initial commit

third_party/eigen/doc/snippets/.krazy

@@ -0,0 +1,2 @@
+EXCLUDE copyright
+EXCLUDE license

third_party/eigen/doc/snippets/AngleAxis_mimic_euler.cpp

@@ -0,0 +1,4 @@
+Matrix3f m;
+m = AngleAxisf(0.25 * EIGEN_PI, Vector3f::UnitX()) * AngleAxisf(0.5 * EIGEN_PI, Vector3f::UnitY()) *
+    AngleAxisf(0.33 * EIGEN_PI, Vector3f::UnitZ());
+cout << m << endl << "is unitary: " << m.isUnitary() << endl;

third_party/eigen/doc/snippets/Array_initializer_list_23_cxx11.cpp

@@ -0,0 +1,2 @@
+ArrayXXi a{{1, 2, 3}, {3, 4, 5}};
+cout << a << endl;

third_party/eigen/doc/snippets/Array_initializer_list_vector_cxx11.cpp

@@ -0,0 +1,2 @@
+Array<int, Dynamic, 1> v{{1, 2, 3, 4, 5}};
+cout << v << endl;

third_party/eigen/doc/snippets/Array_variadic_ctor_cxx11.cpp

@@ -0,0 +1,3 @@
+Array<int, 1, 6> a(1, 2, 3, 4, 5, 6);
+Array<int, 3, 1> b{1, 2, 3};
+cout << a << "\n\n" << b << endl;

third_party/eigen/doc/snippets/BiCGSTAB_simple.cpp

@@ -0,0 +1,11 @@
+int n = 10000;
+VectorXd x(n), b(n);
+SparseMatrix<double> A(n, n);
+/* ... fill A and b ... */
+BiCGSTAB<SparseMatrix<double> > solver;
+solver.compute(A);
+x = solver.solve(b);
+std::cout << "#iterations:     " << solver.iterations() << std::endl;
+std::cout << "estimated error: " << solver.error() << std::endl;
+/* ... update b ... */
+x = solver.solve(b);  // solve again

third_party/eigen/doc/snippets/BiCGSTAB_step_by_step.cpp

@@ -0,0 +1,14 @@
+int n = 10000;
+VectorXd x(n), b(n);
+SparseMatrix<double> A(n, n);
+/* ... fill A and b ... */
+BiCGSTAB<SparseMatrix<double> > solver(A);
+// start from a random solution
+x = VectorXd::Random(n);
+solver.setMaxIterations(1);
+int i = 0;
+do {
+  x = solver.solveWithGuess(b, x);
+  std::cout << i << " : " << solver.error() << std::endl;
+  ++i;
+} while (solver.info() != Success && i < 100);

third_party/eigen/doc/snippets/CMakeLists.txt

@@ -0,0 +1,32 @@
+file(GLOB snippets_SRCS "*.cpp")
+
+add_custom_target(all_snippets)
+
+foreach(snippet_src ${snippets_SRCS})
+  get_filename_component(snippet ${snippet_src} NAME_WE)
+  set(compile_snippet_target compile_${snippet})
+  set(compile_snippet_src ${compile_snippet_target}.cpp)
+
+  file(READ ${snippet_src} snippet_source_code)
+  configure_file(${CMAKE_CURRENT_SOURCE_DIR}/compile_snippet.cpp.in
+                ${CMAKE_CURRENT_BINARY_DIR}/${compile_snippet_src})
+  add_executable(${compile_snippet_target}
+                ${CMAKE_CURRENT_BINARY_DIR}/${compile_snippet_src})
+  if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)
+    target_link_libraries(${compile_snippet_target} ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO})
+  endif()
+  target_link_libraries(${compile_snippet_target} Eigen3::Eigen)
+
+  if(${snippet_src} MATCHES "deprecated")
+    set_target_properties(${compile_snippet_target} PROPERTIES COMPILE_FLAGS "-DEIGEN_NO_DEPRECATED_WARNING")
+  endif()
+  add_custom_command(
+    TARGET ${compile_snippet_target}
+    POST_BUILD
+    COMMAND ${compile_snippet_target}
+    ARGS >${CMAKE_CURRENT_BINARY_DIR}/${snippet}.out
+  )
+  add_dependencies(all_snippets ${compile_snippet_target})
+  set_source_files_properties(${CMAKE_CURRENT_BINARY_DIR}/${compile_snippet_src}
+                              PROPERTIES OBJECT_DEPENDS ${snippet_src})
+endforeach()

third_party/eigen/doc/snippets/ColPivHouseholderQR_solve.cpp

@@ -0,0 +1,8 @@
+Matrix3f m = Matrix3f::Random();
+Matrix3f y = Matrix3f::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is the matrix y:" << endl << y << endl;
+Matrix3f x;
+x = m.colPivHouseholderQr().solve(y);
+assert(y.isApprox(m* x));
+cout << "Here is a solution x to the equation mx=y:" << endl << x << endl;

