F16 Chapter Contents
F16 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF16DPF

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

F16DPF computes the smallest component of an integer vector, along with the index of that component.

## 2  Specification

 SUBROUTINE F16DPF ( N, X, INCX, K, I)
 INTEGER N, X(1+(N-1)*ABS(INCX)), INCX, K, I

## 3  Description

F16DPF computes the smallest component, $i$, of an $n$-element integer vector $x$, and determines the smallest index, $k$, such that
 $i=xk=minjxj.$

## 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  Parameters

1:     $\mathrm{N}$ – INTEGERInput
On entry: $n$, the number of elements in $x$.
2:     $\mathrm{X}\left(1+\left({\mathbf{N}}-1\right)×\left|{\mathbf{INCX}}\right|\right)$ – INTEGER arrayInput
On entry: the $n$-element vector $x$.
If ${\mathbf{INCX}}>0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{X}}\left(\left(\mathit{i}-1\right)×\left|{\mathbf{INCX}}\right|+1\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{N}}$.
If ${\mathbf{INCX}}<0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{X}}\left(\left({\mathbf{N}}-\mathit{i}\right)×\left|{\mathbf{INCX}}\right|+1\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{N}}$.
Intermediate elements of X are not referenced. If ${\mathbf{N}}=0$, X is not referenced.
3:     $\mathrm{INCX}$ – INTEGERInput
On entry: the increment in the subscripts of X between successive elements of $x$.
Constraint: ${\mathbf{INCX}}\ne 0$.
4:     $\mathrm{K}$ – INTEGEROutput
On exit: $k$, the index, from the set $\left\{1,1+\left|{\mathbf{INCX}}\right|,\dots ,1+\left({\mathbf{N}}-1\right)×\left|{\mathbf{INCX}}\right|\right\}$, of the smallest component of $x$. If ${\mathbf{N}}\le 0$ on input then K is returned as $0$.
5:     $\mathrm{I}$ – INTEGEROutput
On exit: $i$, the smallest component of $x$. If ${\mathbf{N}}\le 0$ on input then I is returned as $0$.

## 6  Error Indicators and Warnings

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

## 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 and index of that component for the vector
 $x= 1,10,11,-2,9T .$

### 10.1  Program Text

Program Text (f16dpfe.f90)

### 10.2  Program Data

Program Data (f16dpfe.d)

### 10.3  Program Results

Program Results (f16dpfe.r)