IDL Analyst Reference Guide: Special Functions

IMSL_ERFC

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.

Syntax

Result = IMSL_ERFC(x [, /DOUBLE] [, /INVERSE])

Return Value

The value of the complementary error function erfc(x).

Arguments

x

Expression for which the complementary error function is to be evaluated.

Keywords

DOUBLE

If present and nonzero, double precision is used.

INVERSE

Evaluates the inverse complementary error function erfc^–1(x). The parameter must be in the range 0 < x < 2.

Discussion

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 in Figure 12-3.

x = FINDGEN(100)/99  
PLOT, 6 * x - 3, IMSL_ERFC(6 * x - 3), XTitle = 'x', $  
   YTitle = 'erfc(x)'  

Figure 12-3: Plot of erf(x)

Figure 12-3: Plot of erf(x)

Example 2

Plot the inverse of the complementary error function over (0, 2). The results are shown in Figure 12-4.

x = FINDGEN(100)/99  
PLOT, 2 * x(1:98), IMSL_ERFC(2 * x(1:98), /Inverse), $  
   XTitle = 'x', YTitle = 'erfc!E-1!N(x)'  

Figure 12-4: Plot of erfc–1(x)

Figure 12-4: Plot of erfc–1(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 e is the machine precision.

Warning Errors

MATH_LARGE_ARG_WARN—Parameter |x| should be less than

where e 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.

Version History

  IDL Online Help (March 06, 2007)