autodl-projects/xautodl/datasets/math_adv_funcs.py
2021-05-24 13:06:10 +08:00

129 lines
4.2 KiB
Python

#####################################################
# Copyright (c) Xuanyi Dong [GitHub D-X-Y], 2021.03 #
#####################################################
import math
import abc
import copy
import numpy as np
from typing import Optional
import torch
import torch.utils.data as data
from .math_base_funcs import FitFunc
from .math_base_funcs import QuadraticFunc
from .math_base_funcs import QuarticFunc
class ConstantFunc(FitFunc):
"""The constant function: f(x) = c."""
def __init__(self, constant=None, xstr="x"):
param = dict()
param[0] = constant
super(ConstantFunc, self).__init__(0, None, param, xstr)
def __call__(self, x):
self.check_valid()
return self._params[0]
def fit(self, **kwargs):
raise NotImplementedError
def _getitem(self, x, weights):
raise NotImplementedError
def __repr__(self):
return "{name}({a})".format(name=self.__class__.__name__, a=self._params[0])
class ComposedSinFunc(FitFunc):
"""The composed sin function that outputs:
f(x) = a * sin( b*x ) + c
"""
def __init__(self, params, xstr="x"):
super(ComposedSinFunc, self).__init__(3, None, params, xstr)
def __call__(self, x):
self.check_valid()
a = self._params[0]
b = self._params[1]
c = self._params[2]
return a * math.sin(b * x) + c
def _getitem(self, x, weights):
raise NotImplementedError
def __repr__(self):
return "{name}({a} * sin({b} * {x}) + {c})".format(
name=self.__class__.__name__,
a=self._params[0],
b=self._params[1],
c=self._params[2],
x=self.xstr,
)
class ComposedSinFuncV2(FitFunc):
"""The composed sin function that outputs:
f(x) = amplitude-scale-of(x) * sin( period-phase-shift-of(x) )
- the amplitude scale is a quadratic function of x
- the period-phase-shift is another quadratic function of x
"""
def __init__(self, **kwargs):
super(ComposedSinFuncV2, self).__init__(0, None)
self.fit(**kwargs)
def __call__(self, x):
self.check_valid()
scale = self._params["amplitude_scale"](x)
period_phase = self._params["period_phase_shift"](x)
return scale * math.sin(period_phase)
def fit(self, **kwargs):
num_sin_phase = kwargs.get("num_sin_phase", 7)
sin_speed_use_power = kwargs.get("sin_speed_use_power", True)
min_amplitude = kwargs.get("min_amplitude", 1)
max_amplitude = kwargs.get("max_amplitude", 4)
phase_shift = kwargs.get("phase_shift", 0.0)
# create parameters
if kwargs.get("amplitude_scale", None) is None:
amplitude_scale = QuadraticFunc(
[(0, min_amplitude), (0.5, max_amplitude), (1, min_amplitude)]
)
else:
amplitude_scale = kwargs.get("amplitude_scale")
if kwargs.get("period_phase_shift", None) is None:
fitting_data = []
if sin_speed_use_power:
temp_max_scalar = 2 ** (num_sin_phase - 1)
else:
temp_max_scalar = num_sin_phase - 1
for i in range(num_sin_phase):
if sin_speed_use_power:
value = (2 ** i) / temp_max_scalar
next_value = (2 ** (i + 1)) / temp_max_scalar
else:
value = i / temp_max_scalar
next_value = (i + 1) / temp_max_scalar
for _phase in (0, 0.25, 0.5, 0.75):
inter_value = value + (next_value - value) * _phase
fitting_data.append((inter_value, math.pi * (2 * i + _phase)))
period_phase_shift = QuarticFunc(fitting_data)
else:
period_phase_shift = kwargs.get("period_phase_shift")
self.set(
dict(amplitude_scale=amplitude_scale, period_phase_shift=period_phase_shift)
)
def _getitem(self, x, weights):
raise NotImplementedError
def __repr__(self):
return "{name}({amplitude_scale} * sin({period_phase_shift}))".format(
name=self.__class__.__name__,
amplitude_scale=self._params["amplitude_scale"],
period_phase_shift=self._params["period_phase_shift"],
)