def do_mut_hyper_2_3(fs, to_gtr):
out = StringIO()
# define the path mutation rate matrix
M = mrate.get_sparse_sequence_rate_matrix(2, 3)
print >> out, '*** mutation rate matrix (8-state cube) ***'
print >> out
print >> out, get_rate_matrix_summary(M)
print >> out
print >> out
# kill the last state by natural selection
p_other = (1 - fs.p_mid)/7
p_target = [p_other]*7 + [fs.p_mid]
Q = to_gtr(M, p_target)
print >> out, '*** mutation-selection balance ***'
print >> out
print >> out, get_rate_matrix_summary(Q)
print >> out
print >> out
# define a reference mutation rate matrix
R = mrate.get_sparse_sequence_rate_matrix(2, 3)
nstates = 7
M = np.zeros((nstates, nstates))
for i in range(nstates):
for j in range(nstates):
if i != j:
M[i, j] = R[i, j]
M -= np.diag(np.sum(M, axis=1))
M /= mrate.Q_to_expected_rate(M)
print >> out, '*** reference mutation rate matrix (corner removed) ***'
print >> out
print >> out, get_rate_matrix_summary(M)
print >> out
print >> out
return out.getvalue().rstrip()
def do_mut_hyper_2_3_square(fs, to_gtr):
out = StringIO()
# define the path mutation rate matrix
M = mrate.get_sparse_sequence_rate_matrix(2, 3)
print >> out, '*** mutation rate matrix (8-state cube) ***'
print >> out
print >> out, get_rate_matrix_summary(M)
print >> out
print >> out
# kill the last state by natural selection
p_other = (1 - 4*fs.p_mid)/4
p_target = [p_other]*4 + [fs.p_mid]*4
Q = to_gtr(M, p_target)
print >> out, '*** mutation-selection balance ***'
print >> out
print >> out, get_rate_matrix_summary(Q)
print >> out
print >> out
# define a reference mutation rate matrix
M = mrate.get_sparse_sequence_rate_matrix(2, 2)
print >> out, '*** reference mutation rate matrix (square) ***'
print >> out
print >> out, get_rate_matrix_summary(M)
print >> out
print >> out
return out.getvalue().rstrip()
def do_mut_hyper_2_2(fs, to_gtr):
out = StringIO()
# define the path mutation rate matrix
M = mrate.get_sparse_sequence_rate_matrix(2, 2)
print >> out, '*** mutation rate matrix (4-state square) ***'
print >> out
print >> out, get_rate_matrix_summary(M)
print >> out
print >> out
# kill the last state by natural selection
p_other = (1 - fs.p_mid)/3
p_target = (p_other, p_other, p_other, fs.p_mid)
Q = to_gtr(M, p_target)
print >> out, '*** mutation-selection balance ***'
print >> out
print >> out, get_rate_matrix_summary(Q)
print >> out
print >> out
# define a reference mutation rate matrix
M = mrate.get_path_rate_matrix(3)
print >> out, '*** reference mutation rate matrix (3-state path) ***'
print >> out
print >> out, get_rate_matrix_summary(M)
print >> out
print >> out
return out.getvalue().rstrip()
def get_table_string_and_scripts(fs):
nstates = fs.nresidues**fs.nsites
if nstates > 256:
raise ValueError('the mutation rate matrix is too big')
# get the mutation matrix
Q_mut = mrate.get_sparse_sequence_rate_matrix(fs.nresidues, fs.nsites)
# sample a bunch of mutation-selection rate matrices
Q_sels = []
for selection_index in range(fs.nselections):
# sample the selection parameters
if fs.low_var:
v = 0.2
elif fs.medium_var:
v = 1
elif fs.high_var:
v = 5.0
elif fs.really_high_var:
v = 25.0
s = math.sqrt(v)
if fs.neg_skew:
sels = [-random.expovariate(1 / s) for i in range(nstates)]
elif fs.no_skew:
sels = [random.gauss(0, s) for i in range(nstates)]
elif fs.pos_skew:
sels = [random.expovariate(1 / s) for i in range(nstates)]
# define the mutation-selection rate matrix using Halpern-Bruno
Q = np.zeros_like(Q_mut)
for i in range(nstates):
for j in range(nstates):
if i != j:
tau = math.exp(-(sels[j] - sels[i]))
coeff = math.log(tau) / (1 - 1 / tau)
Q[i, j] = Q_mut[i, j] * coeff
for i in range(nstates):
Q[i, i] = -np.sum(Q[i])
Q_sels.append(Q)
# define the time points
incr = (fs.t_high - fs.t_low) / (fs.ntimes - 1)
times = [fs.t_low + i * incr for i in range(fs.ntimes)]
# compute the statistics
nsels = len(Q_sels)
pairs = [get_time_point_summary(Q_mut, Q_sels, t) for t in times]
mi_sign_lists, time_stats = zip(*pairs)
ncrossing_list = []
# look at how the signs change over time for each selection sample
for signs in zip(*mi_sign_lists):
