61 lines
1.9 KiB
Python
61 lines
1.9 KiB
Python
import numpy as np
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import matplotlib.pyplot as plt
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plt.xkcd()
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fig = plt.figure( figsize=(6,3.5) )
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rng = np.random.RandomState(637281)
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# generate correlated data:
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n = 200
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a = 0.2
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x = rng.randn(n);
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y = rng.randn(n) + a*x;
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rd = np.corrcoef(x, y)[0, 1]
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print rd
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# permutation:
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nperm = 1000
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rs = []
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for i in xrange(nperm) :
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xr=rng.permutation(x)
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yr=rng.permutation(y)
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rs.append( np.corrcoef(xr, yr)[0, 1] )
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# pdf of the correlation coefficients:
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h, b = np.histogram(rs, 20, density=True)
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# significance:
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rq = np.percentile(rs, 95.0);
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ax = fig.add_subplot(1, 1, 1)
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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.annotate('Measured\ncorrelation\nis significant!',
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xy=(rd, 1.1), xycoords='data',
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xytext=(rd, 2.2), textcoords='data', ha='left',
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arrowprops=dict(arrowstyle="->", relpos=(0.2,0.0),
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connectionstyle="angle3,angleA=10,angleB=80") )
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ax.annotate('95% percentile',
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xy=(0.14, 0.9), xycoords='data',
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xytext=(0.2, 4.0), textcoords='data', ha='left',
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arrowprops=dict(arrowstyle="->", relpos=(0.1,0.0),
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connectionstyle="angle3,angleA=30,angleB=70") )
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ax.annotate('Distribution of\nuncorrelated\nsamples',
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xy=(-0.08, 3.6), xycoords='data',
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xytext=(-0.22, 5.0), textcoords='data', ha='left',
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arrowprops=dict(arrowstyle="->", relpos=(0.5,0.0),
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connectionstyle="angle3,angleA=150,angleB=100") )
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ax.bar(b[:-1], h, width=b[1]-b[0], color='#ffff66')
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ax.bar(b[:-1][b[:-1]>=rq], h[b[:-1]>=rq], width=b[1]-b[0], color='#ff9900')
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ax.plot( [rd, rd], [0, 1], 'b', linewidth=4 )
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ax.set_xlim(-0.25, 0.35)
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ax.set_xlabel('Correlation coefficient')
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ax.set_ylabel('Probability density of H0')
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plt.tight_layout()
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plt.savefig('permutecorrelation.pdf')
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#plt.show();
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