# NAG FL Interfacef16jsf (zamax_​val)

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## 1Purpose

f16jsf computes, with respect to absolute value, the largest component of a complex vector, along with the index of that component.

## 2Specification

Fortran Interface
 Subroutine f16jsf ( n, x, incx, k, r)
 Integer, Intent (In) :: n, incx Integer, Intent (Out) :: k Real (Kind=nag_wp), Intent (Out) :: r Complex (Kind=nag_wp), Intent (In) :: x(1+(n-1)*ABS(incx))
#include <nag.h>
 void f16jsf_ (const Integer *n, const Complex x[], const Integer *incx, Integer *k, double *r)
The routine may be called by the names f16jsf, nagf_blast_zamax_val or its BLAST name blas_zamax_val.

## 3Description

f16jsf 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 https://www.netlib.org/blas/blast-forum/blas-report.pdf

## 5Arguments

1: $\mathbf{n}$Integer Input
On entry: $n$, the number of elements in $x$.
2: $\mathbf{x}\left(1+\left({\mathbf{n}}-1\right)×|{\mathbf{incx}}|\right)$Complex (Kind=nag_wp) array Input
On entry: the $n$-element vector $x$.
If ${\mathbf{incx}}>0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{x}}\left(\left(\mathit{i}-1\right)×{\mathbf{incx}}+1\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
If ${\mathbf{incx}}<0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{x}}\left(\left({\mathbf{n}}-\mathit{i}\right)×|{\mathbf{incx}}|+1\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
Intermediate elements of x are not referenced. If ${\mathbf{n}}=0$, x is not referenced.
3: $\mathbf{incx}$Integer Input
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 $\left\{1,2,\dots ,{\mathbf{n}}\right\}$, of the largest component of $x$ with respect to absolute value. If ${\mathbf{n}}\le 0$ on input then k is returned as $0$.
5: $\mathbf{r}$Real (Kind=nag_wp) Output
On exit: $r$, the largest component of $x$ with respect to absolute value. If ${\mathbf{n}}\le 0$ on input then r is returned as $0.0$.

## 6Error Indicators and Warnings

If ${\mathbf{incx}}=0$, an error message is printed and program execution is terminated.

## 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

f16jsf 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
 $x= (-4+2.1i,3.7+4.5i,-6+1.2i) T .$

### 10.1Program Text

Program Text (f16jsfe.f90)

### 10.2Program Data

Program Data (f16jsfe.d)

### 10.3Program Results

Program Results (f16jsfe.r)