Trainable Bezier Curve Multiparameter Regressor

This text details the development of a trainable Bezier curve multiparameter regressor, which involves creating functions for generating curves, adjusting for skew, and evaluating input values. The creation and evaluation process are discussed in detail, providing insights into how this powerful tool can be used in various applications.

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bezier

first, we need a bezier curve connects (0,0) and (1,1)

import numpy as np
import bezier
def bezierCurve(start=(0,0), end=(1,1), skew=0):
# skew: (-0.5,0.5) otherwise this shit will look ugly.
assert skew >=-0.5
assert skew <=0.5
x_start, y_start = start
x_end, y_end = end
x_diff = x_end - x_start
y_diff = y_end - y_start
nodes1 = np.asfortranarray(
[
[x_start, x_diff * (0.5 + skew), x_end],
[y_start, y_diff * (0.5 - skew), y_end],
]
)
curve1 = bezier.Curve(nodes1, degree=2)
curve_params = {'x_start':x_start, 'x_diff':x_diff,'x_end':x_end}
return curve1, curve_params
def evaluateBezierCurve(input_value:float,curve, curve_params:dict)
x_start = curve_params['x_start']
x_end = curve_params['x_end']
assert x_start <= input_value
assert x_end >= input_value
x_diff = curve_params['x_diff']
s = (input_value - x_start)/x_diff
points = curve.evaluate(s)
# we only get the single point.
point = points.T[0]
x,y = point
result = y
return result

then, we define our very recursive or flexible regressor:

def multiParameterExponentialNetwork(*args, input_bias=0.05, curve_function=bezierCurve, curve_function_kwargs = {'start':(0,0),'end':(1,1)'skew':0}, evaluate_function=evaluateBezierCurve):
curve, curve_params = curve_function(**curve_function_kwargs)
value = evaluate_function(input_bias, curve, curve_params)
for index, input_value in enumerate(args):
apply_list = [input_value]*(index+1)
for apply_item in apply_list:
value += (1-value)*function(apply_item, **function_kwargs)
return value