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https://gitlab.com/libeigen/eigen.git
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* Make HouseholderSequence::evalTo works in place
* Clean a bit the Triadiagonalization making sure it the inplace function really works inplace ;), and that only the lower triangular part of the matrix is referenced. * Remove the Tridiagonalization member object of SelfAdjointEigenSolver exploiting the in place capability of HouseholdeSequence. * Update unit test to check SelfAdjointEigenSolver only consider the lower triangular part.
This commit is contained in:
Gael Guennebaud
parent
d2d7465bcf
commit
469382407c
@ -38,7 +38,7 @@
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*
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* \tparam _MatrixType the type of the matrix of which we are computing the
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* eigendecomposition; this is expected to be an instantiation of the Matrix
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* class template. Currently, only real matrices are supported.
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* class template.
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*
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* A matrix \f$ A \f$ is selfadjoint if it equals its adjoint. For real
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* matrices, this means that the matrix is symmetric: it equals its
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@ -55,6 +55,8 @@
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* faster and more accurate than the general purpose eigenvalue algorithms
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* implemented in EigenSolver and ComplexEigenSolver.
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*
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* Only the \b lower \b triangular \b part of the input matrix is referenced.
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*
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* This class can also be used to solve the generalized eigenvalue problem
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* \f$ Av = \lambda Bv \f$. In this case, the matrix \f$ A \f$ should be
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* selfadjoint and the matrix \f$ B \f$ should be positive definite.
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@ -117,7 +119,6 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
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SelfAdjointEigenSolver()
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: m_eivec(),
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m_eivalues(),
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m_tridiag(),
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m_subdiag(),
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m_isInitialized(false)
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{ }
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@ -138,7 +139,6 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
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SelfAdjointEigenSolver(Index size)
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: m_eivec(size, size),
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m_eivalues(size),
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m_tridiag(size),
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m_subdiag(size > 1 ? size - 1 : 1),
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m_isInitialized(false)
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{}
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@ -146,7 +146,7 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
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/** \brief Constructor; computes eigendecomposition of given matrix.
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*
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* \param[in] matrix Selfadjoint matrix whose eigendecomposition is to
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* be computed.
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* be computed. Only the lower triangular part of the matrix is referenced.
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* \param[in] computeEigenvectors If true, both the eigenvectors and the
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* eigenvalues are computed; if false, only the eigenvalues are
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* computed.
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@ -164,7 +164,6 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
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SelfAdjointEigenSolver(const MatrixType& matrix, bool computeEigenvectors = true)
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: m_eivec(matrix.rows(), matrix.cols()),
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m_eivalues(matrix.cols()),
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m_tridiag(matrix.rows()),
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m_subdiag(matrix.rows() > 1 ? matrix.rows() - 1 : 1),
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m_isInitialized(false)
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{
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@ -174,7 +173,9 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
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/** \brief Constructor; computes generalized eigendecomposition of given matrix pencil.
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*
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* \param[in] matA Selfadjoint matrix in matrix pencil.
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* Only the lower triangular part of the matrix is referenced.
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* \param[in] matB Positive-definite matrix in matrix pencil.
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* Only the lower triangular part of the matrix is referenced.
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* \param[in] computeEigenvectors If true, both the eigenvectors and the
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* eigenvalues are computed; if false, only the eigenvalues are
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* computed.
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@ -196,7 +197,6 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
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SelfAdjointEigenSolver(const MatrixType& matA, const MatrixType& matB, bool computeEigenvectors = true)
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: m_eivec(matA.rows(), matA.cols()),
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m_eivalues(matA.cols()),
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m_tridiag(matA.rows()),
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m_subdiag(matA.rows() > 1 ? matA.rows() - 1 : 1),
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m_isInitialized(false)
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{
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@ -206,7 +206,7 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
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/** \brief Computes eigendecomposition of given matrix.
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*
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* \param[in] matrix Selfadjoint matrix whose eigendecomposition is to
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* be computed.
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* be computed. Only the lower triangular part of the matrix is referenced.
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* \param[in] computeEigenvectors If true, both the eigenvectors and the
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* eigenvalues are computed; if false, only the eigenvalues are
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* computed.
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@ -240,7 +240,9 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
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/** \brief Computes generalized eigendecomposition of given matrix pencil.
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*
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* \param[in] matA Selfadjoint matrix in matrix pencil.
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* Only the lower triangular part of the matrix is referenced.
