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| author | Narayan Kamath <narayan@google.com> | 2012-11-02 10:59:05 +0000 |
|---|---|---|
| committer | Xiaotao Duan <xiaotao@google.com> | 2012-11-07 14:17:48 -0800 |
| commit | c981c48f5bc9aefeffc0bcb0cc3934c2fae179dd (patch) | |
| tree | 54d1c7d66098154c1d7c5bd414394ef4cf255810 /doc/snippets | |
| parent | 63f67d748682b46d58be31235a0a2d64d81b998c (diff) | |
| download | eigen-c981c48f5bc9aefeffc0bcb0cc3934c2fae179dd.tar.gz | |
Initial import of eigen 3.1.1android-cts-4.4_r4android-cts-4.2_r2android-4.4_r1.2.0.1android-4.4_r1.2android-4.4_r1.1.0.1android-4.4_r1.1android-4.4_r1.0.1android-4.4_r1android-4.4_r0.9android-4.4_r0.8android-4.3_r2.3android-4.3_r2.2android-4.3_r2.1android-4.3_r2android-4.3_r1.1android-4.3_r1android-4.3_r0.9.1android-4.3_r0.9android-4.2.2_r1.2android-4.2.2_r1.1android-4.2.2_r1kitkat-releasekitkat-cts-releasejb-mr2.0-releasejb-mr2-releasejb-mr1.1-releasejb-mr1.1-dev
Added a README.android and a MODULE_LICENSE_MPL2 file.
Added empty Android.mk and CleanSpec.mk to optimize Android build.
Non MPL2 license code is disabled in ./Eigen/src/Core/util/NonMPL2.h.
Trying to include such files will lead to an error.
Change-Id: I0e148b7c3e83999bcc4dfaa5809d33bfac2aac32
Diffstat (limited to 'doc/snippets')
229 files changed, 1344 insertions, 0 deletions
diff --git a/doc/snippets/.krazy b/doc/snippets/.krazy new file mode 100644 index 000000000..00b99405d --- /dev/null +++ b/doc/snippets/.krazy @@ -0,0 +1,2 @@ +EXCLUDE copyright +EXCLUDE license diff --git a/doc/snippets/AngleAxis_mimic_euler.cpp b/doc/snippets/AngleAxis_mimic_euler.cpp new file mode 100644 index 000000000..456de7f7e --- /dev/null +++ b/doc/snippets/AngleAxis_mimic_euler.cpp @@ -0,0 +1,5 @@ +Matrix3f m; +m = AngleAxisf(0.25*M_PI, Vector3f::UnitX()) + * AngleAxisf(0.5*M_PI, Vector3f::UnitY()) + * AngleAxisf(0.33*M_PI, Vector3f::UnitZ()); +cout << m << endl << "is unitary: " << m.isUnitary() << endl; diff --git a/doc/snippets/CMakeLists.txt b/doc/snippets/CMakeLists.txt new file mode 100644 index 000000000..92a22ea61 --- /dev/null +++ b/doc/snippets/CMakeLists.txt @@ -0,0 +1,30 @@ +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() + get_target_property(compile_snippet_executable + ${compile_snippet_target} LOCATION) + add_custom_command( + TARGET ${compile_snippet_target} + POST_BUILD + COMMAND ${compile_snippet_executable} + ARGS >${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(snippet_src) + +ei_add_target_property(compile_tut_arithmetic_transpose_aliasing COMPILE_FLAGS -DEIGEN_NO_DEBUG)
\ No newline at end of file diff --git a/doc/snippets/ColPivHouseholderQR_solve.cpp b/doc/snippets/ColPivHouseholderQR_solve.cpp new file mode 100644 index 000000000..b7b204a18 --- /dev/null +++ b/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; diff --git a/doc/snippets/ComplexEigenSolver_compute.cpp b/doc/snippets/ComplexEigenSolver_compute.cpp new file mode 100644 index 000000000..11d6bd399 --- /dev/null +++ b/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; diff --git a/doc/snippets/ComplexEigenSolver_eigenvalues.cpp b/doc/snippets/ComplexEigenSolver_eigenvalues.cpp new file mode 100644 index 000000000..5509bd897 --- /dev/null +++ b/doc/snippets/ComplexEigenSolver_eigenvalues.cpp @@ -0,0 +1,4 @@ +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; diff --git a/doc/snippets/ComplexEigenSolver_eigenvectors.cpp b/doc/snippets/ComplexEigenSolver_eigenvectors.cpp new file mode 100644 index 000000000..bb1c2ccf1 --- /dev/null +++ b/doc/snippets/ComplexEigenSolver_eigenvectors.cpp @@ -0,0 +1,4 @@ +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(1) << endl; diff --git a/doc/snippets/ComplexSchur_compute.cpp b/doc/snippets/ComplexSchur_compute.cpp new file mode 100644 index 000000000..3a5170101 --- /dev/null +++ b/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; diff --git a/doc/snippets/ComplexSchur_matrixT.cpp b/doc/snippets/ComplexSchur_matrixT.cpp new file mode 100644 index 000000000..8380571ac --- /dev/null +++ b/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; diff --git a/doc/snippets/ComplexSchur_matrixU.cpp b/doc/snippets/ComplexSchur_matrixU.cpp new file mode 100644 index 000000000..ba3d9c22e --- /dev/null +++ b/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; diff --git a/doc/snippets/Cwise_abs.cpp b/doc/snippets/Cwise_abs.cpp new file mode 100644 index 000000000..0aeec3a40 --- /dev/null +++ b/doc/snippets/Cwise_abs.cpp @@ -0,0 +1,2 @@ +Array3d v(1,-2,-3); +cout << v.abs() << endl; diff --git a/doc/snippets/Cwise_abs2.cpp b/doc/snippets/Cwise_abs2.cpp new file mode 100644 index 000000000..2c4f9b344 --- /dev/null +++ b/doc/snippets/Cwise_abs2.cpp @@ -0,0 +1,2 @@ +Array3d v(1,-2,-3); +cout << v.abs2() << endl; diff --git a/doc/snippets/Cwise_acos.cpp b/doc/snippets/Cwise_acos.cpp new file mode 100644 index 000000000..34432cbac --- /dev/null +++ b/doc/snippets/Cwise_acos.cpp @@ -0,0 +1,2 @@ +Array3d v(0, sqrt(2.)/2, 1); +cout << v.acos() << endl; diff --git a/doc/snippets/Cwise_boolean_and.cpp b/doc/snippets/Cwise_boolean_and.cpp new file mode 100644 index 000000000..df6b60d92 --- /dev/null +++ b/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; diff --git a/doc/snippets/Cwise_boolean_or.cpp b/doc/snippets/Cwise_boolean_or.cpp new file mode 100644 index 000000000..83eb0068e --- /dev/null +++ b/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; diff --git a/doc/snippets/Cwise_cos.cpp b/doc/snippets/Cwise_cos.cpp new file mode 100644 index 000000000..f589f0724 --- /dev/null +++ b/doc/snippets/Cwise_cos.cpp @@ -0,0 +1,2 @@ +Array3d v(M_PI, M_PI/2, M_PI/3); +cout << v.cos() << endl; diff --git a/doc/snippets/Cwise_cube.cpp b/doc/snippets/Cwise_cube.cpp new file mode 100644 index 000000000..85e41dcce --- /dev/null +++ b/doc/snippets/Cwise_cube.cpp @@ -0,0 +1,2 @@ +Array3d v(2,3,4); +cout << v.cube() << endl; diff --git a/doc/snippets/Cwise_equal_equal.cpp b/doc/snippets/Cwise_equal_equal.cpp new file mode 100644 index 000000000..0ba96f660 --- /dev/null +++ b/doc/snippets/Cwise_equal_equal.cpp @@ -0,0 +1,2 @@ +Array3d v(1,2,3), w(3,2,1); +cout << (v==w) << endl; diff --git a/doc/snippets/Cwise_exp.cpp b/doc/snippets/Cwise_exp.cpp new file mode 100644 index 000000000..db23618f9 --- /dev/null +++ b/doc/snippets/Cwise_exp.cpp @@ -0,0 +1,2 @@ +Array3d v(1,2,3); +cout << v.exp() << endl; diff --git a/doc/snippets/Cwise_greater.cpp b/doc/snippets/Cwise_greater.cpp new file mode 100644 index 000000000..40ad0296d --- /dev/null +++ b/doc/snippets/Cwise_greater.cpp @@ -0,0 +1,2 @@ +Array3d v(1,2,3), w(3,2,1); +cout << (v>w) << endl; diff --git a/doc/snippets/Cwise_greater_equal.cpp b/doc/snippets/Cwise_greater_equal.cpp new file mode 100644 index 000000000..6a08f8948 --- /dev/null +++ b/doc/snippets/Cwise_greater_equal.cpp @@ -0,0 +1,2 @@ +Array3d v(1,2,3), w(3,2,1); +cout << (v>=w) << endl; diff --git a/doc/snippets/Cwise_inverse.cpp b/doc/snippets/Cwise_inverse.cpp new file mode 100644 index 000000000..3967a7ecf --- /dev/null +++ b/doc/snippets/Cwise_inverse.cpp @@ -0,0 +1,2 @@ +Array3d v(2,3,4); +cout << v.inverse() << endl; diff --git a/doc/snippets/Cwise_less.cpp b/doc/snippets/Cwise_less.cpp new file mode 100644 index 000000000..cafd3b6e0 --- /dev/null +++ b/doc/snippets/Cwise_less.cpp @@ -0,0 +1,2 @@ +Array3d v(1,2,3), w(3,2,1); +cout << (v<w) << endl; diff --git a/doc/snippets/Cwise_less_equal.cpp b/doc/snippets/Cwise_less_equal.cpp new file mode 100644 index 000000000..1600e397e --- /dev/null +++ b/doc/snippets/Cwise_less_equal.cpp @@ -0,0 +1,2 @@ +Array3d v(1,2,3), w(3,2,1); +cout << (v<=w) << endl; diff --git a/doc/snippets/Cwise_log.cpp b/doc/snippets/Cwise_log.cpp new file mode 100644 index 000000000..f7aca72fd --- /dev/null +++ b/doc/snippets/Cwise_log.cpp @@ -0,0 +1,2 @@ +Array3d v(1,2,3); +cout << v.log() << endl; diff --git a/doc/snippets/Cwise_max.cpp b/doc/snippets/Cwise_max.cpp new file mode 100644 index 000000000..6602881e8 --- /dev/null +++ b/doc/snippets/Cwise_max.cpp @@ -0,0 +1,2 @@ +Array3d v(2,3,4), w(4,2,3); +cout << v.max(w) << endl; diff --git a/doc/snippets/Cwise_min.cpp b/doc/snippets/Cwise_min.cpp new file mode 100644 index 000000000..1c01c764e --- /dev/null +++ b/doc/snippets/Cwise_min.cpp @@ -0,0 +1,2 @@ +Array3d v(2,3,4), w(4,2,3); +cout << v.min(w) << endl; diff --git a/doc/snippets/Cwise_minus.cpp b/doc/snippets/Cwise_minus.cpp new file mode 100644 index 000000000..b89b9fbb7 --- /dev/null +++ b/doc/snippets/Cwise_minus.cpp @@ -0,0 +1,2 @@ +Array3d v(1,2,3); +cout << v-5 << endl; diff --git a/doc/snippets/Cwise_minus_equal.cpp b/doc/snippets/Cwise_minus_equal.cpp new file mode 100644 index 000000000..dfde49dc3 --- /dev/null +++ b/doc/snippets/Cwise_minus_equal.cpp @@ -0,0 +1,3 @@ +Array3d v(1,2,3); +v -= 5; +cout << v << endl; diff --git a/doc/snippets/Cwise_not_equal.cpp b/doc/snippets/Cwise_not_equal.cpp new file mode 100644 index 000000000..57a407aac --- /dev/null +++ b/doc/snippets/Cwise_not_equal.cpp @@ -0,0 +1,2 @@ +Array3d v(1,2,3), w(3,2,1); +cout << (v!=w) << endl; diff --git a/doc/snippets/Cwise_plus.cpp b/doc/snippets/Cwise_plus.cpp new file mode 100644 index 000000000..9d4732743 --- /dev/null +++ b/doc/snippets/Cwise_plus.cpp @@ -0,0 +1,2 @@ +Array3d v(1,2,3); +cout << v+5 << endl; diff --git a/doc/snippets/Cwise_plus_equal.cpp b/doc/snippets/Cwise_plus_equal.cpp new file mode 100644 index 000000000..d744b1e89 --- /dev/null +++ b/doc/snippets/Cwise_plus_equal.cpp @@ -0,0 +1,3 @@ +Array3d v(1,2,3); +v += 5; +cout << v << endl; diff --git a/doc/snippets/Cwise_pow.cpp b/doc/snippets/Cwise_pow.cpp new file mode 100644 index 000000000..a723ed8b5 --- /dev/null +++ b/doc/snippets/Cwise_pow.cpp @@ -0,0 +1,2 @@ +Array3d v(8,27,64); +cout << v.pow(0.333333) << endl; diff --git a/doc/snippets/Cwise_product.cpp b/doc/snippets/Cwise_product.cpp new file mode 100644 index 000000000..714d66d21 --- /dev/null +++ b/doc/snippets/Cwise_product.cpp @@ -0,0 +1,4 @@ +Array33i a = Array33i::Random(), b = Array33i::Random(); +Array33i c = a * b; +cout << "a:\n" << a << "\nb:\n" << b << "\nc:\n" << c << endl; + diff --git a/doc/snippets/Cwise_quotient.cpp b/doc/snippets/Cwise_quotient.cpp new file mode 100644 index 000000000..7cb9f7f2a --- /dev/null +++ b/doc/snippets/Cwise_quotient.cpp @@ -0,0 +1,2 @@ +Array3d v(2,3,4), w(4,2,3); +cout << v/w << endl; diff --git a/doc/snippets/Cwise_sin.cpp b/doc/snippets/Cwise_sin.cpp new file mode 100644 index 000000000..46fa908cb --- /dev/null +++ b/doc/snippets/Cwise_sin.cpp @@ -0,0 +1,2 @@ +Array3d v(M_PI, M_PI/2, M_PI/3); +cout << v.sin() << endl; diff --git a/doc/snippets/Cwise_slash_equal.cpp b/doc/snippets/Cwise_slash_equal.cpp new file mode 100644 index 000000000..2efd32d84 --- /dev/null +++ b/doc/snippets/Cwise_slash_equal.cpp @@ -0,0 +1,3 @@ +Array3d v(3,2,4), w(5,4,2); +v /= w; +cout << v << endl; diff --git a/doc/snippets/Cwise_sqrt.cpp b/doc/snippets/Cwise_sqrt.cpp new file mode 100644 index 000000000..97bafe8b3 --- /dev/null +++ b/doc/snippets/Cwise_sqrt.cpp @@ -0,0 +1,2 @@ +Array3d v(1,2,4); +cout << v.sqrt() << endl; diff --git a/doc/snippets/Cwise_square.cpp b/doc/snippets/Cwise_square.cpp new file mode 100644 index 000000000..f704c5e0b --- /dev/null +++ b/doc/snippets/Cwise_square.cpp @@ -0,0 +1,2 @@ +Array3d v(2,3,4); +cout << v.square() << endl; diff --git a/doc/snippets/Cwise_tan.cpp b/doc/snippets/Cwise_tan.cpp new file mode 100644 index 000000000..b758ef04a --- /dev/null +++ b/doc/snippets/Cwise_tan.cpp @@ -0,0 +1,2 @@ +Array3d v(M_PI, M_PI/2, M_PI/3); +cout << v.tan() << endl; diff --git a/doc/snippets/Cwise_times_equal.cpp b/doc/snippets/Cwise_times_equal.cpp new file mode 100644 index 000000000..147556c73 --- /dev/null +++ b/doc/snippets/Cwise_times_equal.cpp @@ -0,0 +1,3 @@ +Array3d v(1,2,3), w(2,3,0); +v *= w; +cout << v << endl; diff --git a/doc/snippets/DenseBase_LinSpaced.cpp b/doc/snippets/DenseBase_LinSpaced.cpp new file mode 100644 index 000000000..8e54b17fc --- /dev/null +++ b/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; diff --git a/doc/snippets/DenseBase_LinSpaced_seq.cpp b/doc/snippets/DenseBase_LinSpaced_seq.cpp new file mode 100644 index 000000000..f55c5085d --- /dev/null +++ b/doc/snippets/DenseBase_LinSpaced_seq.