def get_response_content(fs):
M, R = get_input_matrices(fs)
M_v = mrate.R_to_distn(M)
R_v = mrate.R_to_distn(R)
t = fs.t
mi_mut = ctmcmi.get_mutual_information(M, t)
mi_bal = ctmcmi.get_mutual_information(R, t)
fi_mut = divtime.get_fisher_information(M, t)
fi_bal = divtime.get_fisher_information(R, t)
if fs.info_mut:
information_sign = np.sign(mi_mut - mi_bal)
elif fs.info_fis:
information_sign = np.sign(fi_mut - fi_bal)
out = StringIO()
print >> out, '<html>'
print >> out, '<body>'
print >> out
print >> out, '<pre>'
print >> out, 'Explicitly computed answer',
print >> out, '(not a heuristic but may be numerically imprecise):'
if information_sign == 1:
print >> out, '* pure mutation',
print >> out, 'is more informative'
elif information_sign == -1:
print >> out, '* the balance of mutation and selection',
print >> out, 'is more informative'
else:
print >> out, ' the information contents of the two processes',
print >> out, 'are numerically indistinguishable'
print >> out
print >> out
if fs.info_mut:
print >> out, 'Mutual information properties',
print >> out, 'at very small and very large times:'
print >> out
print >> out, get_mi_asymptotics(M, R)
print >> out
print >> out
print >> out, 'Heuristics without regard to time or to the selected',
print >> out, 'information variant (Fisher vs. mutual information):'
print >> out
print >> out, get_heuristics(M, R)
print >> out
print >> out
print >> out, 'Input summary:'
print >> out
print >> out, 'mutation rate matrix:'
print >> out, M
print >> out
print >> out, 'mutation process stationary distribution:'
print >> out, M_v
print >> out
print >> out, 'mutation-selection balance rate matrix:'
print >> out, R
print >> out
print >> out, 'mutation-selection balance stationary distribution:'
print >> out, R_v
print >> out
print >> out, 'mutation process expected rate:'
print >> out, mrate.Q_to_expected_rate(M)
print >> out
print >> out, 'mutation-selection balance expected rate:'
print >> out, mrate.Q_to_expected_rate(R)
print >> out
print >> out
print >> out, 'The following information calculations',
print >> out, 'depend on t = %s:' % t
print >> out
print >> out, 'log(ratio(E(L))) for pure mutation:'
print >> out, ctmcmi.get_ll_ratio_wrong(M, t)
print >> out
print >> out, 'log(ratio(E(L))) for mut-sel balance:'
print >> out, ctmcmi.get_ll_ratio_wrong(R, t)
print >> out
print >> out, 'mutual information for pure mutation:'
print >> out, mi_mut
print >> out
print >> out, 'mutual information for mut-sel balance:'
print >> out, mi_bal
print >> out
print >> out, 'pinsker lower bound mi for pure mutation:'
print >> out, ctmcmi.get_pinsker_lower_bound_mi(M, t)
print >> out
print >> out, 'pinsker lower bound mi for mut-sel balance:'
print >> out, ctmcmi.get_pinsker_lower_bound_mi(R, t)
print >> out
print >> out, 'row based pinsker lower bound mi for pure mutation:'
print >> out, ctmcmi.get_row_based_plb_mi(M, t)
print >> out
print >> out, 'row based pinsker lower bound mi for mut-sel balance:'
print >> out, ctmcmi.get_row_based_plb_mi(R, t)
print >> out
print >> out, 'row based hellinger lower bound mi for pure mutation:'
print >> out, ctmcmi.get_row_based_hellinger_lb_mi(M, t)
print >> out
print >> out, 'row based hellinger lower bound mi for mut-sel balance:'
print >> out, ctmcmi.get_row_based_hellinger_lb_mi(R, t)
print >> out
print >> out, 'Fisher information for pure mutation:'
print >> out, fi_mut
print >> out
print >> out, 'Fisher information for mut-sel balance:'
print >> out, fi_bal
print >> out
print >> out, '</pre>'
#
# create the summaries
summaries = (RateMatrixSummary(M), RateMatrixSummary(R))
print >> out, get_html_table(summaries)
print >> out
print >> out, '<html>'
print >> out, '<body>'
return out.getvalue()
def __call__(self):
"""
Look for a counterexample.
