基于cholesky分解的拉丁超立方随机抽样用matlab怎么实现
时间: 2024-05-05 12:16:37 浏览: 4
以下是基于Cholesky分解的拉丁超立方随机抽样的Matlab实现代码:
```
function [X] = lhsdesign(n, p)
% LHSDESIGN Latin Hypercube Sampling
% X = lhsdesign(n, p) returns an n-by-p matrix, X, for use in
% Latin hypercube sampling. Rows of X are randomly permuted.
%
% Latin hypercube sampling ensures that each row of X is a random
% permutation of the digits 1 through n in each column, and that
% each row has only one digit per column.
% Generate a n-by-p matrix of uniformly distributed random numbers
U = rand(n,p);
% Initialize the output matrix
X = zeros(n,p);
% Generate the Latin hypercube samples
for j = 1:p
idx = randperm(n); % random permutation of indices
P = (idx'-U(:,j))/n; % perturb the uniform samples
X(:,j) = P(randperm(n)); % randomly permute the samples
end
% Randomly permute the rows of X
X = X(randperm(n), :);
% Apply Cholesky decomposition to X
R = chol(X'*X);
X = X/R;
end
```
该函数使用Cholesky分解来确保每个样本都与其他样本相互独立。在调用该函数时,n是样本数,p是特征数。该函数返回一个n-by-p的矩阵,其中每行都是一个样本,每列都是一个特征。