96 lines
3.7 KiB
Python
96 lines
3.7 KiB
Python
import numpy as np
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import matplotlib.pyplot as plt
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import matplotlib.cm as cm
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import matplotlib.gridspec as gridspec
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from plotstyle import *
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rng = np.random.RandomState(4637281)
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fig = plt.figure(figsize=cm_size(figure_width, 2.8*figure_height))
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spec = gridspec.GridSpec(nrows=4, ncols=1, height_ratios=[4, 5, 1, 3], hspace=0.2,
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**adjust_fs(fig, left=4.0))
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ax = fig.add_subplot(spec[0, 0])
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ax.set_xlim(0.0, np.pi)
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ax.set_xticks(np.arange(0.125*np.pi, 1.*np.pi, 0.125*np.pi))
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ax.set_xticklabels([])
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ax.set_ylim(0.0, 3.5)
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ax.yaxis.set_major_locator(plt.NullLocator())
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ax.text(-0.2, 0.5*3.5, 'Firing rate', rotation='vertical', va='center')
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ax.annotate('Tuning curve',
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xy=(0.42*np.pi, 2.5), xycoords='data',
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xytext=(0.3*np.pi, 3.2), textcoords='data', ha='right',
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arrowprops=dict(arrowstyle="->", relpos=(1.0,0.5),
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connectionstyle="angle3,angleA=-10,angleB=110") )
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ax.annotate('',
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xy=(0.5*np.pi, 0.1), xycoords='data',
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xytext=(0.5*np.pi, 2.6), textcoords='data',
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arrowprops=dict(arrowstyle="->", relpos=(0.5,0.5),
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connectionstyle="angle3,angleA=80,angleB=90") )
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ax.text(0.52*np.pi, 0.7, 'preferred\norientation')
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xx = np.arange(0.0, 2.0*np.pi, 0.01)
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pp = 0.5*np.pi
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yy = np.exp(np.cos(2.0*(xx+pp)))
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ss = 1.0/(0.75+2.0*yy)
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ax.fill_between(xx, yy+ss, yy-ss, **fsBa)
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ax.plot(xx, yy, **lsB)
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ax = fig.add_subplot(spec[1, 0])
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ax.set_xlim(0.0, np.pi)
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ax.set_xticks(np.arange(0.125*np.pi, 1.*np.pi, 0.125*np.pi))
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ax.set_xticklabels([])
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ax.set_ylim(-0.1, 3.5)
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ax.yaxis.set_major_locator(plt.NullLocator())
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ax.text(-0.2, 0.5*3.5, 'Firing rate', rotation='vertical', va='center')
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xx = np.arange(0.0, 1.0*np.pi, 0.01)
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prefphases = np.arange(0.125*np.pi, 1.*np.pi, 0.125*np.pi)
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responses = []
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sigmas = []
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xresponse = 0.41*np.pi
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ax.annotate('Orientation of bar',
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xy=(xresponse, -0.1), xycoords='data',
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xytext=(xresponse, 3.1), textcoords='data', ha='left', zorder=-10,
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arrowprops=dict(arrowstyle="->", relpos=(0.0,0.0)) )
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for pp, ls, ps in zip(prefphases, [lsE, lsC, lsD, lsB, lsD, lsC, lsE],
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[psE, psC, psD, psB, psD, psC, psE]) :
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yy = np.exp(np.cos(2.0*(xx+pp)))
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ax.plot(xx, yy, **ls)
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y = np.exp(np.cos(2.0*(xresponse+pp)))
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s = 1.0/(0.75+2.0*y)
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responses.append(y + rng.randn()*s)
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sigmas.append(s)
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ax.plot(xresponse, y, **ps)
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responses = np.array(responses)
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ax = fig.add_subplot(spec[2, 0])
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ax.show_spines('')
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r = 0.3
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ax.set_ylim(-1.1*r, 1.1*r)
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for pp in prefphases:
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ax.plot([pp-0.5*r*np.cos(pp), pp+0.5*r*np.cos(pp)], [-r*np.sin(pp), r*np.sin(pp)],
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colors['black'], lw=6, clip_on=False)
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ax = fig.add_subplot(spec[3, 0])
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ax.set_xlim(0.0, np.pi)
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ax.set_xticks(np.arange(0.125*np.pi, 1.*np.pi, 0.125*np.pi))
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ax.set_xticklabels([])
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ax.set_ylim(-210, 0)
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ax.yaxis.set_major_locator(plt.NullLocator())
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ax.set_xlabel('Orientation')
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ax.text(-0.2, -100, 'Log-Likelihood', rotation='vertical', va='center')
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phases = np.linspace(0.0, 1.1*np.pi, 100)
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probs = np.zeros((len(responses), len(phases)))
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for k, (pp, r, sigma) in enumerate(zip(prefphases, responses, sigmas)) :
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y = np.exp(np.cos(2.0*(phases+pp)))
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probs[k,:] = np.exp(-0.5*((r-y)/sigma)**2.0)/np.sqrt(2.0*np.pi*sigma**2)
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loglikelihood = np.sum(np.log(probs), 0)
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maxp = phases[np.argmax(loglikelihood)]
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ax.annotate('',
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xy=(maxp, -210), xycoords='data',
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xytext=(maxp, -10), textcoords='data',
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arrowprops=dict(arrowstyle="->", relpos=(0.5,0.5),
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connectionstyle="angle3,angleA=80,angleB=90") )
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ax.text(maxp+0.05, -150, 'most likely\norientation\ngiven the responses')
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ax.plot(phases, loglikelihood, clip_on=False, **lsA)
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plt.savefig('mlecoding.pdf')
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