def test_wright_fisher(self):
N_diallelic = 3
s = 0.03
# compute the wright fisher transition matrix directly
Ma = np.exp(wfengine.create_genic_diallelic(N_diallelic, s))
MatrixUtil.assert_transition_matrix(Ma)
# compute the wright fisher transition matrix less directly
N = 2 * N_diallelic
fi = 1.0
fj = 1.0 - s
log_distns = np.zeros((N + 1, 2))
for h in range(0, N + 1):
probs = genic_diallelic(fi, fj, h, (N - h))
log_distns[h] = np.log(np.array(probs))
Mb = np.exp(wfengine.expand_multinomials(N, log_distns))
MatrixUtil.assert_transition_matrix(Mb)
# compare the transition matrices
self.assertTrue(np.allclose(Ma, Mb))
def test_wright_fisher(self):
N_diallelic = 3
s = 0.03
# compute the wright fisher transition matrix directly
Ma = np.exp(wfengine.create_genic_diallelic(N_diallelic, s))
MatrixUtil.assert_transition_matrix(Ma)
# compute the wright fisher transition matrix less directly
N = 2*N_diallelic
fi = 1.0
fj = 1.0 - s
log_distns = np.zeros((N+1, 2))
for h in range(0, N+1):
probs = genic_diallelic(fi, fj, h, (N-h))
log_distns[h] = np.log(np.array(probs))
Mb = np.exp(wfengine.expand_multinomials(N, log_distns))
MatrixUtil.assert_transition_matrix(Mb)
# compare the transition matrices
self.assertTrue(np.allclose(Ma, Mb))
def get_response_content(fs):
initial_composition = (fs.nAB, fs.nAb, fs.naB, fs.nab)
npop = sum(initial_composition)
nstates = get_state_space_size(npop)
# Check for minimum population size.
if npop < 1:
raise ValueError('there should be at least one individual')
# Check the complexity;
# solving a system of linear equations takes about n^3 effort.
if npop > 32:
raise ValueError('sorry this population size is too large')
# Compute the transition matrix.
tm = time.time()
child_distns = get_child_distns(npop, fs.sAB, fs.sAb, fs.saB, fs.r)
log_child_distns = np.log(child_distns)
print time.time() - tm, 'seconds to compute the log child distributions'
tm = time.time()
log_P = wfengine.expand_multinomials(npop, log_child_distns)
print time.time() - tm, 'seconds to compute the log transition matrix'
tm = time.time()
P = np.exp(log_P)
print time.time() - tm, 'seconds to entrywise exponentiate the matrix'
# Precompute the map from compositions to state index.
compositions = list(gen_population_compositions(npop))
c_to_i = dict((c, i) for i, c in enumerate(compositions))
# Compute the exact probabilities of fixation.
tm = time.time()
fixation_distribution = solve(npop, P)[c_to_i[initial_composition]]
print time.time() - tm, 'seconds to solve the linear system'
# Write the output
out = StringIO()
print >> out, 'distribution over eventual allele fixations:'
for p, name in zip(fixation_distribution, ('AB', 'Ab', 'aB', 'ab')):
print >> out, name, ':', p
"""
print >> out, 'probability of eventual fixation (as opposed to extinction)'
print >> out, 'of allele B in the population:'
print >> out, p_fixation
print >> out
print >> out, 'Kimura would give the approximation'
print >> out, k_top / k_bot
print >> out
"""
"""
# Compute low-population approximations of probability of fixation of B.
pB = fs.nB / float(fs.nB + fs.nb)
for nsmall, name in (
(10, 'low population size'),
(20, 'medium population size'),
):
if nsmall >= npop:
continue
s_small = fs.s * npop / float(nsmall)
# Compute all low-population approximations.
x = solve(nsmall, s_small)
f_linear = interpolate.interp1d(range(nsmall+1), x, kind='linear')
f_cubic = interpolate.interp1d(range(nsmall+1), x, kind='cubic')
print >> out, 'linearly interpolated %s (N=%s)' % (name, nsmall)
print >> out, 'approximation of probability of eventual'
print >> out, 'fixation (as opposed to extinction)'
print >> out, 'of allele B in the population:'
print >> out, f_linear(pB*nsmall)
print >> out
print >> out, 'cubic interpolation:'
print >> out, f_cubic(pB*nsmall)
print >> out
"""
return out.getvalue()
def get_response_content(fs):
initial_composition = (fs.nAB, fs.nAb, fs.naB, fs.nab)
npop = sum(initial_composition)
nstates = get_state_space_size(npop)
# Check for minimum population size.
if npop < 1:
raise ValueError('there should be at least one individual')
# Check the complexity;
# solving a system of linear equations takes about n^3 effort.
if npop > 32:
raise ValueError('sorry this population size is too large')
# Compute the transition matrix.
tm = time.time()
child_distns = get_child_distns(npop, fs.sAB, fs.sAb, fs.saB, fs.r)
log_child_distns = np.log(child_distns)
print time.time() - tm, 'seconds to compute the log child distributions'
tm = time.time()
log_P = wfengine.expand_multinomials(npop, log_child_distns)
print time.time() - tm, 'seconds to compute the log transition matrix'
tm = time.time()
P = np.exp(log_P)
print time.time() - tm, 'seconds to entrywise exponentiate the matrix'
# Precompute the map from compositions to state index.
compositions = list(gen_population_compositions(npop))
c_to_i = dict((c, i) for i, c in enumerate(compositions))
# Compute the exact probabilities of fixation.
tm = time.time()
fixation_distribution = solve(npop, P)[c_to_i[initial_composition]]
print time.time() - tm, 'seconds to solve the linear system'
# Write the output
out = StringIO()
print >> out, 'distribution over eventual allele fixations:'
for p, name in zip(fixation_distribution, ('AB', 'Ab', 'aB', 'ab')):
print >> out, name, ':', p
"""
print >> out, 'probability of eventual fixation (as opposed to extinction)'
print >> out, 'of allele B in the population:'
print >> out, p_fixation
print >> out
print >> out, 'Kimura would give the approximation'
print >> out, k_top / k_bot
print >> out
"""
"""
# Compute low-population approximations of probability of fixation of B.
pB = fs.nB / float(fs.nB + fs.nb)
for nsmall, name in (
(10, 'low population size'),
(20, 'medium population size'),
):
if nsmall >= npop:
continue
s_small = fs.s * npop / float(nsmall)
# Compute all low-population approximations.
x = solve(nsmall, s_small)
f_linear = interpolate.interp1d(range(nsmall+1), x, kind='linear')
f_cubic = interpolate.interp1d(range(nsmall+1), x, kind='cubic')
print >> out, 'linearly interpolated %s (N=%s)' % (name, nsmall)
print >> out, 'approximation of probability of eventual'
print >> out, 'fixation (as opposed to extinction)'
print >> out, 'of allele B in the population:'
print >> out, f_linear(pB*nsmall)
print >> out
print >> out, 'cubic interpolation:'
print >> out, f_cubic(pB*nsmall)
print >> out
"""
return out.getvalue()