| /aosp_15_r20/external/eigen/Eigen/src/Eigenvalues/ |
| H A D | MatrixBaseEigenvalues.h | 27 return ComplexEigenSolver<PlainObject>(m_eval, false).eigenvalues(); in run()
39 return EigenSolver<PlainObject>(m_eval, false).eigenvalues();
45 /** \brief Computes the eigenvalues of a matrix
46 * \returns Column vector containing the eigenvalues.
49 * This function computes the eigenvalues with the help of the EigenSolver
53 * The eigenvalues are repeated according to their algebraic multiplicity,
54 * so there are as many eigenvalues as rows in the matrix.
62 * \sa EigenSolver::eigenvalues(), ComplexEigenSolver::eigenvalues(),
63 * SelfAdjointView::eigenvalues()
67 MatrixBase<Derived>::eigenvalues() const
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| H A D | GeneralizedEigenSolver.h | 24 * \brief Computes the generalized eigenvalues and eigenvectors of a pair of general matrices
30 …* The generalized eigenvalues and eigenvectors of a matrix pair \f$ A \f$ and \f$ B \f$ are scalars
32 * \f$ D \f$ is a diagonal matrix with the eigenvalues on the diagonal, and
37 * The generalized eigenvalues and eigenvectors of a matrix pair may be complex, even when the
39 …* singular. To workaround this difficulty, the eigenvalues are provided as a pair of complex \f$ \…
45 * Call the function compute() to compute the generalized eigenvalues and eigenvectors of
48 * eigenvalues and eigenvectors at construction time. Once the eigenvalue and
49 * eigenvectors are computed, they can be retrieved with the eigenvalues() and
56 * \sa MatrixBase::eigenvalues(), class ComplexEigenSolver, class SelfAdjointEigenSolver
86 /** \brief Type for vector of real scalar values eigenvalues as returned by betas().
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| H A D | ComplexEigenSolver.h | 24 * \brief Computes eigenvalues and eigenvectors of general complex matrices
30 * The eigenvalues and eigenvectors of a matrix \f$ A \f$ are scalars
32 * \f$. If \f$ D \f$ is a diagonal matrix with the eigenvalues on
39 * eigenvalues and eigenvectors of a given function. The
73 /** \brief Type for vector of eigenvalues as returned by eigenvalues().
120 * eigenvalues are computed; if false, only the eigenvalues are
149 * \f$ as returned by eigenvalues(). The eigenvectors are normalized to
160 …sert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues."); in eigenvectors()
164 /** \brief Returns the eigenvalues of given matrix.
166 * \returns A const reference to the column vector containing the eigenvalues.
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| H A D | SelfAdjointEigenSolver.h | 34 * \brief Computes eigenvalues and eigenvectors of selfadjoint matrices
42 * transpose. This class computes the eigenvalues and eigenvectors of a
44 * \f$ v \f$ such that \f$ Av = \lambda v \f$. The eigenvalues of a
46 * the eigenvalues on the diagonal, and \f$ V \f$ is a matrix with the
61 * Call the function compute() to compute the eigenvalues and eigenvectors of
64 * the eigenvalues and eigenvectors at construction time. Once the eigenvalue
65 * and eigenvectors are computed, they can be retrieved with the eigenvalues()
74 * \sa MatrixBase::eigenvalues(), class EigenSolver, class ComplexEigenSolver
104 /** \brief Type for vector of eigenvalues as returned by eigenvalues().
137 * eigenvalues and eigenvectors will be computed.
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| H A D | EigenSolver.h | 23 * \brief Computes eigenvalues and eigenvectors of general matrices
29 * The eigenvalues and eigenvectors of a matrix \f$ A \f$ are scalars
31 * \f$ D \f$ is a diagonal matrix with the eigenvalues on the diagonal, and
36 * The eigenvalues and eigenvectors of a matrix may be complex, even when the
46 * Call the function compute() to compute the eigenvalues and eigenvectors of
49 * eigenvalues and eigenvectors at construction time. Once the eigenvalue and
50 * eigenvectors are computed, they can be retrieved with the eigenvalues() and
62 * \sa MatrixBase::eigenvalues(), class ComplexEigenSolver, class SelfAdjointEigenSolver
92 /** \brief Type for vector of eigenvalues as returned by eigenvalues().
