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11 #ifndef EIGEN_SELFADJOINTEIGENSOLVER_H
12 #define EIGEN_SELFADJOINTEIGENSOLVER_H
18 template<
typename _MatrixType>
19 class GeneralizedSelfAdjointEigenSolver;
24 template<
typename MatrixType,
typename DiagType,
typename SubDiagType>
82 Size = MatrixType::RowsAtCompileTime,
171 template<
typename InputType>
214 template<
typename InputType>
411 template<
int StorageOrder,
typename RealScalar,
typename Scalar,
typename Index>
416 template<
typename MatrixType>
417 template<
typename InputType>
422 check_template_parameters();
430 &&
"invalid option parameter");
433 m_eivalues.resize(
n,1);
438 m_eivalues.coeffRef(0,0) =
numext::real(m_eivec.coeff(0,0));
439 if(computeEigenvectors)
440 m_eivec.setOnes(
n,
n);
442 m_isInitialized =
true;
443 m_eigenvectorsOk = computeEigenvectors;
456 m_subdiag.resize(
n-1);
457 m_hcoeffs.resize(
n-1);
465 m_isInitialized =
true;
466 m_eigenvectorsOk = computeEigenvectors;
470 template<
typename MatrixType>
479 if (computeEigenvectors)
481 m_eivec.setIdentity(
diag.size(),
diag.size());
485 m_isInitialized =
true;
486 m_eigenvectorsOk = computeEigenvectors;
502 template<
typename MatrixType,
typename DiagType,
typename SubDiagType>
525 const RealScalar scaled_subdiag = precision_inv * subdiag[
i];
542 if(
iter > maxIterations *
n)
break;
545 while (start>0 && subdiag[start-1]!=0)
548 internal::tridiagonal_qr_step<MatrixType::Flags&RowMajorBit ? RowMajor : ColMajor>(
diag.data(), subdiag.data(), start,
end, computeEigenvectors ? eivec.data() : (
Scalar*)0,
n);
550 if (
iter <= maxIterations *
n)
563 diag.segment(
i,
n-
i).minCoeff(&k);
567 if(computeEigenvectors)
568 eivec.col(
i).swap(eivec.col(k+
i));
575 template<
typename SolverType,
int Size,
bool IsComplex>
struct direct_selfadjoint_eigenvalues
607 Scalar c0 =
m(0,0)*
m(1,1)*
m(2,2) +
Scalar(2)*
m(1,0)*
m(2,0)*
m(2,1) -
m(0,0)*
m(2,1)*
m(2,1) -
m(1,1)*
m(2,0)*
m(2,0) -
m(2,2)*
m(1,0)*
m(1,0);
608 Scalar c1 =
m(0,0)*
m(1,1) -
m(1,0)*
m(1,0) +
m(0,0)*
m(2,2) -
m(2,0)*
m(2,0) +
m(1,1)*
m(2,2) -
m(2,1)*
m(2,1);
619 Scalar q = a_over_3*a_over_3*a_over_3 - half_b*half_b;
628 roots(0) = c2_over_3 - rho*(cos_theta + s_sqrt3*sin_theta);
629 roots(1) = c2_over_3 - rho*(cos_theta - s_sqrt3*sin_theta);
630 roots(2) = c2_over_3 +
Scalar(2)*rho*cos_theta;
640 mat.diagonal().cwiseAbs().maxCoeff(&
i0);
643 representative =
mat.col(
i0);
646 n0 = (c0 = representative.cross(
mat.col((
i0+1)%3))).squaredNorm();
647 n1 = (
c1 = representative.cross(
mat.col((
i0+2)%3))).squaredNorm();
660 &&
"invalid option parameter");
669 MatrixType scaledMat =
mat.template selfadjointView<Lower>();
670 scaledMat.diagonal().array() -= shift;
678 if(computeEigenvectors)
683 eivecs.setIdentity();
702 tmp.diagonal().array () -=
eivals(k);
704 extract_kernel(tmp, eivecs.col(k), eivecs.col(
l));
712 eivecs.col(
l) -= eivecs.col(k).dot(eivecs.col(
l))*eivecs.col(
l);
713 eivecs.col(
l).normalize();
718 tmp.diagonal().array () -=
eivals(
l);
