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48 lines
1.0 KiB
Python
48 lines
1.0 KiB
Python
from __future__ import division, print_function, absolute_import
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import numpy as np
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import scipy.stats
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from scipy.special import i0
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def von_mises_cdf_series(k,x,p):
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x = float(x)
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s = np.sin(x)
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c = np.cos(x)
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sn = np.sin(p*x)
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cn = np.cos(p*x)
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R = 0
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V = 0
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for n in range(p-1,0,-1):
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sn, cn = sn*c - cn*s, cn*c + sn*s
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R = 1./(2*n/k + R)
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V = R*(sn/n+V)
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return 0.5+x/(2*np.pi) + V/np.pi
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def von_mises_cdf_normalapprox(k,x,C1):
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b = np.sqrt(2/np.pi)*np.exp(k)/i0(k)
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z = b*np.sin(x/2.)
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return scipy.stats.norm.cdf(z)
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def von_mises_cdf(k,x):
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ix = 2*np.pi*np.round(x/(2*np.pi))
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x = x-ix
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k = float(k)
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# These values should give 12 decimal digits
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CK = 50
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a = [28., 0.5, 100., 5.0]
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C1 = 50.1
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if k < CK:
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p = int(np.ceil(a[0]+a[1]*k-a[2]/(k+a[3])))
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F = np.clip(von_mises_cdf_series(k,x,p),0,1)
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else:
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F = von_mises_cdf_normalapprox(k,x,C1)
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return F+ix
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