!>
!>              UPLO = 'U' or 'u'   The upper triangular part of A is
!>                                  supplied in AP.
!>
!>              UPLO = 'L' or 'l'   The lower triangular part of A is
!>                                  supplied in AP.
!>
```

*N*

```
!>          N is INTEGER
!>           On entry, N specifies the order of the matrix A.
!>           N must be at least zero.
!>
```

*ALPHA*

```
!>          ALPHA is DOUBLE PRECISION.
!>           On entry, ALPHA specifies the scalar alpha.
!>
```

*X*

```
!>          X is DOUBLE PRECISION array, dimension at least
!>           ( 1 + ( n - 1 )*abs( INCX ) ).
!>           Before entry, the incremented array X must contain the n
!>           element vector x.
!>
```

*INCX*

```
!>          INCX is INTEGER
!>           On entry, INCX specifies the increment for the elements of
!>           X. INCX must not be zero.
!>
```

*Y*

```
!>          Y is DOUBLE PRECISION array, dimension at least
!>           ( 1 + ( n - 1 )*abs( INCY ) ).
!>           Before entry, the incremented array Y must contain the n
!>           element vector y.
!>
```

*INCY*

```
!>          INCY is INTEGER
!>           On entry, INCY specifies the increment for the elements of
!>           Y. INCY must not be zero.
!>
```

*AP*

```
!>          AP is DOUBLE PRECISION array, dimension at least
!>           ( ( n*( n + 1 ) )/2 ).
!>           Before entry with  UPLO = 'U' or 'u', the array AP must
!>           contain the upper triangular part of the symmetric matrix
!>           packed sequentially, column by column, so that AP( 1 )
!>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
!>           and a( 2, 2 ) respectively, and so on. On exit, the array
!>           AP is overwritten by the upper triangular part of the
!>           updated matrix.
!>           Before entry with UPLO = 'L' or 'l', the array AP must
!>           contain the lower triangular part of the symmetric matrix
!>           packed sequentially, column by column, so that AP( 1 )
!>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
!>           and a( 3, 1 ) respectively, and so on. On exit, the array
!>           AP is overwritten by the lower triangular part of the
!>           updated matrix.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

```
!>
!>  Level 2 Blas routine.
!>
!>  -- Written on 22-October-1986.
!>     Jack Dongarra, Argonne National Lab.
!>     Jeremy Du Croz, Nag Central Office.
!>     Sven Hammarling, Nag Central Office.
!>     Richard Hanson, Sandia National Labs.
!>
```

Definition at line **141** of file **dspr2.f**.

### subroutine sspr2 (character uplo, integer n, real alpha, real, dimension(\*) x, integer incx, real, dimension(\*) y, integer incy, real, dimension(\*) ap)

**SSPR2**

**Purpose:**

```
!>
!> SSPR2  performs the symmetric rank 2 operation
!>
!>    A := alpha*x*y**T + alpha*y*x**T + A,
!>
!> where alpha is a scalar, x and y are n element vectors and A is an
!> n by n symmetric matrix, supplied in packed form.
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>           On entry, UPLO specifies whether the upper or lower
!>           triangular part of the matrix A is supplied in the packed
!>           array AP as follows:
!>
!>              UPLO = 'U' or 'u'   The upper triangular part of A is
!>                                  supplied in AP.
!>
!>              UPLO = 'L' or 'l'   The lower triangular part of A is
!>                                  supplied in AP.
!>
```

*N*

```
!>          N is INTEGER
!>           On entry, N specifies the order of the matrix A.
!>           N must be at least zero.
!>
```

*ALPHA*

```
!>          ALPHA is REAL
!>           On entry, ALPHA specifies the scalar alpha.
!>
```

*X*

```
!>          X is REAL array, dimension at least
!>           ( 1 + ( n - 1 )*abs( INCX ) ).
!>           Before entry, the incremented array X must contain the n
!>           element vector x.
!>
```

*INCX*

```
!>          INCX is INTEGER
!>           On entry, INCX specifies the increment for the elements of
!>           X. INCX must not be zero.
!>
```

*Y*

```
!>          Y is REAL array, dimension at least
!>           ( 1 + ( n - 1 )*abs( INCY ) ).
!>           Before entry, the incremented array Y must contain the n
!>           element vector y.
!>
```

*INCY*

```
!>          INCY is INTEGER
!>           On entry, INCY specifies the increment for the elements of
!>           Y. INCY must not be zero.
!>
```