135 * eigenvalues are computed; if false, only the eigenvalues are
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| H A D | GeneralizedSelfAdjointEigenSolver.h | 23 * \brief Computes eigenvalues and eigenvectors of the generalized selfadjoint eigen problem
35 * Call the function compute() to compute the eigenvalues and eigenvectors of
38 * constructor which computes the eigenvalues and eigenvectors at construction time.
39 * Once the eigenvalue and eigenvectors are computed, they can be retrieved with the eigenvalues()
67 * eigenvalues and eigenvectors will be computed.
90 * to compute the eigenvalues and (if requested) the eigenvectors of the
124 * According to \p options, this function computes eigenvalues and (if requested)
133 * The eigenvalues() function can be used to retrieve
134 * the eigenvalues. If \p options contains ComputeEigenvectors, then the
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| /aosp_15_r20/external/eigen/test/ |
| H A D | eigensolver_selfadjoint.cpp | 14 #include <Eigen/Eigenvalues>
31 VERIFY(eiSymm.eigenvalues().cwiseAbs().maxCoeff() <= (std::numeric_limits<RealScalar>::min)()); in selfadjointeigensolver_essential_check()
36 (eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal())/scaling); in selfadjointeigensolver_essential_check()
38 VERIFY_IS_APPROX(m.template selfadjointView<Lower>().eigenvalues(), eiSymm.eigenvalues()); in selfadjointeigensolver_essential_check()
46 if(! eiSymm.eigenvalues().isApprox(eiDirect.eigenvalues(), eival_eps) ) in selfadjointeigensolver_essential_check()
48 std::cerr << "reference eigenvalues: " << eiSymm.eigenvalues().transpose() << "\n" in selfadjointeigensolver_essential_check()
49 << "obtained eigenvalues: " << eiDirect.eigenvalues().transpose() << "\n" in selfadjointeigensolver_essential_check()
50 … << "diff: " << (eiSymm.eigenvalues()-eiDirect.eigenvalues()).transpose() << "\n" in selfadjointeigensolver_essential_check()
51 …<< "error (eps): " << (eiSymm.eigenvalues()-eiDirect.eigenvalues()).norm() / eiSymm.eige… in selfadjointeigensolver_essential_check()
55 … VERIFY(eiDirect.eigenvalues().cwiseAbs().maxCoeff() <= (std::numeric_limits<RealScalar>::min)()); in selfadjointeigensolver_essential_check()
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| H A D | eigensolver_generic.cpp | 13 #include <Eigen/Eigenvalues>
25 eig.eigenvectors() * eig.eigenvalues().asDiagonal()); in check_eigensolver_for_given_mat()
27 VERIFY_IS_APPROX(a.eigenvalues(), eig.eigenvalues()); in check_eigensolver_for_given_mat()
50 (ei0.pseudoEigenvectors().template cast<Complex>()) * (ei0.eigenvalues().asDiagonal())); in eigensolver()
59 VERIFY_IS_EQUAL(ei2.eigenvalues(), ei1.eigenvalues()); in eigensolver()
68 VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues()); in eigensolver()
93 VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(),RealScalar(1)); in eigensolver()
104 VERIFY_RAISES_ASSERT(eig.eigenvalues()); in eigensolver_verify_assert()
137 …VERIFY_IS_APPROX(a * eig.eigenvectors()*scale, eig.eigenvectors() * eig.eigenvalues().asDiagonal()… in eigensolver_generic_extra()
140 // check a case where all eigenvalues are null. in eigensolver_generic_extra()
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| H A D | eigensolver_complex.cpp | 13 #include <Eigen/Eigenvalues>
88 VERIFY_IS_APPROX(symmA * ei0.eigenvectors(), ei0.eigenvectors() * ei0.eigenvalues().asDiagonal()); in eigensolver()
92 VERIFY_IS_APPROX(a * ei1.eigenvectors(), ei1.eigenvectors() * ei1.eigenvalues().asDiagonal()); in eigensolver()
93 // Note: If MatrixType is real then a.eigenvalues() uses EigenSolver and thus in eigensolver()
95 verify_is_approx_upto_permutation(a.eigenvalues(), ei1.eigenvalues()); in eigensolver()
101 VERIFY_IS_EQUAL(ei2.eigenvalues(), ei1.eigenvalues()); in eigensolver()
