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→代码实现
== 代码实现 ==
== 代码实现 ==
这里分别针对状态空间和变量空间的因果涌现实例，提供了python代码实现的参考。
这里分别针对状态空间和变量空间的因果涌现实例，提供了python代码实现的参考。
python:<syntaxhighlight lang="python3">
import torch
def Entropia(a):
b = torch.nonzero(a > 0).squeeze(1)
return -torch.sum(a[b]*torch.log2(a[b]))
def effective_information(G1):
"""
Calculate EI value of transition probability matrix
G1: TPM matrix
return the EI value
"""
N = G1.shape[0]
G = torch.zeros_like(G1)
nozero_number = 0
for i in range(N):
if torch.sum(G1[i]) != 0:
G[i] = G1[i] / torch.sum(G1[i])
nozero_number += 1
Wout = torch.zeros(N)
Win = torch.zeros(N)
for i in range(N):
if torch.sum(G[i]) != 0:
Wout[i] = torch.tensor(Entropia(G[i]))
for i in range(N):
for j in range(N):
if G[i][j] != 0:
Win[j] += G[i][j] / nozero_number
Wout_average = torch.sum(Wout) / nozero_number
Win_entropy = Entropia(Win)
return Win_entropy - Wout_average
def calc_tpm(micro_tpm, group):
"""
Parameters
----------
micro_tpm: the transition probability matrix of system in micro level.
group: the coarse-graining methods (e.g., group = [(0, 1, 2), (3,)]: the micro states 0,1,2 are grouped into macro state 0, and the micro state 3 is grouped into macro state 1.
Returns
-------
micro_ei, macro_ei: the EI value of micro, macro TPM.
macro_tpm: the transition probability matrix of system in macro level
"""
# the number of micro/macro states
Nmi = micro_tpm.shape[0]
Nma = len(group)
# generate the mapping matrix from micro to macro
mapping = torch.zeros((Nmi, Nma), dtype=torch.float)
for j in range(Nma):
for i in group[j]:
mapping[i][j] = 1
# apply the mapping matrix to micro_tpm, and get the macro_tpm
macro_tpm = mapping.t() @ micro_tpm @ mapping
# calculate the EI of micro_tpm, macro_tpm
micro_ei = effective_information(micro_tpm)
macro_ei = effective_information(macro_tpm)
return micro_ei, macro_ei, macro_tpm
micro_tpm = torch.tensor([[1/3, 1/3, 1/3, 0], [1/3, 1/3, 1/3, 0], [1/3, 1/3, 1/3, 0], [0, 0, 0, 1]])
group = [(0, 1, 2), (3,)]
micro_ei, macro_ei, macro_tpm = calc_tpm(micro_tpm, group)
</syntaxhighlight>
== 应用 ==
== 应用 ==