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Renormalization.m
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Renormalization.m
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function theta = Renormalization (xi, threshold, covFunc)
% Renormalization 2次形式で与えられるくりこみ法の計算
% (xi(x,y), theta) = 0
% のxiを引数とし幾何学推定解thetaを返す
% 推定変数の数m,データ長nとして
% xiはm行n列,thetaは長さmの縦ベクトル
% thresholdはtheta≒theta_oと判断する閾値
m = size(xi, 1);
n = size(xi, 2);
theta_o = zeros(m, 1);
theta = ones(m, 1);
Wa = ones(1, n);
while true
smM = zeros(m, m);
smN = zeros(m, m);
for alpha = 1 : n
smM = smM + Wa(1, alpha) * xi(:, alpha) * transpose(xi(:, alpha));
smN = smN + Wa(1, alpha) * covFunc(xi(:, alpha));
end
M = (1 / n) .* smM;
N = (1 / n) .* smN;
[eV, eD] = eig(M, N);
[d,ind] = sort(diag(abs(eD)));
eD = eD(ind, ind);
eV = eV(:, ind);
theta = eV(:, 1);
isEnd = true;
for i = 1 : m
isEnd = isEnd & (abs(abs(theta_o(i)) - abs(theta(i))) < threshold);
end
if isEnd
break
end
theta_o = theta;
for alpha = 1 : n
Wa(1, alpha) = 1 / (theta' * covFunc(xi(:, alpha)) * theta);
end
end
end