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NAG Library Routine Document

a02abf (abs)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

▸▿ 10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

1

Purpose

a02abf returns the value of the modulus of the complex number

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

2

Specification

Fortran Interface

Function a02abf (

xr, xi)

Real (Kind=nag_wp)	::	a02abf
Real (Kind=nag_wp), Intent (In)	::	xr, xi

C Header Interface

#include nagmk26.h

double

a02abf_ ( const double *xr, const double *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

Arguments

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

Parallelism and Performance

a02abf is not threaded in any implementation.

9

Further Comments

None.

10

Example

This example finds the modulus of

- 1.7 + 2.6 i

NAG Library Routine Document

a02abf (abs)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results