def R_to_distn_nonspectral(R):
"""
The rate matrix must be irreducible and reversible.
It is not necessarily symmetric.
If the rate matrix is symmetric then this function is overkill
because the stationary distribution would be uniform.
"""
nstates = len(R)
V = set(range(nstates))
E = set()
for i in range(nstates):
for j in range(i):
if R[i, j]:
if not R[j, i]:
raise MatrixUtil.MatrixError(
'the matrix is not reversible')
edge = frozenset((i, j))
E.add(edge)
nd = graph.g_to_nd(V, E)
# construct an arbitrary rooted spanning tree of the states
V_component, D_component = graph.nd_to_dag_component(nd, 0)
if V_component != V:
raise MatrixUtil.MatrixError('the matrix is not irreducible')
# compute the stationary probabilities relative to the first state
weights = [None] * nstates
v_to_children = graph.dag_to_cd(V_component, D_component)
preorder_states = graph.topo_sort(V_component, D_component)
weights[preorder_states[0]] = 1.0
for parent in preorder_states:
for child in v_to_children[parent]:
ratio = R[parent, child] / R[child, parent]
weights[child] = weights[parent] * ratio
total = sum(weights)
return np.array(weights) / total
def R_to_distn_nonspectral(R):
"""
The rate matrix must be irreducible and reversible.
It is not necessarily symmetric.
If the rate matrix is symmetric then this function is overkill
because the stationary distribution would be uniform.
"""
nstates = len(R)
V = set(range(nstates))
E = set()
for i in range(nstates):
for j in range(i):
if R[i, j]:
if not R[j, i]:
raise MatrixUtil.MatrixError('the matrix is not reversible')
edge = frozenset((i,j))
E.add(edge)
nd = graph.g_to_nd(V, E)
# construct an arbitrary rooted spanning tree of the states
V_component, D_component = graph.nd_to_dag_component(nd, 0)
if V_component != V:
raise MatrixUtil.MatrixError('the matrix is not irreducible')
# compute the stationary probabilities relative to the first state
weights = [None] * nstates
v_to_children = graph.dag_to_cd(V_component, D_component)
preorder_states = graph.topo_sort(V_component, D_component)
weights[preorder_states[0]] = 1.0
for parent in preorder_states:
for child in v_to_children[parent]:
ratio = R[parent, child] / R[child, parent]
weights[child] = weights[parent] * ratio
total = sum(weights)
return np.array(weights) / total
def assert_symmetric_irreducible(M):
assert_symmetric(M)
V = set(range(len(M)))
E = set()
for i in range(len(M)):
for j in range(i):
if M[i, j]:
edge = frozenset((i, j))
E.add(edge)
nd = graph.g_to_nd(V, E)
V_component, D_component = graph.nd_to_dag_component(nd, 0)
if V_component != V:
raise MatrixError('the matrix is not irreducible')
def assert_symmetric_irreducible(M):
assert_symmetric(M)
V = set(range(len(M)))
E = set()
for i in range(len(M)):
for j in range(i):
if M[i, j]:
edge = frozenset((i,j))
E.add(edge)
nd = graph.g_to_nd(V, E)
V_component, D_component = graph.nd_to_dag_component(nd, 0)
if V_component != V:
raise MatrixError('the matrix is not irreducible')
