%AOLMM多步預(yù)測函數(shù)
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(shù)據(jù)長度，mtbp,deltaT,tao,d分別是重構(gòu)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(shù)據(jù)
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(diǎn)與各點(diǎn)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(diǎn)的(m+1)個參考鄰近點(diǎn)
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(diǎn)的(m+1)個參考鄰近點(diǎn)的權(quán)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(diǎn)的演化規(guī)律作為中心點(diǎn)的演化規(guī)律以中心點(diǎn)為基準(zhǔn)進(jìn)行預(yù)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(diǎn)的演化加權(quán)和直接作為中心點(diǎn)的演化點(diǎn)進(jìn)行預(yù)報
        end
    end
    %---------------------------------------------------
  %MatrixX(M + step,d)=a+b*roll(N);
    PredictedData(step) = MatrixX(M + step,d);
    FChaosPredict(step) = PredictedData(step);

end