# NAG Library Function Document

## 1Purpose

nag_zamax_val (f16jsc) computes, with respect to absolute value, the largest component of a complex vector, along with the index of that component.

## 2Specification

 #include #include
 void nag_zamax_val (Integer n, const Complex x[], Integer incx, Integer *k, double *r, NagError *fail)

## 3Description

nag_zamax_val (f16jsc) computes, with respect to absolute value, the largest component, $r$, of an $n$-element complex vector $x$, and determines the smallest index, $k$, such that
 $r = Re⁡xk + Im⁡xk = maxj Re⁡xj + Im⁡xj .$

## 4References

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

## 5Arguments

1:    $\mathbf{n}$IntegerInput
On entry: $n$, the number of elements in $x$.
Constraint: ${\mathbf{n}}\ge 0$.
2:    $\mathbf{x}\left[\mathit{dim}\right]$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 $n$-element vector $x$.
If ${\mathbf{incx}}>0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{x}}\left[\left(\mathit{i}-1\right)×{\mathbf{incx}}\right]$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
If ${\mathbf{incx}}<0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{x}}\left[\left({\mathbf{n}}-\mathit{i}\right)×\left|{\mathbf{incx}}\right|\right]$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
Intermediate elements of x are not referenced. If ${\mathbf{n}}=0$, x is not referenced and may be NULL.
3:    $\mathbf{incx}$IntegerInput
On entry: the increment in the subscripts of x between successive elements of $x$.
Constraint: ${\mathbf{incx}}\ne 0$.
4:    $\mathbf{k}$Integer *Output
On exit: $k$, the index, from the set $\left\{0,1,\dots ,{\mathbf{n}}-1\right\}$, of the largest component of $x$ with respect to absolute value. If ${\mathbf{n}}=0$ on input then k is returned as $-1$.
5:    $\mathbf{r}$double *Output
On exit: $r$, the largest component of $x$ with respect to absolute value. If ${\mathbf{n}}=0$ on input then r is returned as $0.0$.
6:    $\mathbf{fail}$NagError *Input/Output
The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

## 6Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
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, ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{n}}\ge 0$.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

## 7Accuracy

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

## 8Parallelism and Performance

nag_zamax_val (f16jsc) is not threaded in any implementation.

None.

## 10Example

This example computes the largest component with respect to absolute value and index of that component for the vector
 $x= -4+2.1i,3.7+4.5i,-6+1.2iT .$

### 10.1Program Text

Program Text (f16jsce.c)

### 10.2Program Data

Program Data (f16jsce.d)

### 10.3Program Results

Program Results (f16jsce.r)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017