NAG Library Routine Document

A02ABF

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

6 Error Indicators and Warnings

7 Accuracy

8 Further Comments

+− 9 Example

9.1 Program Text

9.2 Program Data

9.3 Program Results

1 Purpose

A02ABF returns the value of the modulus of the complex number

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

2 Specification

FUNCTION A02ABF (

XR, XI)

REAL (KIND=nag_wp) A02ABF

REAL (KIND=nag_wp)

XR, XI

3 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})

4 References

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

5 Parameters

1: XR – REAL (KIND=nag_wp)Input
2: XI – REAL (KIND=nag_wp)Input: On entry: $x_{r}$ and $x_{i}$ , the real and imaginary parts of $x$ , respectively.

6 Error Indicators and Warnings

None.

7 Accuracy

The result should be correct to machine precision.

8 Further Comments

None.

9 Example

This example finds the modulus of

- 1.7 + 2.6 i

NAG Library Routine DocumentA02ABF