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; diff --git a/doc/snippets/DenseBase_setLinSpaced.cpp b/doc/snippets/DenseBase_setLinSpaced.cpp new file mode 100644 index 000000000..50871dfcc --- /dev/null +++ b/doc/snippets/DenseBase_setLinSpaced.cpp @@ -0,0 +1,3 @@ +VectorXf v; +v.setLinSpaced(5,0.5f,1.5f).transpose(); +cout << v << endl; diff --git a/doc/snippets/DirectionWise_replicate.cpp b/doc/snippets/DirectionWise_replicate.cpp new file mode 100644 index 000000000..d92d4a350 --- /dev/null +++ b/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; diff --git a/doc/snippets/DirectionWise_replicate_int.cpp b/doc/snippets/DirectionWise_replicate_int.cpp new file mode 100644 index 000000000..f9b1b5355 --- /dev/null +++ b/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; diff --git a/doc/snippets/EigenSolver_EigenSolver_MatrixType.cpp b/doc/snippets/EigenSolver_EigenSolver_MatrixType.cpp new file mode 100644 index 000000000..c1d9fa879 --- /dev/null +++ b/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; diff --git a/doc/snippets/EigenSolver_compute.cpp b/doc/snippets/EigenSolver_compute.cpp new file mode 100644 index 000000000..a5c96e9b4 --- /dev/null +++ b/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; diff --git a/doc/snippets/EigenSolver_eigenvalues.cpp b/doc/snippets/EigenSolver_eigenvalues.cpp new file mode 100644 index 000000000..ed28869a0 --- /dev/null +++ b/doc/snippets/EigenSolver_eigenvalues.cpp @@ -0,0 +1,4 @@ +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; diff --git a/doc/snippets/EigenSolver_eigenvectors.cpp b/doc/snippets/EigenSolver_eigenvectors.cpp new file mode 100644 index 000000000..0fad4dadb --- /dev/null +++ b/doc/snippets/EigenSolver_eigenvectors.cpp @@ -0,0 +1,4 @@ +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(1) << endl; diff --git a/doc/snippets/EigenSolver_pseudoEigenvectors.cpp b/doc/snippets/EigenSolver_pseudoEigenvectors.cpp new file mode 100644 index 000000000..85e2569df --- /dev/null +++ b/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; diff --git a/doc/snippets/FullPivHouseholderQR_solve.cpp b/doc/snippets/FullPivHouseholderQR_solve.cpp new file mode 100644 index 000000000..23bc0749d --- /dev/null +++ b/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; diff --git a/doc/snippets/FullPivLU_image.cpp b/doc/snippets/FullPivLU_image.cpp new file mode 100644 index 000000000..817bc1e2d --- /dev/null +++ b/doc/snippets/FullPivLU_image.cpp @@ -0,0 +1,9 @@ +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; diff --git a/doc/snippets/FullPivLU_kernel.cpp b/doc/snippets/FullPivLU_kernel.cpp new file mode 100644 index 000000000..7086e01e2 --- /dev/null +++ b/doc/snippets/FullPivLU_kernel.cpp @@ -0,0 +1,7 @@ +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; diff --git a/doc/snippets/FullPivLU_solve.cpp b/doc/snippets/FullPivLU_solve.cpp new file mode 100644 index 000000000..c1f88235e --- /dev/null +++ b/doc/snippets/FullPivLU_solve.cpp @@ -0,0 +1,11 @@ +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; diff --git a/doc/snippets/HessenbergDecomposition_compute.cpp b/doc/snippets/HessenbergDecomposition_compute.cpp new file mode 100644 index 000000000..50e37833a --- /dev/null +++ b/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; diff --git a/doc/snippets/HessenbergDecomposition_matrixH.cpp b/doc/snippets/HessenbergDecomposition_matrixH.cpp new file mode 100644 index 000000000..af0136668 --- /dev/null +++ b/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; diff --git a/doc/snippets/HessenbergDecomposition_packedMatrix.cpp b/doc/snippets/HessenbergDecomposition_packedMatrix.cpp new file mode 100644 index 000000000..4fa5957e8 --- /dev/null +++ b/doc/snippets/HessenbergDecomposition_packedMatrix.cpp @@ -0,0 +1,9 @@ +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; diff --git a/doc/snippets/HouseholderQR_solve.cpp b/doc/snippets/HouseholderQR_solve.cpp new file mode 100644 index 000000000..8cce6ce6c --- /dev/null +++ b/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; diff --git a/doc/snippets/HouseholderSequence_HouseholderSequence.cpp b/doc/snippets/HouseholderSequence_HouseholderSequence.cpp new file mode 100644 index 000000000..2632b83b9 --- /dev/null +++ b/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; diff --git a/doc/snippets/IOFormat.cpp b/doc/snippets/IOFormat.cpp new file mode 100644 index 000000000..735f5dd85 --- /dev/null +++ b/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; diff --git a/doc/snippets/JacobiSVD_basic.cpp b/doc/snippets/JacobiSVD_basic.cpp new file mode 100644 index 000000000..ab24b9bca --- /dev/null +++ b/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> svd(m, ComputeThinU | ComputeThinV); +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; diff --git a/doc/snippets/Jacobi_makeGivens.cpp b/doc/snippets/Jacobi_makeGivens.cpp new file mode 100644 index 000000000..4b733c306 --- /dev/null +++ b/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;
\ No newline at end of file diff --git a/doc/snippets/Jacobi_makeJacobi.cpp b/doc/snippets/Jacobi_makeJacobi.cpp new file mode 100644 index 000000000..0cc331d9f --- /dev/null +++ b/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;
\ No newline at end of file diff --git a/doc/snippets/LLT_example.cpp b/doc/snippets/LLT_example.cpp new file mode 100644 index 000000000..46fb40704 --- /dev/null +++ b/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; diff --git a/doc/snippets/LLT_solve.cpp b/doc/snippets/LLT_solve.cpp new file mode 100644 index 000000000..7095d2cc3 --- /dev/null +++ b/doc/snippets/LLT_solve.cpp @@ -0,0 +1,8 @@ +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; diff --git a/doc/snippets/Map_general_stride.cpp b/doc/snippets/Map_general_stride.cpp new file mode 100644 index 000000000..0657e7f84 --- /dev/null +++ b/doc/snippets/Map_general_stride.cpp @@ -0,0 +1,5 @@ +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; diff --git a/doc/snippets/Map_inner_stride.cpp b/doc/snippets/Map_inner_stride.cpp new file mode 100644 index 000000000..d95ae9b3e --- /dev/null +++ b/doc/snippets/Map_inner_stride.cpp @@ -0,0 +1,5 @@ +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; diff --git a/doc/snippets/Map_outer_stride.cpp b/doc/snippets/Map_outer_stride.cpp new file mode 100644 index 000000000..2f6f052c3 --- /dev/null +++ b/doc/snippets/Map_outer_stride.cpp @@ -0,0 +1,3 @@ +int array[12]; +for(int i = 0; i < 12; ++i) array[i] = i; +cout << Map<MatrixXi, 0, OuterStride<> >(array, 3, 3, OuterStride<>(4)) << endl; diff --git a/doc/snippets/Map_placement_new.cpp b/doc/snippets/Map_placement_new.cpp new file mode 100644 index 000000000..2e40eca32 --- /dev/null +++ b/doc/snippets/Map_placement_new.cpp @@ -0,0 +1,5 @@ +int data[] = {1,2,3,4,5,6,7,8,9}; +Map<RowVectorXi> v(data,4); +cout << "The mapped vector v is: " << v << "\n"; +new (&v) Map<RowVectorXi>(data+4,5); +cout << "Now v is: " << v << "\n";
\ No newline at end of file diff --git a/doc/snippets/Map_simple.cpp b/doc/snippets/Map_simple.cpp new file mode 100644 index 000000000..423bb52ad --- /dev/null +++ b/doc/snippets/Map_simple.cpp @@ -0,0 +1,3 @@ +int array[9]; +for(int i = 0; i < 9; ++i) array[i] = i; +cout << Map<Matrix3i>(array) << endl; diff --git a/doc/snippets/MatrixBase_adjoint.cpp b/doc/snippets/MatrixBase_adjoint.cpp new file mode 100644 index 000000000..4680d5938 --- /dev/null +++ b/doc/snippets/MatrixBase_adjoint.cpp @@ -0,0 +1,3 @@ +Matrix2cf m = Matrix2cf::Random(); +cout << "Here is the 2x2 complex matrix m:" << endl << m << endl; +cout << "Here is the adjoint of m:" << endl << m.adjoint() << endl; diff --git a/doc/snippets/MatrixBase_all.cpp b/doc/snippets/MatrixBase_all.cpp new file mode 100644 index 000000000..46f26f189 --- /dev/null +++ b/doc/snippets/MatrixBase_all.cpp @@ -0,0 +1,7 @@ +Vector3f boxMin(Vector3f::Zero()), boxMax(Vector3f::Ones()); +Vector3f p0 = Vector3f::Random(), p1 = Vector3f::Random().cwiseAbs(); +// let's check if p0 and p1 are inside the axis aligned box defined by the corners boxMin,boxMax: +cout << "Is (" << p0.transpose() << ") inside the box: " + << ((boxMin.array()<p0.array()).all() && (boxMax.array()>p0.array()).all()) << endl; +cout << "Is (" << p1.transpose() << ") inside the box: " + << ((boxMin.array()<p1.array()).all() && (boxMax.array()>p1.array()).all()) << endl; diff --git a/doc/snippets/MatrixBase_array.cpp b/doc/snippets/MatrixBase_array.cpp new file mode 100644 index 000000000..f215086db --- /dev/null +++ b/doc/snippets/MatrixBase_array.cpp @@ -0,0 +1,4 @@ +Vector3d v(1,2,3); +v.array() += 3; +v.array() -= 2; +cout << v << endl; diff --git a/doc/snippets/MatrixBase_array_const.cpp b/doc/snippets/MatrixBase_array_const.cpp new file mode 100644 index 000000000..cd3b26a7c --- /dev/null +++ b/doc/snippets/MatrixBase_array_const.cpp @@ -0,0 +1,4 @@ +Vector3d v(-1,2,-3); +cout << "the absolute values:" << endl << v.array().abs() << endl; +cout << "the absolute values plus one:" << endl << v.array().abs()+1 << endl; +cout << "sum of the squares: " << v.array().square().sum() << endl; diff --git a/doc/snippets/MatrixBase_asDiagonal.cpp b/doc/snippets/MatrixBase_asDiagonal.cpp new file mode 100644 index 000000000..b01082db1 --- /dev/null +++ b/doc/snippets/MatrixBase_asDiagonal.cpp @@ -0,0 +1 @@ +cout << Matrix3i(Vector3i(2,5,6).asDiagonal()) << endl; diff --git a/doc/snippets/MatrixBase_block_int_int.cpp b/doc/snippets/MatrixBase_block_int_int.cpp new file mode 100644 index 000000000..f99b6d4ca --- /dev/null +++ b/doc/snippets/MatrixBase_block_int_int.cpp @@ -0,0 +1,5 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.block<2,2>(1,1):" << endl << m.block<2,2>(1,1) << endl; +m.block<2,2>(1,1).setZero(); +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/doc/snippets/MatrixBase_block_int_int_int_int.cpp b/doc/snippets/MatrixBase_block_int_int_int_int.cpp new file mode 100644 index 000000000..7238cbbed --- /dev/null +++ b/doc/snippets/MatrixBase_block_int_int_int_int.cpp @@ -0,0 +1,5 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.block(1, 1, 2, 2):" << endl << m.block(1, 1, 2, 2) << endl; +m.block(1, 1, 2, 2).setZero(); +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/doc/snippets/MatrixBase_bottomLeftCorner_int_int.cpp b/doc/snippets/MatrixBase_bottomLeftCorner_int_int.cpp new file mode 100644 index 000000000..ebae95e1d --- /dev/null +++ b/doc/snippets/MatrixBase_bottomLeftCorner_int_int.cpp @@ -0,0 +1,6 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.bottomLeftCorner(2, 2):" << endl; +cout << m.bottomLeftCorner(2, 2) << endl; +m.bottomLeftCorner(2, 2).setZero(); +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/doc/snippets/MatrixBase_bottomRightCorner_int_int.cpp b/doc/snippets/MatrixBase_bottomRightCorner_int_int.cpp new file mode 100644 index 000000000..bf05093af --- /dev/null +++ b/doc/snippets/MatrixBase_bottomRightCorner_int_int.cpp @@ -0,0 +1,6 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.bottomRightCorner(2, 2):" << endl; +cout << m.bottomRightCorner(2, 2) << endl; +m.bottomRightCorner(2, 2).setZero(); +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/doc/snippets/MatrixBase_bottomRows_int.cpp b/doc/snippets/MatrixBase_bottomRows_int.cpp new file mode 100644 index 000000000..47ca92ec3 --- /dev/null +++ b/doc/snippets/MatrixBase_bottomRows_int.cpp @@ -0,0 +1,6 @@ +Array44i a = Array44i::Random(); +cout << "Here is the array a:" << endl << a << endl; +cout << "Here is a.bottomRows(2):" << endl; +cout << a.bottomRows(2) << endl; +a.bottomRows(2).setZero(); +cout << "Now the array a is:" << endl << a << endl; diff --git a/doc/snippets/MatrixBase_cast.cpp b/doc/snippets/MatrixBase_cast.cpp new file mode 100644 index 000000000..016880b40 --- /dev/null +++ b/doc/snippets/MatrixBase_cast.cpp @@ -0,0 +1,3 @@ +Matrix2d md = Matrix2d::Identity() * 0.45; +Matrix2f mf = Matrix2f::Identity(); +cout << md + mf.cast<double>() << endl; diff --git a/doc/snippets/MatrixBase_col.cpp b/doc/snippets/MatrixBase_col.cpp new file mode 100644 index 000000000..87c91b129 --- /dev/null +++ b/doc/snippets/MatrixBase_col.cpp @@ -0,0 +1,3 @@ +Matrix3d m = Matrix3d::Identity(); +m.col(1) = Vector3d(4,5,6); +cout << m << endl; diff --git a/doc/snippets/MatrixBase_colwise.cpp b/doc/snippets/MatrixBase_colwise.cpp new file mode 100644 index 000000000..a048beffa --- /dev/null +++ b/doc/snippets/MatrixBase_colwise.cpp @@ -0,0 +1,5 @@ +Matrix3d m = Matrix3d::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the sum of each column:" << endl << m.colwise().sum() << endl; +cout << "Here is the maximum absolute value of each column:" + << endl << m.cwiseAbs().colwise().maxCoeff() << endl; diff --git a/doc/snippets/MatrixBase_computeInverseAndDetWithCheck.cpp b/doc/snippets/MatrixBase_computeInverseAndDetWithCheck.cpp new file mode 100644 index 000000000..a7b084fd0 --- /dev/null +++ b/doc/snippets/MatrixBase_computeInverseAndDetWithCheck.cpp @@ -0,0 +1,13 @@ +Matrix3d m = Matrix3d::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +Matrix3d inverse; +bool invertible; +double determinant; +m.computeInverseAndDetWithCheck(inverse,determinant,invertible); +cout << "Its determinant is " << determinant << endl; +if(invertible) { + cout << "It is invertible, and its inverse is:" << endl << inverse << endl; +} +else { + cout << "It is not invertible." << endl; +} diff --git a/doc/snippets/MatrixBase_computeInverseWithCheck.cpp b/doc/snippets/MatrixBase_computeInverseWithCheck.cpp new file mode 100644 index 000000000..873a9f870 --- /dev/null +++ b/doc/snippets/MatrixBase_computeInverseWithCheck.cpp @@ -0,0 +1,11 @@ +Matrix3d m = Matrix3d::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +Matrix3d inverse; +bool invertible; +m.computeInverseWithCheck(inverse,invertible); +if(invertible) { + cout << "It is invertible, and its inverse is:" << endl << inverse << endl; +} +else { + cout << "It is not invertible." << endl; +} diff --git a/doc/snippets/MatrixBase_cwiseAbs.cpp b/doc/snippets/MatrixBase_cwiseAbs.cpp new file mode 100644 index 000000000..28a31600f --- /dev/null +++ b/doc/snippets/MatrixBase_cwiseAbs.cpp @@ -0,0 +1,4 @@ +MatrixXd m(2,3); +m << 2, -4, 6, + -5, 1, 0; +cout << m.cwiseAbs() << endl; diff --git a/doc/snippets/MatrixBase_cwiseAbs2.cpp b/doc/snippets/MatrixBase_cwiseAbs2.cpp new file mode 100644 index 000000000..889a2e2ba --- /dev/null +++ b/doc/snippets/MatrixBase_cwiseAbs2.cpp @@ -0,0 +1,4 @@ +MatrixXd m(2,3); +m << 2, -4, 6, + -5, 1, 0; +cout << m.cwiseAbs2() << endl; diff --git a/doc/snippets/MatrixBase_cwiseEqual.cpp b/doc/snippets/MatrixBase_cwiseEqual.cpp new file mode 100644 index 000000000..eb3656f4c --- /dev/null +++ b/doc/snippets/MatrixBase_cwiseEqual.cpp @@ -0,0 +1,7 @@ +MatrixXi m(2,2); +m << 1, 0, + 1, 1; +cout << "Comparing m with identity matrix:" << endl; +cout << m.cwiseEqual(MatrixXi::Identity(2,2)) << endl; +int count = m.cwiseEqual(MatrixXi::Identity(2,2)).count(); +cout << "Number of coefficients that are equal: " << count << endl; diff --git a/doc/snippets/MatrixBase_cwiseInverse.cpp b/doc/snippets/MatrixBase_cwiseInverse.cpp new file mode 100644 index 000000000..23e08f7b9 --- /dev/null +++ b/doc/snippets/MatrixBase_cwiseInverse.cpp @@ -0,0 +1,4 @@ +MatrixXd m(2,3); +m << 2, 0.5, 1, + 3, 0.25, 1; +cout << m.cwiseInverse() << endl; diff --git a/doc/snippets/MatrixBase_cwiseMax.cpp b/doc/snippets/MatrixBase_cwiseMax.cpp new file mode 100644 index 000000000..3c956818b --- /dev/null +++ b/doc/snippets/MatrixBase_cwiseMax.cpp @@ -0,0 +1,2 @@ +Vector3d v(2,3,4), w(4,2,3); +cout << v.cwiseMax(w) << endl; diff --git a/doc/snippets/MatrixBase_cwiseMin.cpp b/doc/snippets/MatrixBase_cwiseMin.cpp new file mode 100644 index 000000000..82fc761e2 --- /dev/null +++ b/doc/snippets/MatrixBase_cwiseMin.cpp @@ -0,0 +1,2 @@ +Vector3d v(2,3,4), w(4,2,3); +cout << v.cwiseMin(w) << endl; diff --git a/doc/snippets/MatrixBase_cwiseNotEqual.cpp b/doc/snippets/MatrixBase_cwiseNotEqual.cpp new file mode 100644 index 000000000..6a2e4fb6c --- /dev/null +++ b/doc/snippets/MatrixBase_cwiseNotEqual.cpp @@ -0,0 +1,7 @@ +MatrixXi m(2,2); +m << 1, 0, + 1, 1; +cout << "Comparing m with identity matrix:" << endl; +cout << m.cwiseNotEqual(MatrixXi::Identity(2,2)) << endl; +int count = m.cwiseNotEqual(MatrixXi::Identity(2,2)).count(); +cout << "Number of coefficients that are not equal: " << count << endl; diff --git a/doc/snippets/MatrixBase_cwiseProduct.cpp b/doc/snippets/MatrixBase_cwiseProduct.cpp new file mode 100644 index 000000000..1db3a1132 --- /dev/null +++ b/doc/snippets/MatrixBase_cwiseProduct.cpp @@ -0,0 +1,4 @@ +Matrix3i a = Matrix3i::Random(), b = Matrix3i::Random(); +Matrix3i c = a.cwiseProduct(b); +cout << "a:\n" << a << "\nb:\n" << b << "\nc:\n" << c << endl; + diff --git a/doc/snippets/MatrixBase_cwiseQuotient.cpp b/doc/snippets/MatrixBase_cwiseQuotient.cpp new file mode 100644 index 000000000..969121208 --- /dev/null +++ b/doc/snippets/MatrixBase_cwiseQuotient.cpp @@ -0,0 +1,2 @@ +Vector3d v(2,3,4), w(4,2,3); +cout << v.cwiseQuotient(w) << endl; diff --git a/doc/snippets/MatrixBase_cwiseSqrt.cpp b/doc/snippets/MatrixBase_cwiseSqrt.cpp new file mode 100644 index 000000000..4bfd75d50 --- /dev/null +++ b/doc/snippets/MatrixBase_cwiseSqrt.cpp @@ -0,0 +1,2 @@ +Vector3d v(1,2,4); +cout << v.cwiseSqrt() << endl; diff --git a/doc/snippets/MatrixBase_diagonal.cpp b/doc/snippets/MatrixBase_diagonal.cpp new file mode 100644 index 000000000..cd63413f3 --- /dev/null +++ b/doc/snippets/MatrixBase_diagonal.cpp @@ -0,0 +1,4 @@ +Matrix3i m = Matrix3i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here are the coefficients on the main diagonal of m:" << endl + << m.diagonal() << endl; diff --git a/doc/snippets/MatrixBase_diagonal_int.cpp b/doc/snippets/MatrixBase_diagonal_int.cpp new file mode 100644 index 000000000..7b66abf67 --- /dev/null +++ b/doc/snippets/MatrixBase_diagonal_int.cpp @@ -0,0 +1,5 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:" << endl + << m.diagonal(1).transpose() << endl + << m.diagonal(-2).transpose() << endl; diff --git a/doc/snippets/MatrixBase_diagonal_template_int.cpp b/doc/snippets/MatrixBase_diagonal_template_int.cpp new file mode 100644 index 000000000..0e73d1c16 --- /dev/null +++ b/doc/snippets/MatrixBase_diagonal_template_int.cpp @@ -0,0 +1,5 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:" << endl + << m.diagonal<1>().transpose() << endl + << m.diagonal<-2>().transpose() << endl; diff --git a/doc/snippets/MatrixBase_eigenvalues.cpp b/doc/snippets/MatrixBase_eigenvalues.cpp new file mode 100644 index 000000000..039f88701 --- /dev/null +++ b/doc/snippets/MatrixBase_eigenvalues.cpp @@ -0,0 +1,3 @@ +MatrixXd ones = MatrixXd::Ones(3,3); +VectorXcd eivals = ones.eigenvalues(); +cout << "The eigenvalues of the 3x3 matrix of ones are:" << endl << eivals << endl; diff --git a/doc/snippets/MatrixBase_end_int.cpp b/doc/snippets/MatrixBase_end_int.cpp new file mode 100644 index 000000000..03c54a931 --- /dev/null +++ b/doc/snippets/MatrixBase_end_int.cpp @@ -0,0 +1,5 @@ +RowVector4i v = RowVector4i::Random(); +cout << "Here is the vector v:" << endl << v << endl; +cout << "Here is v.tail(2):" << endl << v.tail(2) << endl; +v.tail(2).setZero(); +cout << "Now the vector v is:" << endl << v << endl; diff --git a/doc/snippets/MatrixBase_eval.cpp b/doc/snippets/MatrixBase_eval.cpp new file mode 100644 index 000000000..1df3aa01d --- /dev/null +++ b/doc/snippets/MatrixBase_eval.cpp @@ -0,0 +1,12 @@ +Matrix2f M = Matrix2f::Random(); +Matrix2f m; +m = M; +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Now we want to copy a column into a row." << endl; +cout << "If we do m.col(1) = m.row(0), then m becomes:" << endl; +m.col(1) = m.row(0); +cout << m << endl << "which is wrong!" << endl; +cout << "Now let us instead do m.col(1) = m.row(0).eval(). Then m becomes" << endl; +m = M; +m.col(1) = m.row(0).eval(); +cout << m << endl << "which is right." << endl; diff --git a/doc/snippets/MatrixBase_extract.cpp b/doc/snippets/MatrixBase_extract.cpp new file mode 100644 index 000000000..c96220f72 --- /dev/null +++ b/doc/snippets/MatrixBase_extract.cpp @@ -0,0 +1,13 @@ +#ifndef _MSC_VER + #warning deprecated +#endif +/* deprecated +Matrix3i m = Matrix3i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the upper-triangular matrix extracted from m:" << endl + << m.part<Eigen::UpperTriangular>() << endl; +cout << "Here is the strictly-upper-triangular matrix extracted from m:" << endl + << m.part<Eigen::StrictlyUpperTriangular>() << endl; +cout << "Here is the unit-lower-triangular matrix extracted from m:" << endl + << m.part<Eigen::UnitLowerTriangular>() << endl; +*/
\ No newline at end of file diff --git a/doc/snippets/MatrixBase_fixedBlock_int_int.cpp b/doc/snippets/MatrixBase_fixedBlock_int_int.cpp new file mode 100644 index 000000000..320112748 --- /dev/null +++ b/doc/snippets/MatrixBase_fixedBlock_int_int.cpp @@ -0,0 +1,5 @@ +Matrix4d m = Vector4d(1,2,3,4).asDiagonal(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.fixed<2, 2>(2, 2):" << endl << m.block<2, 2>(2, 2) << endl; +m.block<2, 2>(2, 0) = m.block<2, 2>(2, 2); +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/doc/snippets/MatrixBase_identity.cpp b/doc/snippets/MatrixBase_identity.cpp new file mode 100644 index 000000000..b5c1e59c9 --- /dev/null +++ b/doc/snippets/MatrixBase_identity.cpp @@ -0,0 +1 @@ +cout << Matrix<double, 3, 4>::Identity() << endl; diff --git a/doc/snippets/MatrixBase_identity_int_int.cpp b/doc/snippets/MatrixBase_identity_int_int.cpp new file mode 100644 index 000000000..918649d64 --- /dev/null +++ b/doc/snippets/MatrixBase_identity_int_int.cpp @@ -0,0 +1 @@ +cout << MatrixXd::Identity(4, 3) << endl; diff --git a/doc/snippets/MatrixBase_inverse.cpp b/doc/snippets/MatrixBase_inverse.cpp new file mode 100644 index 000000000..a56142ee0 --- /dev/null +++ b/doc/snippets/MatrixBase_inverse.cpp @@ -0,0 +1,3 @@ +Matrix3d m = Matrix3d::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Its inverse is:" << endl << m.inverse() << endl; diff --git a/doc/snippets/MatrixBase_isDiagonal.cpp b/doc/snippets/MatrixBase_isDiagonal.cpp new file mode 100644 index 000000000..5b1d59977 --- /dev/null +++ b/doc/snippets/MatrixBase_isDiagonal.cpp @@ -0,0 +1,6 @@ +Matrix3d m = 10000 * Matrix3d::Identity(); +m(0,2) = 1; +cout << "Here's the matrix m:" << endl << m << endl; +cout << "m.isDiagonal() returns: " << m.isDiagonal() << endl; +cout << "m.isDiagonal(1e-3) returns: " << m.isDiagonal(1e-3) << endl; + diff --git a/doc/snippets/MatrixBase_isIdentity.cpp b/doc/snippets/MatrixBase_isIdentity.cpp new file mode 100644 index 000000000..17b756c97 --- /dev/null +++ b/doc/snippets/MatrixBase_isIdentity.cpp @@ -0,0 +1,5 @@ +Matrix3d m = Matrix3d::Identity(); +m(0,2) = 1e-4; +cout << "Here's the matrix m:" << endl << m << endl; +cout << "m.isIdentity() returns: " << m.isIdentity() << endl; +cout << "m.isIdentity(1e-3) returns: " << m.isIdentity(1e-3) << endl; diff --git a/doc/snippets/MatrixBase_isOnes.cpp b/doc/snippets/MatrixBase_isOnes.cpp new file mode 100644 index 000000000..f82f62809 --- /dev/null +++ b/doc/snippets/MatrixBase_isOnes.cpp @@ -0,0 +1,5 @@ +Matrix3d m = Matrix3d::Ones(); +m(0,2) += 1e-4; +cout << "Here's the matrix m:" << endl << m << endl; +cout << "m.isOnes() returns: " << m.isOnes() << endl; +cout << "m.isOnes(1e-3) returns: " << m.isOnes(1e-3) << endl; diff --git a/doc/snippets/MatrixBase_isOrthogonal.cpp b/doc/snippets/MatrixBase_isOrthogonal.cpp new file mode 100644 index 000000000..b22af066c --- /dev/null +++ b/doc/snippets/MatrixBase_isOrthogonal.cpp @@ -0,0 +1,6 @@ +Vector3d v(1,0,0); +Vector3d w(1e-4,0,1); +cout << "Here's the vector v:" << endl << v << endl; +cout << "Here's the vector w:" << endl << w << endl; +cout << "v.isOrthogonal(w) returns: " << v.isOrthogonal(w) << endl; +cout << "v.isOrthogonal(w,1e-3) returns: " << v.isOrthogonal(w,1e-3) << endl; diff --git a/doc/snippets/MatrixBase_isUnitary.cpp b/doc/snippets/MatrixBase_isUnitary.cpp new file mode 100644 index 000000000..3877da347 --- /dev/null +++ b/doc/snippets/MatrixBase_isUnitary.cpp @@ -0,0 +1,5 @@ +Matrix3d m = Matrix3d::Identity(); +m(0,2) = 1e-4; +cout << "Here's the matrix m:" << endl << m << endl; +cout << "m.isUnitary() returns: " << m.isUnitary() << endl; +cout << "m.isUnitary(1e-3) returns: " << m.isUnitary(1e-3) << endl; diff --git a/doc/snippets/MatrixBase_isZero.cpp b/doc/snippets/MatrixBase_isZero.cpp new file mode 100644 index 000000000..c2cfe2201 --- /dev/null +++ b/doc/snippets/MatrixBase_isZero.cpp @@ -0,0 +1,5 @@ +Matrix3d m = Matrix3d::Zero(); +m(0,2) = 1e-4; +cout << "Here's the matrix m:" << endl << m << endl; +cout << "m.isZero() returns: " << m.isZero() << endl; +cout << "m.isZero(1e-3) returns: " << m.isZero(1e-3) << endl; diff --git a/doc/snippets/MatrixBase_leftCols_int.cpp b/doc/snippets/MatrixBase_leftCols_int.cpp new file mode 100644 index 000000000..6ea984e4e --- /dev/null +++ b/doc/snippets/MatrixBase_leftCols_int.cpp @@ -0,0 +1,6 @@ +Array44i a = Array44i::Random(); +cout << "Here is the array a:" << endl << a << endl; +cout << "Here is a.leftCols(2):" << endl; +cout << a.leftCols(2) << endl; +a.leftCols(2).setZero(); +cout << "Now the array a is:" << endl << a << endl; diff --git a/doc/snippets/MatrixBase_marked.cpp b/doc/snippets/MatrixBase_marked.cpp new file mode 100644 index 000000000..f60712178 --- /dev/null +++ b/doc/snippets/MatrixBase_marked.cpp @@ -0,0 +1,14 @@ +#ifndef _MSC_VER + #warning deprecated +#endif +/* +Matrix3d m = Matrix3d::Zero(); +m.part<Eigen::UpperTriangular>().setOnes(); +cout << "Here is the matrix m:" << endl << m << endl; +Matrix3d n = Matrix3d::Ones(); +n.part<Eigen::LowerTriangular>() *= 2; +cout << "Here is the matrix n:" << endl << n << endl; +cout << "And now here is m.inverse()*n, taking advantage of the fact that" + " m is upper-triangular:" << endl + << m.marked<Eigen::UpperTriangular>().solveTriangular(n); +*/
\ No newline at end of file diff --git a/doc/snippets/MatrixBase_noalias.cpp b/doc/snippets/MatrixBase_noalias.cpp new file mode 100644 index 000000000..3b54a79a6 --- /dev/null +++ b/doc/snippets/MatrixBase_noalias.cpp @@ -0,0 +1,3 @@ +Matrix2d a, b, c; a << 1,2,3,4; b << 5,6,7,8; +c.noalias() = a * b; // this computes the product directly to c +cout << c << endl; diff --git a/doc/snippets/MatrixBase_ones.cpp b/doc/snippets/MatrixBase_ones.cpp new file mode 100644 index 000000000..02c767c95 --- /dev/null +++ b/doc/snippets/MatrixBase_ones.cpp @@ -0,0 +1,2 @@ +cout << Matrix2d::Ones() << endl; +cout << 6 * RowVector4i::Ones() << endl; diff --git a/doc/snippets/MatrixBase_ones_int.cpp b/doc/snippets/MatrixBase_ones_int.cpp new file mode 100644 index 000000000..2ef188e7d --- /dev/null +++ b/doc/snippets/MatrixBase_ones_int.cpp @@ -0,0 +1,2 @@ +cout << 6 * RowVectorXi::Ones(4) << endl; +cout << VectorXf::Ones(2) << endl; diff --git a/doc/snippets/MatrixBase_ones_int_int.cpp b/doc/snippets/MatrixBase_ones_int_int.cpp new file mode 100644 index 000000000..60f5a31eb --- /dev/null +++ b/doc/snippets/MatrixBase_ones_int_int.cpp @@ -0,0 +1 @@ +cout << MatrixXi::Ones(2,3) << endl; diff --git a/doc/snippets/MatrixBase_operatorNorm.cpp b/doc/snippets/MatrixBase_operatorNorm.cpp new file mode 100644 index 000000000..355246f0d --- /dev/null +++ b/doc/snippets/MatrixBase_operatorNorm.cpp @@ -0,0 +1,3 @@ +MatrixXd ones = MatrixXd::Ones(3,3); +cout << "The operator norm of the 3x3 matrix of ones is " + << ones.operatorNorm() << endl; diff --git a/doc/snippets/MatrixBase_part.cpp b/doc/snippets/MatrixBase_part.cpp new file mode 100644 index 000000000..d3e7f482e --- /dev/null +++ b/doc/snippets/MatrixBase_part.cpp @@ -0,0 +1,13 @@ +#ifndef _MSC_VER + #warning deprecated +#endif +/* +Matrix3d m = Matrix3d::Zero(); +m.part<Eigen::StrictlyUpperTriangular>().setOnes(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "And let us now compute m*m.adjoint() in a very optimized way" << endl + << "taking advantage of the symmetry." << endl; +Matrix3d n; +n.part<Eigen::SelfAdjoint>() = (m*m.adjoint()).lazy(); +cout << "The result is:" << endl << n << endl; +*/
\ No newline at end of file diff --git a/doc/snippets/MatrixBase_prod.cpp b/doc/snippets/MatrixBase_prod.cpp new file mode 100644 index 000000000..d2f27bdc3 --- /dev/null +++ b/doc/snippets/MatrixBase_prod.cpp @@ -0,0 +1,3 @@ +Matrix3d m = Matrix3d::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the product of all the coefficients:" << endl << m.prod() << endl; diff --git a/doc/snippets/MatrixBase_random.cpp b/doc/snippets/MatrixBase_random.cpp new file mode 100644 index 000000000..65fc524f1 --- /dev/null +++ b/doc/snippets/MatrixBase_random.cpp @@ -0,0 +1 @@ +cout << 100 * Matrix2i::Random() << endl; diff --git a/doc/snippets/MatrixBase_random_int.cpp b/doc/snippets/MatrixBase_random_int.cpp new file mode 100644 index 000000000..f161d03c2 --- /dev/null +++ b/doc/snippets/MatrixBase_random_int.cpp @@ -0,0 +1 @@ +cout << VectorXi::Random(2) << endl; diff --git a/doc/snippets/MatrixBase_random_int_int.cpp b/doc/snippets/MatrixBase_random_int_int.cpp new file mode 100644 index 000000000..3f0f7dd5d --- /dev/null +++ b/doc/snippets/MatrixBase_random_int_int.cpp @@ -0,0 +1 @@ +cout << MatrixXi::Random(2,3) << endl; diff --git a/doc/snippets/MatrixBase_replicate.cpp b/doc/snippets/MatrixBase_replicate.cpp new file mode 100644 index 000000000..3ce52bcd5 --- /dev/null +++ b/doc/snippets/MatrixBase_replicate.cpp @@ -0,0 +1,4 @@ +MatrixXi m = MatrixXi::Random(2,3); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "m.replicate<3,2>() = ..." << endl; +cout << m.replicate<3,2>() << endl; diff --git a/doc/snippets/MatrixBase_replicate_int_int.cpp b/doc/snippets/MatrixBase_replicate_int_int.cpp new file mode 100644 index 000000000..b1dbc70bc --- /dev/null +++ b/doc/snippets/MatrixBase_replicate_int_int.cpp @@ -0,0 +1,4 @@ +Vector3i v = Vector3i::Random(); +cout << "Here is the vector v:" << endl << v << endl; +cout << "v.replicate(2,5) = ..." << endl; +cout << v.replicate(2,5) << endl; diff --git a/doc/snippets/MatrixBase_reverse.cpp b/doc/snippets/MatrixBase_reverse.cpp new file mode 100644 index 000000000..f545a2837 --- /dev/null +++ b/doc/snippets/MatrixBase_reverse.cpp @@ -0,0 +1,8 @@ +MatrixXi m = MatrixXi::Random(3,4); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the reverse of m:" << endl << m.reverse() << endl; +cout << "Here is the coefficient (1,0) in the reverse of m:" << endl + << m.reverse()(1,0) << endl; +cout << "Let us overwrite this coefficient with the value 4." << endl; +m.reverse()(1,0) = 4; +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/doc/snippets/MatrixBase_rightCols_int.cpp b/doc/snippets/MatrixBase_rightCols_int.cpp new file mode 100644 index 000000000..cb513401b --- /dev/null +++ b/doc/snippets/MatrixBase_rightCols_int.cpp @@ -0,0 +1,6 @@ +Array44i a = Array44i::Random(); +cout << "Here is the array a:" << endl << a << endl; +cout << "Here is a.rightCols(2):" << endl; +cout << a.rightCols(2) << endl; +a.rightCols(2).setZero(); +cout << "Now the array a is:" << endl << a << endl; diff --git a/doc/snippets/MatrixBase_row.cpp b/doc/snippets/MatrixBase_row.cpp new file mode 100644 index 000000000..b15e6260c --- /dev/null +++ b/doc/snippets/MatrixBase_row.cpp @@ -0,0 +1,3 @@ +Matrix3d m = Matrix3d::Identity(); +m.row(1) = Vector3d(4,5,6); +cout << m << endl; diff --git a/doc/snippets/MatrixBase_rowwise.cpp b/doc/snippets/MatrixBase_rowwise.cpp new file mode 100644 index 000000000..ae93964ea --- /dev/null +++ b/doc/snippets/MatrixBase_rowwise.cpp @@ -0,0 +1,5 @@ +Matrix3d m = Matrix3d::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the sum of each row:" << endl << m.rowwise().sum() << endl; +cout << "Here is the maximum absolute value of each row:" + << endl << m.cwiseAbs().rowwise().maxCoeff() << endl; diff --git a/doc/snippets/MatrixBase_segment_int_int.cpp b/doc/snippets/MatrixBase_segment_int_int.cpp new file mode 100644 index 000000000..70cd6d266 --- /dev/null +++ b/doc/snippets/MatrixBase_segment_int_int.cpp @@ -0,0 +1,5 @@ +RowVector4i v = RowVector4i::Random(); +cout << "Here is the vector v:" << endl << v << endl; +cout << "Here is v.segment(1, 2):" << endl << v.segment(1, 2) << endl; +v.segment(1, 2).setZero(); +cout << "Now the vector v is:" << endl << v << endl; diff --git a/doc/snippets/MatrixBase_select.cpp b/doc/snippets/MatrixBase_select.cpp new file mode 100644 index 000000000..ae5477f02 --- /dev/null +++ b/doc/snippets/MatrixBase_select.cpp @@ -0,0 +1,6 @@ +MatrixXi m(3, 3); +m << 1, 2, 3, + 4, 5, 6, + 7, 8, 9; +m = (m.array() >= 5).select(-m, m); +cout << m << endl; diff --git a/doc/snippets/MatrixBase_set.cpp b/doc/snippets/MatrixBase_set.cpp new file mode 100644 index 000000000..50ecf5fb9 --- /dev/null +++ b/doc/snippets/MatrixBase_set.cpp @@ -0,0 +1,13 @@ +Matrix3i m1; +m1 << 1, 2, 3, + 4, 5, 6, + 7, 8, 9; +cout << m1 << endl << endl; +Matrix3i m2 = Matrix3i::Identity(); +m2.block(0,0, 2,2) << 10, 11, 12, 13; +cout << m2 << endl << endl; +Vector2i v1; +v1 << 14, 15; +m2 << v1.transpose(), 16, + v1, m1.block(1,1,2,2); +cout << m2 << endl; diff --git a/doc/snippets/MatrixBase_setIdentity.cpp b/doc/snippets/MatrixBase_setIdentity.cpp new file mode 100644 index 000000000..4fd0aa24a --- /dev/null +++ b/doc/snippets/MatrixBase_setIdentity.cpp @@ -0,0 +1,3 @@ +Matrix4i m = Matrix4i::Zero(); +m.block<3,3>(1,0).setIdentity(); +cout << m << endl; diff --git a/doc/snippets/MatrixBase_setOnes.cpp b/doc/snippets/MatrixBase_setOnes.cpp new file mode 100644 index 000000000..4cef9c1eb --- /dev/null +++ b/doc/snippets/MatrixBase_setOnes.cpp @@ -0,0 +1,3 @@ +Matrix4i m = Matrix4i::Random(); +m.row(1).setOnes(); +cout << m << endl; diff --git a/doc/snippets/MatrixBase_setRandom.cpp b/doc/snippets/MatrixBase_setRandom.cpp new file mode 100644 index 000000000..e2c257d44 --- /dev/null +++ b/doc/snippets/MatrixBase_setRandom.cpp @@ -0,0 +1,3 @@ +Matrix4i m = Matrix4i::Zero(); +m.col(1).setRandom(); +cout << m << endl; diff --git a/doc/snippets/MatrixBase_setZero.cpp