NAG Library Function Document
nag_kelvin_bei_vector (s19apc) returns an array of values for the Kelvin function .
||nag_kelvin_bei_vector (Integer n,
const double x,
nag_kelvin_bei_vector (s19apc) evaluates an approximation to the Kelvin function for an array of arguments , for .
Note: , so the approximation need only consider .
The function is based on several Chebyshev expansions:
and , , , and are expansions in the variable .
When is sufficiently close to zero, the result is computed as . If this result would underflow, the result returned is .
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 function must fail.
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
n – IntegerInput
, the number of points.
x[n] – const doubleInput
On entry: the argument of the function, for .
f[n] – doubleOutput
On exit: , the function values.
ivalid[n] – IntegerOutput
contains the error code for
- No error.
- is too large for an accurate result to be returned. contains zero. The threshold value is the same as for NE_REAL_ARG_GT in nag_kelvin_bei (s19abc), as defined in the Users' Note for your implementation.
fail – NagError *Input/Output
The NAG error argument (see Section 3.6
in the Essential Introduction).
6 Error Indicators and Warnings
On entry, argument had an illegal value.
On entry, .
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
On entry, at least one value of x
for more information.
Since the function is oscillatory, the absolute error rather than the relative error is important. Let
be the absolute error in the function, and
be the relative error in the argument. If
is somewhat larger than the machine precision
, then we have:
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 impossible to calculate the functions with any accuracy when . Note that this value of is much smaller than the minimum value of for which the function overflows.
This example reads values of x
from a file, evaluates the function at each value of
and prints the results.
9.1 Program Text
Program Text (s19apce.c)
9.2 Program Data
Program Data (s19apce.d)
9.3 Program Results
Program Results (s19apce.r)