NAG CL Interfaces18crc (bessel_​k1_​scaled_​vector)

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1Purpose

s18crc returns an array of values of the scaled modified Bessel function ${e}^{x}{K}_{1}\left(x\right)$.

2Specification

 #include
 void s18crc (Integer n, const double x[], double f[], Integer ivalid[], NagError *fail)
The function may be called by the names: s18crc, nag_specfun_bessel_k1_scaled_vector or nag_bessel_k1_scaled_vector.

3Description

s18crc evaluates an approximation to ${e}^{{x}_{i}}{K}_{1}\left({x}_{i}\right)$, where ${K}_{1}$ is a modified Bessel function of the second kind for an array of arguments ${x}_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$. The scaling factor ${e}^{x}$ removes most of the variation in ${K}_{1}\left(x\right)$.
The function uses the same Chebyshev expansions as s18arc, which returns an array of the unscaled values of ${K}_{1}\left(x\right)$.

4References

NIST Digital Library of Mathematical Functions

5Arguments

1: $\mathbf{n}$Integer Input
On entry: $n$, the number of points.
Constraint: ${\mathbf{n}}\ge 0$.
2: $\mathbf{x}\left[{\mathbf{n}}\right]$const double Input
On entry: the argument ${x}_{\mathit{i}}$ of the function, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
Constraint: ${\mathbf{x}}\left[\mathit{i}-1\right]>0.0$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
3: $\mathbf{f}\left[{\mathbf{n}}\right]$double Output
On exit: ${e}^{{x}_{i}}{K}_{1}\left({x}_{i}\right)$, the function values.
4: $\mathbf{ivalid}\left[{\mathbf{n}}\right]$Integer Output
On exit: ${\mathbf{ivalid}}\left[\mathit{i}-1\right]$ contains the error code for ${x}_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
${\mathbf{ivalid}}\left[i-1\right]=0$
No error.
${\mathbf{ivalid}}\left[i-1\right]=1$
On entry, ${x}_{i}\le 0.0$, ${K}_{1}\left({x}_{i}\right)$ is undefined. ${\mathbf{f}}\left[\mathit{i}-1\right]$ contains $0.0$.
${\mathbf{ivalid}}\left[i-1\right]=2$
${x}_{i}$ is too close to zero, as determined by the value of the safe-range parameter X02AMC: there is a danger of causing overflow. ${\mathbf{f}}\left[\mathit{i}-1\right]$ contains the reciprocal of the safe-range parameter.
5: $\mathbf{fail}$NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument $⟨\mathit{\text{value}}⟩$ had an illegal value.
NE_INT
On entry, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{n}}\ge 0$.
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.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
NW_IVALID
On entry, at least one value of x was invalid.

7Accuracy

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.

8Parallelism and Performance

s18crc is not threaded in any implementation.

None.

10Example

This example reads values of x from a file, evaluates the function at each value of ${x}_{i}$ and prints the results.

10.1Program Text

Program Text (s18crce.c)

10.2Program Data

Program Data (s18crce.d)

10.3Program Results

Program Results (s18crce.r)