"""
n = self.nstates
# sample a random rate and time and stationary distribution
r = random.expovariate(1)
t = random.expovariate(1)
v = np.random.exponential(1, n)
v /= np.sum(v)
# construct the F81 rate matrix
R = r * np.outer(np.ones(n), v)
R -= np.diag(np.sum(R, axis=1))
# get some information criterion values
mi_general = ctmcmi.get_mutual_information(R, t)
fi_general = divtime.get_fisher_information(R, t)
pollock_general = get_gtr_pollock(R, t)
mi_f81 = get_f81_mi(r, v, t)
fi_f81 = get_f81_fi(r, v, t)
pollock_f81 = get_f81_pollock(r, v, t)
if n == 2:
fi_f81_2state = get_f81_fi_2state(r, v, t)
# check for contradictions
try:
if not np.allclose(mi_general, mi_f81):
raise Contradiction('mutual information')
if not np.allclose(fi_general, fi_f81):
raise Contradiction('fisher information')
if not np.allclose(pollock_general, pollock_f81):
raise Contradiction('neg slope identity proportion')
if n == 2:
if not np.allclose(fi_general, fi_f81_2state):
raise Contradiction('fisher information (2-state)')
except Contradiction as e:
out = StringIO()
print >> out, 'found', str(e), 'contradiction'
print >> out
print >> out, 'GTR mutual information:'
print >> out, mi_general
print >> out
print >> out, 'F81 mutual information:'
print >> out, mi_f81
print >> out
print >> out, 'GTR Fisher information:'
print >> out, fi_general
print >> out
print >> out, 'F81 Fisher information:'
print >> out, fi_f81
print >> out
if n == 2:
print >> out, 'F81 2-state Fisher information:'
print >> out, fi_f81_2state
print >> out
print >> out, 'GTR neg slope identity proportion:'
print >> out, pollock_general
print >> out
print >> out, 'F81 neg slope identity proportion:'
print >> out, pollock_f81
print >> out
self.counterexample = out.getvalue()
return True
return False
def __call__(self):
"""
Look for a counterexample.
"""
n = self.nstates
# sample a random rate and time and stationary distribution
r = random.expovariate(1)
t = random.expovariate(1)
v = np.random.exponential(1, n)
v /= np.sum(v)
# construct the F81 rate matrix
R = r * np.outer(np.ones(n), v)
R -= np.diag(np.sum(R, axis=1))
# get some information criterion values
mi_general = ctmcmi.get_mutual_information(R, t)
fi_general = divtime.get_fisher_information(R, t)
pollock_general = get_gtr_pollock(R, t)
mi_f81 = get_f81_mi(r, v, t)
fi_f81 = get_f81_fi(r, v, t)
pollock_f81 = get_f81_pollock(r, v, t)
if n == 2:
fi_f81_2state = get_f81_fi_2state(r, v, t)
# check for contradictions
try:
if not np.allclose(mi_general, mi_f81):
raise Contradiction('mutual information')
if not np.allclose(fi_general, fi_f81):
raise Contradiction('fisher information')
if not np.allclose(pollock_general, pollock_f81):
raise Contradiction('neg slope identity proportion')
if n == 2:
if not np.allclose(fi_general, fi_f81_2state):
raise Contradiction('fisher information (2-state)')
except Contradiction as e:
out = StringIO()
print >> out, 'found', str(e), 'contradiction'
print >> out
print >> out, 'GTR mutual information:'
print >> out, mi_general
print >> out
print >> out, 'F81 mutual information:'
print >> out, mi_f81
print >> out
print >> out, 'GTR Fisher information:'
