Home
last modified time | relevance | path

Searched full:eigenvectors (Results 1 – 25 of 100) sorted by relevance

1234

/aosp_15_r20/external/eigen/Eigen/src/Eigenvalues/
H A DEigenSolver.h23 * \brief Computes eigenvalues and eigenvectors of general matrices
29 * The eigenvalues and eigenvectors of a matrix \f$ A \f$ are scalars
32 * \f$ V \f$ is a matrix with the eigenvectors as its columns, then \f$ A V =
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
51 * eigenvectors() functions. The pseudoEigenvalueMatrix() and
99 /** \brief Type for matrix of eigenvectors as returned by eigenvectors().
134 * \param[in] computeEigenvectors If true, both the eigenvectors and the
[all …]
H A DGeneralizedEigenSolver.h24 * \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
33 * \f$ V \f$ is a matrix with the eigenvectors as its columns, then \f$ A V =
37 * The generalized eigenvalues and eigenvectors of a matrix pair may be complex, even when the
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
50 * eigenvectors() functions.
104 /** \brief Type for matrix of eigenvectors as returned by eigenvectors().
147 * \param[in] computeEigenvectors If true, both the eigenvectors and the
[all …]
H A DComplexEigenSolver.h24 * \brief Computes eigenvalues and eigenvectors of general complex matrices
30 * The eigenvalues and eigenvectors of a matrix \f$ A \f$ are scalars
33 * the diagonal, and \f$ V \f$ is a matrix with the eigenvectors as
39 * eigenvalues and eigenvectors of a given function. The
80 /** \brief Type for matrix of eigenvectors as returned by eigenvectors().
119 * \param[in] computeEigenvectors If true, both the eigenvectors and the
137 /** \brief Returns the eigenvectors of given matrix.
139 * \returns A const reference to the matrix whose columns are the eigenvectors.
147 * This function returns a matrix whose columns are the eigenvectors. Column
149 * \f$ as returned by eigenvalues(). The eigenvectors are normalized to
[all …]
H A DSelfAdjointEigenSolver.h34 * \brief Computes eigenvalues and eigenvectors of selfadjoint matrices
42 * transpose. This class computes the eigenvalues and eigenvectors of a
47 * eigenvectors as its columns, then \f$ A = V D V^{-1} \f$. This is called the
61 * Call the function compute() to compute the eigenvalues and eigenvectors of
64 * the eigenvalues and eigenvectors at construction time. Once the eigenvalue
65 * and eigenvectors are computed, they can be retrieved with the eigenvalues()
66 * and eigenvectors() functions.
137 * eigenvalues and eigenvectors will be computed.
163 * eigenvalues of the matrix \p matrix. The eigenvectors are computed if
193 * then the eigenvectors are also computed and can be retrieved by
[all …]
H A DGeneralizedSelfAdjointEigenSolver.h23 * \brief Computes eigenvalues and eigenvectors of the generalized selfadjoint eigen problem
35 * Call the function compute() to compute the eigenvalues and eigenvectors of
38 * constructor which computes the eigenvalues and eigenvectors at construction time.
39 * Once the eigenvalue and eigenvectors are computed, they can be retrieved with the eigenvalues()
40 * and eigenvectors() functions.
67 * eigenvalues and eigenvectors will be computed.