third_party/eigen/doc/snippets/ComplexEigenSolver_compute.cpp

@@ -0,0 +1,16 @@
+MatrixXcf A = MatrixXcf::Random(4, 4);
+cout << "Here is a random 4x4 matrix, A:" << endl << A << endl << endl;
+
+ComplexEigenSolver<MatrixXcf> ces;
+ces.compute(A);
+cout << "The eigenvalues of A are:" << endl << ces.eigenvalues() << endl;
+cout << "The matrix of eigenvectors, V, is:" << endl << ces.eigenvectors() << endl << endl;
+
+complex<float> lambda = ces.eigenvalues()[0];
+cout << "Consider the first eigenvalue, lambda = " << lambda << endl;
+VectorXcf v = ces.eigenvectors().col(0);
+cout << "If v is the corresponding eigenvector, then lambda * v = " << endl << lambda * v << endl;
+cout << "... and A * v = " << endl << A * v << endl << endl;
+
+cout << "Finally, V * D * V^(-1) = " << endl
+     << ces.eigenvectors() * ces.eigenvalues().asDiagonal() * ces.eigenvectors().inverse() << endl;

third_party/eigen/doc/snippets/ComplexEigenSolver_eigenvalues.cpp

@@ -0,0 +1,3 @@
+MatrixXcf ones = MatrixXcf::Ones(3, 3);
+ComplexEigenSolver<MatrixXcf> ces(ones, /* computeEigenvectors = */ false);
+cout << "The eigenvalues of the 3x3 matrix of ones are:" << endl << ces.eigenvalues() << endl;

third_party/eigen/doc/snippets/ComplexEigenSolver_eigenvectors.cpp

@@ -0,0 +1,3 @@
+MatrixXcf ones = MatrixXcf::Ones(3, 3);
+ComplexEigenSolver<MatrixXcf> ces(ones);
+cout << "The first eigenvector of the 3x3 matrix of ones is:" << endl << ces.eigenvectors().col(0) << endl;

third_party/eigen/doc/snippets/ComplexSchur_compute.cpp

@@ -0,0 +1,6 @@
+MatrixXcf A = MatrixXcf::Random(4, 4);
+ComplexSchur<MatrixXcf> schur(4);
+schur.compute(A);
+cout << "The matrix T in the decomposition of A is:" << endl << schur.matrixT() << endl;
+schur.compute(A.inverse());
+cout << "The matrix T in the decomposition of A^(-1) is:" << endl << schur.matrixT() << endl;

third_party/eigen/doc/snippets/ComplexSchur_matrixT.cpp

@@ -0,0 +1,4 @@
+MatrixXcf A = MatrixXcf::Random(4, 4);
+cout << "Here is a random 4x4 matrix, A:" << endl << A << endl << endl;
+ComplexSchur<MatrixXcf> schurOfA(A, false);  // false means do not compute U
+cout << "The triangular matrix T is:" << endl << schurOfA.matrixT() << endl;

third_party/eigen/doc/snippets/ComplexSchur_matrixU.cpp

@@ -0,0 +1,4 @@
+MatrixXcf A = MatrixXcf::Random(4, 4);
+cout << "Here is a random 4x4 matrix, A:" << endl << A << endl << endl;
+ComplexSchur<MatrixXcf> schurOfA(A);
+cout << "The unitary matrix U is:" << endl << schurOfA.matrixU() << endl;

third_party/eigen/doc/snippets/Cwise_abs.cpp

@@ -0,0 +1,2 @@
+Array3d v(1, -2, -3);
+cout << v.abs() << endl;

third_party/eigen/doc/snippets/Cwise_abs2.cpp

@@ -0,0 +1,2 @@
+Array3d v(1, -2, -3);
+cout << v.abs2() << endl;

third_party/eigen/doc/snippets/Cwise_acos.cpp

@@ -0,0 +1,2 @@
+Array3d v(0, sqrt(2.) / 2, 1);
+cout << v.acos() << endl;

third_party/eigen/doc/snippets/Cwise_arg.cpp

@@ -0,0 +1,3 @@
+ArrayXcf v = ArrayXcf::Random(3);
+cout << v << endl << endl;
+cout << arg(v) << endl;

third_party/eigen/doc/snippets/Cwise_array_atan2_array.cpp

@@ -0,0 +1,3 @@
+Array<double, 1, 3> x(8, -25, 3), y(1. / 3., 0.5, -2.);
+cout << "atan2([" << x << "], [" << y << "]) = " << x.atan2(y) << endl;  // using ArrayBase::pow
+cout << "atan2([" << x << "], [" << y << "] = " << atan2(x, y) << endl;  // using Eigen::pow

third_party/eigen/doc/snippets/Cwise_array_power_array.cpp

@@ -0,0 +1,3 @@
+Array<double, 1, 3> x(8, 25, 3), e(1. / 3., 0.5, 2.);
+cout << "[" << x << "]^[" << e << "] = " << x.pow(e) << endl;   // using ArrayBase::pow
+cout << "[" << x << "]^[" << e << "] = " << pow(x, e) << endl;  // using Eigen::pow