721 extract_kernel(tmp, eivecs.col(
l),
dummy);
725 eivecs.col(1) = eivecs.col(2).cross(eivecs.col(0)).normalized();
734 solver.m_isInitialized =
true;
735 solver.m_eigenvectorsOk = computeEigenvectors;
740 template<
typename SolverType>
767 &&
"invalid option parameter");
776 scaledMat.coeffRef(0,1) =
mat.coeff(1,0);
777 scaledMat.diagonal().array() -= shift;
786 if(computeEigenvectors)
790 eivecs.setIdentity();
794 scaledMat.diagonal().array () -=
eivals(1);
800 eivecs.col(1) << -scaledMat(1,0), scaledMat(0,0);
805 eivecs.col(1) << -scaledMat(1,1), scaledMat(1,0);
809 eivecs.col(0) << eivecs.col(1).unitOrthogonal();
818 solver.m_isInitialized =
true;
819 solver.m_eigenvectorsOk = computeEigenvectors;
825 template<
typename MatrixType>
837 template<
int StorageOrder,
typename RealScalar,
typename Scalar,
typename Index>
869 rot.makeGivens(
x,
z);
877 subdiag[k] =
rot.c() * sdk -
rot.s() * dkp1;
880 subdiag[k - 1] =
rot.c() * subdiag[k-1] -
rot.s() *
z;
886 z = -
rot.s() * subdiag[k+1];
887 subdiag[k + 1] =
rot.c() * subdiag[k+1];
895 q.applyOnTheRight(k,k+1,
rot);
904 #endif // EIGEN_SELFADJOINTEIGENSOLVER_H
EIGEN_DEVICE_FUNC SelfAdjointEigenSolver & computeDirect(const MatrixType &matrix, int options=ComputeEigenvectors)
Computes eigendecomposition of given matrix using a closed-form algorithm.
#define EIGEN_DEVICE_FUNC
Namespace containing all symbols from the Eigen library.
SolverType::EigenvectorsType EigenvectorsType
static EIGEN_DEVICE_FUNC void run(SolverType &eig, const typename SolverType::MatrixType &A, int options)
EIGEN_DEVICE_FUNC Derived & derived()
const AutoDiffScalar< Matrix< typename internal::traits< typename internal::remove_all< DerTypeA >::type >::Scalar, Dynamic, 1 > > atan2(const AutoDiffScalar< DerTypeA > &a, const AutoDiffScalar< DerTypeB > &b)
Tridiagonal decomposition of a selfadjoint matrix.
#define EIGEN_USING_STD(FUNC)
Array< double, 1, 3 > e(1./3., 0.5, 2.)
SolverType::EigenvectorsType EigenvectorsType
Jet< T, N > sin(const Jet< T, N > &f)
SolverType::Scalar Scalar
SelfAdjointEigenSolver & computeFromTridiagonal(const RealVectorType &diag, const SubDiagonalType &subdiag, int options=ComputeEigenvectors)
Computes the eigen decomposition from a tridiagonal symmetric matrix.
static EIGEN_DEVICE_FUNC void computeRoots(const MatrixType &m, VectorType &roots)
EIGEN_DEVICE_FUNC ComputationInfo computeFromTridiagonal_impl(DiagType &diag, SubDiagType &subdiag, const Index maxIterations, bool computeEigenvectors, MatrixType &eivec)
Matrix diag(const std::vector< Matrix > &Hs)
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SolverType::RealVectorType VectorType
NumTraits< Scalar >::Real RealScalar
Real scalar type for _MatrixType.
TridiagonalizationType::SubDiagonalType SubDiagonalType
EIGEN_DEVICE_FUNC SelfAdjointEigenSolver & compute(const EigenBase< InputType > &matrix, int options=ComputeEigenvectors)
Computes eigendecomposition of given matrix.
const EIGEN_DEVICE_FUNC RealVectorType & eigenvalues() const
Returns the eigenvalues of given matrix.