110 VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues()); in eigensolver()
115 VERIFY((eiz.eigenvalues().cwiseEqual(0)).all()); in eigensolver()
139 VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(),RealScalar(1)); in eigensolver()
148 VERIFY_RAISES_ASSERT(eig.eigenvalues()); in eigensolver_verify_assert()
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| H A D | eigensolver_generalized_real.cpp | 13 #include <Eigen/Eigenvalues>
40 VERIFY_IS_EQUAL(eig.eigenvalues().imag().cwiseAbs().maxCoeff(), 0); in generalized_eigensolver_real()
42 VectorType realEigenvalues = eig.eigenvalues().real(); in generalized_eigensolver_real()
44 VERIFY_IS_APPROX(realEigenvalues, symmEig.eigenvalues()); in generalized_eigensolver_real()
47 … typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType D = eig.eigenvalues().asDiagonal(); in generalized_eigensolver_real()
67 … typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType D = eig.eigenvalues().asDiagonal(); in generalized_eigensolver_real()
84 VERIFY_IS_APPROX(eig1.eigenvalues(), eig2.eigenvalues()); in generalized_eigensolver_real()
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| /aosp_15_r20/external/eigen/unsupported/Eigen/src/Eigenvalues/ |
| H A D | ArpackSelfAdjointEigenSolver.h | 42 /** \brief Type for vector of eigenvalues as returned by eigenvalues().
64 …/** \brief Constructor; computes generalized eigenvalues of given matrix with respect to another m…
66 * \param[in] A Self-adjoint matrix whose eigenvalues / eigenvectors will
70 * \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.
74 * largest algebraic, or smallest algebraic eigenvalues. Alternatively, this
76 * eigenvalues closest to this value will be found.
78 * \param[in] tol What tolerance to find the eigenvalues to. Default is 0, which
82 …* to compute the eigenvalues of the matrix \p A with respect to \p B. The eigenvectors are compute…
99 /** \brief Constructor; computes eigenvalues of given matrix.
101 * \param[in] A Self-adjoint matrix whose eigenvalues / eigenvectors will
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| /aosp_15_r20/external/libchrome/ui/gfx/geometry/ |
| H A D | matrix3_f.cc | 163 float eigenvalues[3]; in SolveEigenproblem() local
171 eigenvalues[0] = data_[M00]; in SolveEigenproblem()
172 eigenvalues[1] = data_[M11]; in SolveEigenproblem()
173 eigenvalues[2] = data_[M22]; in SolveEigenproblem()
198 eigenvalues[0] = q + 2 * p * static_cast<float>(cos(phi)); in SolveEigenproblem()
199 eigenvalues[2] = in SolveEigenproblem()
201 eigenvalues[1] = 3 * q - eigenvalues[0] - eigenvalues[2]; in SolveEigenproblem()
204 // Put eigenvalues in the descending order. in SolveEigenproblem()
206 if (eigenvalues[2] > eigenvalues[1]) { in SolveEigenproblem()
207 std::swap(eigenvalues[2], eigenvalues[1]); in SolveEigenproblem()
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| /aosp_15_r20/external/eigen/Eigen/ |
| H A D | Eigenvalues | 21 /** \defgroup Eigenvalues_Module Eigenvalues module
27 * - MatrixBase::eigenvalues(),
31 * #include <Eigen/Eigenvalues>
36 #include "src/Eigenvalues/Tridiagonalization.h"
37 #include "src/Eigenvalues/RealSchur.h"
38 #include "src/Eigenvalues/EigenSolver.h"
39 #include "src/Eigenvalues/SelfAdjointEigenSolver.h"
40 #include "src/Eigenvalues/GeneralizedSelfAdjointEigenSolver.h"
41 #include "src/Eigenvalues/HessenbergDecomposition.h"
42 #include "src/Eigenvalues/ComplexSchur.h"
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| /aosp_15_r20/external/apache-commons-math/src/main/java/org/apache/commons/math3/linear/ |
| H A D | EigenDecomposition.java | 55 * eigenvalues in 1-by-1 blocks and any complex eigenvalues, lambda + i*mu, in 2-by-2 blocks:
212 * eigenvalues are on the diagonal while complex values are on 2x2 blocks { {real +imaginary},
277 * Gets a copy of the real parts of the eigenvalues of the original matrix.