third_party/eigen/doc/snippets/Cwise_asin.cpp

@@ -0,0 +1,2 @@
+Array3d v(0, sqrt(2.) / 2, 1);
+cout << v.asin() << endl;

third_party/eigen/doc/snippets/Cwise_atan.cpp

@@ -0,0 +1,2 @@
+ArrayXd v = ArrayXd::LinSpaced(5, 0, 1);
+cout << v.atan() << endl;

third_party/eigen/doc/snippets/Cwise_boolean_and.cpp

@@ -0,0 +1,2 @@
+Array3d v(-1, 2, 1), w(-3, 2, 3);
+cout << ((v < w) && (v < 0)) << endl;

third_party/eigen/doc/snippets/Cwise_boolean_not.cpp

@@ -0,0 +1,5 @@
+Array3d v(1, 2, 3);
+v(1) *= 0.0 / 0.0;
+v(2) /= 0.0;
+cout << v << endl << endl;
+cout << !isfinite(v) << endl;

third_party/eigen/doc/snippets/Cwise_boolean_or.cpp

@@ -0,0 +1,2 @@
+Array3d v(-1, 2, 1), w(-3, 2, 3);
+cout << ((v < w) || (v < 0)) << endl;

third_party/eigen/doc/snippets/Cwise_cbrt.cpp

@@ -0,0 +1,2 @@
+Array3d v(1, 2, 4);
+cout << v.cbrt() << endl;

third_party/eigen/doc/snippets/Cwise_ceil.cpp

@@ -0,0 +1,3 @@
+ArrayXd v = ArrayXd::LinSpaced(7, -2, 2);
+cout << v << endl << endl;
+cout << ceil(v) << endl;

third_party/eigen/doc/snippets/Cwise_cos.cpp

@@ -0,0 +1,2 @@
+Array3d v(EIGEN_PI, EIGEN_PI / 2, EIGEN_PI / 3);
+cout << v.cos() << endl;

third_party/eigen/doc/snippets/Cwise_cosh.cpp

@@ -0,0 +1,2 @@
+ArrayXd v = ArrayXd::LinSpaced(5, 0, 1);
+cout << cosh(v) << endl;

third_party/eigen/doc/snippets/Cwise_cube.cpp

@@ -0,0 +1,2 @@
+Array3d v(2, 3, 4);
+cout << v.cube() << endl;

third_party/eigen/doc/snippets/Cwise_equal_equal.cpp

@@ -0,0 +1,2 @@
+Array3d v(1, 2, 3), w(3, 2, 1);
+cout << (v == w) << endl;

third_party/eigen/doc/snippets/Cwise_exp.cpp

@@ -0,0 +1,2 @@
+Array3d v(1, 2, 3);
+cout << v.exp() << endl;

third_party/eigen/doc/snippets/Cwise_floor.cpp

@@ -0,0 +1,3 @@
+ArrayXd v = ArrayXd::LinSpaced(7, -2, 2);
+cout << v << endl << endl;
+cout << floor(v) << endl;

third_party/eigen/doc/snippets/Cwise_greater.cpp

@@ -0,0 +1,2 @@
+Array3d v(1, 2, 3), w(3, 2, 1);
+cout << (v > w) << endl;

third_party/eigen/doc/snippets/Cwise_greater_equal.cpp

@@ -0,0 +1,2 @@
+Array3d v(1, 2, 3), w(3, 2, 1);
+cout << (v >= w) << endl;

third_party/eigen/doc/snippets/Cwise_inverse.cpp

@@ -0,0 +1,2 @@
+Array3d v(2, 3, 4);
+cout << v.inverse() << endl;

third_party/eigen/doc/snippets/Cwise_isFinite.cpp

@@ -0,0 +1,5 @@
+Array3d v(1, 2, 3);
+v(1) *= 0.0 / 0.0;
+v(2) /= 0.0;
+cout << v << endl << endl;
+cout << isfinite(v) << endl;

third_party/eigen/doc/snippets/Cwise_isInf.cpp

@@ -0,0 +1,5 @@
+Array3d v(1, 2, 3);
+v(1) *= 0.0 / 0.0;
+v(2) /= 0.0;
+cout << v << endl << endl;
+cout << isinf(v) << endl;

third_party/eigen/doc/snippets/Cwise_isNaN.cpp

@@ -0,0 +1,5 @@
+Array3d v(1, 2, 3);
+v(1) *= 0.0 / 0.0;
+v(2) /= 0.0;
+cout << v << endl << endl;
+cout << isnan(v) << endl;

third_party/eigen/doc/snippets/Cwise_less.cpp

@@ -0,0 +1,2 @@
+Array3d v(1, 2, 3), w(3, 2, 1);
+cout << (v < w) << endl;

third_party/eigen/doc/snippets/Cwise_less_equal.cpp

@@ -0,0 +1,2 @@
+Array3d v(1, 2, 3), w(3, 2, 1);
+cout << (v <= w) << endl;

