def sim_discrete(tree, Q, anc=None, charname=None, rseed=None):
"""
Simulate discrete character on a tree given transition rate matrix.
Args:
tree (Node): Root node of tree.
Q (np.array): Instantaneous rate matrix
anc (int): Root state. Optional. If None, root state is chosen
from stationary distrubution of Q matrix
rseed (int): Random seed to be passed to np.random. Optional
Returns:
Node: Copy of tree with each node containing its simulated
state and the character history of its subtending branch.
"""
assert tree.isroot, "Given node must be root"
nchar = Q.shape[0]
simtree = tree.copy()
####################################
# Start with ancestral state of root
####################################
if anc is None:
# Randomly pick ancestral state from stationary distribution
anc = rv_discrete(values=(list(range(nchar)), mk.qsd(Q))).rvs()
simtree.sim_char = {}
simtree.sim_char["sim_state"] = anc
simtree.sim_char["sim_hist"] = []
###############################################################
# Go through the tree in preorder sequence and simulate history
###############################################################
if rseed:
np.random.seed(rseed)
for node in simtree.descendants():
prevstate = node.parent.sim_char["sim_state"]
node.sim_char = {}
node.sim_char["sim_state"] = prevstate
node.sim_char["sim_hist"] = []
if node.length == 0:
pass
else:
dt = 0
while 1:
dt += np.random.exponential(1.0 / -Q[prevstate, prevstate])
if dt > node.length:
break
vals = np.concatenate(
(Q[prevstate][:prevstate], Q[prevstate][prevstate + 1:]))
newstate = rv_discrete(
values=(list(range(nchar))[:prevstate] +
list(range(nchar))[prevstate + 1:],
vals / sum(vals))).rvs()
node.sim_char["sim_hist"].append((newstate, dt))
node.sim_char["sim_state"] = newstate
prevstate = newstate
return simtree
def test_qsd_ERQ3_returnsflatpi(self):
Q = np.array([[-.2, .2], [.1, -.1]], dtype=np.double)
calculatedPi = mk.qsd(Q)
expectedPi = np.array([1.0 / 3.0, 2.0 / 3.0])
try:
np.testing.assert_allclose(expectedPi, calculatedPi)
except AssertionError:
self.fail("expectedPi != calculatedPi")
def test_qsd_ARDQ3_matchesphytools(self):
Q = np.array([[-.3, .1, .2], [.05, -.3, .25], [.05, .1, -.15]],
dtype=np.double)
calculatedPi = mk.qsd(Q)
expectedPi = np.array([0.1428571, 0.2500000, 0.6071429])
try:
np.testing.assert_allclose(expectedPi, calculatedPi, atol=1e-5)
except AssertionError:
self.fail("expectedPi != calculatedPi")
def test_qsd_ARDQ4_matchesphytools(self):
Q = np.array([[-.6, .1, .2, .3], [.05, -.4, .25, .1],
[.05, .1, -.15, 0], [.1, .1, .1, -.3]],
dtype=np.double)
calculatedPi = mk.qsd(Q)
expectedPi = np.array([0.08888889, 0.200000, 0.555555555, 0.155555556])
try:
np.testing.assert_allclose(expectedPi, calculatedPi, atol=1e-5)
except AssertionError:
self.fail("expectedPi != calculatedPi")
def test_qsd_ARDQ2_matchesphytools(self):
Q = np.array([[-.3, .1, .2], [.05, -.3, .25], [.05, .1, -.15]],
dtype=np.double)
calculatedPi = mk.qsd(Q)
expectedPi = np.array([0.1428571, 0.2500000, 0.6071429])
try: # Results will vary slightly from phytools (order of 1e-3)
# Possibly due to differences in optimization implementation?
np.testing.assert_allclose(expectedPi, calculatedPi, atol=1e-3)
except AssertionError:
self.fail("expectedPi != calculatedPi")