def anal_Am(np_pmf, pmf_index, sys_index, m):
""" Analytic A_m """
m_ind = len(pmf_index[0]) - 2 - m
if m_ind < 0:
print("require seq_len > 1+m")
return None
s_ind = pmf_index[sys_index][:, [-2, -1]].flatten()
e_ind = np.delete(pmf_index, sys_index, axis=0)[:, m_ind:-1].flatten()
se_ind = np.concatenate((s_ind, e_ind))
margin_index = np.delete(pmf_index.flatten(), se_ind)
margin_pmf = prob.numpy_margin(np_pmf, margin_index)
x_ind = [list(se_ind).index(x) for x in s_ind][0:len(sys_index)]
y_ind = [list(se_ind).index(x)
for x in s_ind][len(sys_index):2 * len(sys_index)]
# print("indices")
# print(pmf_index)
# print(se_ind)
# print(total_ind)
# inf.numpy_conditional_mutual_information()
return inf.numpy_conditional_mutual_information(margin_pmf, x_ind, y_ind)
def anal_step_cond_MI(np_pmf, pmf_index, xind, yind, zind=()):
""" I(X;Y|Z), z optional """
xy_index = list(itt.chain(*xind, *yind, *zind))
margin_index = np.delete(pmf_index.flatten(), xy_index)
margin_pmf = prob.numpy_margin(np_pmf, margin_index)
XIND = [list(xy_index).index(x) for x in list(itt.chain(*xind))]
YIND = [list(xy_index).index(x) for x in list(itt.chain(*yind))]
if zind == ():
return inf.numpy_mutual_information(margin_pmf, XIND, YIND)
return inf.numpy_conditional_mutual_information(margin_pmf, XIND, YIND)
def anal_IF(np_pmf, pmf_index, x_index):
""" Analytic IF(X->Y) = I(Y_{n+1}:X_{n}|Y_{n}) """
pmf_index = np.array(pmf_index)
X_n = pmf_index[x_index][:, -2].flatten()
Y_n = np.delete(pmf_index, x_index, axis=0)[:, -2].flatten()
Y_n1 = np.delete(pmf_index, x_index, axis=0)[:, -1].flatten()
flat_ind = np.sort(np.concatenate((X_n, Y_n, Y_n1)))
margin_index = np.delete(pmf_index.flatten(), flat_ind)
margin_pmf = prob.numpy_margin(np_pmf, margin_index)
x_ind = [list(flat_ind).index(x) for x in X_n]
y_ind = [list(flat_ind).index(y) for y in Y_n1]
return inf.numpy_conditional_mutual_information(margin_pmf, x_ind, y_ind)
def seq_IF(data, flow_from_index, flow_to_index, t_shift=1):
""" IF(E->S) = I(S_{n+1} : E_{n}|S_{n})
Parameters
----------
data : array_like
rows represent variables columns represent time steps
flow_from_index : list
index for X in IF(X->Y)
flow_to_index : list
index for Y in IF(X->Y)
"""
var_index = [flow_to_index, flow_from_index]
step_index = [[t_shift, 0], [0]]
seq_data, seq_index = seq_maker(data,
var_index,
step_index,
return_index=True)
seq_pmf = prob.numpy_pmf(seq_data)
return inf.numpy_conditional_mutual_information(seq_pmf, seq_index[0],
seq_index[2])
def seq_Am(data, sys_index, env_index, m, t_shift=1):
""" I(S_{n+1} ; S_{n} | E_{n}, E_{n-1}, ... ,E_{n-m})
Parameters
----------
data : array_like
rows represent variables columns represent time steps
sys_index : list
index for S in data
env_index : list
index for E in data
"""
var_index = [sys_index, env_index]
step_index = [[t_shift, 0], list(range(0, -(m + 1), -1))]
seq_data, seq_index = seq_maker(data,
var_index,
step_index,
return_index=True)
seq_pmf = prob.numpy_pmf(seq_data)
return inf.numpy_conditional_mutual_information(seq_pmf, seq_index[0],
seq_index[1])