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== 代码实现 ==
== 代码实现 ==
这里分别针对上述状态空间和变量空间的因果涌现实例，提供了计算微观、宏观层次有效信息的python代码，以供参考。
基于状态空间的计算需要给定微观状态的概率转移矩阵，以及状态的
python:<syntaxhighlight lang="python3">
python:<syntaxhighlight lang="python3">
import torch
import torch
import itertools
# 计算信息熵
def Entropia(a):
def Entropia(a):
b = torch.nonzero(a > 0).squeeze(1)
b = torch.nonzero(a > 0).squeeze(1)
return -torch.sum(a[b]*torch.log2(a[b]))
return -torch.sum(a[b]*torch.log2(a[b]))
# 基于状态概率矩阵计算有效信息
def effective_information(G1):
def effective_information(G1):
"""
"""
return Win_entropy - Wout_average
return Win_entropy - Wout_average
# ==========================
# 给定粗粒化方案
# ==========================
# 状态空间的有效信息计算
# 状态空间的宏观TPM生成，以及有效信息计算
def calc_tpm(micro_tpm, group):
def calc_tpm(micro_tpm, group):
"""
"""
# 变量空间的有效信息计算
# 变量空间的微观、宏观TPM生成，以及有效信息计算
def calc_bn_ei(micro_mech, micro, edges, elem_group, mech_group):
def calc_bn_ei(micro_mech, micro, edges, elem_group, mech_group):
"""
"""
Returns
Returns
-------
-------
the EI value of micro and macro level.
micro_ei, macro_ei: the EI value of micro, macro level
S_m, S_M: transition probability matrix of micro, macro level
"""
"""
# generate the statue list of boolean nodes, based on the number of micro elements
# generate the statue list of boolean nodes, based on the number of micro elements
macro_ei = effective_information(S_M)
macro_ei = effective_information(S_M)
return micro_ei, macro_ei
return micro_ei, macro_ei, S_m, S_M
# Example：
# Example：
group = [(0, 1, 2), (3,)]
group = [(0, 1, 2), (3,)]
micro_ei, macro_ei, macro_tpm = calc_tpm(micro_tpm, group)
micro_ei, macro_ei, macro_tpm = calc_tpm(micro_tpm, group)
CE = macro_ei - micro_ei
# Example：提高确定性实例
# Example：提高确定性实例
mech_group = {'00': '0', '01': '0', '10': '0', '11': '1'}
mech_group = {'00': '0', '01': '0', '10': '0', '11': '1'}
micro_ei, macro_ei = calc_bn_ei(micro_mech, micro, edges, elem_group, mech_group)
micro_ei, macro_ei = calc_bn_ei(micro_mech, micro, edges, elem_group, mech_group)
CE = macro_ei - micro_ei
# ==========================
# 贪婪算法寻找最优粗粒化方案（来源：https://github.com/jkbren/einet）
# ==========================
# 需要在Github下载ce_net.py
from ce_net import *
# directly define the micro TPM, or use the generating methods above in function calc_bn_ei.
micro_tpm = np.array([[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]])
# check_network: transfer the TPM numpy ndarray format to digraph
G = check_network(micro_tpm)
# causal_emergence: the function defined in ce_net.py, optimizing the coarse-graining methods using greedy algorithm.
CE = causal_emergence(G)
EI_gain = CE['EI_macro'] - CE['EI_micro']
</syntaxhighlight>
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