12#ifndef EIGEN_COMPLEX_EIGEN_SOLVER_H
13#define EIGEN_COMPLEX_EIGEN_SOLVER_H
15#include "./ComplexSchur.h"
17#include "./InternalHeaderCheck.h"
55 RowsAtCompileTime = MatrixType::RowsAtCompileTime,
56 ColsAtCompileTime = MatrixType::ColsAtCompileTime,
57 Options = MatrixType::Options,
58 MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
59 MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
63 typedef typename MatrixType::Scalar
Scalar;
98 m_isInitialized(false),
99 m_eigenvectorsOk(false),
110 : m_eivec(size, size),
113 m_isInitialized(false),
114 m_eigenvectorsOk(false),
127 template<
typename InputType>
129 : m_eivec(matrix.rows(),matrix.cols()),
130 m_eivalues(matrix.cols()),
131 m_schur(matrix.rows()),
132 m_isInitialized(false),
133 m_eigenvectorsOk(false),
134 m_matX(matrix.rows(),matrix.cols())
161 eigen_assert(m_isInitialized &&
"ComplexEigenSolver is not initialized.");
162 eigen_assert(m_eigenvectorsOk &&
"The eigenvectors have not been computed together with the eigenvalues.");
186 eigen_assert(m_isInitialized &&
"ComplexEigenSolver is not initialized.");
214 template<
typename InputType>
223 eigen_assert(m_isInitialized &&
"ComplexEigenSolver is not initialized.");
224 return m_schur.info();
230 m_schur.setMaxIterations(maxIters);
237 return m_schur.getMaxIterations();
242 EIGEN_STATIC_ASSERT_NON_INTEGER(
Scalar)
247 bool m_isInitialized;
248 bool m_eigenvectorsOk;
252 void doComputeEigenvectors(RealScalar matrixnorm);
253 void sortEigenvalues(
bool computeEigenvectors);
257template<
typename MatrixType>
258template<
typename InputType>
259ComplexEigenSolver<MatrixType>&
263 eigen_assert(matrix.cols() == matrix.rows());
267 m_schur.compute(matrix.derived(), computeEigenvectors);
271 m_eivalues = m_schur.matrixT().diagonal();
272 if(computeEigenvectors)
273 doComputeEigenvectors(m_schur.matrixT().norm());
274 sortEigenvalues(computeEigenvectors);
277 m_isInitialized =
true;
278 m_eigenvectorsOk = computeEigenvectors;
283template<
typename MatrixType>
284void ComplexEigenSolver<MatrixType>::doComputeEigenvectors(RealScalar matrixnorm)
286 const Index n = m_eivalues.size();
288 matrixnorm = numext::maxi(matrixnorm,(std::numeric_limits<RealScalar>::min)());
292 m_matX = EigenvectorType::Zero(n, n);
293 for(
Index k=n-1 ; k>=0 ; k--)
295 m_matX.coeffRef(k,k) = ComplexScalar(1.0,0.0);
297 for(
Index i=k-1 ; i>=0 ; i--)
299 m_matX.coeffRef(i,k) = -m_schur.matrixT().coeff(i,k);
301 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();
302 ComplexScalar z = m_schur.matrixT().coeff(i,i) - m_schur.matrixT().coeff(k,k);
303 if(z==ComplexScalar(0))
307 numext::real_ref(z) = NumTraits<RealScalar>::epsilon() * matrixnorm;
309 m_matX.coeffRef(i,k) = m_matX.coeff(i,k) / z;
314 m_eivec.noalias() = m_schur.matrixU() * m_matX;
316 for(
Index k=0 ; k<n ; k++)
318 m_eivec.col(k).normalize();
323template<
typename MatrixType>
324void ComplexEigenSolver<MatrixType>::sortEigenvalues(
bool computeEigenvectors)
326 const Index n = m_eivalues.size();
327 for (
Index i=0; i<n; i++)
330 m_eivalues.cwiseAbs().tail(n-i).minCoeff(&k);
334 std::swap(m_eivalues[k],m_eivalues[i]);
335 if(computeEigenvectors)
336 m_eivec.col(i).swap(m_eivec.col(k));
Computes eigenvalues and eigenvectors of general complex matrices.
Definition: ComplexEigenSolver.h:48
ComplexEigenSolver & compute(const EigenBase< InputType > &matrix, bool computeEigenvectors=true)
Computes eigendecomposition of given matrix.
std::complex< RealScalar > ComplexScalar
Complex scalar type for MatrixType.
Definition: ComplexEigenSolver.h:73
ComplexEigenSolver(Index size)
Default Constructor with memory preallocation.
Definition: ComplexEigenSolver.h:109
Index getMaxIterations()
Returns the maximum number of iterations.
Definition: ComplexEigenSolver.h:235
ComplexEigenSolver()
Default constructor.
Definition: ComplexEigenSolver.h:94
MatrixType::Scalar Scalar
Scalar type for matrices of type MatrixType.
Definition: ComplexEigenSolver.h:63
ComplexEigenSolver & setMaxIterations(Index maxIters)
Sets the maximum number of iterations allowed.
Definition: ComplexEigenSolver.h:228
ComplexEigenSolver(const EigenBase< InputType > &matrix, bool computeEigenvectors=true)
Constructor; computes eigendecomposition of given matrix.
Definition: ComplexEigenSolver.h:128
const EigenvectorType & eigenvectors() const
Returns the eigenvectors of given matrix.
Definition: ComplexEigenSolver.h:159
Eigen::Index Index
Definition: ComplexEigenSolver.h:65
Matrix< ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime > EigenvectorType
Type for matrix of eigenvectors as returned by eigenvectors().
Definition: ComplexEigenSolver.h:87
MatrixType_ MatrixType
Synonym for the template parameter MatrixType_.
Definition: ComplexEigenSolver.h:52
const EigenvalueType & eigenvalues() const
Returns the eigenvalues of given matrix.
Definition: ComplexEigenSolver.h:184
ComputationInfo info() const
Reports whether previous computation was successful.
Definition: ComplexEigenSolver.h:221
Matrix< ComplexScalar, ColsAtCompileTime, 1, Options &(~RowMajor), MaxColsAtCompileTime, 1 > EigenvalueType
Type for vector of eigenvalues as returned by eigenvalues().
Definition: ComplexEigenSolver.h:80
Performs a complex Schur decomposition of a real or complex square matrix.
Definition: ComplexSchur.h:54
The matrix class, also used for vectors and row-vectors.
Definition: Matrix.h:182
ComputationInfo
Definition: Constants.h:442
@ Success
Definition: Constants.h:444
Namespace containing all symbols from the Eigen library.
Definition: B01_Experimental.dox:1
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:59
Definition: EigenBase.h:32
Derived & derived()
Definition: EigenBase.h:48
Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
Definition: NumTraits.h:235