def wright_distn_helper(M, T, R_mut):
"""
@param M: index to states
@param T: states to index
@param R_mut: scaled mutation rate matrix
@return: stationary distribution of the process
"""
#FIXME: remove dependence on T
lmcs = wrightcore.get_lmcs(M)
lps = wrightcore.create_selection_neutral(M)
log_drift = wrightcore.create_neutral_drift(lmcs, lps, M)
P_drift = np.exp(log_drift)
P_mut = scipy.linalg.expm(R_mut)
P = np.dot(P_mut, P_drift)
v = MatrixUtil.get_stationary_distribution(P)
return v
def wright_distn_helper(M, T, R_mut):
"""
@param M: index to states
@param T: states to index
@param R_mut: scaled mutation rate matrix
@return: stationary distribution of the process
"""
#FIXME: remove dependence on T
lmcs = wrightcore.get_lmcs(M)
lps = wrightcore.create_selection_neutral(M)
log_drift = wrightcore.create_neutral_drift(lmcs, lps, M)
P_drift = np.exp(log_drift)
P_mut = scipy.linalg.expm(R_mut)
P = np.dot(P_mut, P_drift)
v = MatrixUtil.get_stationary_distribution(P)
return v
def do_full_simplex_then_collapse(mutrate, popsize):
#mutrate = 0.01
#mutrate = 0.2
#mutrate = 10
#mutrate = 100
#mutrate = 1
N = popsize
k = 4
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.
R = mutrate * wrightcore.create_mutation(M, T)
# 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)
for state, value in zip(M, v):
print state, value
# collapse the two middle states
nstates_collapsed = multinomstate.get_nstates(N, k-1)
M_collapsed = np.array(list(multinomstate.gen_states(N, k-1)), dtype=int)
T_collapsed = multinomstate.get_inverse_map(M_collapsed)
v_collapsed = np.zeros(nstates_collapsed)
for i, bigstate in enumerate(M):
AB, Ab, aB, ab = bigstate.tolist()
Ab_aB = Ab + aB
j = T_collapsed[AB, Ab_aB, ab]
v_collapsed[j] += v[i]
for state, value in zip(M_collapsed, v_collapsed):
print state, value
# draw an equilateral triangle
#drawtri(M_collapsed, T_collapsed, v_collapsed)
#test_mesh()
return M_collapsed, T_collapsed, v_collapsed
def do_full_simplex_then_collapse(mutrate, popsize):
#mutrate = 0.01
#mutrate = 0.2
#mutrate = 10
#mutrate = 100
#mutrate = 1
N = popsize
k = 4
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.
R = mutrate * wrightcore.create_mutation(M, T)
# 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)
for state, value in zip(M, v):
print state, value
# collapse the two middle states
nstates_collapsed = multinomstate.get_nstates(N, k - 1)
M_collapsed = np.array(list(multinomstate.gen_states(N, k - 1)), dtype=int)
T_collapsed = multinomstate.get_inverse_map(M_collapsed)
v_collapsed = np.zeros(nstates_collapsed)
for i, bigstate in enumerate(M):
AB, Ab, aB, ab = bigstate.tolist()
Ab_aB = Ab + aB
j = T_collapsed[AB, Ab_aB, ab]
v_collapsed[j] += v[i]
for state, value in zip(M_collapsed, v_collapsed):
print state, value
# draw an equilateral triangle
#drawtri(M_collapsed, T_collapsed, v_collapsed)
#test_mesh()
return M_collapsed, T_collapsed, v_collapsed
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