F16 Chapter Contents
F16 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF16JTF (BLAS_ZAMIN_VAL)

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

F16JTF (BLAS_ZAMIN_VAL) computes, with respect to absolute value, the smallest component of a complex vector, along with the index of that component.

## 2  Specification

 SUBROUTINE F16JTF ( N, X, INCX, K, R)
 INTEGER N, INCX, K REAL (KIND=nag_wp) R COMPLEX (KIND=nag_wp) X(1+(N-1)*ABS(INCX))
The routine may be called by its BLAST name blas_zamin_val.

## 3  Description

F16JTF (BLAS_ZAMIN_VAL) 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  Parameters

1:     N – INTEGERInput
On entry: $n$, the number of elements in $x$.
2:     X($1+\left({\mathbf{N}}-1\right)×\left|{\mathbf{INCX}}\right|$) – COMPLEX (KIND=nag_wp) arrayInput
On entry: the vector $x$. Element ${x}_{\mathit{i}}$ is stored in ${\mathbf{X}}\left(\left(\mathit{i}-1\right)×\left|{\mathbf{INCX}}\right|+1\right)$, for $\mathit{i}=1,2,\dots ,n$.
3:     INCX – INTEGERInput
On entry: the increment in the subscripts of X between successive elements of $x$.
Constraint: ${\mathbf{INCX}}\ne 0$.
4:     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 $x$ with respect to absolute value. If ${\mathbf{N}}\le 0$ on input then K is returned as $0$.
5:     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 $0.0$.

## 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)).

None.

## 9  Example

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

### 9.1  Program Text

Program Text (f16jtfe.f90)

### 9.2  Program Data

Program Data (f16jtfe.d)

### 9.3  Program Results

Program Results (f16jtfe.r)