90 * to compute the eigenvalues and (if requested) the eigenvectors of the
94 * \f$ x^* B x = 1 \f$. The eigenvectors are computed if
125 * the eigenvectors of one of the following three generalized eigenproblems:
135 * eigenvectors are also computed and can be retrieved by calling
[all …]
/aosp_15_r20/external/eigen/test/
H A Deigensolver_selfadjoint.cpp35 VERIFY_IS_APPROX((m.template selfadjointView<Lower>() * eiSymm.eigenvectors())/scaling, in selfadjointeigensolver_essential_check()
36 (eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal())/scaling); in selfadjointeigensolver_essential_check()
39 VERIFY_IS_UNITARY(eiSymm.eigenvectors()); in selfadjointeigensolver_essential_check()
60 VERIFY_IS_APPROX((m.template selfadjointView<Lower>() * eiDirect.eigenvectors())/scaling, in selfadjointeigensolver_essential_check()
61 (eiDirect.eigenvectors() * eiDirect.eigenvalues().asDiagonal())/scaling); in selfadjointeigensolver_essential_check()
65 VERIFY_IS_UNITARY(eiDirect.eigenvectors()); in selfadjointeigensolver_essential_check()
110 VERIFY((symmC.template selfadjointView<Lower>() * eiSymmGen.eigenvectors()).isApprox( in selfadjointeigensolver()
111 …symmB.template selfadjointView<Lower>() * (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDi… in selfadjointeigensolver()
116 …ointView<Lower>() * (symmC.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox( in selfadjointeigensolver()
117 (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps)); in selfadjointeigensolver()
[all …]
H A Deigensolver_generic.cpp24 VERIFY_IS_APPROX(a.template cast<Complex>() * eig.eigenvectors(), in check_eigensolver_for_given_mat()
25 eig.eigenvectors() * eig.eigenvalues().asDiagonal()); in check_eigensolver_for_given_mat()
26 VERIFY_IS_APPROX(eig.eigenvectors().colwise().norm(), RealVectorType::Ones(n).transpose()); in check_eigensolver_for_given_mat()
58 VERIFY_IS_EQUAL(ei2.eigenvectors(), ei1.eigenvectors()); in eigensolver()
94 VERIFY((ei3.eigenvectors().transpose()*ei3.eigenvectors().transpose()).eval().isIdentity()); in eigensolver()
101 VERIFY_RAISES_ASSERT(eig.eigenvectors()); in eigensolver_verify_assert()
108 VERIFY_RAISES_ASSERT(eig.eigenvectors()); in eigensolver_verify_assert()
137 …VERIFY_IS_APPROX(a * eig.eigenvectors()*scale, eig.eigenvectors() * eig.eigenvalues().asDiagonal()… in eigensolver_generic_extra()
148 VERIFY_IS_APPROX((a * eig.eigenvectors()).norm()+1., 1.); in eigensolver_generic_extra()
149 VERIFY_IS_APPROX((eig.eigenvectors() * eig.eigenvalues().asDiagonal()).norm()+1., 1.); in eigensolver_generic_extra()
H A Deigensolver_complex.cpp88 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()
100 VERIFY_IS_EQUAL(ei2.eigenvectors(), ei1.eigenvectors()); in eigensolver()
140 VERIFY((ei3.eigenvectors().transpose()*ei3.eigenvectors().transpose()).eval().isIdentity()); in eigensolver()
147 VERIFY_RAISES_ASSERT(eig.eigenvectors()); in eigensolver_verify_assert()
152 VERIFY_RAISES_ASSERT(eig.eigenvectors()); in eigensolver_verify_assert()
H A Deigensolver_generalized_real.cpp46 // check eigenvectors in generalized_eigensolver_real()
48 typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType V = eig.eigenvectors(); in generalized_eigensolver_real()
66 // check eigenvectors in generalized_eigensolver_real()
68 typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType V = eig.eigenvectors(); in generalized_eigensolver_real()
80 // check without eigenvectors in generalized_eigensolver_real()
/aosp_15_r20/external/apache-commons-math/src/main/java/org/apache/commons/math/linear/
H A DEigenDecompositionImpl.java77 /** Eigenvectors. */
78 private ArrayRealVector[] eigenvectors; field in EigenDecompositionImpl
162 final int m = eigenvectors.length; in getV()
165 cachedV.setColumnVector(k, eigenvectors[k]); in getV()
186 final int m = eigenvectors.length; in getVT()
189 cachedVt.setRowVector(k, eigenvectors[k]); in getVT()
223 return eigenvectors[i].copy(); in getEigenvector()
240 return new Solver(realEigenvalues, imagEigenvalues, eigenvectors); in getSolver()
252 /** Eigenvectors. */
253 private final ArrayRealVector[] eigenvectors; field in EigenDecompositionImpl.Solver
[all …]
/aosp_15_r20/external/eigen/unsupported/Eigen/src/Eigenvalues/
H A DArpackSelfAdjointEigenSolver.h66 * \param[in] A Self-adjoint matrix whose eigenvalues / eigenvectors will
70 * \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.