third_party/eigen/doc/snippets/Cwise_log.cpp

@@ -0,0 +1,2 @@
+Array3d v(1, 2, 3);
+cout << v.log() << endl;

third_party/eigen/doc/snippets/Cwise_log10.cpp

@@ -0,0 +1,2 @@
+Array4d v(-1, 0, 1, 2);
+cout << log10(v) << endl;

third_party/eigen/doc/snippets/Cwise_max.cpp

@@ -0,0 +1,2 @@
+Array3d v(2, 3, 4), w(4, 2, 3);
+cout << v.max(w) << endl;

third_party/eigen/doc/snippets/Cwise_min.cpp

@@ -0,0 +1,2 @@
+Array3d v(2, 3, 4), w(4, 2, 3);
+cout << v.min(w) << endl;

third_party/eigen/doc/snippets/Cwise_minus.cpp

@@ -0,0 +1,2 @@
+Array3d v(1, 2, 3);
+cout << v - 5 << endl;

third_party/eigen/doc/snippets/Cwise_minus_equal.cpp

@@ -0,0 +1,3 @@
+Array3d v(1, 2, 3);
+v -= 5;
+cout << v << endl;

third_party/eigen/doc/snippets/Cwise_not_equal.cpp

@@ -0,0 +1,2 @@
+Array3d v(1, 2, 3), w(3, 2, 1);
+cout << (v != w) << endl;

third_party/eigen/doc/snippets/Cwise_plus.cpp

@@ -0,0 +1,2 @@
+Array3d v(1, 2, 3);
+cout << v + 5 << endl;

third_party/eigen/doc/snippets/Cwise_plus_equal.cpp

@@ -0,0 +1,3 @@
+Array3d v(1, 2, 3);
+v += 5;
+cout << v << endl;

third_party/eigen/doc/snippets/Cwise_pow.cpp

@@ -0,0 +1,2 @@
+Array3d v(8, 27, 64);
+cout << v.pow(0.333333) << endl;

third_party/eigen/doc/snippets/Cwise_product.cpp

@@ -0,0 +1,3 @@
+Array33i a = Array33i::Random(), b = Array33i::Random();
+Array33i c = a * b;
+cout << "a:\n" << a << "\nb:\n" << b << "\nc:\n" << c << endl;

third_party/eigen/doc/snippets/Cwise_quotient.cpp

@@ -0,0 +1,2 @@
+Array3d v(2, 3, 4), w(4, 2, 3);
+cout << v / w << endl;

third_party/eigen/doc/snippets/Cwise_rint.cpp

@@ -0,0 +1,3 @@
+ArrayXd v = ArrayXd::LinSpaced(7, -2, 2);
+cout << v << endl << endl;
+cout << rint(v) << endl;

third_party/eigen/doc/snippets/Cwise_round.cpp

@@ -0,0 +1,3 @@
+ArrayXd v = ArrayXd::LinSpaced(7, -2, 2);
+cout << v << endl << endl;
+cout << round(v) << endl;

third_party/eigen/doc/snippets/Cwise_scalar_power_array.cpp

@@ -0,0 +1,2 @@
+Array<double, 1, 3> e(2, -3, 1. / 3.);
+cout << "10^[" << e << "] = " << pow(10, e) << endl;

third_party/eigen/doc/snippets/Cwise_sign.cpp

@@ -0,0 +1,2 @@
+Array3d v(-3, 5, 0);
+cout << v.sign() << endl;

third_party/eigen/doc/snippets/Cwise_sin.cpp

@@ -0,0 +1,2 @@
+Array3d v(EIGEN_PI, EIGEN_PI / 2, EIGEN_PI / 3);
+cout << v.sin() << endl;

third_party/eigen/doc/snippets/Cwise_sinh.cpp

@@ -0,0 +1,2 @@
+ArrayXd v = ArrayXd::LinSpaced(5, 0, 1);
+cout << sinh(v) << endl;

third_party/eigen/doc/snippets/Cwise_slash_equal.cpp

@@ -0,0 +1,3 @@
+Array3d v(3, 2, 4), w(5, 4, 2);
+v /= w;
+cout << v << endl;

third_party/eigen/doc/snippets/Cwise_sqrt.cpp

@@ -0,0 +1,2 @@
+Array3d v(1, 2, 4);
+cout << v.sqrt() << endl;

third_party/eigen/doc/snippets/Cwise_square.cpp

@@ -0,0 +1,2 @@
+Array3d v(2, 3, 4);
+cout << v.square() << endl;

third_party/eigen/doc/snippets/Cwise_tan.cpp

@@ -0,0 +1,2 @@
+Array3d v(EIGEN_PI, EIGEN_PI / 2, EIGEN_PI / 3);
+cout << v.tan() << endl;

third_party/eigen/doc/snippets/Cwise_tanh.cpp

@@ -0,0 +1,2 @@
+ArrayXd v = ArrayXd::LinSpaced(5, 0, 1);
+cout << tanh(v) << endl;

