昨天周末晚上没有出去，码了一小段，先留着kangkang。

import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
from tqdm import tqdm

# wrapper class for an interval
# readability is more important than efficiency, so I won't use many tricks
class Interval:
# [@left, @right)
def __init__(self, left, right):
self.left = left
self.right = right

# whether a point is in this interval
def contain(self, x):
return self.left <= x < self.right

# length of this interval
def size(self):
return self.right - self.left

# domain of the square wave, [0, 2)
DOMAIN = Interval(0.0, 2.0)

# square wave function
def square_wave(x):
if 0.5 < x < 1.5:
return 1
return 0

# get @n samples randomly from the square wave
def sample(n):
samples = []
for i in range(0, n):
x = np.random.uniform(DOMAIN.left, DOMAIN.right)
y = square_wave(x)
samples.append([x, y])
return samples

# wrapper class for value function
class ValueFunction:
# @domain: domain of this function, an instance of Interval
# @alpha: basic step size for one update
def __init__(self, feature_width, domain=DOMAIN, alpha=0.2, num_of_features=50):
self.feature_width = feature_width
self.num_of_featrues = num_of_features
self.features = []
self.alpha = alpha
self.domain = domain

# there are many ways to place those feature windows,
# following is just one possible way
step = (domain.size() - feature_width) / (num_of_features - 1)
left = domain.left
for i in range(0, num_of_features - 1):
self.features.append(Interval(left, left + feature_width))
left += step
self.features.append(Interval(left, domain.right))

# initialize weight for each feature
self.weights = np.zeros(num_of_features)

# for point @x, return the indices of corresponding feature windows
def get_active_features(self, x):
active_features = []
for i in range(0, len(self.features)):
if self.features[i].contain(x):
active_features.append(i)
return active_features

# estimate the value for point @x
def value(self, x):
active_features = self.get_active_features(x)
return np.sum(self.weights[active_features])

# update weights given sample of point @x
# @delta: y - x
def update(self, delta, x):
active_features = self.get_active_features(x)
delta *= self.alpha / len(active_features)
for index in active_features:
self.weights[index] += delta

# train @value_function with a set of samples @samples
def approximate(samples, value_function):
for x, y in samples:
delta = y - value_function.value(x)
value_function.update(delta, x)

# Figure 9.8
def figure_9_8():
num_of_samples = [10, 40, 160, 640, 2560, 10240]
feature_widths = [0.2, 0.4, 1.0]
plt.figure(figsize=(30, 20))
axis_x = np.arange(DOMAIN.left, DOMAIN.right, 0.02)
for index, num_of_sample in enumerate(num_of_samples):
print(num_of_sample, 'samples')
samples = sample(num_of_sample)
value_functions = [ValueFunction(feature_width) for feature_width in feature_widths]
plt.subplot(2, 3, index + 1)
plt.title('%d samples' % (num_of_sample))
for value_function in value_functions:
approximate(samples, value_function)
values = [value_function.value(x) for x in axis_x]
plt.plot(axis_x, values, label='feature width %.01f' % (value_function.feature_width))
plt.legend()

plt.savefig('../images/figure_9_8.png')
plt.close()

if __name__ == '__main__':
figure_9_8()

有更好的想法，再编辑完善一下，嘿嘿

巴特西

昨天周末晚上没有出去，码了一小段，先留着kangkang。

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