SolverType::Scalar Scalar
cout<< "Here is the matrix m:"<< endl<< m<< endl;Matrix< ptrdiff_t, 3, 1 > res
Rotation given by a cosine-sine pair.
static EIGEN_DEVICE_FUNC void check_template_parameters()
int EIGEN_BLAS_FUNC() rot(int *n, RealScalar *px, int *incx, RealScalar *py, int *incy, RealScalar *pc, RealScalar *ps)
BiCGSTAB< SparseMatrix< double > > solver
TridiagonalizationType::SubDiagonalType m_subdiag
Jet< T, N > cos(const Jet< T, N > &f)
SolverType::RealVectorType VectorType
EIGEN_DEVICE_FUNC ComputationInfo info() const
Reports whether previous computation was successful.
static EIGEN_DEVICE_FUNC void run(SolverType &solver, const MatrixType &mat, int options)
internal::plain_col_type< MatrixType, RealScalar >::type RealVectorType
Type for vector of eigenvalues as returned by eigenvalues().
SolverType::MatrixType MatrixType
Matrix< Scalar, Size, Size, ColMajor, MaxColsAtCompileTime, MaxColsAtCompileTime > EigenvectorsType
const EIGEN_DEVICE_FUNC EigenvectorsType & eigenvectors() const
Returns the eigenvectors of given matrix.
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Computes eigenvalues and eigenvectors of selfadjoint matrices.
EIGEN_DEVICE_FUNC const Scalar & q
static const Line3 l(Rot3(), 1, 1)
EIGEN_DEVICE_FUNC MatrixType operatorInverseSqrt() const
Computes the inverse square root of the matrix.
SelfAdjointEigenSolver< PlainMatrixType > eig(mat, computeVectors?ComputeEigenvectors:EigenvaluesOnly)
A matrix or vector expression mapping an existing array of data.
TridiagonalizationType::CoeffVectorType m_hcoeffs
EIGEN_DEVICE_FUNC void tridiagonalization_inplace(MatrixType &matA, CoeffVectorType &hCoeffs)
SolverType::MatrixType MatrixType
Map< Matrix< T, Dynamic, Dynamic, ColMajor >, 0, OuterStride<> > matrix(T *data, int rows, int cols, int stride)
NumTraits< Scalar >::Real RealScalar
EIGEN_DEVICE_FUNC MatrixType operatorSqrt() const
Computes the positive-definite square root of the matrix.
EIGEN_DEVICE_FUNC bool abs2(bool x)
A matrix or vector expression mapping an existing expression.
EIGEN_STRONG_INLINE void swap(T &a, T &b)
static EIGEN_DEVICE_FUNC bool extract_kernel(MatrixType &mat, Ref< VectorType > res, Ref< VectorType > representative)
iterator iter(handle obj)
EIGEN_DEVICE_FUNC SelfAdjointEigenSolver(Index size)
Constructor, pre-allocates memory for dynamic-size matrices.
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE internal::enable_if< NumTraits< T >::IsSigned||NumTraits< T >::IsComplex, typename NumTraits< T >::Real >::type abs(const T &x)
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T maxi(const T &x, const T &y)
static const int m_maxIterations
Maximum number of iterations.
static const EIGEN_DEPRECATED end_t end
static EIGEN_DEVICE_FUNC void run(SolverType &solver, const MatrixType &mat, int options)
A triangularView< Lower >().adjoint().solveInPlace(B)
EIGEN_DEVICE_FUNC SelfAdjointEigenSolver(const EigenBase< InputType > &matrix, int options=ComputeEigenvectors)
Constructor; computes eigendecomposition of given matrix.
static EIGEN_DEVICE_FUNC void tridiagonal_qr_step(RealScalar *diag, RealScalar *subdiag, Index start, Index end, Scalar *matrixQ, Index n)
Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
Jet< T, N > sqrt(const Jet< T, N > &f)
RealVectorType m_eivalues
void computeRoots(const Matrix &m, Roots &roots)
MatrixType::Scalar Scalar
Scalar type for matrices of type _MatrixType.
static EIGEN_DEVICE_FUNC void computeRoots(const MatrixType &m, VectorType &roots)
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
#define EIGEN_STATIC_ASSERT_NON_INTEGER(TYPE)
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autogenerated on Fri Nov 1 2024 03:35:03