12#ifndef EIGEN_COMPLEX_EIGEN_SOLVER_H
13#define EIGEN_COMPLEX_EIGEN_SOLVER_H
15#include "./ComplexSchur.h"
53 RowsAtCompileTime = MatrixType::RowsAtCompileTime,
54 ColsAtCompileTime = MatrixType::ColsAtCompileTime,
55 Options = MatrixType::Options,
56 MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
57 MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
61 typedef typename MatrixType::Scalar
Scalar;
62 typedef typename NumTraits<Scalar>::Real RealScalar;
96 m_isInitialized(false),
97 m_eigenvectorsOk(false),
108 : m_eivec(size, size),
111 m_isInitialized(false),
112 m_eigenvectorsOk(false),
125 template<
typename InputType>
127 : m_eivec(matrix.rows(),matrix.cols()),
128 m_eivalues(matrix.cols()),
129 m_schur(matrix.rows()),
130 m_isInitialized(false),
131 m_eigenvectorsOk(false),
132 m_matX(matrix.rows(),matrix.cols())
159 eigen_assert(m_isInitialized &&
"ComplexEigenSolver is not initialized.");
160 eigen_assert(m_eigenvectorsOk &&
"The eigenvectors have not been computed together with the eigenvalues.");
184 eigen_assert(m_isInitialized &&
"ComplexEigenSolver is not initialized.");
212 template<
typename InputType>
221 eigen_assert(m_isInitialized &&
"ComplexEigenSolver is not initialized.");
222 return m_schur.
info();
240 static void check_template_parameters()
242 EIGEN_STATIC_ASSERT_NON_INTEGER(
Scalar);
247 ComplexSchur<MatrixType> m_schur;
248 bool m_isInitialized;
249 bool m_eigenvectorsOk;
253 void doComputeEigenvectors(RealScalar matrixnorm);
254 void sortEigenvalues(
bool computeEigenvectors);
258template<
typename MatrixType>
259template<
typename InputType>
260ComplexEigenSolver<MatrixType>&
261ComplexEigenSolver<MatrixType>::compute(
const EigenBase<InputType>& matrix,
bool computeEigenvectors)
263 check_template_parameters();
266 eigen_assert(matrix.cols() == matrix.rows());
270 m_schur.compute(matrix.derived(), computeEigenvectors);
272 if(m_schur.info() == Success)
274 m_eivalues = m_schur.matrixT().diagonal();
275 if(computeEigenvectors)
276 doComputeEigenvectors(m_schur.matrixT().norm());
277 sortEigenvalues(computeEigenvectors);
280 m_isInitialized =
true;
281 m_eigenvectorsOk = computeEigenvectors;
286template<
typename MatrixType>
287void ComplexEigenSolver<MatrixType>::doComputeEigenvectors(RealScalar matrixnorm)
289 const Index n = m_eivalues.size();
291 matrixnorm = numext::maxi(matrixnorm,(std::numeric_limits<RealScalar>::min)());
295 m_matX = EigenvectorType::Zero(n, n);
296 for(Index k=n-1 ; k>=0 ; k--)
298 m_matX.coeffRef(k,k) = ComplexScalar(1.0,0.0);
300 for(Index i=k-1 ; i>=0 ; i--)
302 m_matX.coeffRef(i,k) = -m_schur.matrixT().coeff(i,k);
304 m_matX.coeffRef(i,k) -= (m_schur.matrixT().row(i).segment(i+1,k-i-1) * m_matX.col(k).segment(i+1,k-i-1)).value();
305 ComplexScalar z = m_schur.matrixT().coeff(i,i) - m_schur.matrixT().coeff(k,k);
306 if(z==ComplexScalar(0))
310 numext::real_ref(z) = NumTraits<RealScalar>::epsilon() * matrixnorm;
312 m_matX.coeffRef(i,k) = m_matX.coeff(i,k) / z;
317 m_eivec.noalias() = m_schur.matrixU() * m_matX;
319 for(Index k=0 ; k<n ; k++)
321 m_eivec.col(k).normalize();
326template<
typename MatrixType>
327void ComplexEigenSolver<MatrixType>::sortEigenvalues(
bool computeEigenvectors)
329 const Index n = m_eivalues.size();
330 for (Index i=0; i<n; i++)
333 m_eivalues.cwiseAbs().tail(n-i).minCoeff(&k);
337 std::swap(m_eivalues[k],m_eivalues[i]);
338 if(computeEigenvectors)
339 m_eivec.col(i).swap(m_eivec.col(k));
Computes eigenvalues and eigenvectors of general complex matrices.
Definition: ComplexEigenSolver.h:46
const EigenvalueType & eigenvalues() const
Returns the eigenvalues of given matrix.
Definition: ComplexEigenSolver.h:182
ComplexEigenSolver & setMaxIterations(Index maxIters)
Sets the maximum number of iterations allowed.
Definition: ComplexEigenSolver.h:226
ComplexEigenSolver()
Default constructor.
Definition: ComplexEigenSolver.h:92
std::complex< RealScalar > ComplexScalar
Complex scalar type for MatrixType.
Definition: ComplexEigenSolver.h:71
const EigenvectorType & eigenvectors() const
Returns the eigenvectors of given matrix.
Definition: ComplexEigenSolver.h:157
MatrixType::Scalar Scalar
Scalar type for matrices of type MatrixType.
Definition: ComplexEigenSolver.h:61
Matrix< ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime > EigenvectorType
Type for matrix of eigenvectors as returned by eigenvectors().
Definition: ComplexEigenSolver.h:85
ComplexEigenSolver(const EigenBase< InputType > &matrix, bool computeEigenvectors=true)
Constructor; computes eigendecomposition of given matrix.
Definition: ComplexEigenSolver.h:126
ComplexEigenSolver(Index size)
Default Constructor with memory preallocation.
Definition: ComplexEigenSolver.h:107
Eigen::Index Index
Definition: ComplexEigenSolver.h:63
Matrix< ComplexScalar, ColsAtCompileTime, 1, Options &(~RowMajor), MaxColsAtCompileTime, 1 > EigenvalueType
Type for vector of eigenvalues as returned by eigenvalues().
Definition: ComplexEigenSolver.h:78
ComputationInfo info() const
Reports whether previous computation was successful.
Definition: ComplexEigenSolver.h:219
_MatrixType MatrixType
Synonym for the template parameter _MatrixType.
Definition: ComplexEigenSolver.h:50
Index getMaxIterations()
Returns the maximum number of iterations.
Definition: ComplexEigenSolver.h:233
ComplexEigenSolver & compute(const EigenBase< InputType > &matrix, bool computeEigenvectors=true)
Computes eigendecomposition of given matrix.
Index getMaxIterations()
Returns the maximum number of iterations.
Definition: ComplexSchur.h:235
ComputationInfo info() const
Reports whether previous computation was successful.
Definition: ComplexSchur.h:217
ComplexSchur & setMaxIterations(Index maxIters)
Sets the maximum number of iterations allowed.
Definition: ComplexSchur.h:228
The matrix class, also used for vectors and row-vectors.
Definition: Matrix.h:180
ComputationInfo
Definition: Constants.h:440
Namespace containing all symbols from the Eigen library.
Definition: Core:141
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:74
Definition: EigenBase.h:30
Derived & derived()
Definition: EigenBase.h:46