Error Function (Erf)

Functions
template<typename T >
T	EGXMath::Erf (const T &x)
	Error function. The cummlitive distribution function for a guassian/normal distribution. \[ erf(x)\equiv \frac{2}{\sqrt{\pi}}\int_0^x e^{-t^2}dt \] . More...
template<typename T >
T	EGXMath::InverseErf (const T &x)
	Inverese error function. The inverse of the error function. \[ erf^{-1}(erf(x)) = x \] . More...
template<typename T >
T	EGXMath::Erfc (const T &x)
	Complementary error function. \[ erfc(x)\equiv 1-erf(x) \] \[ erfc(x)=\frac{2}{\sqrt{\pi}}\int_x^\infty e^{-t^2}dt \] . More...
template<typename T >
T	EGXMath::InverseErfc (const T &x)
	Inverse complementary error function. The inverse of the complementary error function. \[erfc^{-1}(erfc(x)) = x\] . More...

Detailed Description

Function Documentation

Erf()

template<typename T >

T EGXMath::Erf

(

const T &

x

)

Error function. The cummlitive distribution function for a guassian/normal distribution.

\[ erf(x)\equiv \frac{2}{\sqrt{\pi}}\int_0^x e^{-t^2}dt \]

.

See http://mathworld.wolfram.com/Erf.html

Parameters

x	\(x\ (dimensionless)\) is the argument of the function.

Returns

\(erf(x)\ (dimensionless)\) is the value after applying the error function. Ranges from -1 < x < 1.

See also

InverseErf() for inverse error function.

Erfc() for complementary error function.

InverseErfc() for inverse complementary error function.

Gaussian() for gaussian/normal distribution.

Erfc()

template<typename T >

T EGXMath::Erfc

(

const T &

x

)

Complementary error function.

\[ erfc(x)\equiv 1-erf(x) \]

\[ erfc(x)=\frac{2}{\sqrt{\pi}}\int_x^\infty e^{-t^2}dt \]

.

See http://mathworld.wolfram.com/Erfc.html

Parameters

x	\(x\ (dimensionless)\) is the argument of the function.

Returns

\(erfc(x)\ (dimensionless)\) is the value after applying the complementary error function. Ranges from -1 < x < 1.

See also

Erf() for error function.

InverseErf() for inverse error function.

InverseErfc() for inverse complementary error function.

Gaussian() for gaussian/normal distribution.

InverseErf()

template<typename T >

T EGXMath::InverseErf

(

const T &

x

)

Inverese error function. The inverse of the error function.

\[ erf^{-1}(erf(x)) = x \]

.

See http://mathworld.wolfram.com/InverseErf.html

Parameters

x	\(x\ (dimensionless)\) is the argument of the function. Ranges from -1 < x < 1.

Returns

\(erf^{-1}(x)\ (dimensionless)\) is the value after applying the inverse error function.

See also

Erf() for error function.

Erfc() for complementary error function.

InverseErfc() for inverse complementary error function.

Gaussian() for gaussian/normal distribution.

InverseErfc()

template<typename T >

T EGXMath::InverseErfc

(

const T &

x

)

Inverse complementary error function. The inverse of the complementary error function.

\[erfc^{-1}(erfc(x)) = x\]

.

See http://mathworld.wolfram.com/InverseErfc.html

Parameters

x	\(x\ (dimensionless)\) is the argument of the function. Ranges from -1 < x < 1.

Returns

\(erfc^{-1}(x)\ (dimensionless)\) is the value after applying the inverse complementary error function.

See also

Erf() for error function.

InverseErf() for inverse error function.

Erfc() for complementary error function.

Gaussian() for gaussian/normal distribution.