1 | #include <Eigen/Sparse>
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2 | #include <vector>
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3 | #include <QImage>
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4 |
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5 | typedef Eigen::SparseMatrix<double> SpMat; // declares a column-major sparse matrix type of double
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6 | typedef Eigen::Triplet<double> T;
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7 |
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8 | void insertCoefficient(int id, int i, int j, double w, std::vector<T>& coeffs,
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9 | Eigen::VectorXd& b, const Eigen::VectorXd& boundary)
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10 | {
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11 | int n = boundary.size();
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12 | int id1 = i+j*n;
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13 |
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14 | if(i==-1 || i==n) b(id) -= w * boundary(j); // constrained coefficient
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15 | else if(j==-1 || j==n) b(id) -= w * boundary(i); // constrained coefficient
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16 | else coeffs.push_back(T(id,id1,w)); // unknown coefficient
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17 | }
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18 |
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19 | void buildProblem(std::vector<T>& coefficients, Eigen::VectorXd& b, int n)
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20 | {
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21 | b.setZero();
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22 | Eigen::ArrayXd boundary = Eigen::ArrayXd::LinSpaced(n, 0,M_PI).sin().pow(2);
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23 | for(int j=0; j<n; ++j)
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24 | {
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25 | for(int i=0; i<n; ++i)
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26 | {
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27 | int id = i+j*n;
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28 | insertCoefficient(id, i-1,j, -1, coefficients, b, boundary);
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29 | insertCoefficient(id, i+1,j, -1, coefficients, b, boundary);
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30 | insertCoefficient(id, i,j-1, -1, coefficients, b, boundary);
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31 | insertCoefficient(id, i,j+1, -1, coefficients, b, boundary);
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32 | insertCoefficient(id, i,j, 4, coefficients, b, boundary);
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33 | }
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34 | }
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35 | }
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36 |
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37 | void saveAsBitmap(const Eigen::VectorXd& x, int n, const char* filename)
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38 | {
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39 | Eigen::Array<unsigned char,Eigen::Dynamic,Eigen::Dynamic> bits = (x*255).cast<unsigned char>();
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40 | QImage img(bits.data(), n,n,QImage::Format_Indexed8);
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41 | img.setColorCount(256);
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42 | for(int i=0;i<256;i++) img.setColor(i,qRgb(i,i,i));
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43 | img.save(filename);
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44 | }
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