b/doc/snippets/MatrixBase_setZero.cpp new file mode 100644 index 000000000..9b5b9583c --- /dev/null +++ b/doc/snippets/MatrixBase_setZero.cpp @@ -0,0 +1,3 @@ +Matrix4i m = Matrix4i::Random(); +m.row(1).setZero(); +cout << m << endl; diff --git a/doc/snippets/MatrixBase_start_int.cpp b/doc/snippets/MatrixBase_start_int.cpp new file mode 100644 index 000000000..c261d2b4e --- /dev/null +++ b/doc/snippets/MatrixBase_start_int.cpp @@ -0,0 +1,5 @@ +RowVector4i v = RowVector4i::Random(); +cout << "Here is the vector v:" << endl << v << endl; +cout << "Here is v.head(2):" << endl << v.head(2) << endl; +v.head(2).setZero(); +cout << "Now the vector v is:" << endl << v << endl; diff --git a/doc/snippets/MatrixBase_template_int_bottomRows.cpp b/doc/snippets/MatrixBase_template_int_bottomRows.cpp new file mode 100644 index 000000000..f9ea892da --- /dev/null +++ b/doc/snippets/MatrixBase_template_int_bottomRows.cpp @@ -0,0 +1,6 @@ +Array44i a = Array44i::Random(); +cout << "Here is the array a:" << endl << a << endl; +cout << "Here is a.bottomRows<2>():" << endl; +cout << a.bottomRows<2>() << endl; +a.bottomRows<2>().setZero(); +cout << "Now the array a is:" << endl << a << endl; diff --git a/doc/snippets/MatrixBase_template_int_end.cpp b/doc/snippets/MatrixBase_template_int_end.cpp new file mode 100644 index 000000000..f5ccb00f6 --- /dev/null +++ b/doc/snippets/MatrixBase_template_int_end.cpp @@ -0,0 +1,5 @@ +RowVector4i v = RowVector4i::Random(); +cout << "Here is the vector v:" << endl << v << endl; +cout << "Here is v.tail(2):" << endl << v.tail<2>() << endl; +v.tail<2>().setZero(); +cout << "Now the vector v is:" << endl << v << endl; diff --git a/doc/snippets/MatrixBase_template_int_int_bottomLeftCorner.cpp b/doc/snippets/MatrixBase_template_int_int_bottomLeftCorner.cpp new file mode 100644 index 000000000..847892a27 --- /dev/null +++ b/doc/snippets/MatrixBase_template_int_int_bottomLeftCorner.cpp @@ -0,0 +1,6 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.bottomLeftCorner<2,2>():" << endl; +cout << m.bottomLeftCorner<2,2>() << endl; +m.bottomLeftCorner<2,2>().setZero(); +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/doc/snippets/MatrixBase_template_int_int_bottomRightCorner.cpp b/doc/snippets/MatrixBase_template_int_int_bottomRightCorner.cpp new file mode 100644 index 000000000..abacb014e --- /dev/null +++ b/doc/snippets/MatrixBase_template_int_int_bottomRightCorner.cpp @@ -0,0 +1,6 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.bottomRightCorner<2,2>():" << endl; +cout << m.bottomRightCorner<2,2>() << endl; +m.bottomRightCorner<2,2>().setZero(); +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/doc/snippets/MatrixBase_template_int_int_topLeftCorner.cpp b/doc/snippets/MatrixBase_template_int_int_topLeftCorner.cpp new file mode 100644 index 000000000..1899d902d --- /dev/null +++ b/doc/snippets/MatrixBase_template_int_int_topLeftCorner.cpp @@ -0,0 +1,6 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.topLeftCorner<2,2>():" << endl; +cout << m.topLeftCorner<2,2>() << endl; +m.topLeftCorner<2,2>().setZero(); +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/doc/snippets/MatrixBase_template_int_int_topRightCorner.cpp b/doc/snippets/MatrixBase_template_int_int_topRightCorner.cpp new file mode 100644 index 000000000..c3a177110 --- /dev/null +++ b/doc/snippets/MatrixBase_template_int_int_topRightCorner.cpp @@ -0,0 +1,6 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.topRightCorner<2,2>():" << endl; +cout << m.topRightCorner<2,2>() << endl; +m.topRightCorner<2,2>().setZero(); +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/doc/snippets/MatrixBase_template_int_leftCols.cpp b/doc/snippets/MatrixBase_template_int_leftCols.cpp new file mode 100644 index 000000000..1c425d917 --- /dev/null +++ b/doc/snippets/MatrixBase_template_int_leftCols.cpp @@ -0,0 +1,6 @@ +Array44i a = Array44i::Random(); +cout << "Here is the array a:" << endl << a << endl; +cout << "Here is a.leftCols<2>():" << endl; +cout << a.leftCols<2>() << endl; +a.leftCols<2>().setZero(); +cout << "Now the array a is:" << endl << a << endl; diff --git a/doc/snippets/MatrixBase_template_int_rightCols.cpp b/doc/snippets/MatrixBase_template_int_rightCols.cpp new file mode 100644 index 000000000..fc8c0d93c --- /dev/null +++ b/doc/snippets/MatrixBase_template_int_rightCols.cpp @@ -0,0 +1,6 @@ +Array44i a = Array44i::Random(); +cout << "Here is the array a:" << endl << a << endl; +cout << "Here is a.rightCols<2>():" << endl; +cout << a.rightCols<2>() << endl; +a.rightCols<2>().setZero(); +cout << "Now the array a is:" << endl << a << endl; diff --git a/doc/snippets/MatrixBase_template_int_segment.cpp b/doc/snippets/MatrixBase_template_int_segment.cpp new file mode 100644 index 000000000..e448b4022 --- /dev/null +++ b/doc/snippets/MatrixBase_template_int_segment.cpp @@ -0,0 +1,5 @@ +RowVector4i v = RowVector4i::Random(); +cout << "Here is the vector v:" << endl << v << endl; +cout << "Here is v.segment<2>(1):" << endl << v.segment<2>(1) << endl; +v.segment<2>(2).setZero(); +cout << "Now the vector v is:" << endl << v << endl; diff --git a/doc/snippets/MatrixBase_template_int_start.cpp b/doc/snippets/MatrixBase_template_int_start.cpp new file mode 100644 index 000000000..d336b3716 --- /dev/null +++ b/doc/snippets/MatrixBase_template_int_start.cpp @@ -0,0 +1,5 @@ +RowVector4i v = RowVector4i::Random(); +cout << "Here is the vector v:" << endl << v << endl; +cout << "Here is v.head(2):" << endl << v.head<2>() << endl; +v.head<2>().setZero(); +cout << "Now the vector v is:" << endl << v << endl; diff --git a/doc/snippets/MatrixBase_template_int_topRows.cpp b/doc/snippets/MatrixBase_template_int_topRows.cpp new file mode 100644 index 000000000..0110251a5 --- /dev/null +++ b/doc/snippets/MatrixBase_template_int_topRows.cpp @@ -0,0 +1,6 @@ +Array44i a = Array44i::Random(); +cout << "Here is the array a:" << endl << a << endl; +cout << "Here is a.topRows<2>():" << endl; +cout << a.topRows<2>() << endl; +a.topRows<2>().setZero(); +cout << "Now the array a is:" << endl << a << endl; diff --git a/doc/snippets/MatrixBase_topLeftCorner_int_int.cpp b/doc/snippets/MatrixBase_topLeftCorner_int_int.cpp new file mode 100644 index 000000000..e52cb3bdb --- /dev/null +++ b/doc/snippets/MatrixBase_topLeftCorner_int_int.cpp @@ -0,0 +1,6 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.topLeftCorner(2, 2):" << endl; +cout << m.topLeftCorner(2, 2) << endl; +m.topLeftCorner(2, 2).setZero(); +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/doc/snippets/MatrixBase_topRightCorner_int_int.cpp b/doc/snippets/MatrixBase_topRightCorner_int_int.cpp new file mode 100644 index 000000000..811fa563e --- /dev/null +++ b/doc/snippets/MatrixBase_topRightCorner_int_int.cpp @@ -0,0 +1,6 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.topRightCorner(2, 2):" << endl; +cout << m.topRightCorner(2, 2) << endl; +m.topRightCorner(2, 2).setZero(); +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/doc/snippets/MatrixBase_topRows_int.cpp b/doc/snippets/MatrixBase_topRows_int.cpp new file mode 100644 index 000000000..f2d75f1cb --- /dev/null +++ b/doc/snippets/MatrixBase_topRows_int.cpp @@ -0,0 +1,6 @@ +Array44i a = Array44i::Random(); +cout << "Here is the array a:" << endl << a << endl; +cout << "Here is a.topRows(2):" << endl; +cout << a.topRows(2) << endl; +a.topRows(2).setZero(); +cout << "Now the array a is:" << endl << a << endl; diff --git a/doc/snippets/MatrixBase_transpose.cpp b/doc/snippets/MatrixBase_transpose.cpp new file mode 100644 index 000000000..88eea83c4 --- /dev/null +++ b/doc/snippets/MatrixBase_transpose.cpp @@ -0,0 +1,8 @@ +Matrix2i m = Matrix2i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the transpose of m:" << endl << m.transpose() << endl; +cout << "Here is the coefficient (1,0) in the transpose of m:" << endl + << m.transpose()(1,0) << endl; +cout << "Let us overwrite this coefficient with the value 0." << endl; +m.transpose()(1,0) = 0; +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/doc/snippets/MatrixBase_zero.cpp b/doc/snippets/MatrixBase_zero.cpp new file mode 100644 index 000000000..606493677 --- /dev/null +++ b/doc/snippets/MatrixBase_zero.cpp @@ -0,0 +1,2 @@ +cout << Matrix2d::Zero() << endl; +cout << RowVector4i::Zero() << endl; diff --git a/doc/snippets/MatrixBase_zero_int.cpp b/doc/snippets/MatrixBase_zero_int.cpp new file mode 100644 index 000000000..370a9ba0a --- /dev/null +++ b/doc/snippets/MatrixBase_zero_int.cpp @@ -0,0 +1,2 @@ +cout << RowVectorXi::Zero(4) << endl; +cout << VectorXf::Zero(2) << endl; diff --git a/doc/snippets/MatrixBase_zero_int_int.cpp b/doc/snippets/MatrixBase_zero_int_int.cpp new file mode 100644 index 000000000..4099c5d4d --- /dev/null +++ b/doc/snippets/MatrixBase_zero_int_int.cpp @@ -0,0 +1 @@ +cout << MatrixXi::Zero(2,3) << endl; diff --git a/doc/snippets/Matrix_resize_NoChange_int.cpp b/doc/snippets/Matrix_resize_NoChange_int.cpp new file mode 100644 index 000000000..acdf18c46 --- /dev/null +++ b/doc/snippets/Matrix_resize_NoChange_int.cpp @@ -0,0 +1,3 @@ +MatrixXd m(3,4); +m.resize(NoChange, 5); +cout << "m: " << m.rows() << " rows, " << m.cols() << " cols" << endl; diff --git a/doc/snippets/Matrix_resize_int.cpp b/doc/snippets/Matrix_resize_int.cpp new file mode 100644 index 000000000..044c78989 --- /dev/null +++ b/doc/snippets/Matrix_resize_int.cpp @@ -0,0 +1,6 @@ +VectorXd v(10); +v.resize(3); +RowVector3d w; +w.resize(3); // this is legal, but has no effect +cout << "v: " << v.rows() << " rows, " << v.cols() << " cols" << endl; +cout << "w: " << w.rows() << " rows, " << w.cols() << " cols" << endl; diff --git a/doc/snippets/Matrix_resize_int_NoChange.cpp b/doc/snippets/Matrix_resize_int_NoChange.cpp new file mode 100644 index 000000000..5c37c9067 --- /dev/null +++ b/doc/snippets/Matrix_resize_int_NoChange.cpp @@ -0,0 +1,3 @@ +MatrixXd m(3,4); +m.resize(5, NoChange); +cout << "m: " << m.rows() << " rows, " << m.cols() << " cols" << endl; diff --git a/doc/snippets/Matrix_resize_int_int.cpp b/doc/snippets/Matrix_resize_int_int.cpp new file mode 100644 index 000000000..bfd474159 --- /dev/null +++ b/doc/snippets/Matrix_resize_int_int.cpp @@ -0,0 +1,9 @@ +MatrixXd m(2,3); +m << 1,2,3,4,5,6; +cout << "here's the 2x3 matrix m:" << endl << m << endl; +cout << "let's resize m to 3x2. This is a conservative resizing because 2*3==3*2." << endl; +m.resize(3,2); +cout << "here's the 3x2 matrix m:" << endl << m << endl; +cout << "now let's resize m to size 2x2. This is NOT a conservative resizing, so it becomes uninitialized:" << endl; +m.resize(2,2); +cout << m << endl; diff --git a/doc/snippets/Matrix_setConstant_int.cpp b/doc/snippets/Matrix_setConstant_int.cpp new file mode 100644 index 000000000..ff5a86c98 --- /dev/null +++ b/doc/snippets/Matrix_setConstant_int.cpp @@ -0,0 +1,3 @@ +VectorXf v; +v.setConstant(3, 5); +cout << v << endl; diff --git a/doc/snippets/Matrix_setConstant_int_int.cpp b/doc/snippets/Matrix_setConstant_int_int.cpp new file mode 100644 index 000000000..32b950cfd --- /dev/null +++ b/doc/snippets/Matrix_setConstant_int_int.cpp @@ -0,0 +1,3 @@ +MatrixXf m; +m.setConstant(3, 3, 5); +cout << m << endl; diff --git a/doc/snippets/Matrix_setIdentity_int_int.cpp b/doc/snippets/Matrix_setIdentity_int_int.cpp new file mode 100644 index 000000000..a65967199 --- /dev/null +++ b/doc/snippets/Matrix_setIdentity_int_int.cpp @@ -0,0 +1,3 @@ +MatrixXf m; +m.setIdentity(3, 3); +cout << m << endl; diff --git a/doc/snippets/Matrix_setOnes_int.cpp b/doc/snippets/Matrix_setOnes_int.cpp new file mode 