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第256行： − − python代码实现:<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>
→状态空间的因果涌现
即存在着0.19比特的因果涌现，或用有效性度量得到0.595的因果涌现。
即存在着0.19比特的因果涌现，或用有效性度量得到0.595的因果涌现。
== 变量角度的因果涌现 ==
== 变量角度的因果涌现 ==