| #include <Eigen/Sparse> |
| #include <vector> |
| #include <QImage> |
| |
| typedef Eigen::SparseMatrix<double> SpMat; // declares a column-major sparse matrix type of double |
| typedef Eigen::Triplet<double> T; |
| |
| void insertCoefficient(int id, int i, int j, double w, std::vector<T>& coeffs, Eigen::VectorXd& b, |
| const Eigen::VectorXd& boundary) { |
| int n = int(boundary.size()); |
| int id1 = i + j * n; |
| |
| if (i == -1 || i == n) |
| b(id) -= w * boundary(j); // constrained coefficient |
| else if (j == -1 || j == n) |
| b(id) -= w * boundary(i); // constrained coefficient |
| else |
| coeffs.push_back(T(id, id1, w)); // unknown coefficient |
| } |
| |
| void buildProblem(std::vector<T>& coefficients, Eigen::VectorXd& b, int n) { |
| b.setZero(); |
| Eigen::ArrayXd boundary = Eigen::ArrayXd::LinSpaced(n, 0, M_PI).sin().pow(2); |
| for (int j = 0; j < n; ++j) { |
| for (int i = 0; i < n; ++i) { |
| int id = i + j * n; |
| insertCoefficient(id, i - 1, j, -1, coefficients, b, boundary); |
| insertCoefficient(id, i + 1, j, -1, coefficients, b, boundary); |
| insertCoefficient(id, i, j - 1, -1, coefficients, b, boundary); |
| insertCoefficient(id, i, j + 1, -1, coefficients, b, boundary); |
| insertCoefficient(id, i, j, 4, coefficients, b, boundary); |
| } |
| } |
| } |
| |
| void saveAsBitmap(const Eigen::VectorXd& x, int n, const char* filename) { |
| Eigen::Array<unsigned char, Eigen::Dynamic, Eigen::Dynamic> bits = (x * 255).cast<unsigned char>(); |
| QImage img(bits.data(), n, n, QImage::Format_Indexed8); |
| img.setColorCount(256); |
| for (int i = 0; i < 256; i++) img.setColor(i, qRgb(i, i, i)); |
| img.save(filename); |
| } |