print >> out, fi_general
print >> out
print >> out, 'F81 Fisher information:'
print >> out, fi_f81
print >> out
if n == 2:
print >> out, 'F81 2-state Fisher information:'
print >> out, fi_f81_2state
print >> out
print >> out, 'GTR neg slope identity proportion:'
print >> out, pollock_general
print >> out
print >> out, 'F81 neg slope identity proportion:'
print >> out, pollock_f81
print >> out
self.counterexample = out.getvalue()
return True
return False
def get_response_content(fs):
M, R = get_input_matrices(fs)
M_v = mrate.R_to_distn(M)
R_v = mrate.R_to_distn(R)
t = fs.t
mi_mut = ctmcmi.get_mutual_information(M, t)
mi_bal = ctmcmi.get_mutual_information(R, t)
fi_mut = divtime.get_fisher_information(M, t)
fi_bal = divtime.get_fisher_information(R, t)
if fs.info_mut:
information_sign = np.sign(mi_mut - mi_bal)
elif fs.info_fis:
information_sign = np.sign(fi_mut - fi_bal)
out = StringIO()
print >> out, '<html>'
print >> out, '<body>'
print >> out
print >> out, '<pre>'
print >> out, 'Explicitly computed answer',
print >> out, '(not a heuristic but may be numerically imprecise):'
if information_sign == 1:
print >> out, '* pure mutation',
print >> out, 'is more informative'
elif information_sign == -1:
print >> out, '* the balance of mutation and selection',
print >> out, 'is more informative'
else:
print >> out, ' the information contents of the two processes',
print >> out, 'are numerically indistinguishable'
print >> out
print >> out
if fs.info_mut:
print >> out, 'Mutual information properties',
print >> out, 'at very small and very large times:'
print >> out
print >> out, get_mi_asymptotics(M, R)
print >> out
print >> out
print >> out, 'Heuristics without regard to time or to the selected',
print >> out, 'information variant (Fisher vs. mutual information):'
print >> out
print >> out, get_heuristics(M, R)
print >> out
print >> out
print >> out, 'Input summary:'
print >> out
print >> out, 'mutation rate matrix:'
print >> out, M
print >> out
print >> out, 'mutation process stationary distribution:'
print >> out, M_v
print >> out
print >> out, 'mutation-selection balance rate matrix:'
print >> out, R
print >> out
print >> out, 'mutation-selection balance stationary distribution:'
print >> out, R_v
print >> out
print >> out, 'mutation process expected rate:'
print >> out, mrate.Q_to_expected_rate(M)
print >> out
print >> out, 'mutation-selection balance expected rate:'
print >> out, mrate.Q_to_expected_rate(R)
print >> out
print >> out
print >> out, 'The following information calculations',
print >> out, 'depend on t = %s:' % t
print >> out
print >> out, 'log(ratio(E(L))) for pure mutation:'
print >> out, ctmcmi.get_ll_ratio_wrong(M, t)
print >> out
print >> out, 'log(ratio(E(L))) for mut-sel balance:'
print >> out, ctmcmi.get_ll_ratio_wrong(R, t)
print >> out
print >> out, 'mutual information for pure mutation:'
print >> out, mi_mut
print >> out
print >> out, 'mutual information for mut-sel balance:'
print >> out, mi_bal
print >> out
print >> out, 'pinsker lower bound mi for pure mutation:'
print >> out, ctmcmi.get_pinsker_lower_bound_mi(M, t)
print >> out