100644 index 000000000..752cb35b2 --- /dev/null +++ b/doc/snippets/Matrix_setOnes_int.cpp @@ -0,0 +1,3 @@ +VectorXf v; +v.setOnes(3); +cout << v << endl; diff --git a/doc/snippets/Matrix_setOnes_int_int.cpp b/doc/snippets/Matrix_setOnes_int_int.cpp new file mode 100644 index 000000000..1ffb66bbd --- /dev/null +++ b/doc/snippets/Matrix_setOnes_int_int.cpp @@ -0,0 +1,3 @@ +MatrixXf m; +m.setOnes(3, 3); +cout << m << endl; diff --git a/doc/snippets/Matrix_setRandom_int.cpp b/doc/snippets/Matrix_setRandom_int.cpp new file mode 100644 index 000000000..e160dd7df --- /dev/null +++ b/doc/snippets/Matrix_setRandom_int.cpp @@ -0,0 +1,3 @@ +VectorXf v; +v.setRandom(3); +cout << v << endl; diff --git a/doc/snippets/Matrix_setRandom_int_int.cpp b/doc/snippets/Matrix_setRandom_int_int.cpp new file mode 100644 index 000000000..80cda11d7 --- /dev/null +++ b/doc/snippets/Matrix_setRandom_int_int.cpp @@ -0,0 +1,3 @@ +MatrixXf m; +m.setRandom(3, 3); +cout << m << endl; diff --git a/doc/snippets/Matrix_setZero_int.cpp b/doc/snippets/Matrix_setZero_int.cpp new file mode 100644 index 000000000..0fb16c1f3 --- /dev/null +++ b/doc/snippets/Matrix_setZero_int.cpp @@ -0,0 +1,3 @@ +VectorXf v; +v.setZero(3); +cout << v << endl; diff --git a/doc/snippets/Matrix_setZero_int_int.cpp b/doc/snippets/Matrix_setZero_int_int.cpp new file mode 100644 index 000000000..ad883b916 --- /dev/null +++ b/doc/snippets/Matrix_setZero_int_int.cpp @@ -0,0 +1,3 @@ +MatrixXf m; +m.setZero(3, 3); +cout << m << endl; diff --git a/doc/snippets/PartialPivLU_solve.cpp b/doc/snippets/PartialPivLU_solve.cpp new file mode 100644 index 000000000..fa3570ab8 --- /dev/null +++ b/doc/snippets/PartialPivLU_solve.cpp @@ -0,0 +1,7 @@ +MatrixXd A = MatrixXd::Random(3,3); +MatrixXd B = MatrixXd::Random(3,2); +cout << "Here is the invertible matrix A:" << endl << A << endl; +cout << "Here is the matrix B:" << endl << B << endl; +MatrixXd X = A.lu().solve(B); +cout << "Here is the (unique) solution X to the equation AX=B:" << endl << X << endl; +cout << "Relative error: " << (A*X-B).norm() / B.norm() << endl; diff --git a/doc/snippets/PartialRedux_count.cpp b/doc/snippets/PartialRedux_count.cpp new file mode 100644 index 000000000..c7b3097e4 --- /dev/null +++ b/doc/snippets/PartialRedux_count.cpp @@ -0,0 +1,3 @@ +Matrix3d m = Matrix3d::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the count of elements larger or equal than 0.5 of each row:" << endl << (m.array() >= 0.5).rowwise().count() << endl; diff --git a/doc/snippets/PartialRedux_maxCoeff.cpp b/doc/snippets/PartialRedux_maxCoeff.cpp new file mode 100644 index 000000000..e8fd3820d --- /dev/null +++ b/doc/snippets/PartialRedux_maxCoeff.cpp @@ -0,0 +1,3 @@ +Matrix3d m = Matrix3d::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the maximum of each column:" << endl << m.colwise().maxCoeff() << endl; diff --git a/doc/snippets/PartialRedux_minCoeff.cpp b/doc/snippets/PartialRedux_minCoeff.cpp new file mode 100644 index 000000000..d717bc0d1 --- /dev/null +++ b/doc/snippets/PartialRedux_minCoeff.cpp @@ -0,0 +1,3 @@ +Matrix3d m = Matrix3d::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the minimum of each column:" << endl << m.colwise().minCoeff() << endl; diff --git a/doc/snippets/PartialRedux_norm.cpp b/doc/snippets/PartialRedux_norm.cpp new file mode 100644 index 000000000..dbcf290a0 --- /dev/null +++ b/doc/snippets/PartialRedux_norm.cpp @@ -0,0 +1,3 @@ +Matrix3d m = Matrix3d::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the norm of each column:" << endl << m.colwise().norm() << endl; diff --git a/doc/snippets/PartialRedux_prod.cpp b/doc/snippets/PartialRedux_prod.cpp new file mode 100644 index 000000000..aacf09cbb --- /dev/null +++ b/doc/snippets/PartialRedux_prod.cpp @@ -0,0 +1,3 @@ +Matrix3d m = Matrix3d::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the product of each row:" << endl << m.rowwise().prod() << endl; diff --git a/doc/snippets/PartialRedux_squaredNorm.cpp b/doc/snippets/PartialRedux_squaredNorm.cpp new file mode 100644 index 000000000..9f3293e65 --- /dev/null +++ b/doc/snippets/PartialRedux_squaredNorm.cpp @@ -0,0 +1,3 @@ +Matrix3d m = Matrix3d::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the square norm of each row:" << endl << m.rowwise().squaredNorm() << endl; diff --git a/doc/snippets/PartialRedux_sum.cpp b/doc/snippets/PartialRedux_sum.cpp new file mode 100644 index 000000000..ec82d3e41 --- /dev/null +++ b/doc/snippets/PartialRedux_sum.cpp @@ -0,0 +1,3 @@ +Matrix3d m = Matrix3d::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the sum of each row:" << endl << m.rowwise().sum() << endl; diff --git a/doc/snippets/RealSchur_RealSchur_MatrixType.cpp b/doc/snippets/RealSchur_RealSchur_MatrixType.cpp new file mode 100644 index 000000000..a5530dcc8 --- /dev/null +++ b/doc/snippets/RealSchur_RealSchur_MatrixType.cpp @@ -0,0 +1,10 @@ +MatrixXd A = MatrixXd::Random(6,6); +cout << "Here is a random 6x6 matrix, A:" << endl << A << endl << endl; + +RealSchur<MatrixXd> schur(A); +cout << "The orthogonal matrix U is:" << endl << schur.matrixU() << endl; +cout << "The quasi-triangular matrix T is:" << endl << schur.matrixT() << endl << endl; + +MatrixXd U = schur.matrixU(); +MatrixXd T = schur.matrixT(); +cout << "U * T * U^T = " << endl << U * T * U.transpose() << endl; diff --git a/doc/snippets/RealSchur_compute.cpp b/doc/snippets/RealSchur_compute.cpp new file mode 100644 index 000000000..20c2611b8 --- /dev/null +++ b/doc/snippets/RealSchur_compute.cpp @@ -0,0 +1,6 @@ +MatrixXf A = MatrixXf::Random(4,4); +RealSchur<MatrixXf> schur(4); +schur.compute(A, /* computeU = */ false); +cout << "The matrix T in the decomposition of A is:" << endl << schur.matrixT() << endl; +schur.compute(A.inverse(), /* computeU = */ false); +cout << "The matrix T in the decomposition of A^(-1) is:" << endl << schur.matrixT() << endl; diff --git a/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver.cpp b/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver.cpp new file mode 100644 index 000000000..73a7f6252 --- /dev/null +++ b/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver.cpp @@ -0,0 +1,7 @@ +SelfAdjointEigenSolver<Matrix4f> es; +Matrix4f X = Matrix4f::Random(4,4); +Matrix4f A = X + X.transpose(); +es.compute(A); +cout << "The eigenvalues of A are: " << es.eigenvalues().transpose() << endl; +es.compute(A + Matrix4f::Identity(4,4)); // re-use es to compute eigenvalues of A+I +cout << "The eigenvalues of A+I are: " << es.eigenvalues().transpose() << endl; diff --git a/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType.cpp b/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType.cpp new file mode 100644 index 000000000..3599b17a0 --- /dev/null +++ b/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType.cpp @@ -0,0 +1,17 @@ +MatrixXd X = MatrixXd::Random(5,5); +MatrixXd A = X + X.transpose(); +cout << "Here is a random symmetric 5x5 matrix, A:" << endl << A << endl << endl; + +SelfAdjointEigenSolver<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; + +double lambda = es.eigenvalues()[0]; +cout << "Consider the first eigenvalue, lambda = " << lambda << endl; +VectorXd 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 * v << endl << endl; + +MatrixXd D = es.eigenvalues().asDiagonal(); +MatrixXd V = es.eigenvectors(); +cout << "Finally, V * D * V^(-1) = " << endl << V * D * V.inverse() << endl; diff --git a/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.cpp b/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.cpp new file mode 100644 index 000000000..bbb821e02 --- /dev/null +++ b/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.cpp @@ -0,0 +1,16 @@ +MatrixXd X = MatrixXd::Random(5,5); +MatrixXd A = X + X.transpose(); +cout << "Here is a random symmetric matrix, A:" << endl << A << endl; +X = MatrixXd::Random(5,5); +MatrixXd B = X * X.transpose(); +cout << "and a random postive-definite matrix, B:" << endl << B << endl << endl; + +GeneralizedSelfAdjointEigenSolver<MatrixXd> es(A,B); +cout << "The eigenvalues of the pencil (A,B) are:" << endl << es.eigenvalues() << endl; +cout << "The matrix of eigenvectors, V, is:" << endl << es.eigenvectors() << endl << endl; + +double lambda = es.eigenvalues()[0]; +cout << "Consider the first eigenvalue, lambda = " << lambda << endl; +VectorXd v = es.eigenvectors().col(0); +cout << "If v is the corresponding eigenvector, then A * v = " << endl << A * v << endl; +cout << "... and lambda * B * v = " << endl << lambda * B * v << endl << endl; diff --git a/doc/snippets/SelfAdjointEigenSolver_compute_MatrixType.cpp b/doc/snippets/SelfAdjointEigenSolver_compute_MatrixType.cpp new file mode 100644 index 000000000..2975cc3f2 --- /dev/null +++ b/doc/snippets/SelfAdjointEigenSolver_compute_MatrixType.cpp @@ -0,0 +1,7 @@ +SelfAdjointEigenSolver<MatrixXf> es(4); +MatrixXf X = MatrixXf::Random(4,4); +MatrixXf A = X + X.transpose(); +es.compute(A); +cout << "The eigenvalues of A are: " << es.eigenvalues().transpose() << endl; +es.compute(A + MatrixXf::Identity(4,4)); // re-use es to compute eigenvalues of A+I +cout << "The eigenvalues of A+I are: " << es.eigenvalues().transpose() << endl; diff --git a/doc/snippets/SelfAdjointEigenSolver_compute_MatrixType2.cpp b/doc/snippets/SelfAdjointEigenSolver_compute_MatrixType2.cpp new file mode 100644 index 000000000..07c92a1e4 --- /dev/null +++ b/doc/snippets/SelfAdjointEigenSolver_compute_MatrixType2.cpp @@ -0,0 +1,9 @@ +MatrixXd X = MatrixXd::Random(5,5); +MatrixXd A = X * X.transpose(); +X = MatrixXd::Random(5,5); +MatrixXd B = X * X.transpose(); + +GeneralizedSelfAdjointEigenSolver<MatrixXd> es(A,B,EigenvaluesOnly); +cout << "The eigenvalues of the pencil (A,B) are:" << endl << es.eigenvalues() << endl; +es.compute(B,A,false); +cout << "The eigenvalues of the pencil (B,A) are:" << endl << es.eigenvalues() << endl; diff --git a/doc/snippets/SelfAdjointEigenSolver_eigenvalues.cpp b/doc/snippets/SelfAdjointEigenSolver_eigenvalues.cpp new file mode 100644 index 000000000..0ff33c68d --- /dev/null +++ b/doc/snippets/SelfAdjointEigenSolver_eigenvalues.cpp @@ -0,0 +1,4 @@ +MatrixXd ones = MatrixXd::Ones(3,3); +SelfAdjointEigenSolver<MatrixXd> es(ones); +cout << "The eigenvalues of the 3x3 matrix of ones are:" + << endl << es.eigenvalues() << endl; diff --git a/doc/snippets/SelfAdjointEigenSolver_eigenvectors.cpp b/doc/snippets/SelfAdjointEigenSolver_eigenvectors.cpp new file mode 100644 index 000000000..cfc8b0d54 --- /dev/null +++ b/doc/snippets/SelfAdjointEigenSolver_eigenvectors.cpp @@ -0,0 +1,4 @@ +MatrixXd ones = MatrixXd::Ones(3,3); +SelfAdjointEigenSolver<MatrixXd> es(ones); +cout << "The first eigenvector of the 3x3 matrix of ones is:" + << endl << es.eigenvectors().col(1) << endl; diff --git a/doc/snippets/SelfAdjointEigenSolver_operatorInverseSqrt.cpp b/doc/snippets/SelfAdjointEigenSolver_operatorInverseSqrt.cpp new file mode 100644 index 000000000..114c65fb3 --- /dev/null +++ b/doc/snippets/SelfAdjointEigenSolver_operatorInverseSqrt.cpp @@ -0,0 +1,9 @@ +MatrixXd X = MatrixXd::Random(4,4); +MatrixXd A = X * X.transpose(); +cout << "Here is a random positive-definite matrix, A:" << endl << A << endl << endl; + +SelfAdjointEigenSolver<MatrixXd> es(A); +cout << "The inverse square root of A is: " << endl; +cout << es.operatorInverseSqrt() << endl; +cout << "We can also compute it with operatorSqrt() and inverse(). That yields: " << endl; +cout << es.operatorSqrt().inverse() << endl; diff --git a/doc/snippets/SelfAdjointEigenSolver_operatorSqrt.cpp b/doc/snippets/SelfAdjointEigenSolver_operatorSqrt.cpp new