NAG Library Routine Document
S18CRF returns an array of values of the scaled modified Bessel function .
||N, IVALID(N), IFAIL
S18CRF evaluates an approximation to , where is a modified Bessel function of the second kind for an array of arguments , for . The scaling factor removes most of the variation in .
The routine uses the same Chebyshev expansions as S18ARF
, which returns an array of the unscaled values of
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
- 1: N – INTEGERInput
On entry: , the number of points.
- 2: X(N) – REAL (KIND=nag_wp) arrayInput
On entry: the argument of the function, for .
, for .
- 3: F(N) – REAL (KIND=nag_wp) arrayOutput
On exit: , the function values.
- 4: IVALID(N) – INTEGER arrayOutput
contains the error code for
- No error.
|On entry,||, is undefined. contains .|
- is too close to zero, as determined by the value of the safe-range parameter X02AMF: there is a danger of causing overflow. contains the reciprocal of the safe-range parameter.
- 5: IFAIL – INTEGERInput/Output
must be set to
. If you are unfamiliar with this parameter you should refer to Section 3.3
in the Essential Introduction 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 parameter, the recommended value is
. When the value is used it is essential to test the value of IFAIL 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
, explanatory error messages are output on the current error message unit (as defined by X04AAF
Errors or warnings detected by the routine:
On entry, at least one value of X
for more information.
On entry, .
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.
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 (s18crfe.f90)
9.2 Program Data
Program Data (s18crfe.d)
9.3 Program Results
Program Results (s18crfe.r)