---
name: "zspr"
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/zspr.f"
---

# zspr(3)

Part of [zspr.f(3)](/zspr.f/3.md).

## NAME

SRC/zspr.f

## SYNOPSIS

### Functions/Subroutines

subroutine **zspr** (uplo, n, alpha, x, incx, ap)\
 **ZSPR** performs the symmetrical rank-1 update of a complex symmetric packed matrix.

## Function/Subroutine Documentation

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

**ZSPR** performs the symmetrical rank-1 update of a complex symmetric packed matrix.

**Purpose:**

```
!>
!> ZSPR    performs the symmetric rank 1 operation
!>
!>    A := alpha*x*x**H + A,
!>
!> where alpha is a complex scalar, x is an n element vector 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.
!>
!>           Unchanged on exit.
!>
```

*N*

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

*ALPHA*

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

*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.
!>           Unchanged on exit.
!>
```

*INCX*

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

*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 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.
!>           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.

Definition at line **131** of file **zspr.f**.

## Author

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