[136] | 1 | #include <Eigen/Sparse>
|
---|
| 2 | #include <vector>
|
---|
| 3 | #include <QImage>
|
---|
| 4 |
|
---|
| 5 | typedef Eigen::SparseMatrix<double> SpMat; // declares a column-major sparse matrix type of double
|
---|
| 6 | typedef Eigen::Triplet<double> T;
|
---|
| 7 |
|
---|
| 8 | void insertCoefficient(int id, int i, int j, double w, std::vector<T>& coeffs,
|
---|
| 9 | Eigen::VectorXd& b, const Eigen::VectorXd& boundary)
|
---|
| 10 | {
|
---|
| 11 | int n = boundary.size();
|
---|
| 12 | int id1 = i+j*n;
|
---|
| 13 |
|
---|
| 14 | if(i==-1 || i==n) b(id) -= w * boundary(j); // constrained coefficient
|
---|
| 15 | else if(j==-1 || j==n) b(id) -= w * boundary(i); // constrained coefficient
|
---|
| 16 | else coeffs.push_back(T(id,id1,w)); // unknown coefficient
|
---|
| 17 | }
|
---|
| 18 |
|
---|
| 19 | void buildProblem(std::vector<T>& coefficients, Eigen::VectorXd& b, int n)
|
---|
| 20 | {
|
---|
| 21 | b.setZero();
|
---|
| 22 | Eigen::ArrayXd boundary = Eigen::ArrayXd::LinSpaced(n, 0,M_PI).sin().pow(2);
|
---|
| 23 | for(int j=0; j<n; ++j)
|
---|
| 24 | {
|
---|
| 25 | for(int i=0; i<n; ++i)
|
---|
| 26 | {
|
---|
| 27 | int id = i+j*n;
|
---|
| 28 | insertCoefficient(id, i-1,j, -1, coefficients, b, boundary);
|
---|
| 29 | insertCoefficient(id, i+1,j, -1, coefficients, b, boundary);
|
---|
| 30 | insertCoefficient(id, i,j-1, -1, coefficients, b, boundary);
|
---|
| 31 | insertCoefficient(id, i,j+1, -1, coefficients, b, boundary);
|
---|
| 32 | insertCoefficient(id, i,j, 4, coefficients, b, boundary);
|
---|
| 33 | }
|
---|
| 34 | }
|
---|
| 35 | }
|
---|
| 36 |
|
---|
| 37 | void saveAsBitmap(const Eigen::VectorXd& x, int n, const char* filename)
|
---|
| 38 | {
|
---|
| 39 | Eigen::Array<unsigned char,Eigen::Dynamic,Eigen::Dynamic> bits = (x*255).cast<unsigned char>();
|
---|
| 40 | QImage img(bits.data(), n,n,QImage::Format_Indexed8);
|
---|
| 41 | img.setColorCount(256);
|
---|
| 42 | for(int i=0;i<256;i++) img.setColor(i,qRgb(i,i,i));
|
---|
| 43 | img.save(filename);
|
---|
| 44 | }
|
---|