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erfcx

Scaled complementary error function

Syntax

Description

example

erfcx(x) returns the value of the Scaled Complementary Error Function for each element of x. Use the erfcx function to replace expressions containing exp(x^2)*erfc(x) to avoid underflow or overflow errors.

Examples

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Find Scaled Complementary Error Function

erfcx(5)
ans =

    0.1107

Find the scaled complementary error function of the elements of a vector.

V = [-Inf -1 0 1 10 Inf];
erfcx(V)
ans =

       Inf    5.0090    1.0000    0.4276    0.0561         0

Find the scaled complementary error function of the elements of a matrix.

M = [-0.5 15; 3.2 1];
erfcx(M)
ans =

    1.9524    0.0375
    0.1687    0.4276

Avoid Roundoff Errors Using Scaled Complementary Error Function

You can use the scaled complementary error function erfcx in place of exp(x^2)*erfc(x) to avoid underflow or overflow errors.

Show how to avoid roundoff errors by calculating exp(35^2)*erfc(35) using erfcx(35). The original calculation returns NaN while erfcx(35) returns the correct result.

x = 35;
exp(x^2)*erfc(x)
erfcx(x)
ans =

   NaN


ans =

    0.0161

Input Arguments

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x — Inputreal number | vector of real numbers | matrix of real numbers | multidimensional array of real numbers

Input, specified as a real number, or a vector, matrix, or multidimensional array of real numbers. x cannot be sparse.

Data Types: single | double

More About

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Scaled Complementary Error Function

The scaled complementary error function erfcx(x) is defined as

erfcx(x)=ex2erfc(x).

For large X, erfcx(X) is approximately (1π)1x.

Tips

  • For expressions of the form exp(-x^2)*erfcx(x), use the complementary error function erfc instead. This substitution maintains accuracy by avoiding roundoff errors for large values of x.

See Also

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Introduced before R2006a

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