optimatic.utils package¶

Submodules¶

Numerical differentiation

optimatic.utils.differentiate.central_diff(f, h, epsilon=0.0001)[source]¶

Calculates the value of \(f^{\prime}(x=h)\) using the central difference method:

\[f^{\prime}(h) \approx \frac{f(h + \epsilon) - f(h - \epsilon)} {2 \epsilon}\]

Parameters:	f – The function to differentiate h – The value to evaluate the derivative at epsilon – The value to use for epsilon

optimatic.utils.differentiate.forward_diff(f, h, epsilon=0.0001)[source]¶

Calculates the value of \(f^{\prime}(x=h)\) using the foward difference method:

\[f^{\prime}(h) \approx \frac{f(h + \epsilon) - f(h)}{\epsilon}\]

Parameters:	f – The function to differentiate h – The value to evaluate the derivative at epsilon – The value to use for epsilon

Methods for generating data to fit using optimisation algorithms

optimatic.utils.generate.random_polynomial(degree, x, scale=5, noisy=True)[source]¶

Generates a polynomial of the given degree with random coefficients, then adds some noise.

Return coefficients:
Parameters:	degree – The degree of the polynomial to generate x – An array of x values to evaluate the polynomial \(y(x)\) at scale – The stdev of the normal distribution from which the parameters wil be sampled noisy – Whether or not to add noise to the generated data. If true, noise will be sampled from a normal distribution with stdev scale/2
Return y:	The generated data points
	The coefficients of the polynomial