nag_blast_zamin_val (f16jt) computes, with respect to absolute value, the smallest component of a complex vector, along with the index of that component.

Syntax

[k, r] = f16jt(n, x, incx)

[k, r] = nag_blast_zamin_val(n, x, incx)

Description

nag_blast_zamin_val (f16jt) 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 x_{k}| + |Im x_{k}| = \min_{j} |Re x_{j}| + |Im x_{j}| .

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

Parameters

Compulsory Input Parameters

1: $n$ – int64int32nag_int scalar: $n$ , the number of elements in $x$ .
2: $x (1 + (n - 1) \times |incx|)$ – complex array: The vector $x$ . Element $x_{i}$ is stored in $x ((i - 1) \times |incx| + 1)$ , for $i = 1, 2, \dots, n$ .
3: $incx$ – int64int32nag_int scalar: The increment in the subscripts of x between successive elements of $x$ .

Constraint: $incx \neq 0$ .

Optional Input Parameters

None.

Output Parameters

1: $k$ – int64int32nag_int scalar: $k$ , the index, from the set $\{1, 2, \dots, n\}$ , of the smallest component of $x$ with respect to absolute value. If $n \leq 0$ on input then k is returned as $0$ .
2: $r$ – double scalar: $r$ , the smallest component of $x$ with respect to absolute value. If $n \leq 0$ on input then r is returned as $0.0$ .

Error Indicators and Warnings

incx = 0

, an error message is printed and program execution is terminated.

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)).

Further Comments

None.

Example

This example computes the smallest component with respect to absolute value and index of that component for the vector

x = {(- 4 + 2.1 i, 3.7 + 4.5 i, - 6 + 1.2 i)}^{T} .

Open in the MATLAB editor: f16jt_example

function f16jt_example


fprintf('f16jt example results\n\n');

% minabs complex and location
n    = int64(3);
x    = [ -4 + 2.1i      3.7 + 4.5i      -6 + 1.2i];
incx = int64(1);

[xloc, xmin] = f16jt(n, x, incx);

fprintf('minabs(x) = |x(%4d)| = %5.1f\n', xloc, xmin);

f16jt example results

minabs(x) = |x(   1)| =   6.1

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox