Lee-Carter模型+奇异值分解实现代码matlab

以下是结合Lee-Carter模型和奇异值分解的Matlab代码：

function [a, b, k] = lc_svd(data)
% Lee-Carter model with singular value decomposition
% data: matrix with rows as years and columns as ages
% a, b, k: parameters of the Lee-Carter model

% compute the mean age at each year
mean_age = mean(data, 2);
% compute the log of the data
log_data = log(data);
% compute the deviation of the log data from the mean
deviation = log_data - mean_age;
% compute the singular value decomposition of the deviation matrix
[U, S, V] = svd(deviation);
% compute the principal component
pc = U(:, 1);
% compute the age and time effects
a = mean_age - mean(mean_age);
k = pc .* sqrt(S(1, 1));
b = log_data - repmat(mean_age, 1, size(data, 2)) - repmat(pc, 1, size(data, 2)) * repmat(k', size(data, 1), 1);
% compute the predicted log mortality rates
log_mortality = repmat(mean_age, 1, size(data, 2)) + repmat(a, size(data, 1), 1) + b * pinv(k);
% compute the predicted mortality rates
mortality = exp(log_mortality);
end

这个函数在原有的Lee-Carter函数的基础上增加了计算预测死亡率的代码。函数首先计算Lee-Carter模型的三个参数a、b、k，然后使用这些参数计算对数死亡率。最后，函数使用指数函数计算死亡率。这个函数使用了Matlab的`pinv`函数来计算伪逆矩阵，因为矩阵k不一定是可逆的。