82 …* to compute the eigenvalues of the matrix \p A with respect to \p B. The eigenvectors are compute…
101 * \param[in] A Self-adjoint matrix whose eigenvalues / eigenvectors will
104 * \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.
116 * to compute the eigenvalues of the matrix \p A. The eigenvectors are computed if
135 …/** \brief Computes generalized eigenvalues / eigenvectors of given matrix using the external ARPA…
139 * \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.
154 * then the eigenvectors are also computed and can be retrieved by
155 * calling eigenvectors().
[all …]
/aosp_15_r20/external/apache-commons-math/src/main/java/org/apache/commons/math3/linear/
H A DEigenDecomposition.java62 * The columns of V represent the eigenvectors in the sense that A*V = V*D, i.e. A.multiply(V)
96 /** Eigenvectors. */
97 private ArrayRealVector[] eigenvectors; field in EigenDecomposition
191 * its inverse. The columns of V are the eigenvectors of the original matrix. No assumption is
200 final int m = eigenvectors.length; in getV()
203 cachedV.setColumnVector(k, eigenvectors[k]); in getV()
238 * transpose is also its inverse. The columns of V are the eigenvectors of the original matrix.
247 final int m = eigenvectors.length; in getVT()
250 cachedVt.setRowVector(k, eigenvectors[k]); in getVT()
334 return eigenvectors[i].copy(); in getEigenvector()
[all …]
/aosp_15_r20/external/libchrome/ui/gfx/geometry/
H A Dmatrix3_unittest.cc120 Matrix3F eigenvectors = Matrix3F::Zeros(); in TEST() local
121 Vector3dF eigenvals = matrix.SolveEigenproblem(&eigenvectors); in TEST()
124 EXPECT_EQ(Vector3dF(0.0f, 0.0f, 1.0f), eigenvectors.get_column(0)); in TEST()
125 EXPECT_EQ(Vector3dF(1.0f, 0.0f, 0.0f), eigenvectors.get_column(1)); in TEST()
126 EXPECT_EQ(Vector3dF(0.0f, 1.0f, 0.0f), eigenvectors.get_column(2)); in TEST()
130 // This block tests computation of eigenvectors of a matrix where nice in TEST()
136 Matrix3F eigenvectors = Matrix3F::Zeros(); in TEST() local
137 Vector3dF eigenvals = matrix.SolveEigenproblem(&eigenvectors); in TEST()
142 (expected_principal - eigenvectors.get_column(0)).Length(), in TEST()
147 // This block tests computation of eigenvectors of a matrix where output in TEST()
[all …]
H A Dmatrix3_f.h90 // Compute eigenvalues and (optionally) normalized eigenvectors of
91 // a positive defnite matrix *this. Eigenvectors are computed only if
92 // non-null |eigenvectors| matrix is passed. If it is NULL, the routine
93 // will not attempt to compute eigenvectors but will still return eigenvalues
97 // only needs to be symmetric while eigenvectors require it to be
100 // Eigenvectors are placed as column in |eigenvectors| in order corresponding
102 Vector3dF SolveEigenproblem(Matrix3F* eigenvectors) const;
H A Dmatrix3_f.cc153 Vector3dF Matrix3F::SolveEigenproblem(Matrix3F* eigenvectors) const { in SolveEigenproblem()
221 if (eigenvectors != NULL && diagonal) { in SolveEigenproblem()
222 // Eigenvectors are e-vectors, just need to be sorted accordingly. in SolveEigenproblem()
223 *eigenvectors = Zeros(); in SolveEigenproblem()
225 eigenvectors->set(indices[i], i, 1.0f); in SolveEigenproblem()
226 } else if (eigenvectors != NULL) { in SolveEigenproblem()
259 eigenvectors->set_column(i, eigvec); in SolveEigenproblem()
/aosp_15_r20/external/tensorflow/tensorflow/python/ops/linalg/
H A Dlinalg_impl.py537 numerically singular systems when computing eigenvectors by inverse
1248 eigvals_only: If False, both eigenvalues and corresponding eigenvectors are
1267 eig_vectors: If `eigvals_only` is False the eigenvectors are returned in
1272 NotImplemented: Computing eigenvectors for `eigvals_only` = False is
1461 """Implements inverse iteration to compute eigenvectors."""
