# zspr.f - Man Page

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

NAG Ltd.

Definition at line 131 of file zspr.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zspr(3) is an alias of zspr.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK