Performs a complex Schur decomposition of a real or complex square matrix. More...

Public Types
enum	{ RowsAtCompileTime , ColsAtCompileTime , Options , MaxRowsAtCompileTime , MaxColsAtCompileTime }

typedef Matrix< ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime >	ComplexMatrixType
	Type for the matrices in the Schur decomposition. More...

typedef std::complex< RealScalar >	ComplexScalar
	Complex scalar type for `MatrixType_`. More...

typedef Eigen::Index	Index

typedef MatrixType_	MatrixType

typedef NumTraits< Scalar >::Real	RealScalar

typedef MatrixType::Scalar	Scalar
	Scalar type for matrices of type `MatrixType_`. More...

Public Member Functions
template<typename InputType >
	ComplexSchur (const EigenBase< InputType > &matrix, bool computeU=true)
	Constructor; computes Schur decomposition of given matrix. More...

	ComplexSchur (Index size=RowsAtCompileTime==Dynamic ? 1 :RowsAtCompileTime)
	Default constructor. More...

template<typename InputType >
ComplexSchur< MatrixType > &	compute (const EigenBase< InputType > &matrix, bool computeU)

template<typename InputType >
ComplexSchur &	compute (const EigenBase< InputType > &matrix, bool computeU=true)
	Computes Schur decomposition of given matrix. More...

template<typename HessMatrixType , typename OrthMatrixType >
ComplexSchur< MatrixType > &	computeFromHessenberg (const HessMatrixType &matrixH, const OrthMatrixType &matrixQ, bool computeU)

template<typename HessMatrixType , typename OrthMatrixType >
ComplexSchur &	computeFromHessenberg (const HessMatrixType &matrixH, const OrthMatrixType &matrixQ, bool computeU=true)
	Compute Schur decomposition from a given Hessenberg matrix. More...

Index	getMaxIterations ()
	Returns the maximum number of iterations. More...

ComputationInfo	info () const
	Reports whether previous computation was successful. More...

const ComplexMatrixType &	matrixT () const
	Returns the triangular matrix in the Schur decomposition. More...

const ComplexMatrixType &	matrixU () const
	Returns the unitary matrix in the Schur decomposition. More...

ComplexSchur &	setMaxIterations (Index maxIters)
	Sets the maximum number of iterations allowed. More...

Static Public Attributes
static const int	m_maxIterationsPerRow
	Maximum number of iterations per row. More...

Protected Attributes
HessenbergDecomposition< MatrixType >	m_hess

ComputationInfo	m_info

bool	m_isInitialized

ComplexMatrixType	m_matT

ComplexMatrixType	m_matU

bool	m_matUisUptodate

Index	m_maxIters

Private Member Functions
ComplexScalar	computeShift (Index iu, Index iter)

void	reduceToTriangularForm (bool computeU)

bool	subdiagonalEntryIsNeglegible (Index i)

Detailed Description

template<typename MatrixType_>
class Eigen::ComplexSchur< MatrixType_ >

Performs a complex Schur decomposition of a real or complex square matrix.

This is defined in the Eigenvalues module.

#include <Eigen/Eigenvalues>

Eigenvalues

Template Parameters

MatrixType_ the type of the matrix of which we are computing the Schur decomposition; this is expected to be an instantiation of the Matrix class template.

Given a real or complex square matrix A, this class computes the Schur decomposition: \( A = U T U^*\) where U is a unitary complex matrix, and T is a complex upper triangular matrix. The diagonal of the matrix T corresponds to the eigenvalues of the matrix A.

Call the function compute() to compute the Schur decomposition of a given matrix. Alternatively, you can use the ComplexSchur(const MatrixType&, bool) constructor which computes the Schur decomposition at construction time. Once the decomposition is computed, you can use the matrixU() and matrixT() functions to retrieve the matrices U and V in the decomposition.

Note: This code is inspired from Jampack

See also: class RealSchur, class EigenSolver, class ComplexEigenSolver

Definition at line 53 of file ComplexSchur.h.

Member Typedef Documentation

◆ ComplexMatrixType

template<typename MatrixType_ >

typedef Matrix<ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime> Eigen::ComplexSchur< MatrixType_ >::ComplexMatrixType

Type for the matrices in the Schur decomposition.

This is a square matrix with entries of type ComplexScalar. The size is the same as the size of MatrixType_.

Definition at line 83 of file ComplexSchur.h.

◆ ComplexScalar

template<typename MatrixType_ >

typedef std::complex<RealScalar> Eigen::ComplexSchur< MatrixType_ >::ComplexScalar

Complex scalar type for MatrixType_.

This is std::complex<Scalar> if Scalar is real (e.g., float or double) and just Scalar if Scalar is complex.

Definition at line 76 of file ComplexSchur.h.

◆ Index

template<typename MatrixType_ >

typedef Eigen::Index Eigen::ComplexSchur< MatrixType_ >::Index

Deprecated:: since Eigen 3.3

Definition at line 68 of file ComplexSchur.h.

◆ MatrixType

template<typename MatrixType_ >

typedef MatrixType_ Eigen::ComplexSchur< MatrixType_ >::MatrixType

Definition at line 56 of file ComplexSchur.h.

◆ RealScalar

template<typename MatrixType_ >

typedef NumTraits<Scalar>::Real Eigen::ComplexSchur< MatrixType_ >::RealScalar

Definition at line 67 of file ComplexSchur.h.

◆ Scalar

template<typename MatrixType_ >

typedef MatrixType::Scalar Eigen::ComplexSchur< MatrixType_ >::Scalar

Scalar type for matrices of type MatrixType_.

Definition at line 66 of file ComplexSchur.h.

Member Enumeration Documentation

◆ anonymous enum

template<typename MatrixType_ >

anonymous enum

Enumerator
RowsAtCompileTime
ColsAtCompileTime
Options
MaxRowsAtCompileTime
MaxColsAtCompileTime

Definition at line 57 of file ComplexSchur.h.

          {
       RowsAtCompileTime = MatrixType::RowsAtCompileTime,
       ColsAtCompileTime = MatrixType::ColsAtCompileTime,
       Options = MatrixType::Options,
       MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
       MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
     };

Constructor & Destructor Documentation

◆ ComplexSchur() [1/2]

template<typename MatrixType_ >

Eigen::ComplexSchur< MatrixType_ >::ComplexSchur ( Index size = RowsAtCompileTime==Dynamic ? 1 : RowsAtCompileTime )

inlineexplicit

Default constructor.

Parameters

[in] size Positive integer, size of the matrix whose Schur decomposition will be computed.

The default constructor is useful in cases in which the user intends to perform decompositions via compute(). The size parameter is only used as a hint. It is not an error to give a wrong size, but it may impair performance.

See also: compute() for an example.

Definition at line 96 of file ComplexSchur.h.

                                                                       : RowsAtCompileTime)
       : m_matT(size,size),
         m_matU(size,size),
         m_hess(size),
         m_isInitialized(false),
         m_matUisUptodate(false),
         m_maxIters(-1)
     {}

◆ ComplexSchur() [2/2]

template<typename MatrixType_ >

template<typename InputType >

Eigen::ComplexSchur< MatrixType_ >::ComplexSchur	(	const EigenBase< InputType > &	matrix,
		bool	computeU = `true`
	)

inlineexplicit

Constructor; computes Schur decomposition of given matrix.

Parameters

[in]	matrix	Square matrix whose Schur decomposition is to be computed.
[in]	computeU	If true, both T and U are computed; if false, only T is computed.

This constructor calls compute() to compute the Schur decomposition.

See also: matrixT() and matrixU() for examples.

Definition at line 115 of file ComplexSchur.h.

       : m_matT(matrix.rows(),matrix.cols()),
         m_matU(matrix.rows(),matrix.cols()),
         m_hess(matrix.rows()),
         m_isInitialized(false),
         m_matUisUptodate(false),
         m_maxIters(-1)
     {
       compute(matrix.derived(), computeU);
     }

Member Function Documentation

◆ compute() [1/2]

template<typename MatrixType_ >

template<typename InputType >

ComplexSchur<MatrixType>& Eigen::ComplexSchur< MatrixType_ >::compute	(	const EigenBase< InputType > &	matrix,
		bool	computeU
	)

Definition at line 324 of file ComplexSchur.h.

 {
   m_matUisUptodate = false;
   eigen_assert(matrix.cols() == matrix.rows());
  
   if(matrix.cols() == 1)
   {
     m_matT = matrix.derived().template cast<ComplexScalar>();
     if(computeU)  m_matU = ComplexMatrixType::Identity(1,1);
     m_info = Success;
     m_isInitialized = true;
     m_matUisUptodate = computeU;
     return *this;
   }
  
   internal::complex_schur_reduce_to_hessenberg<MatrixType, NumTraits<Scalar>::IsComplex>::run(*this, matrix.derived(), computeU);
   computeFromHessenberg(m_matT, m_matU, computeU);
   return *this;
 }

◆ compute() [2/2]

template<typename MatrixType_ >

template<typename InputType >

ComplexSchur& Eigen::ComplexSchur< MatrixType_ >::compute	(	const EigenBase< InputType > &	matrix,
		bool	computeU = `true`
	)

Computes Schur decomposition of given matrix.

Parameters

[in]	matrix	Square matrix whose Schur decomposition is to be computed.
[in]	computeU	If true, both T and U are computed; if false, only T is computed.

Returns: Reference to *this

The Schur decomposition is computed by first reducing the matrix to Hessenberg form using the class HessenbergDecomposition. The Hessenberg matrix is then reduced to triangular form by performing QR iterations with a single shift. The cost of computing the Schur decomposition depends on the number of iterations; as a rough guide, it may be taken on the number of iterations; as a rough guide, it may be taken to be \(25n^3\) complex flops, or \(10n^3\) complex flops if computeU is false.

Example:

MatrixXcf A = MatrixXcf::Random(4,4);
ComplexSchur<MatrixXcf> schur(4);
schur.compute(A);
cout << "The matrix T in the decomposition of A is:" << endl << schur.matrixT() << endl;
schur.compute(A.inverse());
cout << "The matrix T in the decomposition of A^(-1) is:" << endl << schur.matrixT() << endl;

Output:

The matrix T in the decomposition of A is:
 (-0.691,-1.63)  (0.763,-0.144) (-0.104,-0.836) (-0.462,-0.378)
          (0,0)   (-0.758,1.22)  (-0.65,-0.772)  (-0.244,0.113)
          (0,0)           (0,0)   (0.137,0.505) (0.0687,-0.404)
          (0,0)           (0,0)           (0,0)   (1.52,-0.402)
The matrix T in the decomposition of A^(-1) is:
    (0.501,-1.84)    (-1.01,-0.984)       (0.636,1.3)    (-0.676,0.352)
            (0,0)   (-0.369,-0.593)     (0.0733,0.18) (-0.0658,-0.0263)
            (0,0)             (0,0)    (-0.222,0.521)    (-0.191,0.121)
            (0,0)             (0,0)             (0,0)     (0.614,0.162)

See also: compute(const MatrixType&, bool, Index)

◆ computeFromHessenberg() [1/2]

template<typename MatrixType_ >

template<typename HessMatrixType , typename OrthMatrixType >

ComplexSchur<MatrixType>& Eigen::ComplexSchur< MatrixType_ >::computeFromHessenberg	(	const HessMatrixType &	matrixH,
		const OrthMatrixType &	matrixQ,
		bool	computeU
	)

Definition at line 346 of file ComplexSchur.h.

 {
   m_matT = matrixH;
   if(computeU)
     m_matU = matrixQ;
   reduceToTriangularForm(computeU);
   return *this;
 }

◆ computeFromHessenberg() [2/2]

template<typename MatrixType_ >

template<typename HessMatrixType , typename OrthMatrixType >

ComplexSchur& Eigen::ComplexSchur< MatrixType_ >::computeFromHessenberg	(	const HessMatrixType &	matrixH,
		const OrthMatrixType &	matrixQ,
		bool	computeU = `true`
	)

Compute Schur decomposition from a given Hessenberg matrix.

Parameters

[in]	matrixH	Matrix in Hessenberg form H
[in]	matrixQ	orthogonal matrix Q that transform a matrix A to H : A = Q H Q^T
	computeU	Computes the matriX U of the Schur vectors

Returns: Reference to *this

This routine assumes that the matrix is already reduced in Hessenberg form matrixH using either the class HessenbergDecomposition or another mean. It computes the upper quasi-triangular matrix T of the Schur decomposition of H When computeU is true, this routine computes the matrix U such that A = U T U^T = (QZ) T (QZ)^T = Q H Q^T where A is the initial matrix

NOTE Q is referenced if computeU is true; so, if the initial orthogonal matrix is not available, the user should give an identity matrix (Q.setIdentity())

See also: compute(const MatrixType&, bool)

◆ computeShift()

template<typename MatrixType >

ComplexSchur< MatrixType >::ComplexScalar Eigen::ComplexSchur< MatrixType >::computeShift	(	Index	iu,
		Index	iter
	)

private

Compute the shift in the current QR iteration.

Definition at line 283 of file ComplexSchur.h.

 {
   using std::abs;
   if (iter == 10 || iter == 20) 
   {
     // exceptional shift, taken from http://www.netlib.org/eispack/comqr.f
     return abs(numext::real(m_matT.coeff(iu,iu-1))) + abs(numext::real(m_matT.coeff(iu-1,iu-2)));
   }
  
   // compute the shift as one of the eigenvalues of t, the 2x2
   // diagonal block on the bottom of the active submatrix
   Matrix<ComplexScalar,2,2> t = m_matT.template block<2,2>(iu-1,iu-1);
   RealScalar normt = t.cwiseAbs().sum();
   t /= normt;     // the normalization by sf is to avoid under/overflow
  
   ComplexScalar b = t.coeff(0,1) * t.coeff(1,0);
   ComplexScalar c = t.coeff(0,0) - t.coeff(1,1);
   ComplexScalar disc = sqrt(c*c + RealScalar(4)*b);
   ComplexScalar det = t.coeff(0,0) * t.coeff(1,1) - b;
   ComplexScalar trace = t.coeff(0,0) + t.coeff(1,1);
   ComplexScalar eival1 = (trace + disc) / RealScalar(2);
   ComplexScalar eival2 = (trace - disc) / RealScalar(2);
   RealScalar eival1_norm = numext::norm1(eival1);
   RealScalar eival2_norm = numext::norm1(eival2);
   // A division by zero can only occur if eival1==eival2==0.
   // In this case, det==0, and all we have to do is checking that eival2_norm!=0
   if(eival1_norm > eival2_norm)
     eival2 = det / eival1;
   else if(!numext::is_exactly_zero(eival2_norm))
     eival1 = det / eival2;
  
   // choose the eigenvalue closest to the bottom entry of the diagonal
   if(numext::norm1(eival1-t.coeff(1,1)) < numext::norm1(eival2-t.coeff(1,1)))
     return normt * eival1;
   else
     return normt * eival2;
 }

◆ getMaxIterations()

template<typename MatrixType_ >

Index Eigen::ComplexSchur< MatrixType_ >::getMaxIterations ( )

inline

Returns the maximum number of iterations.

Definition at line 237 of file ComplexSchur.h.

     {
       return m_maxIters;
     }

◆ info()

template<typename MatrixType_ >

ComputationInfo Eigen::ComplexSchur< MatrixType_ >::info ( ) const

inline

Reports whether previous computation was successful.

Returns: Success if computation was successful, NoConvergence otherwise.

Definition at line 219 of file ComplexSchur.h.

     {
       eigen_assert(m_isInitialized && "ComplexSchur is not initialized.");
       return m_info;
     }

◆ matrixT()

template<typename MatrixType_ >

const ComplexMatrixType& Eigen::ComplexSchur< MatrixType_ >::matrixT ( ) const

inline

Returns the triangular matrix in the Schur decomposition.

Returns: A const reference to the matrix T.

It is assumed that either the constructor ComplexSchur(const MatrixType& matrix, bool computeU) or the member function compute(const MatrixType& matrix, bool computeU) has been called before to compute the Schur decomposition of a matrix.

Note that this function returns a plain square matrix. If you want to reference only the upper triangular part, use:

schur.matrixT().triangularView<Upper>()

Eigen::Upper

@ Upper

Definition: Constants.h:213

Example:

MatrixXcf A = MatrixXcf::Random(4,4);
cout << "Here is a random 4x4 matrix, A:" << endl << A << endl << endl;
ComplexSchur<MatrixXcf> schurOfA(A, false); // false means do not compute U
cout << "The triangular matrix T is:" << endl << schurOfA.matrixT() << endl;

Output:

Here is a random 4x4 matrix, A:
  (-0.211,0.68)  (0.108,-0.444)   (0.435,0.271) (-0.198,-0.687)
  (0.597,0.566) (0.258,-0.0452)  (0.214,-0.717)  (-0.782,-0.74)
 (-0.605,0.823)  (0.0268,-0.27) (-0.514,-0.967)  (-0.563,0.998)
  (0.536,-0.33)   (0.832,0.904)  (0.608,-0.726)  (0.678,0.0259)

The triangular matrix T is:
 (-0.691,-1.63)  (0.763,-0.144) (-0.104,-0.836) (-0.462,-0.378)
          (0,0)   (-0.758,1.22)  (-0.65,-0.772)  (-0.244,0.113)
          (0,0)           (0,0)   (0.137,0.505) (0.0687,-0.404)
          (0,0)           (0,0)           (0,0)   (1.52,-0.402)

Definition at line 164 of file ComplexSchur.h.

     {
       eigen_assert(m_isInitialized && "ComplexSchur is not initialized.");
       return m_matT;
     }

◆ matrixU()

template<typename MatrixType_ >

const ComplexMatrixType& Eigen::ComplexSchur< MatrixType_ >::matrixU ( ) const

inline

Returns the unitary matrix in the Schur decomposition.

Returns: A const reference to the matrix U.

