The IMSL_ERFC function evaluates the real complementary error function erfc(x). Using a keyword, the inverse complementary error function erfc–1(x) can be evaluated.
This routine requires an IDL Advanced Math and Stats license. For more information, contact your sales or technical support representative.
The complementary error function erfc(x) is defined as:
where parameter x must not be so large that the result underflows. Approximately, x should be less than:
where s is the smallest representable floating-point number.
The inverse complementary error function y = erfc–1(x) is such that x = erfc(y).
Examples
Example 1
Plot the complementary error function over [–3, 3]. The results are shown following.
x = FINDGEN(100)/99
PLOT, 6 * x - 3, IMSL_ERFC(6 * x - 3), XTitle = 'x', $
YTitle = 'erfc(x)'
Example 2
Plot the inverse of the complementary error function over (0, 2). The results are shown following.
x = FINDGEN(100)/99
PLOT, 2 * x(1:98), IMSL_ERFC(2 * x(1:98), /Inverse), $
XTitle = 'x', YTitle = 'erfc!E-1!N(x)'
Errors
Alert Errors
MATH_LARGE_ARG_UNDERFLOW: Parameter x must not be so large that the result underflows. Very approximately, x should be less than:
where ε is the machine precision.
Warning Errors
MATH_LARGE_ARG_WARN: Parameter |x| should be less than:
where ε is the machine precision, to prevent the answer from being less accurate than half precision.
Fatal Errors
MATH_ERF_ALGORITHM: Algorithm failed to converge.
MATH_SMALL_ARG_OVERFLOW: Computation of:
must not overflow.
MATH_REAL_OUT_OF_RANGE: Function is defined only for 0 < x < 2.
Syntax
Result = IMSL_ERFC(X [, /DOUBLE] [, /INVERSE]
Return Value
The value of the error function erfc(x).
Arguments
X
Expression for which the complimentary error function is to be evaluated.
Keywords
DOUBLE (optional)
If present and nonzero, double precision is used.
INVERSE (optional)
Evaluates the inverse complementary error function erfc–1(x). The parameter must be in the range 0 < x < 2.
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