f16 Chapter Contents
f16 Chapter Introduction
NAG Library Manual

# NAG Library Function Documentnag_zamin_val (f16jtc)

## 1  Purpose

nag_zamin_val (f16jtc) computes, with respect to absolute value, the smallest component of a complex vector, along with the index of that component.

## 2  Specification

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

## 3  Description

nag_zamin_val (f16jtc) computes, with respect to absolute value, the smallest component, $r$, of an $n$-element complex vector $x$, and determines the smallest index, $k$, such that
 $r=Re⁡xk+Im⁡xk=minjRe⁡xj+Im⁡xj.$

## 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:     nIntegerInput
On entry: $n$, the number of elements in $x$.
Constraint: ${\mathbf{n}}\ge 0$.
2:     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 $x$. Element ${x}_{\mathit{i}}$ is stored in ${\mathbf{x}}\left[\left(\mathit{i}-1\right)×\left|{\mathbf{incx}}\right|\right]$, for $\mathit{i}=1,2,\dots ,n$.
3:     incxIntegerInput
On entry: the increment in the subscripts of x between successive elements of $x$.
Constraint: ${\mathbf{incx}}\ne 0$.
4:     kInteger *Output
On exit: $k$, the index, from the set $\left\{0,\left|{\mathbf{incx}}\right|,\dots ,\left({\mathbf{n}}-1\right)×\left|{\mathbf{incx}}\right|\right\}$, of the smallest component of $x$ with respect to absolute value. If ${\mathbf{n}}=0$ on input then k is returned as $-1$.
5:     rdouble *Output
On exit: $r$, the smallest component of $x$ with respect to absolute value. If ${\mathbf{n}}=0$ on input then r is returned as $0.0$.
6:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

## 6  Error Indicators and Warnings

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: ${\mathbf{n}}\ge 0$.

## 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

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

### 10.1  Program Text

Program Text (f16jtce.c)

### 10.2  Program Data

Program Data (f16jtce.d)

### 10.3  Program Results

Program Results (f16jtce.r)