279 * @return a copy of the real parts of the eigenvalues of the original matrix.
302 * Gets a copy of the imaginary parts of the eigenvalues of the original matrix.
304 * @return a copy of the imaginary parts of the eigenvalues of the original matrix.
383 * DecompositionSolver} only supports real eigenvalues.
387 * eigenvalues
410 * @param realEigenvalues Real parts of the eigenvalues.
411 * @param imagEigenvalues Imaginary parts of the eigenvalues.
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| /aosp_15_r20/external/tensorflow/third_party/eigen3/ |
| H A D | LICENSE | 191 ./lapack/eigenvalues.cpp
362 ./Eigen/src/Eigenvalues/RealSchur.h
363 ./Eigen/src/Eigenvalues/ComplexEigenSolver.h
364 ./Eigen/src/Eigenvalues/GeneralizedEigenSolver.h
365 ./Eigen/src/Eigenvalues/ComplexSchur.h
366 ./Eigen/src/Eigenvalues/RealQZ.h
367 ./Eigen/src/Eigenvalues/EigenSolver.h
368 ./Eigen/src/Eigenvalues/HessenbergDecomposition.h
369 ./Eigen/src/Eigenvalues/GeneralizedSelfAdjointEigenSolver.h
370 ./Eigen/src/Eigenvalues/Tridiagonalization.h
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| /aosp_15_r20/external/tensorflow/tensorflow/python/ops/ |
| H A D | linalg_ops.py | 383 The eigenvalues
387 Computes the eigenvalues and right eigenvectors of the innermost
397 e: Eigenvalues. Shape is `[..., N]`. The eigenvalues are not necessarily
413 """Computes the eigenvalues of one or more matrices.
418 eigenvectors are used to compute the gradient w.r.t. the eigenvalues. See
426 e: Eigenvalues. Shape is `[..., N]`. The vector `e[..., :]` contains the `N`
427 eigenvalues of `tensor[..., :, :]`.
443 Computes the eigenvalues and eigenvectors of the innermost N-by-N matrices
453 e: Eigenvalues. Shape is `[..., N]`. Sorted in non-decreasing order.
465 """Computes the eigenvalues of one or more self-adjoint matrices.
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| /aosp_15_r20/external/eigen/doc/snippets/ |
| H A D | EigenSolver_compute.cpp | 4 cout << "The eigenvalues of A are: " << es.eigenvalues().transpose() << endl;
5 es.compute(A + MatrixXf::Identity(4,4), false); // re-use es to compute eigenvalues of A+I
6 cout << "The eigenvalues of A+I are: " << es.eigenvalues().transpose() << endl;
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| H A D | SelfAdjointEigenSolver_SelfAdjointEigenSolver.cpp | 5 cout << "The eigenvalues of A are: " << es.eigenvalues().transpose() << endl;
6 es.compute(A + Matrix4f::Identity(4,4)); // re-use es to compute eigenvalues of A+I
7 cout << "The eigenvalues of A+I are: " << es.eigenvalues().transpose() << endl;
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| H A D | SelfAdjointEigenSolver_compute_MatrixType.cpp | 5 cout << "The eigenvalues of A are: " << es.eigenvalues().transpose() << endl;
6 es.compute(A + MatrixXf::Identity(4,4)); // re-use es to compute eigenvalues of A+I
7 cout << "The eigenvalues of A+I are: " << es.eigenvalues().transpose() << endl;
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| /aosp_15_r20/external/pytorch/torch/linalg/ |
| H A D | __init__.py | 452 This is the case when all its eigenvalues are different.
