def __call__(self):
"""
Look for a counterexample.
"""
# Sample a rate matrix.
# Use a trick by Robert Kern to left and right multiply by diagonals.
# http://mail.scipy.org/pipermail/numpy-discussion/2007-March/
# 026809.html
S = MatrixUtil.sample_pos_sym_matrix(self.nstates)
v = mrate.sample_distn(self.nstates)
R = (v**-0.5)[:,np.newaxis] * S * (v**0.5)
R -= np.diag(np.sum(R, axis=1))
# Construct a parent-independent process
# with the same max rate and stationary distribution
# as the sampled process.
#max_rate = max(-np.diag(R))
#expected_rate = np.dot(v, -np.diag(R))
#logical_entropy = np.dot(v, 1-v)
#randomization_rate = expected_rate / logical_entropy
Q = self.simplification(R)
#Q = np.outer(np.ones(self.nstates), v)
#Q -= np.diag(np.sum(Q, axis=1))
#Q *= max(np.diag(R) / np.diag(Q))
# sample a random time
t = random.expovariate(1)
# Check that the mutual information of the
# parent independent process is smaller.
mi_R = ctmcmi.get_expected_ll_ratio(R, t)
mi_Q = ctmcmi.get_expected_ll_ratio(Q, t)
if np.allclose(mi_R, mi_Q):
self.n_too_close += 1
return False
if mi_R < mi_Q:
out = StringIO()
print >> out, 'found a counterexample'
print >> out
print >> out, 'sampled symmetric matrix S:'
print >> out, S
print >> out
print >> out, 'sampled stationary distribution v:'
print >> out, v
print >> out
print >> out, 'implied rate matrix R:'
print >> out, R
print >> out
print >> out, 'parent independent process Q:'
print >> out, Q
print >> out
print >> out, 'sampled time t:', t
print >> out
print >> out, 'mutual information of sampled process:', mi_R
print >> out, 'mutual information of p.i. process:', mi_Q
print >> out
self.counterexample = out.getvalue().rstrip()
return True
def __call__(self):
"""
Look for a counterexample.
"""
# Sample a rate matrix.
# Use a trick by Robert Kern to left and right multiply by diagonals.
# http://mail.scipy.org/pipermail/numpy-discussion/2007-March/
# 026809.html
S = MatrixUtil.sample_pos_sym_matrix(self.nstates)
v = mrate.sample_distn(self.nstates)
R = (v**-0.5)[:, np.newaxis] * S * (v**0.5)
R -= np.diag(np.sum(R, axis=1))
# Construct a parent-independent process
# with the same max rate and stationary distribution
# as the sampled process.
#max_rate = max(-np.diag(R))
#expected_rate = np.dot(v, -np.diag(R))
#logical_entropy = np.dot(v, 1-v)
#randomization_rate = expected_rate / logical_entropy
Q = self.simplification(R)
#Q = np.outer(np.ones(self.nstates), v)
#Q -= np.diag(np.sum(Q, axis=1))
#Q *= max(np.diag(R) / np.diag(Q))
# sample a random time
t = random.expovariate(1)
# Check that the mutual information of the
# parent independent process is smaller.
mi_R = ctmcmi.get_expected_ll_ratio(R, t)
mi_Q = ctmcmi.get_expected_ll_ratio(Q, t)
if np.allclose(mi_R, mi_Q):
self.n_too_close += 1
return False
if mi_R < mi_Q:
out = StringIO()
print >> out, 'found a counterexample'
print >> out
print >> out, 'sampled symmetric matrix S:'
print >> out, S
print >> out
print >> out, 'sampled stationary distribution v:'
print >> out, v
print >> out
print >> out, 'implied rate matrix R:'
print >> out, R
print >> out
print >> out, 'parent independent process Q:'
print >> out, Q
print >> out
print >> out, 'sampled time t:', t
print >> out
print >> out, 'mutual information of sampled process:', mi_R
print >> out, 'mutual information of p.i. process:', mi_Q
print >> out
self.counterexample = out.getvalue().rstrip()
return True
def __call__(self):
"""
Look for a counterexample.
