A02AAF (PDF version)
A02 Chapter Contents
A02 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

A02AAF

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.

 Contents

    1  Purpose
    7  Accuracy

1  Purpose

A02AAF evaluates the square root of the complex number x=xr,xi.

2  Specification

SUBROUTINE A02AAF ( XR, XI, YR, YI)
REAL (KIND=nag_wp)  XR, XI, YR, YI

3  Description

The method of evaluating y=x depends on the value of xr.
For xr0,
yr=xr+xr2+xi2 2,  yi=xi2yr .  
For xr<0,
yi=signxi×xr+xr2+xi2 2 ,  yr=xi2yi .  
Overflow is avoided when squaring xi and xr by calling A02ABF to evaluate xr2+xi2.

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: xr and xi, the real and imaginary parts of x, respectively.
3:     YR – REAL (KIND=nag_wp)Output
4:     YI – REAL (KIND=nag_wp)Output
On exit: yr and yi, the real and imaginary parts of y, respectively.

6  Error Indicators and Warnings

None.

7  Accuracy

The result should be correct to machine precision.

8  Parallelism and Performance

Not applicable.

9  Further Comments

The time taken by A02AAF is negligible.

10  Example

This example finds the square root of -1.7+2.6i.

10.1  Program Text

Program Text (a02aafe.f90)

10.2  Program Data

Program Data (a02aafe.d)

10.3  Program Results

Program Results (a02aafe.r)


A02AAF (PDF version)
A02 Chapter Contents
A02 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2015