NAG Library Manual, Mark 28.5

Interfaces: FL CL CPP AD PY MB

NAG FL Interface Introduction

A02 (Complex) Chapter Contents

A02 (Complex) Chapter Introduction

a02ab: FL CL CPP AD PY MB

NAG FL Interface
a02abf (abs)

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NAG Library Manual, Mark 28.5

Interfaces: FL CL CPP AD PY MB

NAG FL Interface Introduction

A02 (Complex) Chapter Contents

A02 (Complex) Chapter Introduction

a02ab: FL CL CPP AD PY MB

▸▿ Contents

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

8 Parallelism and Performance

9 Further Comments

▸▿ 10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

© The Numerical Algorithms Group Ltd. 2022

1 Purpose

a02abf returns the value of the modulus of the complex number

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

.

2 Specification

Fortran Interface

Function a02abf (

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

C Header Interface

#include <nag.h>

double

a02abf_ (const double *xr, const double *xi)

The routine may be called by the names a02abf or nagf_complex_abs.

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

Background information to multithreading can be found in the Multithreading documentation.

a02abf is not threaded in any implementation.

9 Further Comments

None.

10 Example

This example finds the modulus of

- 1.7 + 2.6 i

.

10.1 Program Text

Program Text (a02abfe.f90)

10.2 Program Data

Program Data (a02abfe.d)

10.3 Program Results

Program Results (a02abfe.r)

NAG Library Manual, Mark 28.5

Interfaces: FL CL CPP AD PY MB

NAG FL Interface Introduction

A02 (Complex) Chapter Contents

A02 (Complex) Chapter Introduction

a02ab: FL CL CPP AD PY MB

© The Numerical Algorithms Group Ltd. 2022