third_party/eigen/doc/snippets/Cwise_times_equal.cpp

@@ -0,0 +1,3 @@
+Array3d v(1, 2, 3), w(2, 3, 0);
+v *= w;
+cout << v << endl;

third_party/eigen/doc/snippets/Cwise_trunc.cpp

@@ -0,0 +1,3 @@
+ArrayXd v = ArrayXd::LinSpaced(7, -2, 2);
+cout << v << endl << endl;
+cout << trunc(v) << endl;

third_party/eigen/doc/snippets/DenseBase_LinSpaced.cpp

@@ -0,0 +1,2 @@
+cout << VectorXi::LinSpaced(4, 7, 10).transpose() << endl;
+cout << VectorXd::LinSpaced(5, 0.0, 1.0).transpose() << endl;

third_party/eigen/doc/snippets/DenseBase_LinSpacedInt.cpp

@@ -0,0 +1,8 @@
+cout << "Even spacing inputs:" << endl;
+cout << VectorXi::LinSpaced(8, 1, 4).transpose() << endl;
+cout << VectorXi::LinSpaced(8, 1, 8).transpose() << endl;
+cout << VectorXi::LinSpaced(8, 1, 15).transpose() << endl;
+cout << "Uneven spacing inputs:" << endl;
+cout << VectorXi::LinSpaced(8, 1, 7).transpose() << endl;
+cout << VectorXi::LinSpaced(8, 1, 9).transpose() << endl;
+cout << VectorXi::LinSpaced(8, 1, 16).transpose() << endl;

third_party/eigen/doc/snippets/DenseBase_LinSpaced_seq_deprecated.cpp

@@ -0,0 +1,2 @@
+cout << VectorXi::LinSpaced(Sequential, 4, 7, 10).transpose() << endl;
+cout << VectorXd::LinSpaced(Sequential, 5, 0.0, 1.0).transpose() << endl;

third_party/eigen/doc/snippets/DenseBase_setLinSpaced.cpp

@@ -0,0 +1,3 @@
+VectorXf v;
+v.setLinSpaced(5, 0.5f, 1.5f);
+cout << v << endl;

third_party/eigen/doc/snippets/DirectionWise_hnormalized.cpp

@@ -0,0 +1,6 @@
+Matrix4Xd M = Matrix4Xd::Random(4, 5);
+Projective3d P(Matrix4d::Random());
+cout << "The matrix M is:" << endl << M << endl << endl;
+cout << "M.colwise().hnormalized():" << endl << M.colwise().hnormalized() << endl << endl;
+cout << "P*M:" << endl << P * M << endl << endl;
+cout << "(P*M).colwise().hnormalized():" << endl << (P * M).colwise().hnormalized() << endl << endl;

third_party/eigen/doc/snippets/DirectionWise_replicate.cpp

@@ -0,0 +1,4 @@
+MatrixXi m = MatrixXi::Random(2, 3);
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "m.colwise().replicate<3>() = ..." << endl;
+cout << m.colwise().replicate<3>() << endl;

third_party/eigen/doc/snippets/DirectionWise_replicate_int.cpp

@@ -0,0 +1,4 @@
+Vector3i v = Vector3i::Random();
+cout << "Here is the vector v:" << endl << v << endl;
+cout << "v.rowwise().replicate(5) = ..." << endl;
+cout << v.rowwise().replicate(5) << endl;

third_party/eigen/doc/snippets/EigenSolver_EigenSolver_MatrixType.cpp

@@ -0,0 +1,16 @@
+MatrixXd A = MatrixXd::Random(6, 6);
+cout << "Here is a random 6x6 matrix, A:" << endl << A << endl << endl;
+
+EigenSolver<MatrixXd> es(A);
+cout << "The eigenvalues of A are:" << endl << es.eigenvalues() << endl;
+cout << "The matrix of eigenvectors, V, is:" << endl << es.eigenvectors() << endl << endl;
+
+complex<double> lambda = es.eigenvalues()[0];
+cout << "Consider the first eigenvalue, lambda = " << lambda << endl;
+VectorXcd v = es.eigenvectors().col(0);
+cout << "If v is the corresponding eigenvector, then lambda * v = " << endl << lambda * v << endl;
+cout << "... and A * v = " << endl << A.cast<complex<double> >() * v << endl << endl;
+
+MatrixXcd D = es.eigenvalues().asDiagonal();
+MatrixXcd V = es.eigenvectors();
+cout << "Finally, V * D * V^(-1) = " << endl << V * D * V.inverse() << endl;

third_party/eigen/doc/snippets/EigenSolver_compute.cpp

@@ -0,0 +1,6 @@
+EigenSolver<MatrixXf> es;
+MatrixXf A = MatrixXf::Random(4, 4);
+es.compute(A, /* computeEigenvectors = */ false);
+cout << "The eigenvalues of A are: " << es.eigenvalues().transpose() << endl;
+es.compute(A + MatrixXf::Identity(4, 4), false);  // re-use es to compute eigenvalues of A+I
+cout << "The eigenvalues of A+I are: " << es.eigenvalues().transpose() << endl;

