82 lines
2.7 KiB
Python
82 lines
2.7 KiB
Python
import matplotlib.pyplot as plt
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import numpy as np
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def create_data():
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m = 0.75
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n= -40
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x = np.concatenate( (np.arange(10.,110., 2.5), np.arange(0.,120., 2.0)) )
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y = m * x + n;
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rng = np.random.RandomState(37281)
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noise = rng.randn(len(x))*15
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y += noise
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return x, y, m, n
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def plot_data(ax, x, y, m, n):
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ax.spines["right"].set_visible(False)
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ax.spines["top"].set_visible(False)
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ax.yaxis.set_ticks_position('left')
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ax.xaxis.set_ticks_position('bottom')
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ax.tick_params(direction="out", width=1.25)
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ax.tick_params(direction="out", width=1.25)
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ax.set_xlabel('Input x')
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ax.set_ylabel('Output y')
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ax.set_xlim(0, 120)
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ax.set_ylim(-80, 80)
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ax.set_xticks(np.arange(0,121, 40))
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ax.set_yticks(np.arange(-80,81, 40))
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ax.annotate('Error',
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xy=(x[34]+1, y[34]+15), xycoords='data',
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xytext=(80, -50), textcoords='data', ha='left',
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arrowprops=dict(arrowstyle="->", relpos=(0.9,1.0),
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connectionstyle="angle3,angleA=50,angleB=-30") )
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ax.scatter(x[:40], y[:40], color='b', s=10, zorder=0)
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inxs = [3, 13, 16, 19, 25, 34, 36]
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ax.scatter(x[inxs], y[inxs], color='b', s=40, zorder=10)
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xx = np.asarray([2, 118])
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ax.plot(xx, m*xx+n, color='#CC0000', lw=2)
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for i in inxs :
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xx = [x[i], x[i]]
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yy = [m*x[i]+n, y[i]]
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ax.plot(xx, yy, color='#FF9900', lw=2, zorder=5)
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def plot_error_hist(ax, x, y, m, n):
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ax.spines["right"].set_visible(False)
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ax.spines["top"].set_visible(False)
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ax.yaxis.set_ticks_position('left')
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ax.xaxis.set_ticks_position('bottom')
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ax.tick_params(direction="out", width=1.25)
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ax.tick_params(direction="out", width=1.25)
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ax.set_xlabel('Squared error')
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ax.set_ylabel('Frequency')
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bins = np.arange(0.0, 602.0, 50.0)
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ax.set_xlim(bins[0], bins[-1])
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ax.set_ylim(0, 35)
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ax.set_xticks(np.arange(bins[0], bins[-1], 100))
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ax.set_yticks(np.arange(0, 36, 10))
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errors = (y-(m*x+n))**2.0
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mls = np.mean(errors)
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ax.annotate('Mean\nsquared\nerror',
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xy=(mls, 0.5), xycoords='data',
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xytext=(350, 20), textcoords='data', ha='left',
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arrowprops=dict(arrowstyle="->", relpos=(0.0,0.2),
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connectionstyle="angle3,angleA=10,angleB=90") )
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ax.hist(errors, bins, color='#FF9900')
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if __name__ == "__main__":
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x, y, m, n = create_data()
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plt.xkcd()
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fig = plt.figure()
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ax = fig.add_subplot(1, 2, 1)
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plot_data(ax, x, y, m, n)
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ax = fig.add_subplot(1, 2, 2)
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plot_error_hist(ax, x, y, m, n)
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fig.set_facecolor("white")
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fig.set_size_inches(7., 2.6)
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fig.tight_layout()
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fig.savefig("linear_least_squares.pdf")
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plt.close()
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