f16 Chapter Contents
f16 Chapter Introduction
NAG Library Manual

# NAG Library Function Documentnag_zger (f16smc)

## 1  Purpose

nag_zger (f16smc) performs a rank-1 update on a complex general matrix.

## 2  Specification

 #include #include
 void nag_zger (Nag_OrderType order, Nag_ConjType conj, Integer m, Integer n, Complex alpha, const Complex x[], Integer incx, const Complex y[], Integer incy, Complex beta, Complex a[], Integer pda, NagError *fail)

## 3  Description

nag_zger (f16smc) performs the rank-1 update operation
 $A←αxyT+βA,$
or
 $A←αxyH+βA,$
where $A$ is an $m$ by $n$ complex matrix, $x$ is an $m$ element complex vector, $y$ is an $n$-element complex vector, and $\alpha$ and $\beta$ are complex scalars.

## 4  References

Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001) Basic Linear Algebra Subprograms Technical (BLAST) Forum Standard University of Tennessee, Knoxville, Tennessee http://www.netlib.org/blas/blast-forum/blas-report.pdf

## 5  Arguments

1:     orderNag_OrderTypeInput
On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by ${\mathbf{order}}=\mathrm{Nag_RowMajor}$. See Section 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.
Constraint: ${\mathbf{order}}=\mathrm{Nag_RowMajor}$ or $\mathrm{Nag_ColMajor}$.
2:     conjNag_ConjTypeInput
On entry: the argument conj specifies whether the elements ${y}_{i}$ are used unconjugated or conjugated, as follows:
${\mathbf{conj}}=\mathrm{Nag_NoConj}$
The elements ${y}_{i}$ are not conjugated.
${\mathbf{conj}}=\mathrm{Nag_Conj}$
The complex conjugate of the elements ${y}_{i}$ are used.
Constraint: ${\mathbf{conj}}=\mathrm{Nag_NoConj}$ or $\mathrm{Nag_Conj}$.
3:     mIntegerInput
On entry: $m$, the number of rows of the matrix $A$.
Constraint: ${\mathbf{m}}\ge 0$.
4:     nIntegerInput
On entry: $n$, the number of columns of the matrix $A$.
Constraint: ${\mathbf{n}}\ge 0$.
5:     alphaComplexInput
On entry: the scalar $\alpha$.
6:     x[$\mathit{dim}$]const ComplexInput
Note: the dimension, dim, 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 vector $x$.
7:     incxIntegerInput
On entry: the increment in the subscripts of x between successive elements of $x$.
Constraint: ${\mathbf{incx}}\ne 0$.
8:     y[$\mathit{dim}$]const ComplexInput
Note: the dimension, dim, 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 vector $y$.
9:     incyIntegerInput
On entry: the increment in the subscripts of y between successive elements of $y$.
Constraint: ${\mathbf{incy}}\ne 0$.
10:   betaComplexInput
On entry: the scalar $\beta$.
11:   a[$\mathit{dim}$]ComplexInput/Output
Note: the dimension, dim, of the array a must be at least
• $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{pda}}×{\mathbf{n}}\right)$ when ${\mathbf{order}}=\mathrm{Nag_ColMajor}$;
• $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{m}}×{\mathbf{pda}}\right)$ when ${\mathbf{order}}=\mathrm{Nag_RowMajor}$.
If ${\mathbf{order}}=\mathrm{Nag_ColMajor}$, ${A}_{ij}$ is stored in ${\mathbf{a}}\left[\left(j-1\right)×{\mathbf{pda}}+i-1\right]$.
If ${\mathbf{order}}=\mathrm{Nag_RowMajor}$, ${A}_{ij}$ is stored in ${\mathbf{a}}\left[\left(i-1\right)×{\mathbf{pda}}+j-1\right]$.
On entry: the $m$ by $n$ matrix $A$.
On exit: the updated matrix $A$.
12:   pdaIntegerInput
On entry: the stride separating row or column elements (depending on the value of order) in the array a.
Constraints:
• if ${\mathbf{order}}=\mathrm{Nag_ColMajor}$, ${\mathbf{pda}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{m}}\right)$;
• if ${\mathbf{order}}=\mathrm{Nag_RowMajor}$, ${\mathbf{pda}}\ge {\mathbf{n}}$.
13:   failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

## 6  Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
On entry, argument $⟨\mathit{\text{value}}⟩$ had an illegal value.
NE_INT
On entry, ${\mathbf{incx}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{incx}}\ne 0$.
On entry, ${\mathbf{incy}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{incy}}\ne 0$.
On entry, ${\mathbf{m}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{m}}\ge 0$.
On entry, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{n}}\ge 0$.
NE_INT_2
On entry, ${\mathbf{pda}}=⟨\mathit{\text{value}}⟩$, ${\mathbf{m}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{pda}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{m}}\right)$.
On entry, ${\mathbf{pda}}=⟨\mathit{\text{value}}⟩$ and ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{pda}}\ge {\mathbf{n}}$.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

## 7  Accuracy

The BLAS standard requires accurate implementations which avoid unnecessary over/underflow (see Section 2.7 of Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001)).

Not applicable.

None.

## 10  Example

Perform rank-1 update of complex matrix $A$ using vectors $x$ and $y$:
 $A ← A - x yH ,$
where $A$ is the $3$ by $2$ complex matrix given by
 $A = 4.0+4.0i 2.0+2.0i 4.0+7.0i 4.0+3.0i 11.0+3.0i 9.0+7.0i ,$
and the vectors $x$ and $y$ are
 $x = 2.0+1.0i 3.0+2.0i 5.0-1.0i$
and
 $y = 2.0+1.0i 1.0-2.0i .$
The vector $y$ is stored in every second element of array y (${\mathbf{incy}}=2$).

### 10.1  Program Text

Program Text (f16smce.c)

### 10.2  Program Data

Program Data (f16smce.d)

### 10.3  Program Results

Program Results (f16smce.r)