print >> out, 'pinsker lower bound mi for mut-sel balance:'
print >> out, ctmcmi.get_pinsker_lower_bound_mi(R, t)
print >> out
print >> out, 'row based pinsker lower bound mi for pure mutation:'
print >> out, ctmcmi.get_row_based_plb_mi(M, t)
print >> out
print >> out, 'row based pinsker lower bound mi for mut-sel balance:'
print >> out, ctmcmi.get_row_based_plb_mi(R, t)
print >> out
print >> out, 'row based hellinger lower bound mi for pure mutation:'
print >> out, ctmcmi.get_row_based_hellinger_lb_mi(M, t)
print >> out
print >> out, 'row based hellinger lower bound mi for mut-sel balance:'
print >> out, ctmcmi.get_row_based_hellinger_lb_mi(R, t)
print >> out
print >> out, 'Fisher information for pure mutation:'
print >> out, fi_mut
print >> out
print >> out, 'Fisher information for mut-sel balance:'
print >> out, fi_bal
print >> out
print >> out, '</pre>'
#
# create the summaries
summaries = (RateMatrixSummary(M), RateMatrixSummary(R))
print >> out, get_html_table(summaries)
print >> out
print >> out, '<html>'
print >> out, '<body>'
return out.getvalue()
def sample_row():
n = 4
# sample the exchangeability
S = np.zeros((n, n))
S[1,0] = random.expovariate(1)
S[2,0] = random.expovariate(1)
S[2,1] = random.expovariate(1)
S[3,0] = random.expovariate(1)
S[3,1] = random.expovariate(1)
S[3,2] = random.expovariate(1)
# sample the mutation stationary distribution
mdistn = np.array([random.expovariate(1) for i in range(n)])
mdistn /= np.sum(mdistn)
# sample the mutation selection balance stationary distribution
bdistn = np.array([random.expovariate(1) for i in range(n)])
bdistn /= np.sum(bdistn)
# sample the time
t = random.expovariate(1)
# sample the info type
infotype = random.choice(('infotype.mi', 'infotype.fi'))
# Compute some intermediate variables
# from which the summary statistics and the label are computed.
S = S + S.T
M = S * mdistn
M -= np.diag(np.sum(M, axis=1))
R = mrate.to_gtr_halpern_bruno(M, bdistn)
shannon_ent_mut = -sum(p*log(p) for p in mdistn)
shannon_ent_bal = -sum(p*log(p) for p in bdistn)
logical_ent_mut = 1.0 - sum(p*p for p in mdistn)
logical_ent_bal = 1.0 - sum(p*p for p in bdistn)
expected_rate_mut = mrate.Q_to_expected_rate(M)
expected_rate_bal = mrate.Q_to_expected_rate(R)
spectral_rate_mut = 1 / mrate.R_to_relaxation_time(M)
spectral_rate_bal = 1 / mrate.R_to_relaxation_time(R)
mi_mut = ctmcmi.get_mutual_information(M, t)
mi_bal = ctmcmi.get_mutual_information(R, t)
fi_mut = divtime.get_fisher_information(M, t)
fi_bal = divtime.get_fisher_information(R, t)
# compute the summary statistics
summary_entries = [
shannon_ent_bal - shannon_ent_mut,
logical_ent_bal - logical_ent_mut,
log(shannon_ent_bal) - log(shannon_ent_mut),
log(logical_ent_bal) - log(logical_ent_mut),
expected_rate_bal - expected_rate_mut,
spectral_rate_bal - spectral_rate_mut,
log(expected_rate_bal) - log(expected_rate_mut),
log(spectral_rate_bal) - log(spectral_rate_mut),
mi_bal - mi_mut,
fi_bal - fi_mut,
math.log(mi_bal) - math.log(mi_mut),
math.log(fi_bal) - math.log(fi_mut),
]
# get the definition entries
definition_entries = [
S[1,0], S[2,0], S[2,1], S[3,0], S[3,1], S[3,2],
