NAG FL Interfacef16jtf (zamin_​val)

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1Purpose

f16jtf computes, with respect to absolute value, the smallest component of a complex vector, along with the index of that component.

2Specification

Fortran Interface
 Subroutine f16jtf ( 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 f16jtf_ (const Integer *n, const Complex x[], const Integer *incx, Integer *k, double *r)
The routine may be called by the names f16jtf, nagf_blast_zamin_val or its BLAST name blas_zamin_val.

3Description

f16jtf 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
 $r=|Re⁡xk|+|Im⁡xk|=minj|Re⁡xj|+|Im⁡xj|.$

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 smallest 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 smallest 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

f16jtf is not threaded in any implementation.

None.

10Example

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

10.1Program Text

Program Text (f16jtfe.f90)

10.2Program Data

Program Data (f16jtfe.d)

10.3Program Results

Program Results (f16jtfe.r)