NAG Library Routine Document
S15ADF returns the value of the complementary error function, , via the function name.
|REAL (KIND=nag_wp) S15ADF
S15ADF calculates an approximate value for the complement of the error function
be the root of the equation
the value of
is based on the following rational Chebyshev expansion for
denotes a rational function of degree
in the numerator and
in the denominator.
the value of
is based on a rational Chebyshev expansion for
the value is based on the expansion
it is based on the expansion
For each expansion, the specific values of
are selected to be minimal such that the maximum relative error in the expansion is of the order
is the maximum number of decimal digits that can be accurately represented for the particular implementation (see X02BEF
there is a danger of setting underflow in
(the value of
is given in the Users' Note
for your implementation). For
, S15ADF returns
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
Cody W J (1969) Rational Chebyshev approximations for the error function Math.Comp. 23 631–637
- 1: X – REAL (KIND=nag_wp)Input
On entry: the argument of the function.
- 2: 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
There are no failure exits from S15ADF. The parameter IFAIL
has been included for consistency with other routines in this chapter.
are relative errors in the argument and result, respectively, then in principle
That is, the relative error in the argument,
, is amplified by a factor
in the result.
The behaviour of this factor is shown in Figure 1
It should be noted that near
this factor behaves as
and hence the accuracy is largely determined by the machine precision
. Also for large negative
, where the factor is
, accuracy is mainly limited by machine precision
. However, for large positive
, the factor becomes
and to an extent relative accuracy is necessarily lost. The absolute accuracy
is given by
so absolute accuracy is guaranteed for all
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.
9.1 Program Text
Program Text (s15adfe.f90)
9.2 Program Data
Program Data (s15adfe.d)
9.3 Program Results
Program Results (s15adfe.r)