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%最小二乘支持向量機（LSSVM）軟測量，崔宇，200901
%該函數的作用：用訓練樣本集進行訓練，然后對測試樣本集進行預測，返回預測輸出值
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%【輸入】： XTrain   - 訓練集樣本_鍋爐工況數據
%          yTrain   - 訓練集樣本_飛灰含碳(或煙氣含氧)真實值
%          XTest    - 測試集樣本_鍋爐工況
%          Gama     - 懲罰系數（LS-SVM參數，也叫正規化參數）
%          Sigma    - RBF核函數參數（LS-SVM參數）
%【輸出】：yPredict - 飛灰含碳(或煙氣含氧)軟測量模型預測值

function yPredict= LSSVM(XTrain,yTrain,XTest,Gama,Sigma);

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%初始化
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% t = cputime;
SampleNumber = size(XTrain,1);   %訓練樣本數（各論文中的“L”）

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%LSSVM方法中，線性方程組等號左邊的系數矩陣
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InputMatrix =ones(SampleNumber + 1,SampleNumber + 1);  %初始化線性方程組等號左邊的矩陣
InputMatrix(1,1) =0;
KernelXTrain = zeros(SampleNumber,SampleNumber);  %初始化線性方程組等號左邊的矩陣中的子陣
%對線性方程等號左邊的矩陣中的子陣進行賦值
for i = 1:SampleNumber
    
    for j = 1:SampleNumber
        
        if i < j,                   
            KernelXTrain(i,j) = sum((XTrain(j,:) - XTrain(i,:)).^2); %歐式距離的平方
        else
            KernelXTrain(i,j) = KernelXTrain(j,i);
        end
        
    end

end
%計算線性方程組等號左邊矩陣
KernelXTrain = exp(KernelXTrain/-Sigma);
KernelXTrain =KernelXTrain + 1 / Gama * eye(SampleNumber);
InputMatrix(2:SampleNumber + 1,2:SampleNumber + 1) = KernelXTrain;

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%LSSVM方法中，線性方程組等號右邊的系數矩陣
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OutMatrix = zeros(SampleNumber + 1,size(yTrain,2)); %初始化線性方程組等號右邊的矩陣
%計算線性方程組右邊矩陣
for i = 1:size(yTrain,2)
    OutMatrix(:,i) = [0;yTrain(:,i)];
end    
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%%求解LSSVM中的線性方程組
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Coefficient = inv(InputMatrix) * OutMatrix;
a = Coefficient(2:SampleNumber + 1,:);
b=zeros(size(XTest,1),1);
for i = 1:size(XTest,1)
    b(i,:) = Coefficient(1,:);
end

% cputime - t
% t1= cputime;

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%%計算測試集鍋爐工況核函數
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KernelXTest= zeros(size(XTest,1),SampleNumber);
for i = 1:size(XTest,1)
    
    for j = 1:SampleNumber
        KernelXTest(i,j) = sum((XTrain(j,:) - XTest(i,:)).^2);  %歐式距離的平方
    end
    
end
KernelXTest = exp(KernelXTest / -Sigma);

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%使用訓練得到的軟測量模型，對某一個（或幾個）工況下的飛灰含碳（或煙氣含氧）進行預測
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yPredict = KernelXTest * a + b;

% (cputime - t1)/SampleNumber

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%存在的若干問題
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