MaterialPropertyLib::SigmoidFunction Class Reference

Detailed Description

Sigmoid function with scalar argument and two constant parameters

The sigmoid function is a smooth step function with the range \([0,1]\) defined by the following formula

\[ (1-S_r) \left[1 + \exp(k(T - T_\mathrm{c})) \right]^{-1} \]

where \(S_r\) is residual saturation, representing the amount of liquid water remaining after the water-ice phase transition is complete. \(T_\mathrm{c}\) is the critical value (e.g. a phase change temperature). The parameter \(k\) is proportional to the slope at the characteristic value and controls thus the steepness. Letting \(k\) go to infinity, the heaviside step function is obtained.

Definition at line 38 of file SigmoidFunction.h.

#include <SigmoidFunction.h>

Public Member Functions
	SigmoidFunction (double const k, double const T_c, double const S_r)
double	value (double const &T) const
double	dValue (double const &T) const
double	d2Value (double const &T) const

Private Attributes
double const	k_
double const	T_c_
double const	S_r

Constructor & Destructor Documentation

SigmoidFunction()

MaterialPropertyLib::SigmoidFunction::SigmoidFunction	(	double const	k,
		double const	T_c,
		double const	S_r )

Definition at line 17 of file SigmoidFunction.cpp.

    : k_(k), T_c_(T_c), S_r(S_r)
{
}

Member Function Documentation

d2Value()

double MaterialPropertyLib::SigmoidFunction::d2Value

(

double const &

T

)

const

Definition at line 49 of file SigmoidFunction.cpp.

{
    double const fT = dValue(T);
    if (fT == 0)
    {
        return 0;
    }
 
    double const f = value(T);
    return fT * (k_ + 2 * fT / f);
}

References dValue(), k_, and value().

Referenced by MaterialPropertyLib::TemperatureDependentFraction::d2Value().

dValue()

double MaterialPropertyLib::SigmoidFunction::dValue

(

double const &

T

)

const

Definition at line 38 of file SigmoidFunction.cpp.

{
    double const f = value(T);
    if (f * f == 0)
    {
        return 0;
    }
    double const x = k_ * (T - T_c_);
    return -k_ * std::exp(x) * (f * f) / (1. - S_r);
}

References k_, S_r, T_c_, and value().

Referenced by d2Value(), and MaterialPropertyLib::TemperatureDependentFraction::dValue().

value()

double MaterialPropertyLib::SigmoidFunction::value

(

double const &

T

)

const

Definition at line 23 of file SigmoidFunction.cpp.

{
    double const x = k_ * (T - T_c_);
 
    // Cutting off at the last x producing a (non-normal) return value because
    // std::exp(x) produces +infinity beyond this point, approximately 709.78.
    // The reason for using hex representation is that the value is unambiguous.
    if (x > 0x1.62e42fefa39efp+9)
    {
        return 0.;
    }
 
    return (1. - S_r) / (1. + std::exp(x));
}

References k_, S_r, and T_c_.

Referenced by d2Value(), dValue(), and MaterialPropertyLib::TemperatureDependentFraction::value().

Member Data Documentation

k_

double const MaterialPropertyLib::SigmoidFunction::k_

private

Definition at line 50 of file SigmoidFunction.h.

Referenced by d2Value(), dValue(), and value().

S_r

double const MaterialPropertyLib::SigmoidFunction::S_r

private

Definition at line 53 of file SigmoidFunction.h.

Referenced by dValue(), and value().

T_c_

double const MaterialPropertyLib::SigmoidFunction::T_c_

private

Definition at line 51 of file SigmoidFunction.h.

Referenced by dValue(), and value().

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The documentation for this class was generated from the following files:

• MaterialLib/MPL/Utils/SigmoidFunction.h
• MaterialLib/MPL/Utils/SigmoidFunction.cpp