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* \param[in] matB Positive-definite matrix in matrix pencil.
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* Only the lower triangular part of the matrix is referenced.
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* \param[in] computeEigenvectors If true, both the eigenvectors and the
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* eigenvalues are computed; if false, only the eigenvalues are
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* computed.
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@ -386,7 +388,6 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
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protected:
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MatrixType m_eivec;
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RealVectorType m_eivalues;
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TridiagonalizationType m_tridiag;
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typename TridiagonalizationType::SubDiagonalType m_subdiag;
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ComputationInfo m_info;
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bool m_isInitialized;
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@ -418,8 +419,6 @@ SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>::compute(
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assert(matrix.cols() == matrix.rows());
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Index n = matrix.cols();
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m_eivalues.resize(n,1);
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if(computeEigenvectors)
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m_eivec.resize(n,n);
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if(n==1)
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{
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@ -432,12 +431,13 @@ SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>::compute(
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return *this;
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}
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m_tridiag.compute(matrix);
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// declare some aliases
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RealVectorType& diag = m_eivalues;
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diag = m_tridiag.diagonal();
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m_subdiag = m_tridiag.subDiagonal();
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if (computeEigenvectors)
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m_eivec = m_tridiag.matrixQ();
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MatrixType& mat = m_eivec;
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mat = matrix;
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m_subdiag.resize(n-1);
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ei_tridiagonalization_inplace(mat, diag, m_subdiag, computeEigenvectors);
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Index end = n-1;
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Index start = 0;
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@ -487,7 +487,7 @@ SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>::compute(
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{
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std::swap(m_eivalues[i], m_eivalues[k+i]);
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if(computeEigenvectors)
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m_eivec.col(i).swap(m_eivec.col(k+i));
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m_eivec.col(i).swap(m_eivec.col(k+i));
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}
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}
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}
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@ -507,7 +507,7 @@ compute(const MatrixType& matA, const MatrixType& matB, bool computeEigenvectors
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LLT<MatrixType> cholB(matB);
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// compute C = inv(L) A inv(L')
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MatrixType matC = matA;
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MatrixType matC = matA.template selfadjointView<Lower>();
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cholB.matrixL().template solveInPlace<OnTheLeft>(matC);
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cholB.matrixU().template solveInPlace<OnTheRight>(matC);
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@ -154,7 +154,7 @@ template<typename _MatrixType> class Tridiagonalization
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{
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m_matrix = matrix;
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m_hCoeffs.resize(matrix.rows()-1, 1);
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_compute(m_matrix, m_hCoeffs);
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ei_tridiagonalization_inplace(m_matrix, m_hCoeffs);
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m_isInitialized = true;
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return *this;
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}
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@ -285,43 +285,6 @@ template<typename _MatrixType> class Tridiagonalization
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*/
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const SubDiagonalReturnType subDiagonal() const;
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/** \brief Performs a full decomposition in place
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*
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* \param[in,out] mat On input, the selfadjoint matrix whose tridiagonal
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* decomposition is to be computed. On output, the orthogonal matrix Q
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* in the decomposition if \p extractQ is true.
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* \param[out] diag The diagonal of the tridiagonal matrix T in the
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* decomposition.
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* \param[out] subdiag The subdiagonal of the tridiagonal matrix T in
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* the decomposition.
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* \param[in] extractQ If true, the orthogonal matrix Q in the
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* decomposition is computed and stored in \p mat.
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*
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* Compute the tridiagonal matrix of \p mat in place. The tridiagonal
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* matrix T is passed to the output parameters \p diag and \p subdiag. If
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* \p extractQ is true, then the orthogonal matrix Q is passed to \p mat.
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*
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* The vectors \p diag and \p subdiag are not resized. The function
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* assumes that they are already of the correct size. The length of the
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* vector \p diag should equal the number of rows in \p mat, and the
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* length of the vector \p subdiag should be one left.
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*
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* This implementation contains an optimized path for real 3-by-3 matrices
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* which is especially useful for plane fitting.
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*
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* \note Notwithstanding the name, the current implementation copies
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* \p mat to a temporary matrix and uses that matrix to compute the
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* decomposition.
