NAG Library Routine Document
s18aff (bessel_i1_real)
1
Purpose
s18aff returns a value for the modified Bessel function , via the function name.
2
Specification
Fortran Interface
| Real (Kind=nag_wp) | :: | s18aff | | Integer, Intent (Inout) | :: | ifail | | Real (Kind=nag_wp), Intent (In) | :: | x |
|
C Header Interface
|
#include <nagmk26.h>
| double |
s18aff_ (const double *x, Integer *ifail) |
|
3
Description
s18aff evaluates an approximation to the modified Bessel function of the first kind .
Note: , so the approximation need only consider .
The routine is based on three Chebyshev expansions:
For
,
For
,
For
,
For small
,
. This approximation is used when
is sufficiently small for the result to be correct to
machine precision.
For large , the routine must fail because cannot be represented without overflow.
4
References
5
Arguments
- 1: – Real (Kind=nag_wp)Input
-
On entry: the argument of the function.
- 2: – IntegerInput/Output
-
On entry:
ifail must be set to
,
. 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
is recommended. If the output of error messages is undesirable, then the value
is recommended. Otherwise, if you are not familiar with this argument, the recommended value is
.
When the value is used it is essential to test the value of ifail on exit.
On exit:
unless the routine detects an error or a warning has been flagged (see
Section 6).
6
Error Indicators and Warnings
If on entry
or
, explanatory error messages are output on the current error message unit (as defined by
x04aaf).
Errors or warnings detected by the routine:
-
On entry, .
Constraint: .
is too large and the function returns the approximate value of at the nearest valid argument.
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.
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.
Dynamic memory allocation failed.
See
Section 3.7 in How to Use the NAG Library and its Documentation for further information.
7
Accuracy
Let and be the relative errors in the argument and result respectively.
If
is somewhat larger than the
machine precision (i.e., if
is due to data errors etc.), then
and
are approximately related by:
Figure 1 shows the behaviour of the error amplification factor
However, if is of the same order as machine precision, then rounding errors could make slightly larger than the above relation predicts.
For small , and there is no amplification of errors.
For large , and we have strong amplification of errors. However, the routine must fail for quite moderate values of because would overflow; hence in practice the loss of accuracy for large is not excessive. Note that for large , the errors will be dominated by those of the standard function exp.
8
Parallelism and Performance
s18aff is not threaded in any implementation.
None.
10
Example
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.
10.1
Program Text
Program Text (s18affe.f90)
10.2
Program Data
Program Data (s18affe.d)
10.3
Program Results
Program Results (s18affe.r)
