initial commit

third_party/eigen/doc/special_examples/CMakeLists.txt

@@ -0,0 +1,31 @@
+if(NOT EIGEN_TEST_NOQT)
+  find_package(Qt4)
+  if(QT4_FOUND)
+    include(${QT_USE_FILE})
+  endif()
+endif()
+
+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} Eigen3::Eigen)
+
+  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()
+
+add_executable(random_cpp11 random_cpp11.cpp)
+target_link_libraries(random_cpp11 ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO} Eigen3::Eigen)
+add_dependencies(all_examples random_cpp11)
+
+add_custom_command(
+  TARGET random_cpp11
+  POST_BUILD
+  COMMAND random_cpp11
+  ARGS >${CMAKE_CURRENT_BINARY_DIR}/random_cpp11.out
+)

third_party/eigen/doc/special_examples/Tutorial_sparse_example.cpp

@@ -0,0 +1,36 @@
+#include <Eigen/Sparse>
+#include <vector>
+#include <iostream>
+
+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) {
+  if (argc != 2) {
+    std::cerr << "Error: expected one and only one argument.\n";
+    return -1;
+  }
+
+  int n = 300;    // size of the image
+  int m = n * n;  // number of unknowns (=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;
+}

third_party/eigen/doc/special_examples/Tutorial_sparse_example_details.cpp

@@ -0,0 +1,42 @@
+#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, EIGEN_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);
+}

third_party/eigen/doc/special_examples/random_cpp11.cpp

@@ -0,0 +1,12 @@
+#include <Eigen/Core>
+#include <iostream>
+#include <random>
+
+int main() {
+  std::default_random_engine generator;
+  std::poisson_distribution<int> distribution(4.1);
+  auto poisson = [&]() { return distribution(generator); };
+
+  Eigen::RowVectorXi v = Eigen::RowVectorXi::NullaryExpr(10, poisson);
+  std::cout << v << "\n";
+}