function [ln_r,ln_C]=G_P(data,N,tau,min_m,max_m,ss) % the function is used to calculate correlation dimention with G-P algorithm % data:the time series % N: the length of the time series % tau: the time delay % min_m:the least embedded dimention m % max_m:the largest embedded dimention m % ss:the stepsize of r %skyhawk for m=min_m:max_m Y=reconstitution(data,N,m,tau);%reconstitute state space M=N-(m-1)*tau;%the number of points in state space for i=1:M-1 for j=i+1:M d(i,j)=max(abs(Y(:,i)-Y(:,j)));%calculate the distance of each two end %points in state space end max_d=max(max(d));%the max distance of all points d(1,1)=max_d; min_d=min(min(d));%the min distance of all points delt=(max_d-min_d)/ss;%the stepsize of r for k=1:ss r=min_d+k*delt; C(k)=correlation_integral(Y,M,r);%calculate the correlation integral ln_C(m,k)=log(C(k));%lnC(r) ln_r(m,k)=log(r);%lnr fprintf('%d/%d/%d/%d\n',k,ss,m,max_m); end plot(ln_r(m,:),ln_C(m,:)); hold on; end fid=fopen('lnr.txt','w'); 评论1
时间: 2024-04-04 15:33:41 浏览: 16
这段代码是用于计算关联维数的 G-P 算法,其中 data 是时间序列,N 是时间序列长度,tau 是时间延迟,min_m 是最小嵌入维数,max_m 是最大嵌入维数,ss 是 r 的步长。代码中先通过 reconstitution 函数重构状态空间,然后计算出状态空间中每两个点之间的距离,并计算出所有点之间距离的最大值和最小值。接着根据最大值、最小值和步长计算出一系列的 r 值,并分别计算每个 r 值下的关联积分 C。最后将 r 和 lnC(r) 分别存储在 ln_r 和 ln_C 中,并绘制出关联维数的图像。
相关问题
帮我写这两个函数mutual_information(data, tau, m)和false_nearest_neighbors(data, tau, m)
好的,下面是 `mutual_information(data, tau, m)` 和 `false_nearest_neighbors(data, tau, m)` 的代码。
```matlab
function MI = mutual_information(data, tau, m)
% Compute the mutual information of time series data
% data: input time series data
% tau: time delay
% m: embedding dimension
% Construct the phase space
X = embed(data, m, tau);
% Compute the probability density function
pdf = ksdensity(X);
% Compute the mutual information
MI = sum(pdf.*log2(pdf));
end
function fnn = false_nearest_neighbors(data, tau, m)
% Compute the false nearest neighbors of time series data
% data: input time series data
% tau: time delay
% m: embedding dimension
% Construct the phase space
X = embed(data, m, tau);
% Compute the Euclidean distances between neighboring points
dist = pdist(X);
% Compute the false nearest neighbors
fnn = sum(dist(1:end-1) > 10*dist(2:end));
end
function X = embed(data, m, tau)
% Embed a time series into a m-dimensional phase space with time delay tau
% data: input time series data
% m: embedding dimension
% tau: time delay
% Construct the phase space
N = length(data);
X = zeros(N-(m-1)*tau, m);
for i = 1:m
X(:,i) = data((i-1)*tau+1:end-(m-i)*tau);
end
end
```
`mutual_information(data, tau, m)` 函数使用核密度估计来计算概率密度函数,然后计算互信息。`false_nearest_neighbors(data, tau, m)` 函数计算相邻点之间的欧几里得距离,然后计算所有距离的比率是否超过了一个给定的阈值。这个阈值通常被设置为 10。
请注意,`embed(data, m, tau)` 函数也被包含在内,用于将时间序列嵌入到 m 维相空间中。
lambdas = np.arange(0, 10.1, 0.4) pipeline = Pipeline([ ('polynomial_features', PolynomialFeatures(degree=5)), ('ridge_regression', c.SGDLinearRegressor(batch_size=20, eta=0.01, tau_max=1000, epsilon=0.00001, random_state=42)) ])给这段代码加注释
以下是对这段代码的注释:
```python
import numpy as np
from sklearn.pipeline import Pipeline
from sklearn.preprocessing import PolynomialFeatures
import custom_module as c # 自定义模块
# 生成一个从 0 到 10(不含 10),步长为 0.4 的数组,作为 lambda 值
lambdas = np.arange(0, 10.1, 0.4)
# 定义一个 Pipeline,它包含两个步骤:
# 1. 对输入特征进行多项式扩展(degree=5)
# 2. 使用自定义模块 c 中的 SGDLinearRegressor 进行线性回归(batch_size=20, eta=0.01, tau_max=1000, epsilon=0.00001, random_state=42)
pipeline = Pipeline([
('polynomial_features', PolynomialFeatures(degree=5)),
('ridge_regression', c.SGDLinearRegressor(batch_size=20, eta=0.01, tau_max=1000, epsilon=0.00001, random_state=42))
])
```