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*
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* Example (this uses the same matrix as the example in
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* Tridiagonalization(const MatrixType&)):
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* \include Tridiagonalization_decomposeInPlace.cpp
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* Output: \verbinclude Tridiagonalization_decomposeInPlace.out
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*
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* \sa Tridiagonalization(const MatrixType&), compute()
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*/
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static void decomposeInPlace(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ = true);
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protected:
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static void _compute(MatrixType& matA, CoeffVectorType& hCoeffs);
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@ -368,21 +331,36 @@ Tridiagonalization<MatrixType>::matrixT() const
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}
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/** \internal
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* Performs a tridiagonal decomposition of \a matA in place.
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* Performs a tridiagonal decomposition of the selfadjoint matrix \a matA in-place.
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*
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* \param matA the input selfadjoint matrix
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* \param hCoeffs returned Householder coefficients
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* \param[in,out] matA On input the selfadjoint matrix. Only the \b lower triangular part is referenced.
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* On output, the strict upper part is left unchanged, and the lower triangular part
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* represents the T and Q matrices in packed format has detailed below.
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* \param[out] hCoeffs returned Householder coefficients (see below)
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*
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* The result is written in the lower triangular part of \a matA.
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* On output, the tridiagonal selfadjoint matrix T is stored in the diagonal
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* and lower sub-diagonal of the matrix \a matA.
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* The unitary matrix Q is represented in a compact way as a product of
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* Householder reflectors \f$ H_i \f$ such that:
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* \f$ Q = H_{N-1} \ldots H_1 H_0 \f$.
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* The Householder reflectors are defined as
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* \f$ H_i = (I - h_i v_i v_i^T) \f$
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* where \f$ h_i = hCoeffs[i]\f$ is the \f$ i \f$th Householder coefficient and
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* \f$ v_i \f$ is the Householder vector defined by
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* \f$ v_i = [ 0, \ldots, 0, 1, matA(i+2,i), \ldots, matA(N-1,i) ]^T \f$.
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*
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* Implemented from Golub's "Matrix Computations", algorithm 8.3.1.
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*
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* \sa packedMatrix()
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* \sa Tridiagonalization::packedMatrix()
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*/
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template<typename MatrixType>
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void Tridiagonalization<MatrixType>::_compute(MatrixType& matA, CoeffVectorType& hCoeffs)
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template<typename MatrixType, typename CoeffVectorType>
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void ei_tridiagonalization_inplace(MatrixType& matA, CoeffVectorType& hCoeffs)
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{
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assert(matA.rows()==matA.cols());
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ei_assert(matA.rows()==matA.cols());
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ei_assert(matA.rows()==hCoeffs.size()+1);
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typedef typename MatrixType::Index Index;
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typedef typename MatrixType::Scalar Scalar;
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typedef typename MatrixType::RealScalar RealScalar;
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Index n = matA.rows();
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for (Index i = 0; i<n-1; ++i)
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{
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@ -408,67 +386,139 @@ void Tridiagonalization<MatrixType>::_compute(MatrixType& matA, CoeffVectorType&
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}
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}
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template<typename MatrixType>
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void Tridiagonalization<MatrixType>::decomposeInPlace(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ)
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// forward declaration, implementation at the end of this file
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template<typename MatrixType, int Size=MatrixType::ColsAtCompileTime>
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struct ei_tridiagonalization_inplace_selector;
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/** \brief Performs a full tridiagonalization in place
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*
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* \param[in,out] mat On input, the selfadjoint matrix whose tridiagonal
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* decomposition is to be computed. Only the lower triangular part referenced.
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* The rest is left unchanged. On output, the orthogonal matrix Q
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* in the decomposition if \p extractQ is true.
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* \param[out] diag The diagonal of the tridiagonal matrix T in the
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* decomposition.
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* \param[out] subdiag The subdiagonal of the tridiagonal matrix T in
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* the decomposition.
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* \param[in] extractQ If true, the orthogonal matrix Q in the
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* decomposition is computed and stored in \p mat.
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*
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* Computes the tridiagonal decomposition of the selfadjoint matrix \p mat in place
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* such that \f$ mat = Q T Q^* \f$ where \f$ Q \f$ is unitary and \f$ T \f$ a real
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* symmetric tridiagonal matrix.
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*
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* The tridiagonal matrix T is passed to the output parameters \p diag and \p subdiag. If
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* \p extractQ is true, then the orthogonal matrix Q is passed to \p mat. Otherwise the lower
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* part of the matrix \p mat is destroyed.
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*
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* The vectors \p diag and \p subdiag are not resized. The function
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* assumes that they are already of the correct size. The length of the
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* vector \p diag should equal the number of rows in \p mat, and the
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* length of the vector \p subdiag should be one left.