third_party/eigen/doc/snippets/EigenSolver_eigenvalues.cpp

@@ -0,0 +1,3 @@
+MatrixXd ones = MatrixXd::Ones(3, 3);
+EigenSolver<MatrixXd> es(ones, false);
+cout << "The eigenvalues of the 3x3 matrix of ones are:" << endl << es.eigenvalues() << endl;

third_party/eigen/doc/snippets/EigenSolver_eigenvectors.cpp

@@ -0,0 +1,3 @@
+MatrixXd ones = MatrixXd::Ones(3, 3);
+EigenSolver<MatrixXd> es(ones);
+cout << "The first eigenvector of the 3x3 matrix of ones is:" << endl << es.eigenvectors().col(0) << endl;

third_party/eigen/doc/snippets/EigenSolver_pseudoEigenvectors.cpp

@@ -0,0 +1,9 @@
+MatrixXd A = MatrixXd::Random(6, 6);
+cout << "Here is a random 6x6 matrix, A:" << endl << A << endl << endl;
+
+EigenSolver<MatrixXd> es(A);
+MatrixXd D = es.pseudoEigenvalueMatrix();
+MatrixXd V = es.pseudoEigenvectors();
+cout << "The pseudo-eigenvalue matrix D is:" << endl << D << endl;
+cout << "The pseudo-eigenvector matrix V is:" << endl << V << endl;
+cout << "Finally, V * D * V^(-1) = " << endl << V * D * V.inverse() << endl;

third_party/eigen/doc/snippets/FullPivHouseholderQR_solve.cpp

@@ -0,0 +1,8 @@
+Matrix3f m = Matrix3f::Random();
+Matrix3f y = Matrix3f::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is the matrix y:" << endl << y << endl;
+Matrix3f x;
+x = m.fullPivHouseholderQr().solve(y);
+assert(y.isApprox(m* x));
+cout << "Here is a solution x to the equation mx=y:" << endl << x << endl;

third_party/eigen/doc/snippets/FullPivLU_image.cpp

@@ -0,0 +1,7 @@
+Matrix3d m;
+m << 1, 1, 0, 1, 3, 2, 0, 1, 1;
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Notice that the middle column is the sum of the two others, so the "
+     << "columns are linearly dependent." << endl;
+cout << "Here is a matrix whose columns have the same span but are linearly independent:" << endl
+     << m.fullPivLu().image(m) << endl;

third_party/eigen/doc/snippets/FullPivLU_kernel.cpp

@@ -0,0 +1,5 @@
+MatrixXf m = MatrixXf::Random(3, 5);
+cout << "Here is the matrix m:" << endl << m << endl;
+MatrixXf ker = m.fullPivLu().kernel();
+cout << "Here is a matrix whose columns form a basis of the kernel of m:" << endl << ker << endl;
+cout << "By definition of the kernel, m*ker is zero:" << endl << m * ker << endl;

third_party/eigen/doc/snippets/FullPivLU_solve.cpp

@@ -0,0 +1,9 @@
+Matrix<float, 2, 3> m = Matrix<float, 2, 3>::Random();
+Matrix2f y = Matrix2f::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is the matrix y:" << endl << y << endl;
+Matrix<float, 3, 2> x = m.fullPivLu().solve(y);
+if ((m * x).isApprox(y)) {
+  cout << "Here is a solution x to the equation mx=y:" << endl << x << endl;
+} else
+  cout << "The equation mx=y does not have any solution." << endl;

third_party/eigen/doc/snippets/GeneralizedEigenSolver.cpp

@@ -0,0 +1,7 @@
+GeneralizedEigenSolver<MatrixXf> ges;
+MatrixXf A = MatrixXf::Random(4, 4);
+MatrixXf B = MatrixXf::Random(4, 4);
+ges.compute(A, B);
+cout << "The (complex) numerators of the generalzied eigenvalues are: " << ges.alphas().transpose() << endl;
+cout << "The (real) denominatore of the generalzied eigenvalues are: " << ges.betas().transpose() << endl;
+cout << "The (complex) generalzied eigenvalues are (alphas./beta): " << ges.eigenvalues().transpose() << endl;

third_party/eigen/doc/snippets/HessenbergDecomposition_compute.cpp

@@ -0,0 +1,6 @@
+MatrixXcf A = MatrixXcf::Random(4, 4);
+HessenbergDecomposition<MatrixXcf> hd(4);
+hd.compute(A);
+cout << "The matrix H in the decomposition of A is:" << endl << hd.matrixH() << endl;
+hd.compute(2 * A);  // re-use hd to compute and store decomposition of 2A
+cout << "The matrix H in the decomposition of 2A is:" << endl << hd.matrixH() << endl;