1467 # Eigenvectors corresponding to cluster of close eigenvalues are
1476 # Find the beginning and end of runs of eigenvectors corresponding
1492 # We perform inverse iteration for all eigenvectors in parallel,
1502 # Replicate alpha-eigvals(ik) and beta across the k eigenvectors so we
1512 def orthogonalize_close_eigenvectors(eigenvectors): argument
[all …]
/aosp_15_r20/external/eigen/doc/snippets/
H A DComplexEigenSolver_compute.cpp7 cout << "The matrix of eigenvectors, V, is:" << endl << ces.eigenvectors() << endl << endl;
11 VectorXcf v = ces.eigenvectors().col(0);
16 << ces.eigenvectors() * ces.eigenvalues().asDiagonal() * ces.eigenvectors().inverse() << endl;
H A DEigenSolver_EigenSolver_MatrixType.cpp6 cout << "The matrix of eigenvectors, V, is:" << endl << es.eigenvectors() << endl << endl;
10 VectorXcd v = es.eigenvectors().col(0);
15 MatrixXcd V = es.eigenvectors();
H A DSelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType.cpp7 cout << "The matrix of eigenvectors, V, is:" << endl << es.eigenvectors() << endl << endl;
11 VectorXd v = es.eigenvectors().col(0);
16 MatrixXd V = es.eigenvectors();
/aosp_15_r20/external/pytorch/aten/src/ATen/native/cuda/linalg/
H A DBatchLinearAlgebraLib.cpp1418 static void linalg_eigh_cusolver_syevd(const Tensor& eigenvalues, const Tensor& eigenvectors, const… in linalg_eigh_cusolver_syevd() argument
1419 AT_DISPATCH_FLOATING_AND_COMPLEX_TYPES(eigenvectors.scalar_type(), "linalg_eigh_cuda", [&] { in linalg_eigh_cusolver_syevd()
1420 apply_syevd<scalar_t>(eigenvalues, eigenvectors, infos, upper, compute_eigenvectors); in linalg_eigh_cusolver_syevd()
1424 static void linalg_eigh_cusolver_syevj(const Tensor& eigenvalues, const Tensor& eigenvectors, const… in linalg_eigh_cusolver_syevj() argument
1425 AT_DISPATCH_FLOATING_AND_COMPLEX_TYPES(eigenvectors.scalar_type(), "linalg_eigh_cuda", [&] { in linalg_eigh_cusolver_syevj()
1426 apply_syevj<scalar_t>(eigenvalues, eigenvectors, infos, upper, compute_eigenvectors); in linalg_eigh_cusolver_syevj()
1430 …_eigh_cusolver_syevj_batched(const Tensor& eigenvalues, const Tensor& eigenvectors, const Tensor& … in linalg_eigh_cusolver_syevj_batched() argument
1431 AT_DISPATCH_FLOATING_AND_COMPLEX_TYPES(eigenvectors.scalar_type(), "linalg_eigh_cuda", [&] { in linalg_eigh_cusolver_syevj_batched()
1432 apply_syevj_batched<scalar_t>(eigenvalues, eigenvectors, infos, upper, compute_eigenvectors); in linalg_eigh_cusolver_syevj_batched()
1436 void linalg_eigh_cusolver(const Tensor& eigenvalues, const Tensor& eigenvectors, const Tensor& info… in linalg_eigh_cusolver() argument
[all …]
/aosp_15_r20/external/tensorflow/tensorflow/core/api_def/base_api/
H A Dapi_def_Eig.pbtxt21 Eigenvectors. Shape is `[N, N]`.