count = 0
for sign_a, sign_b in iterutils.pairwise(signs):
if sign_a != sign_b:
count += 1
ncrossing_list.append(count)
# get the R scripts
scripts = [
get_r_band_script(nsels, time_stats),
get_r_prop_script(nsels, time_stats),
get_r_cross_script(ncrossing_list)
]
table_string = RUtil.get_table_string(time_stats, g_time_stats_headers)
return table_string, scripts
def get_table_string_and_scripts(fs):
nstates = fs.nresidues ** fs.nsites
if nstates > 256:
raise ValueError('the mutation rate matrix is too big')
# get the mutation matrix
Q_mut = mrate.get_sparse_sequence_rate_matrix(fs.nresidues, fs.nsites)
# sample a bunch of mutation-selection rate matrices
Q_sels = []
for selection_index in range(fs.nselections):
# sample the selection parameters
if fs.low_var:
v = 0.2
elif fs.medium_var:
v = 1
elif fs.high_var:
v = 5.0
elif fs.really_high_var:
v = 25.0
s = math.sqrt(v)
if fs.neg_skew:
sels = [-random.expovariate(1/s) for i in range(nstates)]
elif fs.no_skew:
sels = [random.gauss(0, s) for i in range(nstates)]
elif fs.pos_skew:
sels = [random.expovariate(1/s) for i in range(nstates)]
# define the mutation-selection rate matrix using Halpern-Bruno
Q = np.zeros_like(Q_mut)
for i in range(nstates):
for j in range(nstates):
if i != j:
tau = math.exp(-(sels[j] - sels[i]))
coeff = math.log(tau) / (1 - 1/tau)
Q[i, j] = Q_mut[i, j] * coeff
for i in range(nstates):
Q[i, i] = -np.sum(Q[i])
Q_sels.append(Q)
# define the time points
incr = (fs.t_high - fs.t_low) / (fs.ntimes - 1)
times = [fs.t_low + i*incr for i in range(fs.ntimes)]
# compute the statistics
nsels = len(Q_sels)
pairs = [get_time_point_summary(Q_mut, Q_sels, t) for t in times]
mi_sign_lists, time_stats = zip(*pairs)
ncrossing_list = []
# look at how the signs change over time for each selection sample
for signs in zip(*mi_sign_lists):
count = 0
for sign_a, sign_b in iterutils.pairwise(signs):
if sign_a != sign_b:
count += 1
ncrossing_list.append(count)
# get the R scripts
scripts = [
get_r_band_script(nsels, time_stats),
get_r_prop_script(nsels, time_stats),
get_r_cross_script(ncrossing_list)]
table_string = RUtil.get_table_string(time_stats, g_time_stats_headers)
return table_string, scripts
def get_table_string_and_scripts(fs):
"""
The latex documentbody should have a bunch of tikz pieces in it.
Each tikz piece should have been generated from R.
"""
nstates = fs.nresidues ** fs.nsites
if nstates > 256:
raise ValueError("the mutation rate matrix is too big")
# get the mutation matrix
Q_mut = mrate.get_sparse_sequence_rate_matrix(fs.nresidues, fs.nsites)
# sample a bunch of mutation-selection rate matrices
Q_sels = []
for selection_index in range(fs.nselections):
# sample the selection parameters
if fs.low_var:
v = 0.2
elif fs.medium_var:
v = 1
elif fs.high_var:
v = 5.0
elif fs.really_high_var:
v = 25.0
s = math.sqrt(v)
if fs.neg_skew:
sels = [-random.expovariate(1 / s) for i in range(nstates)]
elif fs.no_skew:
sels = [random.gauss(0, s) for i in range(nstates)]
elif fs.pos_skew:
sels = [random.expovariate(1 / s) for i in range(nstates)]
# define the mutation-selection rate matrix using Halpern-Bruno
Q = np.zeros_like(Q_mut)
for i in range(nstates):
for j in range(nstates):
if i != j:
tau = math.exp(-(sels[j] - sels[i]))
coeff = math.log(tau) / (1 - 1 / tau)
Q[i, j] = Q_mut[i, j] * coeff
for i in range(nstates):
Q[i, i] = -np.sum(Q[i])
Q_sels.append(Q)
# define the time points
incr = (fs.t_high - fs.t_low) / (fs.ntimes - 1)
times = [fs.t_low + i * incr for i in range(fs.ntimes)]
# compute the statistics
nsels = len(Q_sels)
time_stats = [get_time_point_summary(Q_mut, Q_sels, t) for t in times]
# get the R scripts
scripts = [
# get_r_tikz_mi_plot(nsels, time_stats),
get_r_tikz_corr_plot(nsels, time_stats),
get_r_tikz_prop_plot(nsels, time_stats),
get_r_tikz_info_plot(nsels, time_stats),
]
table_string = RUtil.get_table_string(time_stats, g_time_stats_headers)
return table_string, scripts
def get_table_string_and_scripts(fs):
"""
The latex documentbody should have a bunch of tikz pieces in it.