"""
# Sample a rate matrix.
# Use a trick by Robert Kern to left and right multiply by diagonals.
# http://mail.scipy.org/pipermail/numpy-discussion/2007-March/
# 026809.html
S = MatrixUtil.sample_pos_sym_matrix(self.nstates)
v = mrate.sample_distn(self.nstates)
R = (v**-0.5)[:,np.newaxis] * S * (v**0.5)
R -= np.diag(np.sum(R, axis=1))
# sample a random time
rate = 1.0 / self.etime
t = random.expovariate(rate)
# sample one side of the bipartition and get the mutual information
k = random.randrange(1, self.nstates)
A = random.sample(range(self.nstates), k)
mi_non_markov = get_mutual_information(R, A, t)
# get summary statistics of the non-markov process
Q = msimpl.get_fast_two_state(R, A)
mi_markov = ctmcmi.get_expected_ll_ratio(Q, t)
# check if the mutual informations are indistinguishable
if np.allclose(mi_non_markov, mi_markov):
self.n_too_close += 1
return False
if mi_non_markov < mi_markov:
out = StringIO()
print >> out, 'found a counterexample'
print >> out
print >> out, 'sampled symmetric matrix S:'
print >> out, S
print >> out
print >> out, 'sampled stationary distribution v:'
print >> out, v
print >> out
print >> out, 'implied rate matrix R:'
print >> out, R
print >> out
print >> out, 'reduced rate matrix Q'
print >> out, Q
print >> out
print >> out, 'sampled time t:', t
print >> out
print >> out, 'non-markov mutual information:', mi_non_markov
print >> out, 'markov mutual information:', mi_markov
print >> out
self.counterexample = out.getvalue().rstrip()
return True
def __call__(self):
"""
Look for a counterexample.
"""
# Sample a rate matrix.
# Use a trick by Robert Kern to left and right multiply by diagonals.
# http://mail.scipy.org/pipermail/numpy-discussion/2007-March/
# 026809.html
S = MatrixUtil.sample_pos_sym_matrix(self.nstates)
v = mrate.sample_distn(self.nstates)
R = (v**-0.5)[:, np.newaxis] * S * (v**0.5)
R -= np.diag(np.sum(R, axis=1))
# sample a random time
rate = 1.0 / self.etime
t = random.expovariate(rate)
# sample one side of the bipartition and get the mutual information
k = random.randrange(1, self.nstates)
A = random.sample(range(self.nstates), k)
mi_non_markov = get_mutual_information(R, A, t)
# get summary statistics of the non-markov process
Q = msimpl.get_fast_two_state(R, A)
mi_markov = ctmcmi.get_expected_ll_ratio(Q, t)
# check if the mutual informations are indistinguishable
if np.allclose(mi_non_markov, mi_markov):
self.n_too_close += 1
return False
if mi_non_markov < mi_markov:
out = StringIO()
print >> out, 'found a counterexample'
print >> out
print >> out, 'sampled symmetric matrix S:'
print >> out, S
print >> out
print >> out, 'sampled stationary distribution v:'
print >> out, v
print >> out
print >> out, 'implied rate matrix R:'
print >> out, R
print >> out
print >> out, 'reduced rate matrix Q'
print >> out, Q
print >> out
print >> out, 'sampled time t:', t
print >> out
print >> out, 'non-markov mutual information:', mi_non_markov
print >> out, 'markov mutual information:', mi_markov
print >> out
self.counterexample = out.getvalue().rstrip()
return True
def make_table(args, distn_modes):
"""
Make outputs to pass to RUtil.get_table_string.
@param args: user args
@param distn_modes: ordered distribution modes
@return: matrix, headers
"""
# define some variables
t_low = args.t_low
t_high = args.t_high
if t_high <= t_low:
raise ValueError('low time must be smaller than high time')
ntimes = 100
incr = (t_high - t_low) / (ntimes - 1)
n = args.nstates
# define some tables
distn_mode_to_f = {
UNIFORM : get_distn_uniform,
ONE_INC : get_distn_one_inc,
TWO_INC : get_distn_two_inc,
ONE_DEC : get_distn_one_dec,
TWO_DEC : get_distn_two_dec}
selection_mode_to_f = {
BALANCED : mrate.to_gtr_balanced,
HALPERN_BRUNO : mrate.to_gtr_halpern_bruno}
# define the selection modes and calculators
selection_f = selection_mode_to_f[args.selection]
distn_fs = [distn_mode_to_f[m] for m in distn_modes]
# define the headers
headers = ['t'] + [s.replace('_', '.') for s in distn_modes]
# define the numbers in the table
S = np.ones((n, n), dtype=float)
S -= np.diag(np.sum(S, axis=1))
arr = []
for i in range(ntimes):
t = t_low + i * incr
row = [t]
for distn_f in distn_fs:
v = distn_f(n, args.sel_surr)
R = selection_f(S, v)
expected_log_ll_ratio = ctmcmi.get_expected_ll_ratio(R, t)
row.append(expected_log_ll_ratio)
arr.append(row)
return np.array(arr), headers
def make_table(args, distn_modes):
"""
Make outputs to pass to RUtil.get_table_string.