*AP*

```
!>          AP is REAL array, dimension at least
!>           ( ( n*( n + 1 ) )/2 ).
!>           Before entry with  UPLO = 'U' or 'u', the array AP must
!>           contain the upper triangular part of the symmetric matrix
!>           packed sequentially, column by column, so that AP( 1 )
!>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
!>           and a( 2, 2 ) respectively, and so on. On exit, the array
!>           AP is overwritten by the upper triangular part of the
!>           updated matrix.
!>           Before entry with UPLO = 'L' or 'l', the array AP must
!>           contain the lower triangular part of the symmetric matrix
!>           packed sequentially, column by column, so that AP( 1 )
!>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
!>           and a( 3, 1 ) respectively, and so on. On exit, the array
!>           AP is overwritten by the lower triangular part of the
!>           updated matrix.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

```
!>
!>  Level 2 Blas routine.
!>
!>  -- Written on 22-October-1986.
!>     Jack Dongarra, Argonne National Lab.
!>     Jeremy Du Croz, Nag Central Office.
!>     Sven Hammarling, Nag Central Office.
!>     Richard Hanson, Sandia National Labs.
!>
```

Definition at line **141** of file **sspr2.f**.

### subroutine zhpr2 (character uplo, integer n, complex\*16 alpha, complex\*16, dimension(\*) x, integer incx, complex\*16, dimension(\*) y, integer incy, complex\*16, dimension(\*) ap)

**ZHPR2**

**Purpose:**

```
!>
!> ZHPR2  performs the hermitian rank 2 operation
!>
!>    A := alpha*x*y**H + conjg( alpha )*y*x**H + A,
!>
!> where alpha is a scalar, x and y are n element vectors and A is an
!> n by n hermitian matrix, supplied in packed form.
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>           On entry, UPLO specifies whether the upper or lower
!>           triangular part of the matrix A is supplied in the packed
!>           array AP as follows:
!>
!>              UPLO = 'U' or 'u'   The upper triangular part of A is
!>                                  supplied in AP.
!>
!>              UPLO = 'L' or 'l'   The lower triangular part of A is
!>                                  supplied in AP.
!>
```

*N*

```
!>          N is INTEGER
!>           On entry, N specifies the order of the matrix A.
!>           N must be at least zero.
!>
```

*ALPHA*

```
!>          ALPHA is COMPLEX*16
!>           On entry, ALPHA specifies the scalar alpha.
!>
```

*X*

```
!>          X is COMPLEX*16 array, dimension at least
!>           ( 1 + ( n - 1 )*abs( INCX ) ).
!>           Before entry, the incremented array X must contain the n
!>           element vector x.
!>
```

*INCX*

```
!>          INCX is INTEGER
!>           On entry, INCX specifies the increment for the elements of
!>           X. INCX must not be zero.
!>
```

*Y*

```
!>          Y is COMPLEX*16 array, dimension at least
!>           ( 1 + ( n - 1 )*abs( INCY ) ).
!>           Before entry, the incremented array Y must contain the n
!>           element vector y.
!>
```

*INCY*

```
!>          INCY is INTEGER
!>           On entry, INCY specifies the increment for the elements of
!>           Y. INCY must not be zero.
!>
```

*AP*

```
!>          AP is COMPLEX*16 array, dimension at least
!>           ( ( n*( n + 1 ) )/2 ).
!>           Before entry with  UPLO = 'U' or 'u', the array AP must
!>           contain the upper triangular part of the hermitian matrix
!>           packed sequentially, column by column, so that AP( 1 )
!>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
!>           and a( 2, 2 ) respectively, and so on. On exit, the array
!>           AP is overwritten by the upper triangular part of the
!>           updated matrix.
!>           Before entry with UPLO = 'L' or 'l', the array AP must
!>           contain the lower triangular part of the hermitian matrix
!>           packed sequentially, column by column, so that AP( 1 )
!>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
!>           and a( 3, 1 ) respectively, and so on. On exit, the array
!>           AP is overwritten by the lower triangular part of the
!>           updated matrix.
!>           Note that the imaginary parts of the diagonal elements need
!>           not be set, they are assumed to be zero, and on exit they
!>           are set to zero.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

```
!>
!>  Level 2 Blas routine.
!>
!>  -- Written on 22-October-1986.
!>     Jack Dongarra, Argonne National Lab.
!>     Jeremy Du Croz, Nag Central Office.
!>     Sven Hammarling, Nag Central Office.
!>     Richard Hanson, Sandia National Labs.
!>
```

Definition at line **144** of file **zhpr2.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.