file mode 100644 index 000000000..eeacca74b --- /dev/null +++ b/doc/snippets/SelfAdjointEigenSolver_operatorSqrt.cpp @@ -0,0 +1,8 @@ +MatrixXd X = MatrixXd::Random(4,4); +MatrixXd A = X * X.transpose(); +cout << "Here is a random positive-definite matrix, A:" << endl << A << endl << endl; + +SelfAdjointEigenSolver<MatrixXd> es(A); +MatrixXd sqrtA = es.operatorSqrt(); +cout << "The square root of A is: " << endl << sqrtA << endl; +cout << "If we square this, we get: " << endl << sqrtA*sqrtA << endl; diff --git a/doc/snippets/SelfAdjointView_eigenvalues.cpp b/doc/snippets/SelfAdjointView_eigenvalues.cpp new file mode 100644 index 000000000..be1986778 --- /dev/null +++ b/doc/snippets/SelfAdjointView_eigenvalues.cpp @@ -0,0 +1,3 @@ +MatrixXd ones = MatrixXd::Ones(3,3); +VectorXd eivals = ones.selfadjointView<Lower>().eigenvalues(); +cout << "The eigenvalues of the 3x3 matrix of ones are:" << endl << eivals << endl; diff --git a/doc/snippets/SelfAdjointView_operatorNorm.cpp b/doc/snippets/SelfAdjointView_operatorNorm.cpp new file mode 100644 index 000000000..f380f5594 --- /dev/null +++ b/doc/snippets/SelfAdjointView_operatorNorm.cpp @@ -0,0 +1,3 @@ +MatrixXd ones = MatrixXd::Ones(3,3); +cout << "The operator norm of the 3x3 matrix of ones is " + << ones.selfadjointView<Lower>().operatorNorm() << endl; diff --git a/doc/snippets/TopicAliasing_block.cpp b/doc/snippets/TopicAliasing_block.cpp new file mode 100644 index 000000000..03282f4f0 --- /dev/null +++ b/doc/snippets/TopicAliasing_block.cpp @@ -0,0 +1,7 @@ +MatrixXi mat(3,3); +mat << 1, 2, 3, 4, 5, 6, 7, 8, 9; +cout << "Here is the matrix mat:\n" << mat << endl; + +// This assignment shows the aliasing problem +mat.bottomRightCorner(2,2) = mat.topLeftCorner(2,2); +cout << "After the assignment, mat = \n" << mat << endl; diff --git a/doc/snippets/TopicAliasing_block_correct.cpp b/doc/snippets/TopicAliasing_block_correct.cpp new file mode 100644 index 000000000..6fee5801e --- /dev/null +++ b/doc/snippets/TopicAliasing_block_correct.cpp @@ -0,0 +1,7 @@ +MatrixXi mat(3,3); +mat << 1, 2, 3, 4, 5, 6, 7, 8, 9; +cout << "Here is the matrix mat:\n" << mat << endl; + +// The eval() solves the aliasing problem +mat.bottomRightCorner(2,2) = mat.topLeftCorner(2,2).eval(); +cout << "After the assignment, mat = \n" << mat << endl; diff --git a/doc/snippets/TopicAliasing_cwise.cpp b/doc/snippets/TopicAliasing_cwise.cpp new file mode 100644 index 000000000..7049f6c56 --- /dev/null +++ b/doc/snippets/TopicAliasing_cwise.cpp @@ -0,0 +1,20 @@ +MatrixXf mat(2,2); +mat << 1, 2, 4, 7; +cout << "Here is the matrix mat:\n" << mat << endl << endl; + +mat = 2 * mat; +cout << "After 'mat = 2 * mat', mat = \n" << mat << endl << endl; + + +mat = mat - MatrixXf::Identity(2,2); +cout << "After the subtraction, it becomes\n" << mat << endl << endl; + + +ArrayXXf arr = mat; +arr = arr.square(); +cout << "After squaring, it becomes\n" << arr << endl << endl; + +// Combining all operations in one statement: +mat << 1, 2, 4, 7; +mat = (2 * mat - MatrixXf::Identity(2,2)).array().square(); +cout << "Doing everything at once yields\n" << mat << endl << endl; diff --git a/doc/snippets/TopicAliasing_mult1.cpp b/doc/snippets/TopicAliasing_mult1.cpp new file mode 100644 index 000000000..cd7e9004c --- /dev/null +++ b/doc/snippets/TopicAliasing_mult1.cpp @@ -0,0 +1,4 @@ +MatrixXf matA(2,2); +matA << 2, 0, 0, 2; +matA = matA * matA; +cout << matA; diff --git a/doc/snippets/TopicAliasing_mult2.cpp b/doc/snippets/TopicAliasing_mult2.cpp new file mode 100644 index 000000000..a3ff56851 --- /dev/null +++ b/doc/snippets/TopicAliasing_mult2.cpp @@ -0,0 +1,10 @@ +MatrixXf matA(2,2), matB(2,2); +matA << 2, 0, 0, 2; + +// Simple but not quite as efficient +matB = matA * matA; +cout << matB << endl << endl; + +// More complicated but also more efficient +matB.noalias() = matA * matA; +cout << matB; diff --git a/doc/snippets/TopicAliasing_mult3.cpp b/doc/snippets/TopicAliasing_mult3.cpp new file mode 100644 index 000000000..1d12a6c67 --- /dev/null +++ b/doc/snippets/TopicAliasing_mult3.cpp @@ -0,0 +1,4 @@ +MatrixXf matA(2,2); +matA << 2, 0, 0, 2; +matA.noalias() = matA * matA; +cout << matA; diff --git a/doc/snippets/TopicStorageOrders_example.cpp b/doc/snippets/TopicStorageOrders_example.cpp new file mode 100644 index 000000000..0623ef0c2 --- /dev/null +++ b/doc/snippets/TopicStorageOrders_example.cpp @@ -0,0 +1,18 @@ +Matrix<int, 3, 4, ColMajor> Acolmajor; +Acolmajor << 8, 2, 2, 9, + 9, 1, 4, 4, + 3, 5, 4, 5; +cout << "The matrix A:" << endl; +cout << Acolmajor << endl << endl; + +cout << "In memory (column-major):" << endl; +for (int i = 0; i < Acolmajor.size(); i++) + cout << *(Acolmajor.data() + i) << " "; +cout << endl << endl; + +Matrix<int, 3, 4, RowMajor> Arowmajor = Acolmajor; +cout << "In memory (row-major):" << endl; +for (int i = 0; i < Arowmajor.size(); i++) + cout << *(Arowmajor.data() + i) << " "; +cout << endl; + diff --git a/doc/snippets/Tridiagonalization_Tridiagonalization_MatrixType.cpp b/doc/snippets/Tridiagonalization_Tridiagonalization_MatrixType.cpp new file mode 100644 index 000000000..a26012433 --- /dev/null +++ b/doc/snippets/Tridiagonalization_Tridiagonalization_MatrixType.cpp @@ -0,0 +1,9 @@ +MatrixXd X = MatrixXd::Random(5,5); +MatrixXd A = X + X.transpose(); +cout << "Here is a random symmetric 5x5 matrix:" << endl << A << endl << endl; +Tridiagonalization<MatrixXd> triOfA(A); +MatrixXd Q = triOfA.matrixQ(); +cout << "The orthogonal matrix Q is:" << endl << Q << endl; +MatrixXd T = triOfA.matrixT(); +cout << "The tridiagonal matrix T is:" << endl << T << endl << endl; +cout << "Q * T * Q^T = " << endl << Q * T * Q.transpose() << endl; diff --git a/doc/snippets/Tridiagonalization_compute.cpp b/doc/snippets/Tridiagonalization_compute.cpp new file mode 100644 index 000000000..0062a99e8 --- /dev/null +++ b/doc/snippets/Tridiagonalization_compute.cpp @@ -0,0 +1,9 @@ +Tridiagonalization<MatrixXf> tri; +MatrixXf X = MatrixXf::Random(4,4); +MatrixXf A = X + X.transpose(); +tri.compute(A); +cout << "The matrix T in the tridiagonal decomposition of A is: " << endl; +cout << tri.matrixT() << endl; +tri.compute(2*A); // re-use tri to compute eigenvalues of 2A +cout << "The matrix T in the tridiagonal decomposition of 2A is: " << endl; +cout << tri.matrixT() << endl; diff --git a/doc/snippets/Tridiagonalization_decomposeInPlace.cpp b/doc/snippets/Tridiagonalization_decomposeInPlace.cpp new file mode 100644 index 000000000..93dcfca1d --- /dev/null +++ b/doc/snippets/Tridiagonalization_decomposeInPlace.cpp @@ -0,0 +1,10 @@ +MatrixXd X = MatrixXd::Random(5,5); +MatrixXd A = X + X.transpose(); +cout << "Here is a random symmetric 5x5 matrix:" << endl << A << endl << endl; + +VectorXd diag(5); +VectorXd subdiag(4); +internal::tridiagonalization_inplace(A, diag, subdiag, true); +cout << "The orthogonal matrix Q is:" << endl << A << endl; +cout << "The diagonal of the tridiagonal matrix T is:" << endl << diag << endl; +cout << "The subdiagonal of the tridiagonal matrix T is:" << endl << subdiag << endl; diff --git a/doc/snippets/Tridiagonalization_diagonal.cpp b/doc/snippets/Tridiagonalization_diagonal.cpp new file mode 100644 index 000000000..6eec82169 --- /dev/null +++ b/doc/snippets/Tridiagonalization_diagonal.cpp @@ -0,0 +1,13 @@ +MatrixXcd X = MatrixXcd::Random(4,4); +MatrixXcd A = X + X.adjoint(); +cout << "Here is a random self-adjoint 4x4 matrix:" << endl << A << endl << endl; + +Tridiagonalization<MatrixXcd> triOfA(A); +MatrixXd T = triOfA.matrixT(); +cout << "The tridiagonal matrix T is:" << endl << T << endl << endl; + +cout << "We can also extract the diagonals of T directly ..." << endl; +VectorXd diag = triOfA.diagonal(); +cout << "The diagonal is:" << endl << diag << endl; +VectorXd subdiag = triOfA.subDiagonal(); +cout << "The subdiagonal is:" << endl << subdiag << endl; diff --git a/doc/snippets/Tridiagonalization_householderCoefficients.cpp b/doc/snippets/Tridiagonalization_householderCoefficients.cpp new file mode 100644 index 000000000..e5d872880 --- /dev/null +++ b/doc/snippets/Tridiagonalization_householderCoefficients.cpp @@ -0,0 +1,6 @@ +Matrix4d X = Matrix4d::Random(4,4); +Matrix4d A = X + X.transpose(); +cout << "Here is a random symmetric 4x4 matrix:" << endl << A << endl; +Tridiagonalization<Matrix4d> triOfA(A); +Vector3d hc = triOfA.householderCoefficients(); +cout << "The vector of Householder coefficients is:" << endl << hc << endl; diff --git a/doc/snippets/Tridiagonalization_packedMatrix.cpp b/doc/snippets/Tridiagonalization_packedMatrix.cpp new file mode 100644 index 000000000..0f55d0c28 --- /dev/null +++ b/doc/snippets/Tridiagonalization_packedMatrix.cpp @@ -0,0 +1,8 @@ +Matrix4d X = Matrix4d::Random(4,4); +Matrix4d A = X + X.transpose(); +cout << "Here is a random symmetric 4x4 matrix:" << endl << A << endl; +Tridiagonalization<Matrix4d> triOfA(A); +Matrix4d pm = triOfA.packedMatrix(); +cout << "The packed matrix M is:" << endl << pm << endl; +cout << "The diagonal and subdiagonal corresponds to the matrix T, which is:" + << endl << triOfA.matrixT() << endl; diff --git a/doc/snippets/Tutorial_AdvancedInitialization_Block.cpp b/doc/snippets/Tutorial_AdvancedInitialization_Block.cpp new file mode 100644 index 000000000..96e40acfb --- /dev/null +++ b/doc/snippets/Tutorial_AdvancedInitialization_Block.cpp @@ -0,0 +1,5 @@ +MatrixXf matA(2, 2); +matA << 1, 2, 3, 4; +MatrixXf matB(4, 4); +matB << matA, matA/10, matA/10, matA; +std::cout << matB << std::endl; diff --git a/doc/snippets/Tutorial_AdvancedInitialization_CommaTemporary.cpp b/doc/snippets/Tutorial_AdvancedInitialization_CommaTemporary.cpp new file mode 100644 index 000000000..50cff4cb6 --- /dev/null +++ b/doc/snippets/Tutorial_AdvancedInitialization_CommaTemporary.cpp @@ -0,0 +1,4 @@ +MatrixXf mat = MatrixXf::Random(2, 3); +std::cout << mat << std::endl << std::endl; +mat = (MatrixXf(2,2) << 0, 1, 1, 0).finished() * mat; +std::cout << mat << std::endl; diff --git a/doc/snippets/Tutorial_AdvancedInitialization_Join.cpp b/doc/snippets/Tutorial_AdvancedInitialization_Join.cpp new file mode 100644 index 000000000..84e8715cb --- /dev/null +++ b/doc/snippets/Tutorial_AdvancedInitialization_Join.cpp @@ -0,0 +1,11 @@ +RowVectorXd vec1(3); +vec1 << 1, 2, 3; +std::cout << "vec1 = " << vec1 << std::endl; + +RowVectorXd vec2(4); +vec2 << 1, 4, 9, 16;; +std::cout << "vec2 = " << vec2 << std::endl; + +RowVectorXd joined(7); +joined << vec1, vec2; +std::cout << "joined = " << joined << std::endl; diff --git a/doc/snippets/Tutorial_AdvancedInitialization_LinSpaced.cpp b/doc/snippets/Tutorial_AdvancedInitialization_LinSpaced.cpp new file mode 100644 index 000000000..c6a73ab8c --- /dev/null +++ b/doc/snippets/Tutorial_AdvancedInitialization_LinSpaced.cpp @@ -0,0 +1,7 @@ +ArrayXXf table(10, 4); +table.col(0) = ArrayXf::LinSpaced(10, 0, 90); +table.col(1) = M_PI / 180 * table.col(0); +table.col(2) = table.col(1).sin(); +table.col(3) = table.col(1).cos(); +std::cout << " Degrees Radians Sine Cosine\n"; +std::cout << table << std::endl; diff --git a/doc/snippets/Tutorial_AdvancedInitialization_ThreeWays.cpp b/doc/snippets/Tutorial_AdvancedInitialization_ThreeWays.cpp new file mode 100644 index 000000000..cb7457652 --- /dev/null +++ b/doc/snippets/Tutorial_AdvancedInitialization_ThreeWays.cpp @@ -0,0 +1,20 @@ +const int size = 6; +MatrixXd mat1(size, size); +mat1.topLeftCorner(size/2, size/2) = MatrixXd::Zero(size/2, size/2); +mat1.topRightCorner(size/2, size/2) = MatrixXd::Identity(size/2, size/2); +mat1.bottomLeftCorner(size/2, size/2) = MatrixXd::Identity(size/2, size/2); +mat1.bottomRightCorner(size/2, size/2) = MatrixXd::Zero(size/2, size/2); +std::cout << mat1 << std::endl << std::endl; + +MatrixXd mat2(size, size); +mat2.topLeftCorner(size/2, size/2).setZero(); +mat2.topRightCorner(size/2, size/2).setIdentity(); +mat2.bottomLeftCorner(size/2, size/2).setIdentity(); +mat2.bottomRightCorner(size/2, size/2).setZero(); +std::cout << mat2 << std::endl << std::endl; + +MatrixXd mat3(size, size); +mat3 << MatrixXd::Zero(size/2, size/2), MatrixXd::Identity(size/2, size/2), + MatrixXd::Identity(size/2, size/2), MatrixXd::Zero(size/2, size/2); +std::cout << mat3 << std::endl; + diff --git a/doc/snippets/Tutorial_AdvancedInitialization_Zero.cpp b/doc/snippets/Tutorial_AdvancedInitialization_Zero.cpp new file mode 100644 index 000000000..76a36a319 --- /dev/null +++ b/doc/snippets/Tutorial_AdvancedInitialization_Zero.cpp @@ -0,0 +1,13 @@ +std::cout << "A fixed-size array:\n"; +Array33f a1 = Array33f::Zero(); +std::cout << a1 << "\n\n"; + + +std::cout << "A one-dimensional dynamic-size array:\n"; +ArrayXf a2 = ArrayXf::Zero(3); +std::cout << a2 << "\n\n"; + + +std::cout << "A two-dimensional dynamic-size array:\n"; +ArrayXXf a3 = ArrayXXf::Zero(3, 4); +std::cout << a3 << "\n"; diff --git a/doc/snippets/Tutorial_Map_rowmajor.cpp b/doc/snippets/Tutorial_Map_rowmajor.cpp new file mode 100644 index 000000000..fd45ace03 --- /dev/null +++ b/doc/snippets/Tutorial_Map_rowmajor.cpp @@ -0,0 +1,7 @@ +int array[8]; +for(int i = 0; i < 8; ++i) array[i] = i; +cout << "Column-major:\n" << Map<Matrix<int,2,4> >(array) << endl; +cout << "Row-major:\n" << Map<Matrix<int,2,4,RowMajor> >(array) << endl; +cout << "Row-major using stride:\n" << + Map<Matrix<int,2,4>, Unaligned, Stride<1,4> >(array) << endl; + diff --git a/doc/snippets/Tutorial_Map_using.cpp b/doc/snippets/Tutorial_Map_using.cpp new file mode 100644 index 000000000..e5e499f1f --- /dev/null +++ b/doc/snippets/Tutorial_Map_using.cpp @@ -0,0 +1,21 @@ +typedef Matrix<float,1,Dynamic> MatrixType; +typedef Map<MatrixType> MapType; +typedef Map<const MatrixType> MapTypeConst; // a read-only map +const int n_dims = 5; + +MatrixType m1(n_dims), m2(n_dims); +m1.setRandom(); +m2.setRandom(); +float *p = &m2(0); // get the address storing the data for m2 +MapType m2map(p,m2.size()); // m2map shares data with m2 +MapTypeConst m2mapconst(p,m2.size()); // a read-only accessor for m2 + +cout << "m1: " << m1 << endl; +cout << "m2: " << m2 << endl; +cout << "Squared euclidean distance: " << (m1-m2).squaredNorm() << endl; +cout << "Squared euclidean distance, using map: " << + (m1-m2map).squaredNorm() << endl; +m2map(3) = 7; // this will change m2, since they share the same array +cout << "Updated m2: " << m2 << endl; +cout << "m2 coefficient 2, constant accessor: " << m2mapconst(2) << endl; +/* m2mapconst(2) = 5; */ // this yields a compile-time error diff --git a/doc/snippets/Tutorial_commainit_01.cpp b/doc/snippets/Tutorial_commainit_01.cpp new file mode 100644 index 000000000..47ba31dc9 --- /dev/null +++ b/doc/snippets/Tutorial_commainit_01.cpp @@ -0,0 +1,5 @@ +Matrix3f m; +m << 1, 2, 3, + 4, 5, 6, + 7, 8, 9; +std::cout << m; diff --git a/doc/snippets/Tutorial_commainit_01b.cpp b/doc/snippets/Tutorial_commainit_01b.cpp new file mode 100644 index 000000000..2adb2e213 --- /dev/null +++ b/doc/snippets/Tutorial_commainit_01b.cpp @@ -0,0 +1,5 @@ +Matrix3f m; +m.row(0) << 1, 2, 3; +m.block(1,0,2,2) << 4, 5, 7, 8; +m.col(2).tail(2) << 6, 9; +std::cout << m; diff --git a/doc/snippets/Tutorial_commainit_02.cpp b/doc/snippets/Tutorial_commainit_02.cpp new file mode 100644 index 000000000..c960d6ab5 --- /dev/null +++ b/doc/snippets/Tutorial_commainit_02.cpp @@ -0,0 +1,7 @@ +int rows=5, cols=5; +MatrixXf m(rows,cols); +m << (Matrix3f() << 1, 2, 3, 4, 5, 6, 7, 8, 9).finished(), + MatrixXf::Zero(3,cols-3), + MatrixXf::Zero(rows-3,3), + MatrixXf::Identity(rows-3,cols-3); +cout << m; diff --git a/doc/snippets/Tutorial_solve_matrix_inverse.cpp b/doc/snippets/Tutorial_solve_matrix_inverse.cpp new file mode 100644 index 000000000..fff324446 --- /dev/null +++ b/doc/snippets/Tutorial_solve_matrix_inverse.cpp @@ -0,0 +1,6 @@ +Matrix3f A; +Vector3f b; +A << 1,2,3, 4,5,6, 7,8,10; +b << 3, 3, 4; +Vector3f x = A.inverse() * b; +cout << "The solution is:" << endl << x << endl; diff --git a/doc/snippets/Tutorial_solve_multiple_rhs.cpp b/doc/snippets/Tutorial_solve_multiple_rhs.cpp new file mode 100644 index 000000000..5411a44ab --- /dev/null +++ b/doc/snippets/Tutorial_solve_multiple_rhs.cpp @@ -0,0 +1,10 @@ +Matrix3f A(3,3); +A << 1,2,3, 4,5,6, 7,8,10; +Matrix<float,3,2> B; +B << 3,1, 3,1, 4,1; +Matrix<float,3,2> X; +X = A.fullPivLu().solve(B); +cout << "The solution with right-hand side (3,3,4) is:" << endl; +cout << X.col(0) << endl; +cout << "The solution with right-hand side (1,1,1) is:" << endl; +cout << X.col(1) << endl; diff --git a/doc/snippets/Tutorial_solve_reuse_decomposition.cpp b/doc/snippets/Tutorial_solve_reuse_decomposition.cpp new file mode 100644 index 000000000..3ca06453a --- /dev/null +++ b/doc/snippets/Tutorial_solve_reuse_decomposition.cpp @@ -0,0 +1,13 @@ +Matrix3f A(3,3); +A << 1,2,3, 4,5,6, 7,8,10; +PartialPivLU<Matrix3f> luOfA(A); // compute LU decomposition of A +Vector3f b; +b << 3,3,4; +Vector3f x; +x = luOfA.solve(b); +cout << "The solution with right-hand side (3,3,4) is:" << endl; +cout << x << endl; +b << 1,1,1; +x = luOfA.solve(b); +cout << "The solution with right-hand side (1,1,1) is:" << endl; +cout << x << endl; diff --git a/doc/snippets/Tutorial_solve_singular.cpp b/doc/snippets/Tutorial_solve_singular.cpp new file mode 100644 index 000000000..abff1ef73 --- /dev/null +++ b/doc/snippets/Tutorial_solve_singular.cpp @@ -0,0 +1,9 @@ +Matrix3f A; +Vector3f b; +A << 1,2,3, 4,5,6, 7,8,9; +b << 3, 3, 4; +cout << "Here is the matrix A:" << endl << A << endl; +cout << "Here is the vector b:" << endl << b << endl; +Vector3f x; +x = A.lu().solve(b); +cout << "The solution is:" << endl << x << endl; diff --git a/doc/snippets/Tutorial_solve_triangular.cpp b/doc/snippets/Tutorial_solve_triangular.cpp new file mode 100644 index 000000000..9d13f22ec --- /dev/null +++ b/doc/snippets/Tutorial_solve_triangular.cpp @@ -0,0 +1,8 @@ +Matrix3f A; +Vector3f b; +A << 1,2,3, 0,5,6, 0,0,10; +b << 3, 3, 4; +cout << "Here is the matrix A:" << endl << A << endl; +cout << "Here is the vector b:" << endl << b << endl; +Vector3f x = A.triangularView<Upper>().solve(b); +cout << "The solution is:" << endl << x << endl; diff --git a/doc/snippets/Tutorial_solve_triangular_inplace.cpp b/doc/snippets/Tutorial_solve_triangular_inplace.cpp new file mode 100644 index 000000000..16ae633a3 --- /dev/null +++ b/doc/snippets/Tutorial_solve_triangular_inplace.cpp @@ -0,0 +1,6 @@ +Matrix3f A; +Vector3f b; +A << 1,2,3, 0,5,6, 0,0,10; +b << 3, 3, 4; +A.triangularView<Upper>().solveInPlace(b); +cout << "The solution is:" << endl << b << endl; diff --git a/doc/snippets/Vectorwise_reverse.cpp b/doc/snippets/Vectorwise_reverse.cpp new file mode 100644 index 000000000..2f6a35080 --- /dev/null +++ b/doc/snippets/Vectorwise_reverse.cpp @@ -0,0 +1,10 @@ +MatrixXi m = MatrixXi::Random(3,4); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the rowwise reverse of m:" << endl << m.rowwise().reverse() << endl; +cout << "Here is the colwise reverse of m:" << endl << m.colwise().reverse() << endl; + +cout << "Here is the coefficient (1,0) in the rowise reverse of m:" << endl +<< m.rowwise().reverse()(1,0) << endl; +cout << "Let us overwrite this coefficient with the value 4." << endl; +//m.colwise().reverse()(1,0) = 4; +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/doc/snippets/class_FullPivLU.cpp b/doc/snippets/class_FullPivLU.cpp new file mode 100644 index 000000000..fce7fac09 --- /dev/null +++ b/doc/snippets/class_FullPivLU.cpp @@ -0,0 +1,16 @@ +typedef Matrix<double, 5, 3> Matrix5x3; +typedef Matrix<double, 5, 5> Matrix5x5; +Matrix5x3 m = Matrix5x3::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +Eigen::FullPivLU<Matrix5x3> lu(m); +cout << "Here is, up to permutations, its LU decomposition matrix:" + << endl << lu.matrixLU() << endl; +cout << "Here is the L part:" << endl; +Matrix5x5 l = Matrix5x5::Identity(); +l.block<5,3>(0,0).triangularView<StrictlyLower>() = lu.matrixLU(); +cout << l << endl; +cout << "Here is the U part:" << endl; +Matrix5x3 u = lu.matrixLU().triangularView<Upper>(); +cout << u << endl; +cout << "Let us now reconstruct the original matrix m:" << endl; +cout << lu.permutationP().inverse() * l * u * lu.permutationQ().inverse() << endl; diff --git a/doc/snippets/compile_snippet.cpp.in b/doc/snippets/compile_snippet.cpp.in new file mode 100644 index 000000000..894cd526c --- /dev/null +++ b/doc/snippets/compile_snippet.cpp.in @@ -0,0 +1,12 @@ +#include <Eigen/Dense> +#include <iostream> + +using namespace Eigen; +using namespace std; + +int main(int, char**) +{ + cout.precision(3); + ${snippet_source_code} + return 0; +} diff --git a/doc/snippets/tut_arithmetic_redux_minmax.cpp b/doc/snippets/tut_arithmetic_redux_minmax.cpp new file mode 100644 index 000000000..f4ae7f406 --- /dev/null +++ b/doc/snippets/tut_arithmetic_redux_minmax.cpp @@ -0,0 +1,12 @@ + Matrix3f m = Matrix3f::Random(); + std::ptrdiff_t i, j; + float minOfM = m.minCoeff(&i,&j); + cout << "Here is the matrix m:\n" << m << endl; + cout << "Its minimum coefficient (" << minOfM + << ") is at position (" << i << "," << j << ")\n\n"; + + RowVector4i v = RowVector4i::Random(); + int maxOfV = v.maxCoeff(&i); + cout << "Here is the vector v: " << v << endl; + cout << "Its maximum coefficient (" << maxOfV + << ") is at position " << i << endl; diff --git a/doc/snippets/tut_arithmetic_transpose_aliasing.cpp b/doc/snippets/tut_arithmetic_transpose_aliasing.cpp new file mode 100644 index 000000000..c8e4746d0 --- /dev/null +++ b/doc/snippets/tut_arithmetic_transpose_aliasing.cpp @@ -0,0 +1,5 @@ +Matrix2i a; a << 1, 2, 3, 4; +cout << "Here is the matrix a:\n" << a << endl; + +a = a.transpose(); // !!! do NOT do this !!! +cout << "and the result of the aliasing effect:\n" << a << endl;
\ No newline at end of file diff --git a/doc/snippets/tut_arithmetic_transpose_conjugate.cpp b/doc/snippets/tut_arithmetic_transpose_conjugate.cpp new file mode 100644 index 000000000..88496b22d --- /dev/null +++ b/doc/snippets/tut_arithmetic_transpose_conjugate.cpp @@ -0,0 +1,12 @@ +MatrixXcf a = MatrixXcf::Random(2,2); +cout << "Here is the matrix a\n" << a << endl; + +cout << "Here is the matrix a^T\n" << a.transpose() << endl; + + +cout << "Here is the conjugate of a\n" << a.conjugate() << endl; + + +cout << "Here is the matrix a^*\n" << a.adjoint() << endl; + + diff --git a/doc/snippets/tut_arithmetic_transpose_inplace.cpp b/doc/snippets/tut_arithmetic_transpose_inplace.cpp new file mode 100644 index 000000000..7a069ff23 --- /dev/null +++ b/doc/snippets/tut_arithmetic_transpose_inplace.cpp @@ -0,0 +1,6 @@ +MatrixXf a(2,3); a << 1, 2, 3, 4, 5, 6; +cout << "Here is the initial matrix a:\n" << a << endl; + + +a.transposeInPlace(); +cout << "and after being transposed:\n" << a << endl;
\ No newline at end of file diff --git a/doc/snippets/tut_matrix_assignment_resizing.cpp b/doc/snippets/tut_matrix_assignment_resizing.cpp new file mode 100644 index 000000000..cf189983f --- /dev/null +++ b/doc/snippets/tut_matrix_assignment_resizing.cpp @@ -0,0 +1,5 @@ +MatrixXf a(2,2); +std::cout << "a is of size " << a.rows() << "x" << a.cols() << std::endl; +MatrixXf b(3,3); +a = b; +std::cout << "a is now of size " << a.rows() << "x" << a.cols() << std::endl; |