NAG Library Function Document

nag_bessel_k1_scaled_vector (s18crc)

▸▿ 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

nag_bessel_k1_scaled_vector (s18crc) returns an array of values of the scaled modified Bessel function

e^{x} K_{1} (x)

2 Specification

#include <nag.h>

#include <nags.h>

void	nag_bessel_k1_scaled_vector (Integer n, const double x[], double f[], Integer ivalid[], NagError *fail)

3 Description

nag_bessel_k1_scaled_vector (s18crc) evaluates an approximation to

e^{x_{i}} K_{1} (x_{i})

, where

K_{1}

is a modified Bessel function of the second 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

K_{1} (x)

The function uses the same Chebyshev expansions as nag_bessel_k1_vector (s18arc), which returns an array of the unscaled values of

K_{1} (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: $x [n]$ – const doubleInput

On entry: the argument

x_{i}

of the function, for

i = 1, 2, \dots, n

Constraint:

x [i - 1] > 0.0

, for

i = 1, 2, \dots, n

3: $f [n]$ – doubleOutput

On exit:

e^{x_{i}} K_{1} (x_{i})

, the function values.

4: $ivalid [n]$ – IntegerOutput

On exit:

ivalid [i - 1]

contains the error code for

x_{i}

, for

i = 1, 2, \dots, n

$ivalid [i - 1] = 0$

No error.

$ivalid [i - 1] = 1$

On entry,

x_{i} \leq 0.0

K_{1} (x_{i})

is undefined.

f [i - 1]

contains

0.0

$ivalid [i - 1] = 2$

x_{i}

is too close to zero, as determined by the value of the safe-range parameter nag_real_safe_small_number (X02AMC): there is a danger of causing overflow.

f [i - 1]

contains the reciprocal of the safe-range parameter.

5: $fail$ – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.2.1.2 in the Essential Introduction for further information.
NE_BAD_PARAM: On entry, argument $〈value〉$ had an illegal value.
NE_INT: On entry, $n = 〈value〉$ .
Constraint: $n \geq 0$ .
NE_INTERNAL_ERROR: An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

An unexpected error has been triggered by this function. Please contact NAG.
See Section 3.6.6 in the Essential Introduction for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 3.6.5 in the Essential Introduction for further information.
NW_IVALID: On entry, at least one value of x was invalid.
Check ivalid for more 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

Not applicable.

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 Function Documentnag_bessel_k1_scaled_vector (s18crc)

▸▿ 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

NAG Library Function Document

nag_bessel_k1_scaled_vector (s18crc)