third_party/eigen/doc/snippets/HessenbergDecomposition_matrixH.cpp

@@ -0,0 +1,8 @@
+Matrix4f A = MatrixXf::Random(4, 4);
+cout << "Here is a random 4x4 matrix:" << endl << A << endl;
+HessenbergDecomposition<MatrixXf> hessOfA(A);
+MatrixXf H = hessOfA.matrixH();
+cout << "The Hessenberg matrix H is:" << endl << H << endl;
+MatrixXf Q = hessOfA.matrixQ();
+cout << "The orthogonal matrix Q is:" << endl << Q << endl;
+cout << "Q H Q^T is:" << endl << Q * H * Q.transpose() << endl;

third_party/eigen/doc/snippets/HessenbergDecomposition_packedMatrix.cpp

@@ -0,0 +1,8 @@
+Matrix4d A = Matrix4d::Random(4, 4);
+cout << "Here is a random 4x4 matrix:" << endl << A << endl;
+HessenbergDecomposition<Matrix4d> hessOfA(A);
+Matrix4d pm = hessOfA.packedMatrix();
+cout << "The packed matrix M is:" << endl << pm << endl;
+cout << "The upper Hessenberg part corresponds to the matrix H, which is:" << endl << hessOfA.matrixH() << endl;
+Vector3d hc = hessOfA.householderCoefficients();
+cout << "The vector of Householder coefficients is:" << endl << hc << endl;

third_party/eigen/doc/snippets/HouseholderQR_householderQ.cpp

@@ -0,0 +1,7 @@
+MatrixXf A(MatrixXf::Random(5, 3)), thinQ(MatrixXf::Identity(5, 3)), Q;
+A.setRandom();
+HouseholderQR<MatrixXf> qr(A);
+Q = qr.householderQ();
+thinQ = qr.householderQ() * thinQ;
+std::cout << "The complete unitary matrix Q is:\n" << Q << "\n\n";
+std::cout << "The thin matrix Q is:\n" << thinQ << "\n\n";

third_party/eigen/doc/snippets/HouseholderQR_solve.cpp

@@ -0,0 +1,9 @@
+typedef Matrix<float, 3, 3> Matrix3x3;
+Matrix3x3 m = Matrix3x3::Random();
+Matrix3f y = Matrix3f::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is the matrix y:" << endl << y << endl;
+Matrix3f x;
+x = m.householderQr().solve(y);
+assert(y.isApprox(m* x));
+cout << "Here is a solution x to the equation mx=y:" << endl << x << endl;

third_party/eigen/doc/snippets/HouseholderSequence_HouseholderSequence.cpp

@@ -0,0 +1,31 @@
+Matrix3d v = Matrix3d::Random();
+cout << "The matrix v is:" << endl;
+cout << v << endl;
+
+Vector3d v0(1, v(1, 0), v(2, 0));
+cout << "The first Householder vector is: v_0 = " << v0.transpose() << endl;
+Vector3d v1(0, 1, v(2, 1));
+cout << "The second Householder vector is: v_1 = " << v1.transpose() << endl;
+Vector3d v2(0, 0, 1);
+cout << "The third Householder vector is: v_2 = " << v2.transpose() << endl;
+
+Vector3d h = Vector3d::Random();
+cout << "The Householder coefficients are: h = " << h.transpose() << endl;
+
+Matrix3d H0 = Matrix3d::Identity() - h(0) * v0 * v0.adjoint();
+cout << "The first Householder reflection is represented by H_0 = " << endl;
+cout << H0 << endl;
+Matrix3d H1 = Matrix3d::Identity() - h(1) * v1 * v1.adjoint();
+cout << "The second Householder reflection is represented by H_1 = " << endl;
+cout << H1 << endl;
+Matrix3d H2 = Matrix3d::Identity() - h(2) * v2 * v2.adjoint();
+cout << "The third Householder reflection is represented by H_2 = " << endl;
+cout << H2 << endl;
+cout << "Their product is H_0 H_1 H_2 = " << endl;
+cout << H0 * H1 * H2 << endl;
+
+HouseholderSequence<Matrix3d, Vector3d> hhSeq(v, h);
+Matrix3d hhSeqAsMatrix(hhSeq);
+cout << "If we construct a HouseholderSequence from v and h" << endl;
+cout << "and convert it to a matrix, we get:" << endl;
+cout << hhSeqAsMatrix << endl;

third_party/eigen/doc/snippets/IOFormat.cpp

@@ -0,0 +1,14 @@
+std::string sep = "\n----------------------------------------\n";
+Matrix3d m1;
+m1 << 1.111111, 2, 3.33333, 4, 5, 6, 7, 8.888888, 9;
+
+IOFormat CommaInitFmt(StreamPrecision, DontAlignCols, ", ", ", ", "", "", " << ", ";");
+IOFormat CleanFmt(4, 0, ", ", "\n", "[", "]");
+IOFormat OctaveFmt(StreamPrecision, 0, ", ", ";\n", "", "", "[", "]");
+IOFormat HeavyFmt(FullPrecision, 0, ", ", ";\n", "[", "]", "[", "]");
+
+std::cout << m1 << sep;
+std::cout << m1.format(CommaInitFmt) << sep;
+std::cout << m1.format(CleanFmt) << sep;
+std::cout << m1.format(OctaveFmt) << sep;
+std::cout << m1.format(HeavyFmt) << sep;

