F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF06SNF (ZGERC)

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

F06SNF (ZGERC) computes the rank-1 update of a complex general matrix using a conjugated vector.

## 2  Specification

 SUBROUTINE F06SNF ( M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
 INTEGER M, N, INCX, INCY, LDA COMPLEX (KIND=nag_wp) ALPHA, X(*), Y(*), A(LDA,*)
The routine may be called by its BLAS name zgerc.

## 3  Description

F06SNF (ZGERC) performs the rank-1 update operation
 $A←αxyH + A ,$
where $A$ is an $m$ by $n$ complex matrix, $x$ is an $m$ element complex vector, $y$ is an $n$-element complex vector, and $\alpha$ is a complex scalar.

None.

## 5  Parameters

1:     M – INTEGERInput
On entry: $m$, the number of rows of the matrix $A$.
Constraint: ${\mathbf{M}}\ge 0$.
2:     N – INTEGERInput
On entry: $n$, the number of columns of the matrix $A$.
Constraint: ${\mathbf{N}}\ge 0$.
3:     ALPHA – COMPLEX (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 $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{M}}-1\right)×\left|{\mathbf{INCX}}\right|\right)$.
On entry: the $m$ 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 $\mathit{i}=1,2,\dots ,{\mathbf{M}}$.
If ${\mathbf{INCX}}<0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{X}}\left(1–\left({\mathbf{M}}–\mathit{i}\right)×{\mathbf{INCX}}\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{M}}$.
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:     Y($*$) – COMPLEX (KIND=nag_wp) arrayInput
Note: the dimension of the array Y must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{N}}-1\right)×\left|{\mathbf{INCY}}\right|\right)$.
On entry: the $n$-element vector $y$.
If ${\mathbf{INCY}}>0$, ${y}_{\mathit{i}}$ must be stored in ${\mathbf{Y}}\left(1+\left(\mathit{i}-1\right)×{\mathbf{INCY}}\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{N}}$.
If ${\mathbf{INCY}}<0$, ${y}_{\mathit{i}}$ must be stored in ${\mathbf{Y}}\left(1-\left({\mathbf{N}}-\mathit{i}\right)×{\mathbf{INCY}}\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{N}}$.
Intermediate elements of Y are not referenced.
7:     INCY – INTEGERInput
On entry: the increment in the subscripts of Y between successive elements of $y$.
Constraint: ${\mathbf{INCY}}\ne 0$.
8:     A(LDA,$*$) – COMPLEX (KIND=nag_wp) arrayInput/Output
Note: the second dimension of the array A must be at least ${\mathbf{N}}$.
On entry: the $m$ by $n$ matrix $A$.
On exit: the updated matrix $A$.
9:     LDA – INTEGERInput
On entry: the first dimension of the array A as declared in the (sub)program from which F06SNF (ZGERC) is called.
Constraint: ${\mathbf{LDA}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{M}}\right)$.

None.

Not applicable.