@param args: user args
@param distn_modes: ordered distribution modes
@return: matrix, headers
"""
# define some variables
t_low = args.t_low
t_high = args.t_high
if t_high <= t_low:
raise ValueError("low time must be smaller than high time")
ntimes = 100
incr = (t_high - t_low) / (ntimes - 1)
n = args.nstates
# define some tables
distn_mode_to_f = {
UNIFORM: get_distn_uniform,
ONE_INC: get_distn_one_inc,
TWO_INC: get_distn_two_inc,
ONE_DEC: get_distn_one_dec,
TWO_DEC: get_distn_two_dec,
}
selection_mode_to_f = {BALANCED: mrate.to_gtr_balanced, HALPERN_BRUNO: mrate.to_gtr_halpern_bruno}
# define the selection modes and calculators
selection_f = selection_mode_to_f[args.selection]
distn_fs = [distn_mode_to_f[m] for m in distn_modes]
# define the headers
headers = ["t"] + [s.replace("_", ".") for s in distn_modes]
# define the numbers in the table
S = np.ones((n, n), dtype=float)
S -= np.diag(np.sum(S, axis=1))
arr = []
for i in range(ntimes):
t = t_low + i * incr
row = [t]
for distn_f in distn_fs:
v = distn_f(n, args.sel_surr)
R = selection_f(S, v)
expected_log_ll_ratio = ctmcmi.get_expected_ll_ratio(R, t)
row.append(expected_log_ll_ratio)
arr.append(row)
return np.array(arr), headers
def get_response_content(fs):
np.set_printoptions(linewidth=200)
out = StringIO()
R_jc = get_jc_rate_matrix()
t = 0.1
x = 1.6
w = 0.5 * log(x)
v = x_to_distn(x)
R_hb_easy = mrate.to_gtr_halpern_bruno(R_jc, v)
y, z, = mrate.x_to_halpern_bruno_yz(x)
yz_ratio = y / z
R_hb_tedious = get_mut_sel_rate_matrix(y, z)
P_hb_easy = get_trans_mat_expm(R_hb_easy, t)
P_hb_tedious = get_trans_mat_tediously(y, z, t)
P_hb_tedious_c = get_trans_mat_tediously_c(y, z, t)
P_hb_from_x = get_trans_mat_from_x(x, t)
e_ll_jc = ctmcmi.get_expected_ll_ratio(R_jc, t)
e_ll_jc_tedious = get_jc_e_ll(t)
e_ll_hb = ctmcmi.get_expected_ll_ratio(R_hb_easy, t)
e_ll_hb_from_x = get_e_ll_from_x(x, t)
e_ll_hb_from_x_b = get_e_ll_from_x_b(x, t)
e_ll_hb_from_x_htrig = get_e_ll_from_x_htrig(x, t)
# print some values
print >> out, 'Jukes-Cantor mutation matrix:'
print >> out, R_jc
print >> out
print >> out, 'ratio of common to uncommon probabilities:'
print >> out, x
print >> out
print >> out, '1/2 log ratio:'
print >> out, w
print >> out
print >> out, 'fast rate:'
print >> out, y
print >> out
print >> out, 'slow rate:'
print >> out, z
print >> out
print >> out, 'reciprocal of fast rate:'
print >> out, 1.0 / y
print >> out
print >> out, 'ratio of fast to slow rates (should be x):'
print >> out, yz_ratio
print >> out
print >> out, 'mutation-selection rate matrix (easy):'
print >> out, R_hb_easy
print >> out
print >> out, 'mutation-selection rate matrix (tedious):'
print >> out, R_hb_tedious
print >> out
print >> out, 'time:'
print >> out, t
print >> out
print >> out, 'mutation-selection transition matrix (easy):'
print >> out, P_hb_easy
print >> out
print >> out, 'mutation-selection transition matrix (tedious):'
print >> out, P_hb_tedious
print >> out