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*
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* This implementation contains an optimized path for 3-by-3 matrices
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* which is especially useful for plane fitting.
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*
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* \note Currently, it requires two temporary vectors to hold the intermediate
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* Householder coefficients, and to reconstruct the matrix Q from the Householder
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* reflectors.
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*
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* Example (this uses the same matrix as the example in
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* Tridiagonalization::Tridiagonalization(const MatrixType&)):
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* \include Tridiagonalization_decomposeInPlace.cpp
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* Output: \verbinclude Tridiagonalization_decomposeInPlace.out
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*
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* \sa class Tridiagonalization
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*/
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template<typename MatrixType, typename DiagonalType, typename SubDiagonalType>
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void ei_tridiagonalization_inplace(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ)
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{
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typedef typename MatrixType::Index Index;
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Index n = mat.rows();
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ei_assert(mat.cols()==n && diag.size()==n && subdiag.size()==n-1);
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if (n==3 && (!NumTraits<Scalar>::IsComplex) )
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{
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_decomposeInPlace3x3(mat, diag, subdiag, extractQ);
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}
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else
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{
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Tridiagonalization tridiag(mat);
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diag = tridiag.diagonal();
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subdiag = tridiag.subDiagonal();
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if (extractQ)
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mat = tridiag.matrixQ();
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}
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ei_tridiagonalization_inplace_selector<MatrixType>::run(mat, diag, subdiag, extractQ);
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}
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/** \internal
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* Optimized path for 3x3 matrices.
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* General full tridiagonalization
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*/
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template<typename MatrixType, int Size>
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struct ei_tridiagonalization_inplace_selector
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{
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typedef typename Tridiagonalization<MatrixType>::CoeffVectorType CoeffVectorType;
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typedef typename Tridiagonalization<MatrixType>::HouseholderSequenceType HouseholderSequenceType;
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typedef typename MatrixType::Index Index;
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template<typename DiagonalType, typename SubDiagonalType>
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static void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ)
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{
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CoeffVectorType hCoeffs(mat.cols()-1);
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ei_tridiagonalization_inplace(mat,hCoeffs);
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diag = mat.diagonal().real();
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subdiag = mat.template diagonal<-1>().real();
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if(extractQ)
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mat = HouseholderSequenceType(mat, hCoeffs.conjugate(), false, mat.rows() - 1, 1);
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}
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};
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/** \internal
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* Specialization for 3x3 matrices.
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* Especially useful for plane fitting.
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*/
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template<typename MatrixType>
