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
insertCoefficient(int id,int i,int j,double w,std::vector<T> & coeffs,Eigen::VectorXd & b,const Eigen::VectorXd & boundary)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
buildProblem(std::vector<T> & coefficients,Eigen::VectorXd & b,int n)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
saveAsBitmap(const Eigen::VectorXd & x,int n,const char * filename)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 }
45