NAG Library Manual, Mark 30.1

Interfaces: FL CL CPP AD PY MB

NAG FL Interface Introduction

A02 (Complex) Chapter Contents

A02 (Complex) Chapter Introduction

a02aa: FL CL CPP AD PY MB

NAG FL Interface
a02aaf (sqrt)

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NAG Library Manual, Mark 30.1

Interfaces: FL CL CPP AD PY MB

NAG FL Interface Introduction

A02 (Complex) Chapter Contents

A02 (Complex) Chapter Introduction

a02aa: 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. 2024

1 Purpose

a02aaf evaluates the square root of the complex number

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

.

2 Specification

Fortran Interface

Subroutine a02aaf (

xr, xi, yr, yi)

Real (Kind=nag_wp), Intent (In)	::	xr, xi
Real (Kind=nag_wp), Intent (Out)	::	yr, yi

C Header Interface

#include <nag.h>

void	a02aaf_ (const double xr, const double xi, double yr, double yi)

The routine may be called by the names a02aaf or nagf_complex_sqrt.

3 Description

The method of evaluating

y = \sqrt{x}

depends on the value of

x_{r}

.

For

x_{r} \geq 0

,

y_{r} = \sqrt{\frac{x_{r} + \sqrt{x_{r}^{2} + x_{i}^{2}}}{2}}, y_{i} = \frac{x_{i}}{2 y_{r}} .

For

x_{r} < 0

,

y_{i} = sign (x_{i}) \times \sqrt{\frac{| x_{r} | + \sqrt{x_{r}^{2} + x_{i}^{2}}}{2}}, y_{r} = \frac{x_{i}}{2 y_{i}} .

Overflow is avoided when squaring

x_{i}

and

x_{r}

by calling a02abf to evaluate

\sqrt{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.
3: $yr$ – Real (Kind=nag_wp) Output
4: $yi$ – Real (Kind=nag_wp) Output: On exit: $y_{r}$ and $y_{i}$ , 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

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

a02aaf is not threaded in any implementation.

9 Further Comments

The time taken by a02aaf is negligible.

10 Example

This example finds the square root of

- 1.7 + 2.6 i

.

10.1 Program Text

Program Text (a02aafe.f90)

10.2 Program Data

Program Data (a02aafe.d)

10.3 Program Results

Program Results (a02aafe.r)

NAG Library Manual, Mark 30.1

Interfaces: FL CL CPP AD PY MB

NAG FL Interface Introduction

A02 (Complex) Chapter Contents

A02 (Complex) Chapter Introduction

a02aa: FL CL CPP AD PY MB

© The Numerical Algorithms Group Ltd. 2024