def get_response_content(fs):
M, R = get_input_matrices(fs)
# create the R table string and scripts
headers = [
't', 'mi.true.mut', 'mi.true.mutsel', 'mi.analog.mut',
'mi.analog.mutsel'
]
npoints = 100
t_low = 0.0
t_high = 5.0
t_incr = (t_high - t_low) / (npoints - 1)
t_values = [t_low + t_incr * i for i in range(npoints)]
# get the data for the R table
arr = []
for t in t_values:
mi_mut = ctmcmi.get_mutual_information(M, t)
mi_mutsel = ctmcmi.get_mutual_information(R, t)
mi_analog_mut = ctmcmi.get_ll_ratio_wrong(M, t)
mi_analog_mutsel = ctmcmi.get_ll_ratio_wrong(R, t)
row = [t, mi_mut, mi_mutsel, mi_analog_mut, mi_analog_mutsel]
arr.append(row)
# get the R table
table_string = RUtil.get_table_string(arr, headers)
# get the R script
script = get_ggplot()
# create the R plot image
device_name = Form.g_imageformat_to_r_function[fs.imageformat]
retcode, r_out, r_err, image_data = RUtil.run_plotter(
table_string, script, device_name)
if retcode:
raise RUtil.RError(r_err)
return image_data
def get_response_content(fs):
M, R = get_input_matrices(fs)
# create the R table string and scripts
headers = [
't',
'mi.true.mut',
'mi.true.mutsel',
'mi.analog.mut',
'mi.analog.mutsel']
npoints = 100
t_low = 0.0
t_high = 5.0
t_incr = (t_high - t_low) / (npoints - 1)
t_values = [t_low + t_incr*i for i in range(npoints)]
# get the data for the R table
arr = []
for t in t_values:
mi_mut = ctmcmi.get_mutual_information(M, t)
mi_mutsel = ctmcmi.get_mutual_information(R, t)
mi_analog_mut = ctmcmi.get_ll_ratio_wrong(M, t)
mi_analog_mutsel = ctmcmi.get_ll_ratio_wrong(R, t)
row = [t, mi_mut, mi_mutsel, mi_analog_mut, mi_analog_mutsel]
arr.append(row)
# get the R table
table_string = RUtil.get_table_string(arr, headers)
# get the R script
script = get_ggplot()
# create the R plot image
device_name = Form.g_imageformat_to_r_function[fs.imageformat]
retcode, r_out, r_err, image_data = RUtil.run_plotter(
table_string, script, device_name)
if retcode:
raise RUtil.RError(r_err)
return image_data
def test_large_variance(self):
n = 4
v = sample_distribution(n)
S = sample_symmetric_rate_matrix(n)
R = mrate.to_gtr_halpern_bruno(S, v)
"""
a = .1
b = .2
c = .7
R = np.array([
[-(b+c), b, c],
[a, -(a+c), c],
[a, b, -(a+b)]])
"""
t = 2.0
dt = 0.0000001
rtime = mrate.R_to_relaxation_time(R)
var_a = get_ml_variance(R, t)
var_b = get_ml_variance(R, t+dt)
var_slope = (var_b - var_a) / dt
deriv_ratio = get_p_id_deriv_ratio(R, t)
clever_ratio = get_ml_variance_ratio(R, t)
print 'time:', t
print 'variance:', var_a
print 'variance slope:', var_slope
print 'var_slope / var_a:', var_slope / var_a
print 'var_slope / var_a [clever]:', clever_ratio
print 'log variance:', math.log(var_a)
print 'relaxation time:', rtime
print '2 / relaxation_time:', 2 / rtime
print "p_id(t)'' / p_id(t)':", deriv_ratio
print
print '--- new attempt ---'
print 'mutual information:', ctmcmi.get_mutual_information(R, t)
print 'reciprocal of MI:', 1.0 / ctmcmi.get_mutual_information(R, t)
print 'asymptotic variance:', get_asymptotic_variance(R, t)
print 'asymptotic variance (ver. 2):', get_asymptotic_variance_b(R, t)
print 'asymptotic variance (ver. 3):', get_asymptotic_variance_c(R, t)
print 'AV approx (ver. 4):', get_asymptotic_variance_d(R, t)
print 'AV approx (ver. 5):', get_asymptotic_variance_e(R, t)
print
print '--- another thing ---'
fi_slow = get_fisher_info_known_distn(R, v, t)
fi_fast = get_fisher_info_known_distn_fast(R, v, t)
print 'slow asymptotic variance:', 1 / fi_slow
print 'fast asymptotic variance:', 1 / fi_fast
print
