NAG Library Routine Document

1Purpose

f16dpf computes the smallest component of an integer vector, along with the index of that component.

2Specification

Fortran Interface
 Subroutine f16dpf ( n, x, incx, k, i)
 Integer, Intent (In) :: n, x(1+(n-1)*ABS(incx)), incx Integer, Intent (Out) :: k, i
#include nagmk26.h
 void f16dpf_ (const Integer *n, const Integer x[], const Integer *incx, Integer *k, Integer *i)

3Description

f16dpf computes the smallest component, $i$, of an $n$-element integer vector $x$, and determines the smallest index, $k$, such that
 $i=xk=minjxj.$

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

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

f16dpf is not threaded in any implementation.

None.

10Example

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

10.1Program Text

Program Text (f16dpfe.f90)

10.2Program Data

Program Data (f16dpfe.d)

10.3Program Results

Program Results (f16dpfe.r)

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