def collapse_diamond(N, M, v):
"""
Collapse the middle two states.
@param N: population size
@param M: index to state vector
@param v: a distribution over a 3-simplex
@return: a distribution over a 2-simplex
"""
k = 4
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]
return v_collapsed
def collapse_diamond(N, M, v):
"""
Collapse the middle two states.
@param N: population size
@param M: index to state vector
@param v: a distribution over a 3-simplex
@return: a distribution over a 2-simplex
"""
k = 4
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]
return v_collapsed
def collapse_side(N, M, v):
"""
Collapse two pairs of states.
@param N: population size
@param M: index to state vector
@param v: a distribution over a 3-simplex
@return: a distribution over a 1-simplex
"""
k = 4
nstates_collapsed = multinomstate.get_nstates(N, k-2)
M_collapsed = np.array(list(multinomstate.gen_states(N, k-2)), 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
aB_ab = aB + ab
j = T_collapsed[AB_Ab, aB_ab]
v_collapsed[j] += v[i]
return v_collapsed
def collapse_side(N, M, v):
"""
Collapse two pairs of states.
@param N: population size
@param M: index to state vector
@param v: a distribution over a 3-simplex
@return: a distribution over a 1-simplex
"""
k = 4
nstates_collapsed = multinomstate.get_nstates(N, k - 2)
M_collapsed = np.array(list(multinomstate.gen_states(N, k - 2)), 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
aB_ab = aB + ab
j = T_collapsed[AB_Ab, aB_ab]
v_collapsed[j] += v[i]
return 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_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
