# cspr.f man page

cspr.f

## Synopsis

### Functions/Subroutines

subroutine cspr (UPLO, N, ALPHA, X, INCX, AP)
CSPR performs the symmetrical rank-1 update of a complex symmetric packed matrix.

## Function/Subroutine Documentation

### subroutine cspr (character UPLO, integer N, complex ALPHA, complex, dimension( * ) X, integer INCX, complex, dimension( * ) AP)

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

Purpose:

``` CSPR    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
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.```

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.
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 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.

Date:

December 2016

Definition at line 134 of file cspr.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 14 2017 Version 3.8.0 LAPACK