%AOLMM多步預測函數
function [FChaosPredict] = FunctionChaosPredict(Data,N,mtbp,deltaT,tao,d,MaxStep)
%Data是一維信號時間序列，N是信號數據長度，mtbp,deltaT,tao,d分別是重構相空間的平均時間序列、采樣周期、時延及嵌入維

roll=Data;%取橫搖數據
M = N - (d - 1)*tao;
for i = 1 : M
    for j = 1 : d
        MatrixX(i,j) = roll(i + (j - 1)*tao);
    end
end

%計算相空間中第M點與各點的距離
for j = 1 : (M - 1)
    Dis(j) = norm(MatrixX(M,:) - MatrixX(j,:),2);
end
%排序計算相空間中第M點的(m+1)個參考鄰近點
for i = 1 : (d + 1)
    NearDis(i) = Dis(i);
    NearPos(i) = i;
end
for i = (d + 2) : (M - mtbp)
    for j = 1 : (d + 1)
        if (abs(i-j)>mtbp) %& abs(i-j)<10*mtbp
            if(Dis(i) < NearDis(j))
                NearDis(j) = Dis(i);
                NearPos(j) = i;
                break;
            end
        end
    end
end
SortedDis = sort(NearDis);
MinDis = SortedDis(1);
%計算第M點的(m+1)個參考鄰近點的權P[i]
SumP = 0;
for i = 1 : (d + 1)
    P(i) = exp(-NearDis(i)/MinDis);
    SumP = SumP + P(i);
end
P = P/SumP;
%用最小二乘法計算a[],b[]
for step=1:1:MaxStep
    aCoe1 = 0;
    aCoe2 = d;
    bCoe1 = 0;
    bCoe2 = 0;
    e = 0;
    f = 0;
    for i = 1 : (d + 1)
        aCoe1 = aCoe1 + P(i)*sum(MatrixX(NearPos(i),:));
        bCoe1 = bCoe1 + P(i)*(MatrixX(NearPos(i),:)*MatrixX(NearPos(i),:)');
        e = e + P(i)*(MatrixX(NearPos(i) + step,:)*MatrixX(NearPos(i),:)');
        f = f + P(i)*sum(MatrixX(NearPos(i) + step,:));
    end
    bCoe2 = aCoe1;
    CoeMatrix = [aCoe1,bCoe1;aCoe2,bCoe2];
    ResultMatrix = [e;f];
    abResult = CoeMatrix\ResultMatrix;
    a = abResult(1);
    b = abResult(2);
    %----------------------------------------------
    for j = 1 : d
        %     MatrixX(M + step,j) = a + b*MatrixX(M,j); %以歷史上相近點的演化規律作為中心點的演化規律以中心點為基準進行預報

        MatrixX(M + step,j) = 0;
        for i = 1 : (d + 1)
            MatrixX(M + step,j) = MatrixX(M + step,j) + P(i)*(a + b*MatrixX(NearPos(i),j)); %以歷史上相近點的演化加權和直接作為中心點的演化點進行預報
        end
    end
    %---------------------------------------------------
  %MatrixX(M + step,d)=a+b*roll(N);
    PredictedData(step) = MatrixX(M + step,d);
    FChaosPredict(step) = PredictedData(step);

end