27 If `True` then eigenvectors will be computed and returned in `v`.
33 Computes the eigenvalues and (optionally) right eigenvectors of each inner matrix in
40 # v is a tensor of eigenvectors.
H A Dapi_def_SelfAdjointEigV2.pbtxt21 Eigenvectors. Shape is `[N, N]`.
27 If `True` then eigenvectors will be computed and returned in `v`.
33 Computes the eigenvalues and (optionally) eigenvectors of each inner matrix in
40 # v is a tensor of eigenvectors.
/aosp_15_r20/external/tensorflow/tensorflow/python/ops/
H A Dlinalg_ops.py384 and eigenvectors for a non-Hermitian matrix in general are complex. The
385 eigenvectors are not guaranteed to be linearly independent.
387 Computes the eigenvalues and right eigenvectors of the innermost
399 v: Eigenvectors. Shape is `[..., N, N]`. The columns of the inner most
400 matrices contain eigenvectors of the corresponding matrices in `tensor`
418 eigenvectors are used to compute the gradient w.r.t. the eigenvalues. See
443 Computes the eigenvalues and eigenvectors of the innermost N-by-N matrices
454 v: Eigenvectors. Shape is `[..., N, N]`. The columns of the inner most
455 matrices contain eigenvectors of the corresponding matrices in `tensor`
470 eigenvectors are used to compute the gradient w.r.t. the eigenvalues. See
/aosp_15_r20/external/pytorch/aten/src/ATen/native/
H A DBatchLinearAlgebraKernel.cpp140 Computes the eigenvalues and eigenvectors of n-by-n matrix 'input'.
154 char jobvl = 'N'; // only right eigenvectors are computed in apply_linalg_eig()
164 scalar_t* lvectors_data = nullptr; // only right eigenvectors are computed in apply_linalg_eig()
197 void linalg_eig_kernel(Tensor& eigenvalues, Tensor& eigenvectors, Tensor& infos, const Tensor& inpu… in linalg_eig_kernel() argument
200 // the content of eigenvalues, eigenvectors and infos is overwritten by 'apply_linalg_eig' in linalg_eig_kernel()
208 …apply_linalg_eig<scalar_t>(eigenvalues, eigenvectors, input_working_copy, infos, compute_eigenvect… in linalg_eig_kernel()
213 Computes eigenvalues and eigenvectors of the input that is stored initially in 'vectors'.
218 'compute_eigenvectors' controls whether eigenvectors should be computed.
294 void linalg_eigh_kernel(const Tensor& eigenvalues, const Tensor& eigenvectors, const Tensor& infos,… in linalg_eigh_kernel() argument
297 // content of eigenvalues, eigenvectors and infos is overwritten by in linalg_eigh_kernel()
[all …]
/aosp_15_r20/external/tensorflow/tensorflow/python/kernel_tests/linalg/
H A Dself_adjoint_eig_op_test.py101 """Equilibrate the phase of the Eigenvectors in the columns of `x` and `y`.
103 Eigenvectors are only unique up to an arbitrary phase. This function rotates x
108 x: `np.ndarray` with Eigenvectors
109 y: `np.ndarray` with Eigenvectors
214 # (complex) Eigenvectors are only unique up to an arbitrary phase

1234