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void Tridiagonalization<MatrixType>::_decomposeInPlace3x3(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ)
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struct ei_tridiagonalization_inplace_selector<MatrixType,3>
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{
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diag[0] = ei_real(mat(0,0));
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RealScalar v1norm2 = ei_abs2(mat(0,2));
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if (ei_isMuchSmallerThan(v1norm2, RealScalar(1)))
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typedef typename MatrixType::Scalar Scalar;
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typedef typename MatrixType::RealScalar RealScalar;
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template<typename DiagonalType, typename SubDiagonalType>
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static void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ)
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{
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diag[1] = ei_real(mat(1,1));
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diag[2] = ei_real(mat(2,2));
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subdiag[0] = ei_real(mat(0,1));
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subdiag[1] = ei_real(mat(1,2));
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if (extractQ)
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mat.setIdentity();
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}
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else
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{
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RealScalar beta = ei_sqrt(ei_abs2(mat(0,1))+v1norm2);
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RealScalar invBeta = RealScalar(1)/beta;
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Scalar m01 = mat(0,1) * invBeta;
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Scalar m02 = mat(0,2) * invBeta;
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Scalar q = RealScalar(2)*m01*mat(1,2) + m02*(mat(2,2) - mat(1,1));
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diag[1] = ei_real(mat(1,1) + m02*q);
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diag[2] = ei_real(mat(2,2) - m02*q);
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subdiag[0] = beta;
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subdiag[1] = ei_real(mat(1,2) - m01 * q);
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if (extractQ)
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diag[0] = ei_real(mat(0,0));
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RealScalar v1norm2 = ei_abs2(mat(2,0));
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if (ei_isMuchSmallerThan(v1norm2, RealScalar(1)))
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{
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mat(0,0) = 1;
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mat(0,1) = 0;
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mat(0,2) = 0;
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mat(1,0) = 0;
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mat(1,1) = m01;
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mat(1,2) = m02;
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mat(2,0) = 0;
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mat(2,1) = m02;
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mat(2,2) = -m01;
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diag[1] = ei_real(mat(1,1));
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diag[2] = ei_real(mat(2,2));
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subdiag[0] = ei_real(mat(1,0));
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subdiag[1] = ei_real(mat(2,1));
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if (extractQ)
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mat.setIdentity();
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}
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else
|
||||
{
|
||||
RealScalar beta = ei_sqrt(ei_abs2(mat(1,0)) + v1norm2);
|
||||
RealScalar invBeta = RealScalar(1)/beta;
|
||||
Scalar m01 = ei_conj(mat(1,0)) * invBeta;
|
||||
Scalar m02 = ei_conj(mat(2,0)) * invBeta;
|
||||
Scalar q = RealScalar(2)*m01*ei_conj(mat(2,1)) + m02*(mat(2,2) - mat(1,1));
|
||||
diag[1] = ei_real(mat(1,1) + m02*q);
|
||||
diag[2] = ei_real(mat(2,2) - m02*q);
|
||||
subdiag[0] = beta;
|
||||
subdiag[1] = ei_real(ei_conj(mat(2,1)) - m01 * q);
|
||||
if (extractQ)
|
||||
{
|
||||
mat << 1, 0, 0,
|
||||
0, m01, m02,
|
||||
0, m02, -m01;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
/** \internal
|
||||
* Trivial specialization for 1x1 matrices
|
||||
*/
|
||||
template<typename MatrixType>
|
||||
struct ei_tridiagonalization_inplace_selector<MatrixType,1>
|
||||
{
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
|
||||
template<typename DiagonalType, typename SubDiagonalType>
|
||||
static void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType&, bool extractQ)
|
||||
{
|
||||
diag(0,0) = ei_real(mat(0,0));
|
||||
if(extractQ)
|
||||