mdistn[0], mdistn[1], mdistn[2], mdistn[3],
bdistn[0], bdistn[1], bdistn[2], bdistn[3],
infotype,
t,
]
# define the label
if infotype == 'infotype.mi' and mi_mut > mi_bal:
label = 'mut.is.better'
elif infotype == 'infotype.mi' and mi_mut < mi_bal:
label = 'bal.is.better'
elif infotype == 'infotype.fi' and fi_mut > fi_bal:
label = 'mut.is.better'
elif infotype == 'infotype.fi' and fi_mut < fi_bal:
label = 'bal.is.better'
else:
label = 'indistinguishable'
# return the row
return definition_entries + summary_entries + [label]
def sample_row():
n = 4
# sample the exchangeability
S = np.zeros((n, n))
S[1, 0] = random.expovariate(1)
S[2, 0] = random.expovariate(1)
S[2, 1] = random.expovariate(1)
S[3, 0] = random.expovariate(1)
S[3, 1] = random.expovariate(1)
S[3, 2] = random.expovariate(1)
# sample the mutation stationary distribution
mdistn = np.array([random.expovariate(1) for i in range(n)])
mdistn /= np.sum(mdistn)
# sample the mutation selection balance stationary distribution
bdistn = np.array([random.expovariate(1) for i in range(n)])
bdistn /= np.sum(bdistn)
# sample the time
t = random.expovariate(1)
# sample the info type
infotype = random.choice(('infotype.mi', 'infotype.fi'))
# Compute some intermediate variables
# from which the summary statistics and the label are computed.
S = S + S.T
M = S * mdistn
M -= np.diag(np.sum(M, axis=1))
R = mrate.to_gtr_halpern_bruno(M, bdistn)
shannon_ent_mut = -sum(p * log(p) for p in mdistn)
shannon_ent_bal = -sum(p * log(p) for p in bdistn)
logical_ent_mut = 1.0 - sum(p * p for p in mdistn)
logical_ent_bal = 1.0 - sum(p * p for p in bdistn)
expected_rate_mut = mrate.Q_to_expected_rate(M)
expected_rate_bal = mrate.Q_to_expected_rate(R)
spectral_rate_mut = 1 / mrate.R_to_relaxation_time(M)
spectral_rate_bal = 1 / mrate.R_to_relaxation_time(R)
mi_mut = ctmcmi.get_mutual_information(M, t)
mi_bal = ctmcmi.get_mutual_information(R, t)
fi_mut = divtime.get_fisher_information(M, t)
fi_bal = divtime.get_fisher_information(R, t)
# compute the summary statistics
summary_entries = [
shannon_ent_bal - shannon_ent_mut,
logical_ent_bal - logical_ent_mut,
log(shannon_ent_bal) - log(shannon_ent_mut),
log(logical_ent_bal) - log(logical_ent_mut),
expected_rate_bal - expected_rate_mut,
spectral_rate_bal - spectral_rate_mut,
log(expected_rate_bal) - log(expected_rate_mut),
log(spectral_rate_bal) - log(spectral_rate_mut),
mi_bal - mi_mut,
fi_bal - fi_mut,
math.log(mi_bal) - math.log(mi_mut),
math.log(fi_bal) - math.log(fi_mut),
]
# get the definition entries
definition_entries = [
S[1, 0],
S[2, 0],
S[2, 1],
S[3, 0],
S[3, 1],
S[3, 2],
mdistn[0],
mdistn[1],
mdistn[2],
mdistn[3],
bdistn[0],
bdistn[1],
bdistn[2],
bdistn[3],
infotype,
t,
]
# define the label
if infotype == 'infotype.mi' and mi_mut > mi_bal:
label = 'mut.is.better'
elif infotype == 'infotype.mi' and mi_mut < mi_bal:
label = 'bal.is.better'
elif infotype == 'infotype.fi' and fi_mut > fi_bal:
label = 'mut.is.better'
elif infotype == 'infotype.fi' and fi_mut < fi_bal:
label = 'bal.is.better'
else:
label = 'indistinguishable'
# return the row
return definition_entries + summary_entries + [label]
