Package park :: Package fitting :: Module rangemap

Module rangemap

Defines transformations between the a fit space and the parameter space.

The parameter space maps a set of possibly bounded dimensions into a real-valued fitness:

f: [a,b]**n |-> R

The fit space is constrained to map values in the unit box:

f': [0,1]**n |-> R

Here we can define f' using the zero-one mapper:

f' = ZeroOneMapper(f,a,b)
f'(v) = f(x)

An asymptote function maps x to [0,1], preserving at least 12 digits of precision.

Using this mapping, the optimizer can operate in a well known space independent of parameter precision. This allows the use of reasonable constants for items such as a step size and initial value.

Note: we do not yet support fitness functions with analytic derivatives. Given df/dp and mapping function f'(v) = f(M(v)) then df'/dv = df/dM dM/dv. So the derivatives need to be multiplied by the derivative of the parameter mapper. Not difficult computationally, but the definition of the fitness function does not currently support this organization.

Classes
	ArctanAsymptote Arctan asymptote function for mapping (-inf,inf) to [0,1].
	Asymptote Logarithmic asymptote function.
	ZeroOneMapper Map function range into [0,1]**n.

Functions

fp_forward(x)
Linearize floating point values using an exponential scale.

source code

fp_inverse(v)
Restore floating point value from linear form on an exponential scale.

source code

zero_one_mapper(base_function, low, high, asymptote=<class 'park.fitting.rangemap.ArctanAsymptote'>)
Map function range into [0,1]**n.

source code

bounded(function, low, high)
Evaluate a function with bounds checking.

source code

Variables
	fp_max = `2047`
	fp_min = `-2047`

Function Details

fp_forward(x)

source code

Linearize floating point values using an exponential scale.

Convert sign*m*2^e to sign*(e+1023+m), yielding a value in [-2047,2047]

fp_inverse(v)

source code

Restore floating point value from linear form on an exponential scale.

Convert sign*(e+1023+m) to sign*m*2^e, yielding a value in [-1e308,1e308]

zero_one_mapper(base_function, low, high, asymptote=<class 'park.fitting.rangemap.ArctanAsymptote'>)

source code


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

Returns a pair of functions f and inv.  The function f takes an
encoded value in
 encode, which takes x and returns a value
in [0,1] and decode, which takes a value in [0,1] and returns x.

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.

bounded(function, low, high)

source code

Evaluate a function with bounds checking.

This can be used to turn any unconstrained optimizer into a constrained 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.

Note: unused function which may be removed in future versions.