Each tikz piece should have been generated from R.
"""
nstates = fs.nresidues ** fs.nsites
if nstates > 256:
raise ValueError('the mutation rate matrix is too big')
# get the mutation matrix
Q_mut = mrate.get_sparse_sequence_rate_matrix(fs.nresidues, fs.nsites)
# sample a bunch of mutation-selection rate matrices
Q_sels = []
for selection_index in range(fs.nselections):
# sample the selection parameters
if fs.low_var:
v = 0.2
elif fs.medium_var:
v = 1
elif fs.high_var:
v = 5.0
elif fs.really_high_var:
v = 25.0
s = math.sqrt(v)
if fs.neg_skew:
sels = [-random.expovariate(1/s) for i in range(nstates)]
elif fs.no_skew:
sels = [random.gauss(0, s) for i in range(nstates)]
elif fs.pos_skew:
sels = [random.expovariate(1/s) for i in range(nstates)]
# define the mutation-selection rate matrix using Halpern-Bruno
Q = np.zeros_like(Q_mut)
for i in range(nstates):
for j in range(nstates):
if i != j:
tau = math.exp(-(sels[j] - sels[i]))
coeff = math.log(tau) / (1 - 1/tau)
Q[i, j] = Q_mut[i, j] * coeff
for i in range(nstates):
Q[i, i] = -np.sum(Q[i])
Q_sels.append(Q)
# define the time points
incr = (fs.t_high - fs.t_low) / (fs.ntimes - 1)
times = [fs.t_low + i*incr for i in range(fs.ntimes)]
# compute the statistics
nsels = len(Q_sels)
time_stats = [get_time_point_summary(Q_mut, Q_sels, t) for t in times]
# get the R scripts
scripts = [
#get_r_tikz_mi_plot(nsels, time_stats),
get_r_tikz_corr_plot(nsels, time_stats),
get_r_tikz_prop_plot(nsels, time_stats),
get_r_tikz_info_plot(nsels, time_stats)]
table_string = RUtil.get_table_string(time_stats, g_time_stats_headers)
return table_string, scripts
def get_time_stats(fs):
nstates = fs.nresidues ** fs.nsites
if nstates > 256:
raise ValueError('the mutation rate matrix is too big')
# get the mutation matrix
Q_mut = mrate.get_sparse_sequence_rate_matrix(fs.nresidues, fs.nsites)
# sample a bunch of mutation-selection rate matrices
Q_sels = []
for selection_index in range(fs.nselections):
# sample the selection parameters
if fs.low_var:
v = 0.2
elif fs.medium_var:
v = 1
elif fs.high_var:
v = 5.0
elif fs.really_high_var:
v = 25.0
s = math.sqrt(v)
if fs.neg_skew:
sels = [-random.expovariate(1/s) for i in range(nstates)]
elif fs.no_skew:
sels = [random.gauss(0, s) for i in range(nstates)]
elif fs.pos_skew:
sels = [random.expovariate(1/s) for i in range(nstates)]
# define the mutation-selection rate matrix using Halpern-Bruno
Q = np.zeros_like(Q_mut)
for i in range(nstates):
for j in range(nstates):
if i != j:
tau = math.exp(-(sels[j] - sels[i]))
coeff = math.log(tau) / (1 - 1/tau)
Q[i, j] = Q_mut[i, j] * coeff
for i in range(nstates):
Q[i, i] = -np.sum(Q[i])
Q_sels.append(Q)
# define the time points
incr = (fs.t_high - fs.t_low) / (fs.ntimes - 1)
times = [fs.t_low + i*incr for i in range(fs.ntimes)]
# compute the statistics
time_stats = [get_time_point_summary(Q_mut, Q_sels, t) for t in times]
return time_stats
def get_time_stats(fs):
nstates = fs.nresidues**fs.nsites
if nstates > 256:
raise ValueError('the mutation rate matrix is too big')
# get the mutation matrix
Q_mut = mrate.get_sparse_sequence_rate_matrix(fs.nresidues, fs.nsites)
# sample a bunch of mutation-selection rate matrices
Q_sels = []
for selection_index in range(fs.nselections):
# sample the selection parameters
if fs.low_var:
v = 0.2
elif fs.medium_var:
v = 1
elif fs.high_var:
v = 5.0
elif fs.really_high_var:
v = 25.0
s = math.sqrt(v)
if fs.neg_skew:
sels = [-random.expovariate(1 / s) for i in range(nstates)]
elif fs.no_skew:
sels = [random.gauss(0, s) for i in range(nstates)]