print >> out, 'mutation-selection transition matrix (tedious c):'
print >> out, P_hb_tedious_c
print >> out
print >> out, 'mutation-selection transition matrix (from x):'
print >> out, P_hb_from_x
print >> out
print >> out, 'expected Jukes-Cantor log likelihood ratio:'
print >> out, e_ll_jc
print >> out
print >> out, 'expected Jukes-Cantor log likelihood ratio (tedious):'
print >> out, e_ll_jc_tedious
print >> out
print >> out, 'expected mutation-selection log likelihood ratio:'
print >> out, e_ll_hb
print >> out
print >> out, 'expected mutation-selection ll ratio from x:'
print >> out, e_ll_hb_from_x
print >> out
print >> out, 'expected mutation-selection ll ratio from x (impl b):'
print >> out, e_ll_hb_from_x_b
print >> out
print >> out, 'expected mutation-selection ll ratio from x (htrig):'
print >> out, e_ll_hb_from_x_htrig
print >> out
# check some invariants
if np.allclose(R_hb_easy, R_hb_tedious):
print >> out, 'halpern-bruno rate matrices are equal as expected'
else:
print >> out, '*** halpern-bruno rate matrices are not equal!'
if np.allclose(P_hb_easy, P_hb_tedious):
print >> out, 'halpern-bruno transition matrices are equal as expected'
else:
print >> out, '*** halpern-bruno transition matrices are not equal!'
if np.allclose(P_hb_easy, P_hb_tedious_c):
print >> out, 'halpern-bruno transition matrices are equal as expected'
else:
print >> out, '*** halpern-bruno transition matrices are not equal!'
if np.allclose(P_hb_easy, P_hb_from_x):
print >> out, 'halpern-bruno transition matrices are equal as expected'
else:
print >> out, '*** halpern-bruno trans. mat. from x is not equal!'
# return the results
return out.getvalue()
def process(fs):
nstates = fs.nstates
np.set_printoptions(linewidth=200)
t = fs.t
### sample a random time
##time_mu = 0.01
##t = random.expovariate(1 / time_mu)
# Sample a rate matrix.
# Use a trick by Robert Kern to left and right multiply by diagonals.
# http://mail.scipy.org/pipermail/numpy-discussion/2007-March/
# 026809.html
S = MatrixUtil.sample_pos_sym_matrix(nstates)
v = mrate.sample_distn(nstates)
R = (v**-0.5)[:,np.newaxis] * S * (v**0.5)
R -= np.diag(np.sum(R, axis=1))
# Construct a parent-independent process
# with the same max rate and stationary distribution
# as the sampled process.
if fs.parent_indep:
Q = np.outer(np.ones(nstates), v)
Q -= np.diag(np.sum(Q, axis=1))
pi_rescaling_factor = max(np.diag(R) / np.diag(Q))
Q *= pi_rescaling_factor
Z = msimpl.get_fast_meta_f81_autobarrier(Q)
# Construct a child-independent process
# with the same expected rate
# as the sampled process
if fs.child_indep:
C = np.outer(1/v, np.ones(nstates))
C -= np.diag(np.sum(C, axis=1))
ci_rescaling_factor = np.max(R / C)
#expected_rate = -ndot(np.diag(R), v)
#ci_rescaling_factor = expected_rate / (nstates*(nstates-1))
#ci_rescaling_factor = expected_rate / (nstates*nstates)
C *= ci_rescaling_factor
Q = C
if fs.bipartitioned:
Q = msimpl.get_fast_meta_f81_autobarrier(R)
