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sfs_utils.py
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sfs_utils.py
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import numpy
from math import exp
from scipy.stats import hypergeom
def calculate_ks(n):
return numpy.arange(1,n)*1.0
def calculate_neutral_sfs(n):
return 1.0/calculate_ks(n)
def calculate_folded_ks(n):
ks = calculate_ks(n)
folded_ks = ks[0:(n+1)/2]
return folded_ks
def fold_sfs(fs):
n = len(fs)+1
folded_fs = (fs + fs[::-1])[0:(n+1)/2]
if (n-1) % 2 != 0:
folded_fs[-1] *= 0.5
return folded_fs/folded_fs[0]
def calculate_folded_theta_multiples(n):
ks = calculate_ks(n)
folded_ks = ks[0:(n+1)/2]
theta_multiples = folded_ks*(n-folded_ks)*1.0/n
if (n-1) % 2 != 0:
theta_multiples[-1] = folded_ks[-1]
return theta_multiples/theta_multiples[0]
def calculate_theta_multiples(n):
return calculate_ks(n)
def calculate_maf_estimate(count,n):
return min([count,n-count])*1.0/n
def calculate_pi_estimate(count, n):
return 1.0*count*(n-count)/(n*(n-1)/2)
def calculate_downsampled_estimate(i,n,m):
downsampled_estimate = numpy.zeros(m+1)
js = numpy.arange(max([0,m-(n-i)]),min([i,m])+1)
downsampled_estimate[js] += hypergeom.pmf(js,n,i,m)
return downsampled_estimate[1:-1]
def calculate_pi(fs):
n = len(fs)+1
ks = calculate_ks(n)
return (ks*(n-ks)*fs).sum()/(n*(n-1)/2)
def calculate_maf(f):
n = len(f)+1
ks = numpy.arange(1,n)*1.0
mafs = numpy.array([min(k,n-k) for k in ks])
return (mafs*f).sum()/f.sum()/n
def downsample_sfs(fs, m):
n = len(fs)+1
downsampled_fs = numpy.zeros(m-1)
for i in xrange(1,n):
downsampled_fs += calculate_downsampled_estimate(i,n,m)*fs[i-1]
return downsampled_fs
def calculate_an(n):
return (1/calculate_ks(n)).sum()
def calculate_waterson(sfs):
n = len(sfs)+1
return sfs.sum()/calculate_an(n)
def calculate_schaeffers_d(sfs):
n = (len(sfs)+1)*1.0
a1 = (1.0/numpy.arange(1,n)).sum()
a2 = numpy.square(1.0/numpy.arange(1,n)).sum()
b1 = (n+2)/(3*(n-1))
b2 = 2*(n*n+n+3)/(9*n*(n-1))
c1 = b1-a1
c2 = b2-(n+2)/(a1*n)+a2/a1/a1
e1 = c1/a1
e2 = c2/(a1*a1+a2)
pi = calculate_pi(sfs)
S = sfs.sum()
d = pi-S/a1
dmin = -(2/n-1/a1)*S
return d/dmin
def calculate_tajimas_d(sfs):
n = (len(sfs)+1)*1.0
a1 = (1.0/numpy.arange(1,n)).sum()
a2 = numpy.square(1.0/numpy.arange(1,n)).sum()
b1 = (n+1.0)/(3*(n-1))
b2 = 2*(n*n+n+3.0)/(9*n*(n-1))
c1 = b1-1.0/a1
c2 = b2-(n+2.0)/(a1*n)+a2/a1/a1
e1 = c1/a1
e2 = c2/(a1*a1+a2)
pi = calculate_pi(sfs)
S = sfs.sum()
d = pi-S/a1
norm = S*(e2**0.5)
return d/norm
def calculate_tajimas_d_sufficient(n,pi,S):
a1 = (1.0/numpy.arange(1,n)).sum()
a2 = numpy.square(1.0/numpy.arange(1,n)).sum()
b1 = (n+1.0)/(3*(n-1))
b2 = 2*(n*n+n+3.0)/(9*n*(n-1))
c1 = b1-1.0/a1
c2 = b2-(n+2.0)/(a1*n)+a2/a1/a1
e1 = c1/a1
e2 = c2/(a1*a1+a2)
d = pi-S/a1
norm = S*(e2**0.5)
return d/norm
if __name__=='__main__':
n = 40
m = 10
neutral_sfs = calculate_neutral_sfs(n)
downsampled_sfs = downsample_sfs(neutral_sfs, m)
print "Original:", neutral_sfs
print "Downsampled:", downsampled_sfs