import numpy as np import matplotlib.pyplot as plt import matplotlib.cm as cm plt.xkcd() fig = plt.figure( figsize=(6,6.8) ) rng = np.random.RandomState(4637281) lmarg=0.1 rmarg=0.1 ax = fig.add_axes([lmarg, 0.75, 1.0-rmarg, 0.25]) ax.spines['bottom'].set_position('zero') ax.spines['left'].set_visible(False) ax.spines['right'].set_visible(False) ax.spines['top'].set_visible(False) ax.xaxis.set_ticks_position('bottom') ax.get_yaxis().set_visible(False) ax.set_xlim(0.0, np.pi) ax.set_xticks(np.arange(0.125*np.pi, 1.*np.pi, 0.125*np.pi)) ax.set_xticklabels([]) ax.set_ylim(0.0, 3.5) ax.text(-0.2, 0.5*3.5, 'Activity', rotation='vertical', va='center') ax.annotate('Tuning curve', xy=(0.42*np.pi, 2.5), xycoords='data', xytext=(0.3*np.pi, 3.2), textcoords='data', ha='right', arrowprops=dict(arrowstyle="->", relpos=(1.0,0.5), connectionstyle="angle3,angleA=-10,angleB=110") ) ax.annotate('', xy=(0.5*np.pi, 0.1), xycoords='data', xytext=(0.5*np.pi, 2.6), textcoords='data', arrowprops=dict(arrowstyle="->", relpos=(0.5,0.5), connectionstyle="angle3,angleA=80,angleB=90") ) ax.text(0.52*np.pi, 0.7, 'preferred\norientation') ax.plot([0, 0], [0.0, 3.5], 'k', zorder=10, clip_on=False) xx = np.arange(0.0, 2.0*np.pi, 0.01) pp = 0.5*np.pi yy = np.exp(np.cos(2.0*(xx+pp))) ax.fill_between(xx, yy+0.25*yy, yy-0.25*yy, color=cm.autumn(0.3, 1), alpha=0.5) ax.plot(xx, yy, color=cm.autumn(0.0, 1)) ax = fig.add_axes([lmarg, 0.34, 1.0-rmarg, 0.38]) ax.spines['bottom'].set_position('zero') ax.spines['left'].set_visible(False) ax.spines['right'].set_visible(False) ax.spines['top'].set_visible(False) ax.xaxis.set_ticks_position('bottom') ax.get_yaxis().set_visible(False) ax.set_xlim(0.0, np.pi) ax.set_xticks(np.arange(0.125*np.pi, 1.*np.pi, 0.125*np.pi)) ax.set_xticklabels([]) ax.set_ylim(-1.5, 3.0) ax.text(0.5*np.pi, -1.8, 'Orientation', ha='center') ax.text(-0.2, 0.5*3.5, 'Activity', rotation='vertical', va='center') ax.plot([0, 0], [0.0, 3.0], 'k', zorder=10, clip_on=False) xx = np.arange(0.0, 1.0*np.pi, 0.01) prefphases = np.arange(0.125*np.pi, 1.*np.pi, 0.125*np.pi) responses = [] xresponse = 0.475*np.pi for pp in prefphases : yy = np.exp(np.cos(2.0*(xx+pp))) ax.plot(xx, yy, color=cm.autumn(2.0*np.abs(pp/np.pi-0.5), 1)) y = np.exp(np.cos(2.0*(xresponse+pp))) responses.append(y + rng.randn()*0.25*y) ax.plot(xresponse, y, '.', markersize=20, color=cm.autumn(2.0*np.abs(pp/np.pi-0.5), 1)) r=0.3 y=-0.8 ax.plot([pp-0.5*r*np.cos(pp), pp+0.5*r*np.cos(pp)], [y-r*np.sin(pp), y+r*np.sin(pp)], 'k', lw=6) responses = np.array(responses) ax = fig.add_axes([lmarg, 0.05, 1.0-rmarg, 0.22]) ax.spines['left'].set_visible(False) ax.spines['right'].set_visible(False) ax.spines['top'].set_visible(False) ax.xaxis.set_ticks_position('bottom') ax.get_yaxis().set_visible(False) ax.set_xlim(0.0, np.pi) ax.set_xticks(np.arange(0.125*np.pi, 1.*np.pi, 0.125*np.pi)) ax.set_xticklabels([]) ax.set_ylim(-1600, 0) ax.set_xlabel('Orientiation') ax.text(-0.2, -800, 'Log-Likelihood', rotation='vertical', va='center') ax.plot([0, 0], [-1600, 0], 'k', zorder=10, clip_on=False) phases = np.linspace(0.0, 1.1*np.pi, 100) probs = np.zeros((len(responses), len(phases))) for k, (pp, r) in enumerate(zip(prefphases, responses)) : y = np.exp(np.cos(2.0*(phases+pp))) sigma = 0.1*y probs[k,:] = np.exp(-0.5*((r-y)/sigma)**2.0)/np.sqrt(2.0*np.pi)/sigma loglikelihood = np.sum(np.log(probs), 0) maxl = np.max(loglikelihood) maxp = phases[np.argmax(loglikelihood)] ax.annotate('', xy=(maxp, -1600), xycoords='data', xytext=(maxp, -30), textcoords='data', arrowprops=dict(arrowstyle="->", relpos=(0.5,0.5), connectionstyle="angle3,angleA=80,angleB=90") ) ax.text(maxp+0.05, -1100, 'most likely\norientation\ngiven the responses') ax.plot(phases, loglikelihood, '-b') plt.savefig('mlecoding.pdf') #plt.show();