# Check that the mutual information of the
# parent independent process is smaller.
out = StringIO()
print >> out, 'sampled symmetric part of the rate matrix S:'
print >> out, S
print >> out
print >> out, 'sampled stationary distribution v:'
print >> out, v
print >> out
print >> out, 'shannon entropy of stationary distribution v:'
print >> out, -np.dot(np.log(v), v)
print >> out
print >> out, 'sqrt stationary distribution:'
print >> out, np.sqrt(v)
print >> out
print >> out, 'implied rate matrix R:'
print >> out, R
print >> out
print >> out, 'eigenvalues of R:', scipy.linalg.eigvals(R)
print >> out
print >> out, 'relaxation rate of R:',
print >> out, sorted(np.abs(scipy.linalg.eigvals(R)))[1]
print >> out
print >> out, 'expected rate of R:', mrate.Q_to_expected_rate(R)
print >> out
print >> out, 'cheeger bounds of R:', get_cheeger_bounds(R, v)
print >> out
print >> out, 'randomization rate of R:', get_randomization_rate(R, v)
print >> out
candidates = [get_randomization_candidate(R, v, i) for i in range(nstates)]
if np.allclose(get_randomization_rate(R, v), candidates):
print >> out, 'all candidates are equal to this rate'
else:
print >> out, 'not all candidates are equal to this rate'
print >> out
print >> out, 'simplified rate matrix Q:'
print >> out, Q
print >> out
qv = mrate.R_to_distn(Q)
print >> out, 'stationary distribution of Q:'
print >> out, qv
print >> out
print >> out, 'ratio qv/v:'
print >> out, qv / v
print >> out
print >> out, 'shannon entropy of stationary distribution of Q:'
print >> out, -np.dot(np.log(qv), qv)
print >> out
if fs.parent_indep:
print >> out, 'parent independent rescaling factor:'
print >> out, pi_rescaling_factor
print >> out
if fs.child_indep:
print >> out, 'child independent rescaling factor:'
print >> out, ci_rescaling_factor
print >> out
print >> out, 'eigenvalues of Q:', scipy.linalg.eigvals(Q)
print >> out
print >> out, 'relaxation rate of Q:',
print >> out, sorted(np.abs(scipy.linalg.eigvals(Q)))[1]
print >> out
print >> out, 'expected rate of Q:', mrate.Q_to_expected_rate(Q)
print >> out
print >> out, 'cheeger bounds of Q:', get_cheeger_bounds(Q, v)
print >> out
print >> out, 'randomization rate of Q:', get_randomization_rate(Q, v)
print >> out
candidates = [get_randomization_candidate(Q, v, i) for i in range(nstates)]
if np.allclose(get_randomization_rate(Q, v), candidates):
print >> out, 'all candidates are equal to this rate'
else:
print >> out, 'warning: not all candidates are equal to this rate'
print >> out
print >> out, 'E(rate) of Q divided by logical entropy:',
print >> out, mrate.Q_to_expected_rate(Q) / ndot(v, 1-v)
print >> out
print >> out, 'symmetric matrix similar to Q:'
S = ndot(np.diag(np.sqrt(v)), Q, np.diag(1/np.sqrt(v)))
print >> out, S
print >> out
print >> out, 'eigendecomposition of the similar matrix:'
W, V = scipy.linalg.eigh(S)
print >> out, V
print >> out, np.diag(W)
print >> out, V.T
print >> out
#
print >> out, 'time:', t
print >> out
print >> out, 'stationary distn logical entropy:', ndot(v, 1-v)
print >> out
#
P_by_hand = get_pi_transition_matrix(Q, v, t)
print >> out, 'simplified-process transition matrix computed by hand:'
print >> out, P_by_hand
print >> out
print >> out, 'simplified-process transition matrix computed by expm:'
print >> out, scipy.linalg.expm(Q*t)
print >> out
#
print >> out, 'simplified-process m.i. by hand:'
print >> out, get_pi_mi(Q, v, t)
print >> out
print >> out, 'simplified-process m.i. by expm:'
print >> out, ctmcmi.get_expected_ll_ratio(Q, t)
print >> out
#
print >> out, 'original process m.i. by expm:'
print >> out, ctmcmi.get_expected_ll_ratio(R, t)
print >> out
#
print >> out, 'stationary distn Shannon entropy:'
print >> out, -ndot(v, np.log(v))
print >> out
#
if fs.parent_indep:
print >> out, 'approximate simplified process m.i. 2nd order approx:'
print >> out, get_pi_mi_t2_approx(Q, v, t)
print >> out
print >> out, 'approximate simplified process m.i. "better" approx:'
print >> out, get_pi_mi_t2_diag_approx(Q, v, t)
print >> out
print >> out, '"f81-ization plus barrier" of pure f81-ization:'
print >> out, Z
print >> out
#
return out.getvalue().rstrip()