def test_large_variance(self):
n = 4
v = sample_distribution(n)
S = sample_symmetric_rate_matrix(n)
R = mrate.to_gtr_halpern_bruno(S, v)
"""
a = .1
b = .2
c = .7
R = np.array([
[-(b+c), b, c],
[a, -(a+c), c],
[a, b, -(a+b)]])
"""
t = 2.0
dt = 0.0000001
rtime = mrate.R_to_relaxation_time(R)
var_a = get_ml_variance(R, t)
var_b = get_ml_variance(R, t + dt)
var_slope = (var_b - var_a) / dt
deriv_ratio = get_p_id_deriv_ratio(R, t)
clever_ratio = get_ml_variance_ratio(R, t)
print 'time:', t
print 'variance:', var_a
print 'variance slope:', var_slope
print 'var_slope / var_a:', var_slope / var_a
print 'var_slope / var_a [clever]:', clever_ratio
print 'log variance:', math.log(var_a)
print 'relaxation time:', rtime
print '2 / relaxation_time:', 2 / rtime
print "p_id(t)'' / p_id(t)':", deriv_ratio
print
print '--- new attempt ---'
print 'mutual information:', ctmcmi.get_mutual_information(R, t)
print 'reciprocal of MI:', 1.0 / ctmcmi.get_mutual_information(R, t)
print 'asymptotic variance:', get_asymptotic_variance(R, t)
print 'asymptotic variance (ver. 2):', get_asymptotic_variance_b(R, t)
print 'asymptotic variance (ver. 3):', get_asymptotic_variance_c(R, t)
print 'AV approx (ver. 4):', get_asymptotic_variance_d(R, t)
print 'AV approx (ver. 5):', get_asymptotic_variance_e(R, t)
print
print '--- another thing ---'
fi_slow = get_fisher_info_known_distn(R, v, t)
fi_fast = get_fisher_info_known_distn_fast(R, v, t)
print 'slow asymptotic variance:', 1 / fi_slow
print 'fast asymptotic variance:', 1 / fi_fast
print
def get_time_point_summary(Q_mut, Q_sels, t):
"""
@param Q_mut: the mutation rate matrix
@param Q_sels: sequence of mutation-selection rate matrices
@param t: the time point under consideration
@return: a list of signs, and a sequence of statistics
"""
# Compute the following statistics at this time point:
# t
# mutation MI
# selection MI max
# selection MI high
# selection MI mean
# selection MI low
# selection MI min
# proportion
#
# First compute the mutual information for mut and mut-sel.
nsels = len(Q_sels)
mi_mut = ctmcmi.get_mutual_information(Q_mut, t)
mi_sels = [ctmcmi.get_mutual_information(Q, t) for Q in Q_sels]
mi_signs = [1 if mi_sel > mi_mut else -1 for mi_sel in mi_sels]
# Now that we have computed all of the vectors at this time point,
# we can compute the statistics that we want to report.
statistics = []
statistics.append(t)
statistics.append(mi_mut)
# add the mutual information statistics
sorted_mi = sorted(mi_sels)
n_extreme = nsels / 20
statistics.append(sorted_mi[-1])
statistics.append(sorted_mi[-n_extreme])
statistics.append(sum(sorted_mi) / nsels)
statistics.append(sorted_mi[n_extreme-1])
statistics.append(sorted_mi[0])
# add the proportion
statistics.append(sum(1 for x in mi_signs if x == 1) / float(nsels))
# return the statistics
return mi_signs, statistics
def get_time_point_summary(Q_mut, Q_sels, t):
"""
@param Q_mut: the mutation rate matrix
@param Q_sels: sequence of mutation-selection rate matrices
@param t: the time point under consideration
@return: a list of signs, and a sequence of statistics
"""
# Compute the following statistics at this time point:
# t
# mutation MI
# selection MI max
# selection MI high
# selection MI mean
# selection MI low
# selection MI min
# proportion
#
# First compute the mutual information for mut and mut-sel.
nsels = len(Q_sels)
mi_mut = ctmcmi.get_mutual_information(Q_mut, t)
mi_sels = [ctmcmi.get_mutual_information(Q, t) for Q in Q_sels]
mi_signs = [1 if mi_sel > mi_mut else -1 for mi_sel in mi_sels]