elif fs.pos_skew:
sels = [random.expovariate(1 / s) for i in range(nstates)]
# define the mutation-selection rate matrix using Halpern-Bruno
Q = np.zeros_like(Q_mut)
for i in range(nstates):
for j in range(nstates):
if i != j:
tau = math.exp(-(sels[j] - sels[i]))
coeff = math.log(tau) / (1 - 1 / tau)
Q[i, j] = Q_mut[i, j] * coeff
for i in range(nstates):
Q[i, i] = -np.sum(Q[i])
Q_sels.append(Q)
# define the time points
incr = (fs.t_high - fs.t_low) / (fs.ntimes - 1)
times = [fs.t_low + i * incr for i in range(fs.ntimes)]
# compute the statistics
time_stats = [get_time_point_summary(Q_mut, Q_sels, t) for t in times]
return time_stats
def get_response_content(fs):
nstates = fs.nresidues ** fs.nsites
if nstates > 256:
raise ValueError('the mutation rate matrix is too big')
# get the mutation matrix
Q_mut = mrate.get_sparse_sequence_rate_matrix(fs.nresidues, fs.nsites)
# get the random selection matrix which we will use from now on
Q_sel = sample_rate_matrix(fs, Q_mut)
# define the time points
#incr = (fs.t_high - fs.t_low) / (fs.ntimes - 1)
#times = [fs.t_low + i*incr for i in range(fs.ntimes)]
mut_info = RateProperties(Q_mut)
sel_info = RateProperties(Q_sel)
# compute the intersection time
x_time_top = math.log(2 * nstates - 1)
x_time_bot = 2 * abs(mut_info.lam - sel_info.lam)
x_time = x_time_top / x_time_bot
# compute the upper bound on the judgement time
T_second_order = max(
x_time,
mut_info.time_to_usefulness,
sel_info.time_to_usefulness)
# define the name of the eventually winning process
if mut_info.relaxation_time > sel_info.relaxation_time:
x = 'mutation'
slow_info = mut_info
fast_info = sel_info
else:
x = 'mutation-selection balance'
slow_info = sel_info
fast_info = mut_info
eventual_winner_name = 'the %s process' % x
# get a more sophisticated bound
third_order_x_time = ctmcmitaylor.get_sophisticated_time_bound(
-slow_info.lam,
-fast_info.lam,
slow_info.N,
fast_info.N,
slow_info.p,
fast_info.p)
if third_order_x_time is not None:
T_third_order = max(
third_order_x_time,
mut_info.time_to_uniformity,
sel_info.time_to_uniformity)
else:
T_third_order = None
# Define a naive crossing time.
# This is not a bound on the true mutual information doomsday,
# but it shows a limit of our approach.
# It is the bound on the spectral taylor approximation
# given only the second eigenvalues and not the other ones.
naive_x_time_top = math.log(nstates - 1)
naive_x_time_bot = 2 * abs(mut_info.lam - sel_info.lam)
naive_x_time = naive_x_time_top / naive_x_time_bot
# write the report
np.set_printoptions(linewidth=200)
out = StringIO()
print >> out, '*** mutation rate matrix info ***'
print >> out
print >> out, mut_info
print >> out
print >> out
print >> out, '*** mutation-selection balance rate matrix info ***'
print >> out
print >> out, sel_info
print >> out
print >> out
print >> out, '*** note ***'
print >> out
print >> out, 'with the general approach taken here,'
print >> out, 'we will not find an eigenvalue time bound'
print >> out, 'smaller than', naive_x_time
print >> out
print >> out
print >> out, '*** weak inequality ***'
print >> out
print >> out, 'When t >', T_second_order, eventual_winner_name
print >> out, 'has greater mutual information (MI) and approximate MI.'
print >> out
print >> out
print >> out, '*** stronger inequality ***'
print >> out
if T_third_order is None:
print >> out, 'the numerical solver failed to converge'
else:
print >> out, 'When t >', T_third_order, eventual_winner_name
print >> out, 'has greater mutual information (MI) and approximate MI.'
return out.getvalue()
