# fronts.D.power_law¶

fronts.D.power_law(k, a=1.0, epsilon=0.0)

Return a power-law D function.

Given the scalars a, k and $$\varepsilon$$, returns a function D defined as:

$D(\theta) = a\theta^k + \varepsilon$
Parameters
• k (float) – Exponent

• a (float, optional) – Constant factor. The default is 1.

• epsilon (float, optional) – $$\varepsilon$$, the deviation term. The default is 0.

Returns

D

Function to evaluate $$D$$ and its derivatives:

• D(theta) evaluates and returns $$D$$ at theta

• D(theta, 1) returns both the value of $$D$$ and its first derivative at theta

• D(theta, 2) returns the value of $$D$$, its first derivative, and its second derivative at theta

In all cases, the argument theta may be a single float or a NumPy array.

Return type

callable

Notes

Keep in mind that, depending on the parameters, the returned D does not necessarily map every value of $$\theta$$ to a positive value.