# Now that we have computed all of the vectors at this time point,
# we can compute the statistics that we want to report.
statistics = []
statistics.append(t)
statistics.append(mi_mut)
# add the mutual information statistics
sorted_mi = sorted(mi_sels)
n_extreme = nsels / 20
statistics.append(sorted_mi[-1])
statistics.append(sorted_mi[-n_extreme])
statistics.append(sum(sorted_mi) / nsels)
statistics.append(sorted_mi[n_extreme - 1])
statistics.append(sorted_mi[0])
# add the proportion
statistics.append(sum(1 for x in mi_signs if x == 1) / float(nsels))
# return the statistics
return mi_signs, statistics
def get_time_point_summary(Q_mut, Q_sels, t):
"""
@param Q_mut: the mutation rate matrix
@param Q_sels: sequence of mutation-selection rate matrices
@param t: the time point under consideration
@return: a sequence of statistics
"""
# Compute the following statistics at this time point:
# t
# mutation MI
# selection MI max
# selection MI high
# selection MI mean
# selection MI low
# selection MI min
# correlation fn 1
# correlation fn 2
# correlation fn 3
# correlation fn 4
# correlation fn 5
# proportion sign agreement fn 1
# proportion sign agreement fn 2
# proportion sign agreement fn 3
# proportion sign agreement fn 4
# proportion sign agreement fn 5
# informativeness fn 1
# informativeness fn 2
# informativeness fn 3
# informativeness fn 4
# informativeness fn 5
#
# First compute the mutual information for mut and mut-sel.
nsels = len(Q_sels)
mi_mut = ctmcmi.get_mutual_information(Q_mut, t)
mi_sels = [ctmcmi.get_mutual_information(Q, t) for Q in Q_sels]
mi_signs = [1 if mi_sel > mi_mut else -1 for mi_sel in mi_sels]
# Now compute some other functions
v0 = [ctmcmi.get_mutual_information_small_approx_c(Q, t) for Q in Q_sels]
v1 = [ctmcmi.get_mutual_information_small_approx(Q, t) for Q in Q_sels]
v2 = [ctmcmi.get_mutual_information_approx_c(Q, t) for Q in Q_sels]
v3 = [math.exp(-2*t/mrate.R_to_relaxation_time(Q)) for Q in Q_sels]
v4 = [math.exp(-t*mrate.Q_to_expected_rate(Q)) for Q in Q_sels]
# Now that we have computed all of the vectors at this time point,
# we can compute the statistics that we want to report.
statistics = []
statistics.append(t)
statistics.append(mi_mut)
# add the mutual information statistics
sorted_mi = sorted(mi_sels)
n_extreme = nsels / 20
statistics.append(sorted_mi[-1])
statistics.append(sorted_mi[-n_extreme])
statistics.append(sum(sorted_mi) / nsels)
statistics.append(sorted_mi[n_extreme-1])
statistics.append(sorted_mi[0])
# add the correlations
for v in (v0, v1, v2, v3, v4):
r, p = scipy.stats.stats.pearsonr(v, mi_sels)
statistics.append(r)
# add the sign proportions
for v in (v0, v1, v2, v3, v4):
v_signs = [1 if value > mi_mut else -1 for value in v]
total = sum(1 for a, b in zip(mi_signs, v_signs) if a == b)
p = float(total) / nsels
statistics.append(p)
# add the informativenesses
for v in (v0, v1, v2, v3, v4):
v_signs = [1 if value > mi_mut else -1 for value in v]
informativeness = 0
for pair in ((1, 1), (1, -1), (-1, 1), (-1, -1)):
v_value, m_value = pair
v_marginal_count = sum(1 for x in v_signs if x == v_value)
m_marginal_count = sum(1 for x in mi_signs if x == m_value)
joint_count = sum(1 for x in zip(v_signs, mi_signs) if x == pair)
if joint_count:
joint_prob = joint_count / float(nsels)
a = math.log(joint_prob)
b = math.log(v_marginal_count / float(nsels))
c = math.log(m_marginal_count / float(nsels))
informativeness += joint_prob * (a - b - c)
statistics.append(informativeness)
# return the statistics
return statistics
def get_response_content(fs):
out = StringIO()
np.set_printoptions(linewidth=200)
# get the user defined variables
n = fs.nstates
t = fs.divtime
#h = fs.delta
# sample a random rate matrix
v = divtime.sample_distribution(n)
S = divtime.sample_symmetric_rate_matrix(n)
