# NAG CL Interfacef16jtc (zamin_​val)

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## 1Purpose

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

## 2Specification

 #include
 void f16jtc (Integer n, const Complex x[], Integer incx, Integer *k, double *r, NagError *fail)
The function may be called by the names: f16jtc, nag_blast_zamin_val or nag_zamin_val.

## 3Description

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

## 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 $x$.
Constraint: ${\mathbf{n}}\ge 0$.
2: $\mathbf{x}\left[\mathit{dim}\right]$const Complex Input
Note: the dimension, dim, of the array x must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{n}}-1\right)×|{\mathbf{incx}}|\right)$.
On entry: the $n$-element vector $x$.
If ${\mathbf{incx}}>0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{x}}\left[\left(\mathit{i}-1\right)×{\mathbf{incx}}\right]$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
If ${\mathbf{incx}}<0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{x}}\left[\left({\mathbf{n}}-\mathit{i}\right)×|{\mathbf{incx}}|\right]$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
Intermediate elements of x are not referenced. If ${\mathbf{n}}=0$, x is not referenced and may be NULL.
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 $\left\{0,1,\dots ,{\mathbf{n}}-1\right\}$, of the smallest component of $x$ with respect to absolute value. If ${\mathbf{n}}=0$ on input then k is returned as $-1$.
5: $\mathbf{r}$double * 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: $\mathbf{fail}$NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

## 6Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
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: ${\mathbf{n}}\ge 0$.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

## 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

f16jtc 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 (f16jtce.c)

### 10.2Program Data

Program Data (f16jtce.d)

### 10.3Program Results

Program Results (f16jtce.r)