NAG FL Interface
s19aaf (kelvin_ber)
1
Purpose
s19aaf returns a value for the Kelvin function via the function name.
2
Specification
Fortran Interface
| Real (Kind=nag_wp) |
:: |
s19aaf |
| Integer, Intent (Inout) |
:: |
ifail |
| Real (Kind=nag_wp), Intent (In) |
:: |
x |
|
C Header Interface
|
#include <nag.h>
| double |
s19aaf_ (const double *x, Integer *ifail) |
|
C++ Header Interface
|
#include <nag.h> extern "C" {
| double |
s19aaf_ (const double &x, Integer &ifail) |
}
|
The routine may be called by the names s19aaf or nagf_specfun_kelvin_ber.
3
Description
s19aaf evaluates an approximation to the Kelvin function .
Note: , so the approximation need only consider .
The routine is based on several Chebyshev expansions:
For
,
For
,
where
,
,
and , , , and are expansions in the variable .
When is sufficiently close to zero, the result is set directly to .
For large , there is a danger of the result being totally inaccurate, as the error amplification factor grows in an essentially exponential manner; therefore the routine must fail.
4
References
5
Arguments
-
1:
– Real (Kind=nag_wp)
Input
-
On entry: the argument of the function.
-
2:
– Integer
Input/Output
-
On entry:
ifail must be set to
,
. If you are unfamiliar with this argument you should refer to
Section 4 in the Introduction to the NAG Library FL Interface 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 for an accurate result to be returned and the function returns zero.
An unexpected error has been triggered by this routine. Please
contact
NAG.
See
Section 7 in the Introduction to the NAG Library FL Interface for further information.
Your licence key may have expired or may not have been installed correctly.
See
Section 8 in the Introduction to the NAG Library FL Interface for further information.
Dynamic memory allocation failed.
See
Section 9 in the Introduction to the NAG Library FL Interface for further information.
7
Accuracy
Since the function is oscillatory, the absolute error rather than the relative error is important. Let
be the absolute error in the result and
be the relative error in the argument. If
is somewhat larger than the
machine precision, then we have:
(provided
is within machine bounds).
For small the error amplification is insignificant and thus the absolute error is effectively bounded by the machine precision.
For medium and large , the error behaviour is oscillatory and its amplitude grows like . Therefore it is not possible to calculate the function with any accuracy when . Note that this value of is much smaller than the minimum value of for which the function overflows.
8
Parallelism and Performance
s19aaf 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
10.2
Program Data
10.3
Program Results