R = mrate.to_gtr_halpern_bruno(S, v)
# get some properties of the rate matrix
distn = mrate.R_to_distn(R)
spectrum = np.linalg.eigvalsh(mrate.symmetrized(R))
#spectrum, U = np.linalg.eigh(mrate.symmetrized(R))
#spectrum = np.linalg.eigvals(R)
# report some information about the mutual information curve
mi = ctmcmi.get_mutual_information(R, t)
mi_diff = ctmcmi.get_mutual_information_diff(R, t)
mi_diff_b = ctmcmi.get_mutual_information_diff_b(R, t)
mi_diff_c = ctmcmi.get_mutual_information_diff_c(R, t)
print >> out, 'arbitrary large-ish divergence time:'
print >> out, t
print >> out
print >> out, 'randomly sampled reversible rate matrix:'
print >> out, R
print >> out
print >> out, 'stationary distribution:'
print >> out, distn
print >> out
print >> out, 'spectrum of the rate matrix:'
print >> out, spectrum
print >> out
print >> out, 'mutual information at t = %f:' % t
print >> out, mi
print >> out
print >> out, 'mutual information at t = %f (ver. 2):' % t
print >> out, ctmcmi.get_mutual_information_b(R, t)
print >> out
print >> out, 'large t approximation of MI at t = %f:' % t
print >> out, ctmcmi.get_mutual_information_approx(R, t)
print >> out
print >> out, 'large t approximation of MI at t = %f (ver. 2):' % t
print >> out, ctmcmi.get_mutual_information_approx_b(R, t)
print >> out
print >> out, 'large t approximation of MI at t = %f (ver. 3):' % t
print >> out, ctmcmi.cute_MI_alternate(R, t)
print >> out
print >> out, 'large t approximation of MI at t = %f (ver. 4):' % t
print >> out, ctmcmi.get_mutual_information_approx_c(R, t)
print >> out
print >> out, 'small t approximation of MI at t = %f:' % t
print >> out, ctmcmi.get_mutual_information_small_approx(R, t)
print >> out
print >> out, 'small t approximation of MI at t = %f (ver. 2):' % t
print >> out, ctmcmi.get_mutual_information_small_approx_b(R, t)
print >> out
print >> out, 'small t approximation of MI at t = %f (ver. 3):' % t
print >> out, ctmcmi.get_mutual_information_small_approx_c(R, t)
print >> out
print >> out, 'small t approximation of MI at t = %f (ver. 4):' % t
print >> out, ctmcmi.get_mutual_information_small_approx_d(R, t)
print >> out
print >> out, 'mutual information diff at t = %f:' % t
print >> out, mi_diff
print >> out
print >> out, 'mutual information diff at t = %f (ver. 2):' % t
print >> out, mi_diff_b
print >> out
print >> out, 'mutual information diff at t = %f (ver. 3):' % t
print >> out, mi_diff_c
print >> out
print >> out, 'large t approximation of MI diff at t = %f:' % t
print >> out, ctmcmi.get_mutual_information_diff_approx(R, t)
print >> out
print >> out, 'large t approximation of MI diff at t = %f: (ver. 2)' % t
print >> out, ctmcmi.get_mutual_information_diff_approx_b(R, t)
print >> out
print >> out, 'large t approximation of MI diff at t = %f: (ver. 4)' % t
print >> out, ctmcmi.get_mutual_information_diff_approx_c(R, t)
print >> out
print >> out, 'log of mutual information at t = %f:' % t
print >> out, math.log(mi)
print >> out
#print >> out, 'estimated derivative',
#print >> out, 'of log of mutual information at t = %f:' % t
#print >> out, (math.log(mi_c) - math.log(mi_a)) / (2*h)
#print >> out
print >> out, 'estimated derivative of log of MI',
print >> out, 'at t = %f:' % t
print >> out, mi_diff / mi
print >> out
print >> out, 'large t approximation of derivative of log of MI',
print >> out, 'at t = %f:' % t
print >> out, ctmcmi.get_mutual_information_diff_approx(
R, t) / ctmcmi.get_mutual_information_approx(R, t)
print >> out
print >> out, 'large t approximation of derivative of log of MI',
print >> out, 'at t = %f (ver. 2):' % t
print >> out, ctmcmi.get_mutual_information_diff_approx_b(
R, t) / ctmcmi.get_mutual_information_approx_b(R, t)
print >> out
print >> out, 'twice the relevant eigenvalue:'