mat(0,0) = Scalar(1);
|
||||
}
|
||||
};
|
||||
#endif // EIGEN_TRIDIAGONALIZATION_H
|
||||
|
||||
@ -160,18 +160,45 @@ template<typename VectorsType, typename CoeffsType, int Side> class HouseholderS
|
||||
template<typename DestType> void evalTo(DestType& dst) const
|
||||
{
|
||||
Index vecs = m_actualVectors;
|
||||
dst.setIdentity(rows(), rows());
|
||||
// FIXME find a way to pass this temporary if the user want to
|
||||
Matrix<Scalar, DestType::RowsAtCompileTime, 1,
|
||||
AutoAlign|ColMajor, DestType::MaxRowsAtCompileTime, 1> temp(rows());
|
||||
for(Index k = vecs-1; k >= 0; --k)
|
||||
AutoAlign|ColMajor, DestType::MaxRowsAtCompileTime, 1> temp(rows());
|
||||
if( ei_is_same_type<typename ei_cleantype<VectorsType>::type,DestType>::ret
|
||||
&& ei_extract_data(dst) == ei_extract_data(m_vectors))
|
||||
{
|
||||
Index cornerSize = rows() - k - m_shift;
|
||||
if(m_trans)
|
||||
dst.bottomRightCorner(cornerSize, cornerSize)
|
||||
.applyHouseholderOnTheRight(essentialVector(k), m_coeffs.coeff(k), &temp.coeffRef(0));
|
||||
else
|
||||
dst.bottomRightCorner(cornerSize, cornerSize)
|
||||
.applyHouseholderOnTheLeft(essentialVector(k), m_coeffs.coeff(k), &temp.coeffRef(0));
|
||||
// in-place
|
||||
dst.diagonal().setOnes();
|
||||
dst.template triangularView<StrictlyUpper>().setZero();
|
||||
for(Index k = vecs-1; k >= 0; --k)
|
||||
{
|
||||
Index cornerSize = rows() - k - m_shift;
|
||||
if(m_trans)
|
||||
dst.bottomRightCorner(cornerSize, cornerSize)
|
||||
.applyHouseholderOnTheRight(essentialVector(k), m_coeffs.coeff(k), &temp.coeffRef(0));
|
||||
else
|
||||
dst.bottomRightCorner(cornerSize, cornerSize)
|
||||
.applyHouseholderOnTheLeft(essentialVector(k), m_coeffs.coeff(k), &temp.coeffRef(0));
|
||||
|
||||
// clear the off diagonal vector
|
||||
dst.col(k).tail(rows()-k-1).setZero();
|
||||
}
|
||||
// clear the remaining columns if needed
|
||||
for(Index k = 0; k<cols()-vecs ; ++k)
|
||||
dst.col(k).tail(rows()-k-1).setZero();
|
||||
}
|
||||
else
|
||||
{
|
||||
dst.setIdentity(rows(), rows());
|
||||
for(Index k = vecs-1; k >= 0; --k)
|
||||
{
|
||||
Index cornerSize = rows() - k - m_shift;
|
||||
if(m_trans)
|
||||
dst.bottomRightCorner(cornerSize, cornerSize)
|
||||
.applyHouseholderOnTheRight(essentialVector(k), m_coeffs.coeff(k), &temp.coeffRef(0));
|
||||
else
|
||||
dst.bottomRightCorner(cornerSize, cornerSize)
|
||||
.applyHouseholderOnTheLeft(essentialVector(k), m_coeffs.coeff(k), &temp.coeffRef(0));
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
@ -50,10 +50,12 @@ template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m)
|
||||
MatrixType a = MatrixType::Random(rows,cols);
|
||||
MatrixType a1 = MatrixType::Random(rows,cols);
|
||||
MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1;
|
||||
symmA.template triangularView<StrictlyUpper>().setZero();
|
||||
|
||||
MatrixType b = MatrixType::Random(rows,cols);
|
||||
MatrixType b1 = MatrixType::Random(rows,cols);
|
||||
MatrixType symmB = b.adjoint() * b + b1.adjoint() * b1;
|
||||
symmB.template triangularView<StrictlyUpper>().setZero();
|
||||
|
||||
SelfAdjointEigenSolver<MatrixType> eiSymm(symmA);
|
||||
// generalized eigen pb
|
||||
@ -62,6 +64,9 @@ template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m)
|
||||
#ifdef HAS_GSL
|
||||
if (ei_is_same_type<RealScalar,double>::ret)
|
||||
{
|
||||
// restore symmA and symmB.
|
||||
symmA = MatrixType(symmA.template selfadjointView<Lower>());
|
||||
symmB = MatrixType(symmB.template selfadjointView<Lower>());
|
||||
typedef GslTraits<Scalar> Gsl;
|
||||
typename Gsl::Matrix gEvec=0, gSymmA=0, gSymmB=0;
|
||||
typename GslTraits<RealScalar>::Vector gEval=0;
|
||||
@ -103,7 +108,7 @@ template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m)
|
||||
#endif
|
||||
|
||||
VERIFY_IS_EQUAL(eiSymm.info(), Success);
|
||||
VERIFY((symmA * eiSymm.eigenvectors()).isApprox(
|
||||
VERIFY((symmA.template selfadjointView<Lower>() * eiSymm.eigenvectors()).isApprox(
|
||||
eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal(), largerEps));
|
||||
VERIFY_IS_APPROX(symmA.template selfadjointView<Lower>().eigenvalues(), eiSymm.eigenvalues());
|
||||
|
||||
@ -113,12 +118,12 @@ template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m)
|
||||
|
||||
// generalized eigen problem Ax = lBx
|
||||
VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
|
||||
VERIFY((symmA * eiSymmGen.eigenvectors()).isApprox(
|
||||
symmB * (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
|
||||
VERIFY((symmA.template selfadjointView<Lower>() * eiSymmGen.eigenvectors()).isApprox(
|
||||
symmB.template selfadjointView<Lower>() * (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
|
||||
|
||||
MatrixType sqrtSymmA = eiSymm.operatorSqrt();
|
||||
VERIFY_IS_APPROX(symmA, sqrtSymmA*sqrtSymmA);
|
||||
VERIFY_IS_APPROX(sqrtSymmA, symmA*eiSymm.operatorInverseSqrt());
|
||||
VERIFY_IS_APPROX(MatrixType(symmA.template selfadjointView<Lower>()), sqrtSymmA*sqrtSymmA);
|
||||
VERIFY_IS_APPROX(sqrtSymmA, symmA.template selfadjointView<Lower>()*eiSymm.operatorInverseSqrt());
|
||||
|
||||
MatrixType id = MatrixType::Identity(rows, cols);
|
||||
VERIFY_IS_APPROX(id.template selfadjointView<Lower>().operatorNorm(), RealScalar(1));
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user