# 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

Univ. of Colorado Denver

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