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_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
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):
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()