print >> out, 2 * spectrum[-2]
print >> out
print >> out
#print >> out, 'estimated derivative',
#print >> out, 'of mutual information at t = %f:' % t
#print >> out, (mi_c - mi_a) / (2*h)
#print >> out
#print >> out, '(estimated derivative of mutual information) /',
#print >> out, '(mutual information) at t = %f:' % t
#print >> out, (mi_c - mi_a) / (2*h*mi_b)
#print >> out
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 get_response_content(fs):
M = get_input_matrix(fs)
# create the R table string and scripts
headers = ['t']
if fs.show_entropy:
headers.append('ub.entropy')
headers.extend([
'ub.jc.spectral',
'ub.f81.spectral',
'mutual.information',
'lb.2.state.spectral',
'lb.2.state',
'lb.f81',
])
npoints = 100
t_low = fs.start_time
t_high = fs.stop_time
t_incr = (t_high - t_low) / (npoints - 1)
t_values = [t_low + t_incr*i for i in range(npoints)]
# define some extra stuff
v = mrate.R_to_distn(M)
entropy = -np.dot(v, np.log(v))
n = len(M)
gap = sorted(abs(x) for x in np.linalg.eigvals(M))[1]
print 'stationary distn:', v
print 'entropy:', entropy
print 'spectral gap:', gap
M_slow_jc = gap * (1.0 / n) * (np.ones((n,n)) - n*np.eye(n))
M_slow_f81 = gap * np.outer(np.ones(n), v)
M_slow_f81 -= np.diag(np.sum(M_slow_f81, axis=1))
M_f81 = msimpl.get_fast_f81(M)
M_2state = msimpl.get_fast_two_state_autobarrier(M)
M_2state_spectral = -gap * M_2state / np.trace(M_2state)
# get the data for the R table
arr = []
for u in t_values:
# experiment with log time
#t = math.exp(u)
t = u
mi_slow_jc = ctmcmi.get_mutual_information(M_slow_jc, t)
mi_slow_f81 = ctmcmi.get_mutual_information(M_slow_f81, t)
mi_mut = ctmcmi.get_mutual_information(M, t)
mi_2state_spectral = ctmcmi.get_mutual_information(M_2state_spectral, t)
mi_f81 = ctmcmi.get_mutual_information(M_f81, t)
mi_2state = ctmcmi.get_mutual_information(M_2state, t)
row = [u]
if fs.show_entropy:
row.append(entropy)
row.extend([mi_slow_jc, mi_slow_f81,
mi_mut, mi_2state_spectral, mi_2state, mi_f81])
arr.append(row)
# get the R table
table_string = RUtil.get_table_string(arr, headers)
# get the R script
script = get_ggplot()
# create the R plot image
device_name = Form.g_imageformat_to_r_function[fs.imageformat]
retcode, r_out, r_err, image_data = RUtil.run_plotter(
table_string, script, device_name)
if retcode:
raise RUtil.RError(r_err)
return image_data
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 get_response_content(fs):
out = StringIO()
np.set_printoptions(linewidth=200)
# get the user defined variables
n = fs.nstates
# sample a random rate matrix
v = divtime.sample_distribution(n)
S = divtime.sample_symmetric_rate_matrix(n)
R = mrate.to_gtr_halpern_bruno(S, v)
# get some properties of the rate matrix and its re-symmetrization
S = mrate.symmetrized(R)
distn = mrate.R_to_distn(R)
w, U = np.linalg.eigh(S)
D = np.diag(U.T[-1])**2
D_inv = np.diag(np.reciprocal(U.T[-1]))**2
for t in (1.0, 2.0):
P = scipy.linalg.expm(R * t)
M = ndot(D**.5, scipy.linalg.expm(S * t), D**.5)
M_star = ndot(D_inv**.5, scipy.linalg.expm(S * t), D_inv**.5)
M_star_log = np.log(M_star)
M_star_log_w, M_star_log_U = np.linalg.eigh(M_star_log)
E = M * np.log(M_star)
E_w, E_U = np.linalg.eigh(E)
print >> out, 't:'
print >> out, t
print >> out
print >> out, 'randomly sampled rate matrix R'
print >> out, R
print >> out
print >> out, 'symmetrized matrix S'
print >> out, S
print >> out
print >> out, 'stationary distribution diagonal D'
print >> out, D
print >> out
print >> out, 'R = D^-1/2 S D^1/2'
print >> out, ndot(D_inv**.5, S, D**.5)
print >> out
print >> out, 'probability matrix e^(R*t) = P'
print >> out, P
print >> out
print >> out, 'P = D^-1/2 e^(S*t) D^1/2'
print >> out, ndot(D_inv**.5, scipy.linalg.expm(S * t), D**.5)
print >> out
print >> out, 'pairwise distribution matrix M'
