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NAG Library Routine Document

s18csf (bessel_i0_scaled_vector)

▸▿ 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

s18csf returns an array of values of the scaled modified Bessel function

e^{- |x|} I_{0} (x)

2

Specification

Fortran Interface

Subroutine s18csf (

n, x, f, ifail)

Integer, Intent (In)	::	n
Integer, Intent (Inout)	::	ifail
Real (Kind=nag_wp), Intent (In)	::	x(n)
Real (Kind=nag_wp), Intent (Out)	::	f(n)

C Header Interface

#include nagmk26.h

void	s18csf_ ( const Integer n, const double x[], double f[], Integer ifail)

3

Description

s18csf evaluates an approximation to

e^{- |x_{i}|} I_{0} (x_{i})

, where

I_{0}

is a modified Bessel function of the first kind for an array of arguments

x_{i}

, for

i = 1, 2, \dots, n

. The scaling factor

e^{- |x|}

removes most of the variation in

I_{0} (x)

The routine uses the same Chebyshev expansions as s18asf, which returns an array of the unscaled values of

I_{0} (x)

4

References

Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications

5

Arguments

1: $n$ – IntegerInput: On entry: $n$ , the number of points.

Constraint: $n \geq 0$ .
2: $x (n)$ – Real (Kind=nag_wp) arrayInput: On entry: the argument $x_{i}$ of the function, for $i = 1, 2, \dots, n$ .
3: $f (n)$ – Real (Kind=nag_wp) arrayOutput: On exit: $e^{- |x_{i}|} I_{0} (x_{i})$ , the function values.
4: $ifail$ – IntegerInput/Output: On entry: ifail must be set to $0$ , $- 1 or 1$ . If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $- 1 or 1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$ . When the value $- 1 or 1$ is used it is essential to test the value of ifail on exit.

On exit: $ifail = 0$ unless the routine detects an error or a warning has been flagged (see Section 6).

6

Error Indicators and Warnings

If on entry

ifail = 0

- 1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 1$: On entry, $n = 〈value〉$ .
Constraint: $n \geq 0$ .

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

Relative errors in the argument are attenuated when propagated into the function value. When the accuracy of the argument is essentially limited by the machine precision, the accuracy of the function value will be similarly limited by at most a small multiple of the machine precision.

8

Parallelism and Performance

s18csf is not threaded in any implementation.

9

Further Comments

None.

10

Example

This example reads values of x from a file, evaluates the function at each value of

x_{i}

and prints the results.

NAG Library Routine Document

s18csf (bessel_i0_scaled_vector)

▸▿ 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