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Chapter Contents

Chapter Introduction

NAG Toolbox

NAG Toolbox: nag_complex_abs (a02ab)

▸▿ Contents

1 Purpose

2 Syntax

3 Description

4 References

▸▿ 5 Parameters

5.1 Compulsory Input Parameters

5.2 Optional Input Parameters

5.3 Output Parameters

6 Error Indicators and Warnings

7 Accuracy

8 Further Comments

9 Example

Purpose

nag_complex_abs (a02ab) returns the value of the modulus of the complex number

x = (x_{r}, x_{i})

Syntax

[result] = a02ab(xr, xi)

[result] = nag_complex_abs(xr, xi)

Description

The function evaluates

\sqrt{x_{r}^{2} + x_{i}^{2}}

by using

a \sqrt{1 + {(\frac{b}{a})}^{2}}

where

a

is the larger of

|x_{r}|

and

|x_{i}|

, and

b

is the smaller of

|x_{r}|

and

|x_{i}|

. This ensures against unnecessary overflow and loss of accuracy when calculating

(x_{r}^{2} + x_{i}^{2})

References

Wilkinson J H and Reinsch C (1971) Handbook for Automatic Computation II, Linear Algebra Springer–Verlag

Parameters

Compulsory Input Parameters

1: $xr$ – double scalar
2: $xi$ – double scalar: $x_{r}$ and $x_{i}$ , the real and imaginary parts of $x$ , respectively.

Optional Input Parameters

None.

Output Parameters

1: $result$ – double scalar: The result of the function.

Error Indicators and Warnings

None.

Accuracy

The result should be correct to machine precision.

Further Comments

None.

Example

This example finds the modulus of

- 1.7 + 2.6 i

Open in the MATLAB editor: a02ab_example

function a02ab_example


fprintf('a02ab example results\n\n');

xr = -1.7;
xi = 2.6;
x = xr + i*xi;

[absx] = a02ab(xr, xi);

fprintf('The modulus of ');
disp(x);
fprintf('            is ');
disp(absx);

a02ab example results

The modulus of   -1.7000 + 2.6000i

            is     3.1064

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Chapter Contents

Chapter Introduction

NAG Toolbox