Squashed 'third_party/eigen/' content from commit 61d72f6
Change-Id: Iccc90fa0b55ab44037f018046d2fcffd90d9d025
git-subtree-dir: third_party/eigen
git-subtree-split: 61d72f6383cfa842868c53e30e087b0258177257
diff --git a/doc/special_examples/CMakeLists.txt b/doc/special_examples/CMakeLists.txt
new file mode 100644
index 0000000..3ab75db
--- /dev/null
+++ b/doc/special_examples/CMakeLists.txt
@@ -0,0 +1,21 @@
+if(NOT EIGEN_TEST_NOQT)
+ find_package(Qt4)
+ if(QT4_FOUND)
+ include(${QT_USE_FILE})
+ endif()
+endif(NOT EIGEN_TEST_NOQT)
+
+if(QT4_FOUND)
+ add_executable(Tutorial_sparse_example Tutorial_sparse_example.cpp Tutorial_sparse_example_details.cpp)
+ target_link_libraries(Tutorial_sparse_example ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO} ${QT_QTCORE_LIBRARY} ${QT_QTGUI_LIBRARY})
+
+ add_custom_command(
+ TARGET Tutorial_sparse_example
+ POST_BUILD
+ COMMAND ${CMAKE_COMMAND} -E make_directory ${CMAKE_CURRENT_BINARY_DIR}/../html/
+ COMMAND Tutorial_sparse_example ARGS ${CMAKE_CURRENT_BINARY_DIR}/../html/Tutorial_sparse_example.jpeg
+ )
+
+ add_dependencies(all_examples Tutorial_sparse_example)
+endif(QT4_FOUND)
+
diff --git a/doc/special_examples/Tutorial_sparse_example.cpp b/doc/special_examples/Tutorial_sparse_example.cpp
new file mode 100644
index 0000000..002f19f
--- /dev/null
+++ b/doc/special_examples/Tutorial_sparse_example.cpp
@@ -0,0 +1,32 @@
+#include <Eigen/Sparse>
+#include <vector>
+
+typedef Eigen::SparseMatrix<double> SpMat; // declares a column-major sparse matrix type of double
+typedef Eigen::Triplet<double> T;
+
+void buildProblem(std::vector<T>& coefficients, Eigen::VectorXd& b, int n);
+void saveAsBitmap(const Eigen::VectorXd& x, int n, const char* filename);
+
+int main(int argc, char** argv)
+{
+ int n = 300; // size of the image
+ int m = n*n; // number of unknows (=number of pixels)
+
+ // Assembly:
+ std::vector<T> coefficients; // list of non-zeros coefficients
+ Eigen::VectorXd b(m); // the right hand side-vector resulting from the constraints
+ buildProblem(coefficients, b, n);
+
+ SpMat A(m,m);
+ A.setFromTriplets(coefficients.begin(), coefficients.end());
+
+ // Solving:
+ Eigen::SimplicialCholesky<SpMat> chol(A); // performs a Cholesky factorization of A
+ Eigen::VectorXd x = chol.solve(b); // use the factorization to solve for the given right hand side
+
+ // Export the result to a file:
+ saveAsBitmap(x, n, argv[1]);
+
+ return 0;
+}
+
diff --git a/doc/special_examples/Tutorial_sparse_example_details.cpp b/doc/special_examples/Tutorial_sparse_example_details.cpp
new file mode 100644
index 0000000..7d820b4
--- /dev/null
+++ b/doc/special_examples/Tutorial_sparse_example_details.cpp
@@ -0,0 +1,44 @@
+#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 = 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);
+}