Finding Minima of Functions (lib601.minima)

Procedures for finding values of a function to minimize its output.

lib601.minima.bisection(objective, xmin, xmax, threshold=0.0001, h=0.0001)

Find the local minimum of a function objective between xmin and xmax using the bisection method.

Parameters:

• objective – a function from a single numeric parameter to a single numeric output
• xmin – the minimum value of objective’s parameter that should be considered
• xmax – the maximum value of objective’s parameter that should be considered
• threshold – the desired precision of the answer (the “optimum” parameter returned will be within threshold of the theoretical optimum parameter)
• h – the “delta” to use when approximating the derivative of objective

Returns:

a tuple (xBest,fBest), where xBest is the value of x for which f(x) is smallest (accurate to within threshold of the theoretical best x), and fBest is objective(xBest)

lib601.minima.linear(objective, xmin, xmax, numXsteps)

Find the local minimum of a function objective between xmin and xmax using a linear search.

Parameters:

• objective – A function that takes a single number x as an argument and returns a numerical value.
• xmin – The minimum value of x to consider, inclusive.
• xmax – The maximum value of x to consider, inclusive.
• numXsteps – The number of “steps” to try.

Returns:

A tuple (xBest, fBest). xBest is one of the numeric values achieved by starting at xmin and taking numXsteps equal-sized steps up to xmax. The particular value of x returned is the one for which objective(x) is minimized.