import numpy as np import scipy.stats as st import matplotlib.pyplot as plt import matplotlib.gridspec as gridspec import matplotlib.ticker as ticker from plotstyle import * rng = np.random.RandomState(37281) # generate correlated data: n = 200 a = 0.2 x = rng.randn(n); y = rng.randn(n) + a*x; #x = rng.exponential(1.0, n); #y = rng.exponential(2.0, n) + a*x; rd = np.corrcoef(x, y)[0, 1] # permutation: nperm = 1000 rs = [] for i in range(nperm) : xr = rng.permutation(x) yr = rng.permutation(y) rs.append(np.corrcoef(xr, yr)[0, 1]) rr = np.corrcoef(xr, yr)[0, 1] # pdf of the correlation coefficients: h, b = np.histogram(rs, 20, density=True) # significance: rq = np.percentile(rs, 95.0) print('Measured correlation coefficient = %.2f, correlation coefficient at 95%% percentile of permutation = %.2f' % (rd, rq)) ra = 1.0-0.01*st.percentileofscore(rs, rd) print('Measured correlation coefficient %.2f is at %.4f percentile of permutation' % (rd, ra)) rp, ra = st.pearsonr(x, y) print('Measured correlation coefficient %.2f is at %.4f percentile of test' % (rp, ra)) fig = plt.figure(figsize=cm_size(figure_width, 1.8*figure_height)) gs = gridspec.GridSpec(nrows=2, ncols=2, wspace=0.35, hspace=0.8, **adjust_fs(fig, left=5.0, right=1.5, top=1.0, bottom=2.7)) ax = fig.add_subplot(gs[0,0]) ax.text(0.0, 4.0, 'r=%.2f' % rd, ha='center') ax.plot(x, y, **psAm) ax.set_xlim(-4.0, 4.0) ax.set_ylim(-4.0, 4.0) ax.xaxis.set_major_locator(ticker.MultipleLocator(2.0)) ax.yaxis.set_major_locator(ticker.MultipleLocator(2.0)) ax.set_xlabel('x') ax.set_ylabel('y') ax = fig.add_subplot(gs[0,1]) ax.text(0.0, 4.0, 'r=%.2f' % rr, ha='center') ax.plot(xr, yr, **psAm) ax.set_xlim(-4.0, 4.0) ax.set_ylim(-4.0, 4.0) ax.xaxis.set_major_locator(ticker.MultipleLocator(2.0)) ax.yaxis.set_major_locator(ticker.MultipleLocator(2.0)) ax.set_xlabel('Shuffled x') ax.set_ylabel('Shuffled y') ax = fig.add_subplot(gs[1,:]) ax.annotate('Measured\ncorrelation\nis significant!', xy=(rd, 1.1), xycoords='data', xytext=(rd-0.01, 3.0), textcoords='data', ha='left', arrowprops=dict(arrowstyle="->", relpos=(0.3,0.0), connectionstyle="angle3,angleA=10,angleB=80") ) ax.annotate('95% percentile', xy=(0.14, 0.9), xycoords='data', xytext=(0.16, 6.2), textcoords='data', ha='left', arrowprops=dict(arrowstyle="->", relpos=(0.1,0.0), connectionstyle="angle3,angleA=30,angleB=80") ) ax.annotate('Distribution of\nuncorrelated\nsamples', xy=(-0.08, 3.6), xycoords='data', xytext=(-0.22, 5.0), textcoords='data', ha='left', arrowprops=dict(arrowstyle="->", relpos=(0.5,0.0), connectionstyle="angle3,angleA=150,angleB=110") ) ax.bar(b[:-1], h, width=b[1]-b[0], **fsC) ax.bar(b[:-1][b[:-1]>=rq], h[b[:-1]>=rq], width=b[1]-b[0], **fsB) ax.plot( [rd, rd], [0, 1], **lsA) ax.set_xlim(-0.25, 0.35) ax.set_ylim(0.0, 6.0) ax.yaxis.set_major_locator(ticker.MultipleLocator(2.0)) ax.set_xlabel('Correlation coefficient') ax.set_ylabel('PDF of H0') plt.savefig('permutecorrelation.pdf')