print >> out, 'M = D^1/2 e^(S*t) D^1/2'
print >> out, M
print >> out
print >> out, 'sum of entries of M'
print >> out, np.sum(M)
print >> out
print >> out, 'M_star = D^-1/2 e^(S*t) D^-1/2'
print >> out, M_star
print >> out
print >> out, 'entrywise logarithm logij(M_star)'
print >> out, np.log(M_star)
print >> out
print >> out, 'Hadamard product M o logij(M_star) = E'
print >> out, E
print >> out
print >> out, 'spectrum of M:'
print >> out, np.linalg.eigvalsh(M)
print >> out
print >> out, 'spectrum of logij(M_star):'
print >> out, M_star_log_w
print >> out
print >> out, 'corresponding eigenvectors of logij(M_star) as columns:'
print >> out, M_star_log_U
print >> out
print >> out, 'spectrum of E:'
print >> out, E_w
print >> out
print >> out, 'corresponding eigenvectors of E as columns:'
print >> out, E_U
print >> out
print >> out, 'entrywise square roots of stationary distribution:'
print >> out, np.sqrt(v)
print >> out
print >> out, 'sum of entries of E:'
print >> out, np.sum(E)
print >> out
print >> out, 'mutual information:'
print >> out, ctmcmi.get_mutual_information(R, t)
print >> out
print >> out
return out.getvalue()
def get_response_content(fs):
out = StringIO()
np.set_printoptions(linewidth=200)
# get the user defined variables
n = fs.nstates
# sample a random rate matrix
v = divtime.sample_distribution(n)
S = divtime.sample_symmetric_rate_matrix(n)
R = mrate.to_gtr_halpern_bruno(S, v)
# get some properties of the rate matrix and its re-symmetrization
S = mrate.symmetrized(R)
distn = mrate.R_to_distn(R)
w, U = np.linalg.eigh(S)
D = np.diag(U.T[-1])**2
D_inv = np.diag(np.reciprocal(U.T[-1]))**2
for t in (1.0, 2.0):
P = scipy.linalg.expm(R*t)
M = ndot(D**.5, scipy.linalg.expm(S*t), D**.5)
M_star = ndot(D_inv**.5, scipy.linalg.expm(S*t), D_inv**.5)
M_star_log = np.log(M_star)
M_star_log_w, M_star_log_U = np.linalg.eigh(M_star_log)
E = M * np.log(M_star)
E_w, E_U = np.linalg.eigh(E)
print >> out, 't:'
print >> out, t
print >> out
print >> out, 'randomly sampled rate matrix R'
print >> out, R
print >> out
print >> out, 'symmetrized matrix S'
print >> out, S
print >> out
print >> out, 'stationary distribution diagonal D'
print >> out, D
print >> out
print >> out, 'R = D^-1/2 S D^1/2'
print >> out, ndot(D_inv**.5, S, D**.5)
print >> out
print >> out, 'probability matrix e^(R*t) = P'
print >> out, P
print >> out
print >> out, 'P = D^-1/2 e^(S*t) D^1/2'
print >> out, ndot(D_inv**.5, scipy.linalg.expm(S*t), D**.5)
print >> out
print >> out, 'pairwise distribution matrix M'
print >> out, 'M = D^1/2 e^(S*t) D^1/2'
print >> out, M
print >> out
print >> out, 'sum of entries of M'
print >> out, np.sum(M)
print >> out
print >> out, 'M_star = D^-1/2 e^(S*t) D^-1/2'
print >> out, M_star
print >> out
print >> out, 'entrywise logarithm logij(M_star)'
print >> out, np.log(M_star)
print >> out
print >> out, 'Hadamard product M o logij(M_star) = E'
print >> out, E
print >> out
print >> out, 'spectrum of M:'
print >> out, np.linalg.eigvalsh(M)
print >> out
print >> out, 'spectrum of logij(M_star):'
print >> out, M_star_log_w
print >> out
print >> out, 'corresponding eigenvectors of logij(M_star) as columns:'
print >> out, M_star_log_U
print >> out
print >> out, 'spectrum of E:'
print >> out, E_w
print >> out
print >> out, 'corresponding eigenvectors of E as columns:'
print >> out, E_U
print >> out
print >> out, 'entrywise square roots of stationary distribution:'
print >> out, np.sqrt(v)
print >> out
print >> out, 'sum of entries of E:'
print >> out, np.sum(E)
print >> out
print >> out, 'mutual information:'
print >> out, ctmcmi.get_mutual_information(R, t)
print >> out
print >> out
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 __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 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 get_response_content(fs):
