def main():
# use standard notation
Nmu = 1.0
N = 120
mu = Nmu / float(N)
print 'N*mu:', Nmu
print 'N:', N
print
# multiply the rate matrix by this scaling factor
m_factor = mu
# use the moran drift
distn_helper = moran_distn_helper
# get properties of the collapsed diamond process
k = 3
M = np.array(list(multinomstate.gen_states(N, k)), dtype=int)
T = multinomstate.get_inverse_map(M)
R_mut = m_factor * wrightcore.create_mutation_collapsed(M, T)
v = distn_helper(M, T, R_mut)
for Ab_aB in range(N+1):
nremaining = N - Ab_aB
# compute the volume for normalization
volume = 0.0
for AB in range(nremaining+1):
ab = nremaining - AB
volume += v[T[AB, Ab_aB, ab]]
# print some info
print 'X_1 + X_4 =', Ab_aB, '/', N
print 'probability =', volume
print 'Y = X_2 / (1 - (X_1 + X_4)) = X_2 / (X_2 + X_3)'
if not nremaining:
print 'conditional distribution of Y is undefined'
else:
# compute the conditional moments
m1 = 0.0
m2 = 0.0
for AB in range(nremaining+1):
ab = nremaining - AB
p = v[T[AB, Ab_aB, ab]] / volume
x = AB / float(nremaining)
m1 += x*p
m2 += x*x*p
# print some info
print 'conditional E(Y) =', m1
print 'conditional E(Y^2) =', m2
print 'conditional V(Y) =', m2 - m1*m1
print
def main():
# use standard notation
Nmu = 1.0
N = 120
mu = Nmu / float(N)
print 'N*mu:', Nmu
print 'N:', N
print
# multiply the rate matrix by this scaling factor
m_factor = mu
# use the moran drift
distn_helper = moran_distn_helper
# get properties of the collapsed diamond process
k = 3
M = np.array(list(multinomstate.gen_states(N, k)), dtype=int)
T = multinomstate.get_inverse_map(M)
R_mut = m_factor * wrightcore.create_mutation_collapsed(M, T)
v = distn_helper(M, T, R_mut)
for Ab_aB in range(N + 1):
nremaining = N - Ab_aB
# compute the volume for normalization
volume = 0.0
for AB in range(nremaining + 1):
ab = nremaining - AB
volume += v[T[AB, Ab_aB, ab]]
# print some info
print 'X_1 + X_4 =', Ab_aB, '/', N
print 'probability =', volume
print 'Y = X_2 / (1 - (X_1 + X_4)) = X_2 / (X_2 + X_3)'
if not nremaining:
print 'conditional distribution of Y is undefined'
else:
# compute the conditional moments
m1 = 0.0
m2 = 0.0
for AB in range(nremaining + 1):
ab = nremaining - AB
p = v[T[AB, Ab_aB, ab]] / volume
x = AB / float(nremaining)
m1 += x * p
m2 += x * x * p
# print some info
print 'conditional E(Y) =', m1
print 'conditional E(Y^2) =', m2
print 'conditional V(Y) =', m2 - m1 * m1
print
def do_collapsed_simplex(scaled_mut, N):
"""
@param N: population size
"""
k = 3
M = np.array(list(multinomstate.gen_states(N, k)), dtype=int)
T = multinomstate.get_inverse_map(M)
# Create the joint site pair mutation rate matrix.
# This is scaled so that there are about popsize mutations per generation.
R_mut_raw = wrightcore.create_mutation_collapsed(M, T)
R_mut = (scaled_mut / float(N)) * R_mut_raw
# Create the joint site pair drift transition matrix.
lmcs = wrightcore.get_lmcs(M)
lps = wrightcore.create_selection_neutral(M)
#log_drift = wrightcore.create_neutral_drift(lmcs, lps, M)
# Define the drift and mutation transition matrices.
#P_drift = np.exp(log_drift)
#P_mut = scipy.linalg.expm(R)
# Define the composite per-generation transition matrix.
#P = np.dot(P_mut, P_drift)
# Solve a system of equations to find the stationary distribution.
#v = MatrixUtil.get_stationary_distribution(P)
# Try a new thing.
# The raw drift matrix is scaled so that there are about N*N
# replacements per generation.
generation_rate = 1.0
R_drift_raw = wrightcore.create_moran_drift_rate_k3(M, T)
R_drift = (generation_rate / float(N)) * R_drift_raw
#FIXME: you should get the stationary distn directly from the rate matrix
P = scipy.linalg.expm(R_mut + R_drift)
v = MatrixUtil.get_stationary_distribution(P)
"""
for state, value in zip(M, v):
print state, value
"""
# draw an equilateral triangle
#drawtri(M, T, v)
return M, T, v
def do_collapsed_simplex(scaled_mut, N):
"""
@param N: population size
"""
k = 3
M = np.array(list(multinomstate.gen_states(N, k)), dtype=int)
T = multinomstate.get_inverse_map(M)
# Create the joint site pair mutation rate matrix.
# This is scaled so that there are about popsize mutations per generation.
R_mut_raw = wrightcore.create_mutation_collapsed(M, T)
R_mut = (scaled_mut / float(N)) * R_mut_raw
# Create the joint site pair drift transition matrix.
lmcs = wrightcore.get_lmcs(M)
lps = wrightcore.create_selection_neutral(M)
#log_drift = wrightcore.create_neutral_drift(lmcs, lps, M)
# Define the drift and mutation transition matrices.
#P_drift = np.exp(log_drift)
#P_mut = scipy.linalg.expm(R)
# Define the composite per-generation transition matrix.
#P = np.dot(P_mut, P_drift)
# Solve a system of equations to find the stationary distribution.
#v = MatrixUtil.get_stationary_distribution(P)
# Try a new thing.
# The raw drift matrix is scaled so that there are about N*N
# replacements per generation.
generation_rate = 1.0
R_drift_raw = wrightcore.create_moran_drift_rate_k3(M, T)
R_drift = (generation_rate / float(N)) * R_drift_raw
#FIXME: you should get the stationary distn directly from the rate matrix
P = scipy.linalg.expm(R_mut + R_drift)
v = MatrixUtil.get_stationary_distribution(P)
"""
for state, value in zip(M, v):
print state, value
"""
# draw an equilateral triangle
#drawtri(M, T, v)
return M, T, v
def get_collapsed_diamond_process_distn(m_factor, N, distn_helper):
k = 3
M = np.array(list(multinomstate.gen_states(N, k)), dtype=int)
T = multinomstate.get_inverse_map(M)
R_mut = m_factor * wrightcore.create_mutation_collapsed(M, T)
return distn_helper(M, T, R_mut)
def get_collapsed_diamond_process_distn(m_factor, N, distn_helper):
k = 3
M = np.array(list(multinomstate.gen_states(N, k)), dtype=int)
T = multinomstate.get_inverse_map(M)
R_mut = m_factor * wrightcore.create_mutation_collapsed(M, T)
return distn_helper(M, T, R_mut)
