Class ZeroOneMapper

source code

Map function range into [0,1]**n.

Given f: [a,b] -> R Defines f': [0,1] -> R

The method encode(x) returns a value in [0,1] The method decode(v) returns a value in [a,b] The method __call__(v) returns f(decode(v))

For indefinite and semidefinte ranges, an asymptote transformation is needed. Normally this is park.rangemap.Asymptote which supports the full floating point range of values, but is limited to about 12 digits of precision. The arctan function can also be used (see park.rangemap.ArctanAsymptote).

Range is determined by the bounds low and high. Each dimension may be unbounded, semi-definite or bounded. Bounded functions use a linear mapping between low and high. Unbounded functions use an asymptote function, which should be -1 at -inf, 0 at 0 and 1 at +inf, and approximate the identity function between [-0.5,0.5].

This can be used to turn any unconstrained optimizer into a [0,1] bounded optimizer by sending infeasible points to infinity.

Note: Newton-style optimizers will not work in this regime, but instead require a hint about the direction of the unconstrained region.