out = StringIO()
np.set_printoptions(linewidth=200)
# get the user defined variables
n = fs.nstates
t = fs.divtime
#h = fs.delta
# sample a random rate matrix
v = divtime.sample_distribution(n)
S = divtime.sample_symmetric_rate_matrix(n)
R = mrate.to_gtr_halpern_bruno(S, v)
# get some properties of the rate matrix
distn = mrate.R_to_distn(R)
spectrum = np.linalg.eigvalsh(mrate.symmetrized(R))
#spectrum, U = np.linalg.eigh(mrate.symmetrized(R))
#spectrum = np.linalg.eigvals(R)
# report some information about the mutual information curve
mi = ctmcmi.get_mutual_information(R, t)
mi_diff = ctmcmi.get_mutual_information_diff(R, t)
mi_diff_b = ctmcmi.get_mutual_information_diff_b(R, t)
mi_diff_c = ctmcmi.get_mutual_information_diff_c(R, t)
print >> out, 'arbitrary large-ish divergence time:'
print >> out, t
print >> out
print >> out, 'randomly sampled reversible rate matrix:'
print >> out, R
print >> out
print >> out, 'stationary distribution:'
print >> out, distn
print >> out
print >> out, 'spectrum of the rate matrix:'
print >> out, spectrum
print >> out
print >> out, 'mutual information at t = %f:' % t
print >> out, mi
print >> out
print >> out, 'mutual information at t = %f (ver. 2):' % t
print >> out, ctmcmi.get_mutual_information_b(R, t)
print >> out
print >> out, 'large t approximation of MI at t = %f:' % t
print >> out, ctmcmi.get_mutual_information_approx(R, t)
print >> out
print >> out, 'large t approximation of MI at t = %f (ver. 2):' % t
print >> out, ctmcmi.get_mutual_information_approx_b(R, t)
print >> out
print >> out, 'large t approximation of MI at t = %f (ver. 3):' % t
print >> out, ctmcmi.cute_MI_alternate(R, t)
print >> out
print >> out, 'large t approximation of MI at t = %f (ver. 4):' % t
print >> out, ctmcmi.get_mutual_information_approx_c(R, t)
print >> out
print >> out, 'small t approximation of MI at t = %f:' % t
print >> out, ctmcmi.get_mutual_information_small_approx(R, t)
print >> out
print >> out, 'small t approximation of MI at t = %f (ver. 2):' % t
print >> out, ctmcmi.get_mutual_information_small_approx_b(R, t)
print >> out
print >> out, 'small t approximation of MI at t = %f (ver. 3):' % t
print >> out, ctmcmi.get_mutual_information_small_approx_c(R, t)
print >> out
print >> out, 'small t approximation of MI at t = %f (ver. 4):' % t
print >> out, ctmcmi.get_mutual_information_small_approx_d(R, t)
print >> out
print >> out, 'mutual information diff at t = %f:' % t
print >> out, mi_diff
print >> out
print >> out, 'mutual information diff at t = %f (ver. 2):' % t
print >> out, mi_diff_b
print >> out
print >> out, 'mutual information diff at t = %f (ver. 3):' % t
print >> out, mi_diff_c
print >> out
print >> out, 'large t approximation of MI diff at t = %f:' % t
print >> out, ctmcmi.get_mutual_information_diff_approx(R, t)
print >> out
print >> out, 'large t approximation of MI diff at t = %f: (ver. 2)' % t
print >> out, ctmcmi.get_mutual_information_diff_approx_b(R, t)
print >> out
print >> out, 'large t approximation of MI diff at t = %f: (ver. 4)' % t
print >> out, ctmcmi.get_mutual_information_diff_approx_c(R, t)
print >> out
print >> out, 'log of mutual information at t = %f:' % t
print >> out, math.log(mi)
print >> out
#print >> out, 'estimated derivative',
#print >> out, 'of log of mutual information at t = %f:' % t
#print >> out, (math.log(mi_c) - math.log(mi_a)) / (2*h)
#print >> out
print >> out, 'estimated derivative of log of MI',
print >> out, 'at t = %f:' % t
print >> out, mi_diff / mi
print >> out
print >> out, 'large t approximation of derivative of log of MI',
print >> out, 'at t = %f:' % t
print >> out, ctmcmi.get_mutual_information_diff_approx(R,
t) / ctmcmi.get_mutual_information_approx(R, t)