third_party/eigen/doc/snippets/JacobiSVD_basic.cpp

@@ -0,0 +1,9 @@
+MatrixXf m = MatrixXf::Random(3, 2);
+cout << "Here is the matrix m:" << endl << m << endl;
+JacobiSVD<MatrixXf, ComputeThinU | ComputeThinV> svd(m);
+cout << "Its singular values are:" << endl << svd.singularValues() << endl;
+cout << "Its left singular vectors are the columns of the thin U matrix:" << endl << svd.matrixU() << endl;
+cout << "Its right singular vectors are the columns of the thin V matrix:" << endl << svd.matrixV() << endl;
+Vector3f rhs(1, 0, 0);
+cout << "Now consider this rhs vector:" << endl << rhs << endl;
+cout << "A least-squares solution of m*x = rhs is:" << endl << svd.solve(rhs) << endl;

third_party/eigen/doc/snippets/Jacobi_makeGivens.cpp

@@ -0,0 +1,6 @@
+Vector2f v = Vector2f::Random();
+JacobiRotation<float> G;
+G.makeGivens(v.x(), v.y());
+cout << "Here is the vector v:" << endl << v << endl;
+v.applyOnTheLeft(0, 1, G.adjoint());
+cout << "Here is the vector J' * v:" << endl << v << endl;

third_party/eigen/doc/snippets/Jacobi_makeJacobi.cpp

@@ -0,0 +1,8 @@
+Matrix2f m = Matrix2f::Random();
+m = (m + m.adjoint()).eval();
+JacobiRotation<float> J;
+J.makeJacobi(m, 0, 1);
+cout << "Here is the matrix m:" << endl << m << endl;
+m.applyOnTheLeft(0, 1, J.adjoint());
+m.applyOnTheRight(0, 1, J);
+cout << "Here is the matrix J' * m * J:" << endl << m << endl;

third_party/eigen/doc/snippets/LLT_example.cpp

@@ -0,0 +1,12 @@
+MatrixXd A(3, 3);
+A << 4, -1, 2, -1, 6, 0, 2, 0, 5;
+cout << "The matrix A is" << endl << A << endl;
+
+LLT<MatrixXd> lltOfA(A);        // compute the Cholesky decomposition of A
+MatrixXd L = lltOfA.matrixL();  // retrieve factor L  in the decomposition
+// The previous two lines can also be written as "L = A.llt().matrixL()"
+
+cout << "The Cholesky factor L is" << endl << L << endl;
+cout << "To check this, let us compute L * L.transpose()" << endl;
+cout << L * L.transpose() << endl;
+cout << "This should equal the matrix A" << endl;

third_party/eigen/doc/snippets/LLT_solve.cpp

@@ -0,0 +1,7 @@
+typedef Matrix<float, Dynamic, 2> DataMatrix;
+// let's generate some samples on the 3D plane of equation z = 2x+3y (with some noise)
+DataMatrix samples = DataMatrix::Random(12, 2);
+VectorXf elevations = 2 * samples.col(0) + 3 * samples.col(1) + VectorXf::Random(12) * 0.1;
+// and let's solve samples * [x y]^T = elevations in least square sense:
+Matrix<float, 2, 1> xy = (samples.adjoint() * samples).llt().solve((samples.adjoint() * elevations));
+cout << xy << endl;

third_party/eigen/doc/snippets/LeastSquaresNormalEquations.cpp

@@ -0,0 +1,3 @@
+MatrixXf A = MatrixXf::Random(3, 2);
+VectorXf b = VectorXf::Random(3);
+cout << "The solution using normal equations is:\n" << (A.transpose() * A).ldlt().solve(A.transpose() * b) << endl;

third_party/eigen/doc/snippets/LeastSquaresQR.cpp

@@ -0,0 +1,3 @@
+MatrixXf A = MatrixXf::Random(3, 2);
+VectorXf b = VectorXf::Random(3);
+cout << "The solution using the QR decomposition is:\n" << A.colPivHouseholderQr().solve(b) << endl;

third_party/eigen/doc/snippets/Map_general_stride.cpp

@@ -0,0 +1,3 @@
+int array[24];
+for (int i = 0; i < 24; ++i) array[i] = i;
+cout << Map<MatrixXi, 0, Stride<Dynamic, 2> >(array, 3, 3, Stride<Dynamic, 2>(8, 2)) << endl;

third_party/eigen/doc/snippets/Map_inner_stride.cpp

@@ -0,0 +1,4 @@
+int array[12];
+for (int i = 0; i < 12; ++i) array[i] = i;
+cout << Map<VectorXi, 0, InnerStride<2> >(array, 6)  // the inner stride has already been passed as template parameter
+     << endl;