458 The returned eigenvalues are not guaranteed to be in any specific order.
460 .. note:: The eigenvalues and eigenvectors of a real matrix may be complex.
467 eigenvalues are different). If it is not diagonalizable, the returned
468 eigenvalues will be correct but :math:`A \neq V \operatorname{diag}(\Lambda)V^{-1}`.
485 :attr:`A` has distinct eigenvalues.
486 Furthermore, if the distance between any two eigenvalues is close to zero,
487 the gradient will be numerically unstable, as it depends on the eigenvalues
493 :func:`torch.linalg.eigvals` computes only the eigenvalues.
514 …A named tuple `(eigenvalues, eigenvectors)` which corresponds to :math:`\Lambda` and :math:`V` abo…
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| /aosp_15_r20/external/tensorflow/tensorflow/core/api_def/base_api/ |
| H A D | api_def_Eig.pbtxt | 15 Eigenvalues. Shape is `[N]`.
28 Otherwise, only the eigenvalues will be computed.
33 Computes the eigenvalues and (optionally) right eigenvectors of each inner matrix in
34 `input` such that `input[..., :, :] = v[..., :, :] * diag(e[..., :])`. The eigenvalues
39 # e is a tensor of eigenvalues.
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| H A D | api_def_SelfAdjointEigV2.pbtxt | 15 Eigenvalues. Shape is `[N]`.
28 Otherwise, only the eigenvalues will be computed.
33 Computes the eigenvalues and (optionally) eigenvectors of each inner matrix in
34 `input` such that `input[..., :, :] = v[..., :, :] * diag(e[..., :])`. The eigenvalues
39 # e is a tensor of eigenvalues.
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| /aosp_15_r20/external/tensorflow/tensorflow/python/ops/linalg/ |
| H A D | linalg_impl.py | 1238 """Computes the eigenvalues of a Hermitian tridiagonal matrix.
1248 eigvals_only: If False, both eigenvalues and corresponding eigenvectors are
1249 computed. If True, only eigenvalues are computed. Default is True.
1251 determines which eigenvalues to calculate:
1252 'a': all eigenvalues.
1253 ‘v’: eigenvalues in the interval (min, max] given by `select_range`.
1254 'i’: eigenvalues with indices min <= i <= max.
1256 eigenvalues to compute together with select. If select is 'a',
1266 eig_vals: The eigenvalues of the matrix in non-decreasing order.
1300 """Computes all eigenvalues of a Hermitian tridiagonal matrix."""
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| /aosp_15_r20/external/eigen/doc/ |
| H A D | TopicLinearAlgebraDecompositions.dox | 126 <tr><th class="inter" colspan="9">\n Singular values and eigenvalues decompositions</th></tr>
158 <td>Eigenvalues/vectors</td>
170 <td>Eigenvalues/vectors</td>
182 <td>Eigenvalues/vectors</td>
194 <td>Generalized eigenvalues/vectors</td>
255 …>\b 2: </a>Eigenvalues, SVD and Schur decompositions rely on iterative algorithms. Their convergen…
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| /aosp_15_r20/external/eigen/unsupported/Eigen/src/IterativeSolvers/ |
| H A D | DGMRES.h | 13 #include "../../../../Eigen/Eigenvalues"
65 * corresponding to the smallest eigenvalues are used to build a
80 * solver.setEigenv(1); // Set the number of eigenvalues to deflate
166 * Set the number of eigenvalues to deflate at each restart
208 mutable StorageIndex m_neig; //Number of eigenvalues to extract at each restart
209 mutable Index m_r; // Current number of deflated eigenvalues, size of m_U
210 mutable Index m_maxNeig; // Maximum number of eigenvalues to deflate
442 //Count the real number of extracted eigenvalues (with complex conjugates)
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