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