F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF06SPF (ZHER)

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

## 1  Purpose

F06SPF (ZHER) computes the rank-1 update of a complex Hermitian matrix.

## 2  Specification

 SUBROUTINE F06SPF ( UPLO, N, ALPHA, X, INCX, A, LDA)
 INTEGER N, INCX, LDA REAL (KIND=nag_wp) ALPHA COMPLEX (KIND=nag_wp) X(*), A(LDA,*) CHARACTER(1) UPLO
The routine may be called by its BLAS name zher.

## 3  Description

F06SPF (ZHER) performs the Hermitian rank-1 update operation
 $A←αxxH+A ,$
where $A$ is an $n$ by $n$ complex Hermitian matrix, $x$ is an $n$-element complex vector, and $\alpha$ is a real scalar.

None.

## 5  Parameters

1:     UPLO – CHARACTER(1)Input
On entry: specifies whether the upper or lower triangular part of $A$ is stored.
${\mathbf{UPLO}}=\text{'U'}$
The upper triangular part of $A$ is stored.
${\mathbf{UPLO}}=\text{'L'}$
The lower triangular part of $A$ is stored.
Constraint: ${\mathbf{UPLO}}=\text{'U'}$ or $\text{'L'}$.
2:     N – INTEGERInput
On entry: $n$, the order of the matrix $A$.
Constraint: ${\mathbf{N}}\ge 0$.
3:     ALPHA – REAL (KIND=nag_wp)Input
On entry: the scalar $\alpha$.
4:     X($*$) – COMPLEX (KIND=nag_wp) arrayInput
Note: the dimension of the array X must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{N}}-1\right)×\left|{\mathbf{INCX}}\right|\right)$.
On entry: the $n$-element vector $x$.
If ${\mathbf{INCX}}>0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{X}}\left(1+\left(\mathit{i}-1\right)×{\mathbf{INCX}}\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{N}}$.
If ${\mathbf{INCX}}<0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{X}}\left(1-\left({\mathbf{N}}-\mathit{i}\right)×{\mathbf{INCX}}\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{N}}$.
Intermediate elements of X are not referenced.
5:     INCX – INTEGERInput
On entry: the increment in the subscripts of X between successive elements of $x$.
Constraint: ${\mathbf{INCX}}\ne 0$.
6:     A(LDA,$*$) – COMPLEX (KIND=nag_wp) arrayInput/Output
Note: the second dimension of the array A must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{N}}\right)$.
On entry: the $n$ by $n$ Hermitian matrix $A$.
• If ${\mathbf{UPLO}}=\text{'U'}$, the upper triangular part of $A$ must be stored and the elements of the array below the diagonal are not referenced.
• If ${\mathbf{UPLO}}=\text{'L'}$, the lower triangular part of $A$ must be stored and the elements of the array above the diagonal are not referenced.
On exit: the updated matrix $A$. The imaginary parts of the diagonal elements are set to zero.
7:     LDA – INTEGERInput
On entry: the first dimension of the array A as declared in the (sub)program from which F06SPF (ZHER) is called.
Constraint: ${\mathbf{LDA}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{N}}\right)$.

None.

Not applicable.