print >> out
print >> out, 'large t approximation of derivative of log of MI',
print >> out, 'at t = %f (ver. 2):' % t
print >> out, ctmcmi.get_mutual_information_diff_approx_b(R,
t) / ctmcmi.get_mutual_information_approx_b(R, t)
print >> out
print >> out, 'twice the relevant eigenvalue:'
print >> out, 2 * spectrum[-2]
print >> out
print >> out
#print >> out, 'estimated derivative',
#print >> out, 'of mutual information at t = %f:' % t
#print >> out, (mi_c - mi_a) / (2*h)
#print >> out
#print >> out, '(estimated derivative of mutual information) /',
#print >> out, '(mutual information) at t = %f:' % t
#print >> out, (mi_c - mi_a) / (2*h*mi_b)
#print >> out
return out.getvalue()
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 get_time_point_summary(Q_mut, Q_sels, t):
"""
@param Q_mut: the mutation rate matrix
@param Q_sels: sequence of mutation-selection rate matrices
@param t: the time point under consideration
@return: a sequence of statistics
"""
# Compute the following statistics at this time point:
# t
# mutation MI
# selection MI max
# selection MI high
# selection MI mean
# selection MI low
# selection MI min
# correlation fn 1
# correlation fn 2
# correlation fn 3
# correlation fn 4
# correlation fn 5
# proportion sign agreement fn 1
# proportion sign agreement fn 2
# proportion sign agreement fn 3
# proportion sign agreement fn 4
# proportion sign agreement fn 5
# informativeness fn 1
# informativeness fn 2
# informativeness fn 3
# informativeness fn 4
# informativeness fn 5
# mutual information proportion
#
# First compute the mutual information for mut and mut-sel.
nsels = len(Q_sels)
mi_mut = ctmcmi.get_mutual_information(Q_mut, t)
mi_sels = [ctmcmi.get_mutual_information(Q, t) for Q in Q_sels]
mi_signs = [1 if mi_sel > mi_mut else -1 for mi_sel in mi_sels]
# Now compute some other functions
v0 = [ctmcmi.get_mutual_information_small_approx_c(Q, t) for Q in Q_sels]
v1 = [ctmcmi.get_mutual_information_small_approx(Q, t) for Q in Q_sels]
v2 = [ctmcmi.get_mutual_information_approx_c(Q, t) for Q in Q_sels]
v3 = [math.exp(-2*t/mrate.R_to_relaxation_time(Q)) for Q in Q_sels]
v4 = [math.exp(-t*mrate.Q_to_expected_rate(Q)) for Q in Q_sels]
# Now that we have computed all of the vectors at this time point,
# we can compute the statistics that we want to report.
statistics = []
statistics.append(t)
statistics.append(mi_mut)
# add the mutual information statistics
sorted_mi = sorted(mi_sels)
n_extreme = nsels / 20
statistics.append(sorted_mi[-1])
statistics.append(sorted_mi[-n_extreme])
statistics.append(sum(sorted_mi) / nsels)
statistics.append(sorted_mi[n_extreme-1])
statistics.append(sorted_mi[0])
# add the correlations
for v in (v0, v1, v2, v3, v4):
r, p = scipy.stats.stats.pearsonr(v, mi_sels)
statistics.append(r)
# add the sign proportions
for v in (v0, v1, v2, v3, v4):
v_signs = [1 if value > mi_mut else -1 for value in v]
total = sum(1 for a, b in zip(mi_signs, v_signs) if a == b)
p = float(total) / nsels
statistics.append(p)
# add the informativenesses
for v in (v0, v1, v2, v3, v4):
v_signs = [1 if value > mi_mut else -1 for value in v]
informativeness = 0
for pair in ((1, 1), (1, -1), (-1, 1), (-1, -1)):
v_value, m_value = pair
v_marginal_count = sum(1 for x in v_signs if x == v_value)
m_marginal_count = sum(1 for x in mi_signs if x == m_value)
joint_count = sum(1 for x in zip(v_signs, mi_signs) if x == pair)
if joint_count:
joint_prob = joint_count / float(nsels)
a = math.log(joint_prob)
b = math.log(v_marginal_count / float(nsels))
c = math.log(m_marginal_count / float(nsels))
informativeness += joint_prob * (a - b - c)
statistics.append(informativeness)
# add the mutual information sign proportion
statistics.append(sum(1 for x in mi_signs if x == 1) / float(nsels))
return statistics