It is assumed that either the constructor ComplexSchur(const MatrixType& matrix, bool computeU) or the member function compute(const MatrixType& matrix, bool computeU) has been called before to compute the Schur decomposition of a matrix, and that computeU was set to true (the default value).

Example:

MatrixXcf A = MatrixXcf::Random(4,4);
cout << "Here is a random 4x4 matrix, A:" << endl << A << endl << endl;
ComplexSchur<MatrixXcf> schurOfA(A);
cout << "The unitary matrix U is:" << endl << schurOfA.matrixU() << endl;

Output:

Here is a random 4x4 matrix, A:
  (-0.211,0.68)  (0.108,-0.444)   (0.435,0.271) (-0.198,-0.687)
  (0.597,0.566) (0.258,-0.0452)  (0.214,-0.717)  (-0.782,-0.74)
 (-0.605,0.823)  (0.0268,-0.27) (-0.514,-0.967)  (-0.563,0.998)
  (0.536,-0.33)   (0.832,0.904)  (0.608,-0.726)  (0.678,0.0259)

The unitary matrix U is:
 (-0.122,0.271)   (0.354,0.255)    (-0.7,0.321) (0.0909,-0.346)
   (0.247,0.23)  (0.435,-0.395)   (0.184,-0.38)  (0.492,-0.347)
(0.859,-0.0877)  (0.00469,0.21) (-0.256,0.0163)   (0.133,0.355)
 (-0.116,0.195) (-0.484,-0.432)  (-0.183,0.359)   (0.559,0.231)

Definition at line 140 of file ComplexSchur.h.

     {
       eigen_assert(m_isInitialized && "ComplexSchur is not initialized.");
       eigen_assert(m_matUisUptodate && "The matrix U has not been computed during the ComplexSchur decomposition.");
       return m_matU;
     }

◆ reduceToTriangularForm()

template<typename MatrixType >

void Eigen::ComplexSchur< MatrixType >::reduceToTriangularForm ( bool computeU )

private

Definition at line 392 of file ComplexSchur.h.

 {  
   Index maxIters = m_maxIters;
   if (maxIters == -1)
     maxIters = m_maxIterationsPerRow * m_matT.rows();
  
   // The matrix m_matT is divided in three parts. 
   // Rows 0,...,il-1 are decoupled from the rest because m_matT(il,il-1) is zero. 
   // Rows il,...,iu is the part we are working on (the active submatrix).
   // Rows iu+1,...,end are already brought in triangular form.
   Index iu = m_matT.cols() - 1;
   Index il;
   Index iter = 0; // number of iterations we are working on the (iu,iu) element
   Index totalIter = 0; // number of iterations for whole matrix
  
   while(true)
   {
     // find iu, the bottom row of the active submatrix
     while(iu > 0)
     {
       if(!subdiagonalEntryIsNeglegible(iu-1)) break;
       iter = 0;
       --iu;
     }
  
     // if iu is zero then we are done; the whole matrix is triangularized
     if(iu==0) break;
  
     // if we spent too many iterations, we give up
     iter++;
     totalIter++;
     if(totalIter > maxIters) break;
  
     // find il, the top row of the active submatrix
     il = iu-1;
     while(il > 0 && !subdiagonalEntryIsNeglegible(il-1))
     {
       --il;
     }
  
     /* perform the QR step using Givens rotations. The first rotation
        creates a bulge; the (il+2,il) element becomes nonzero. This
        bulge is chased down to the bottom of the active submatrix. */
  
     ComplexScalar shift = computeShift(iu, iter);
     JacobiRotation<ComplexScalar> rot;
     rot.makeGivens(m_matT.coeff(il,il) - shift, m_matT.coeff(il+1,il));
     m_matT.rightCols(m_matT.cols()-il).applyOnTheLeft(il, il+1, rot.adjoint());
     m_matT.topRows((std::min)(il+2,iu)+1).applyOnTheRight(il, il+1, rot);
     if(computeU) m_matU.applyOnTheRight(il, il+1, rot);
  
     for(Index i=il+1 ; i<iu ; i++)
     {
       rot.makeGivens(m_matT.coeffRef(i,i-1), m_matT.coeffRef(i+1,i-1), &m_matT.coeffRef(i,i-1));
       m_matT.coeffRef(i+1,i-1) = ComplexScalar(0);
       m_matT.rightCols(m_matT.cols()-i).applyOnTheLeft(i, i+1, rot.adjoint());
       m_matT.topRows((std::min)(i+2,iu)+1).applyOnTheRight(i, i+1, rot);
       if(computeU) m_matU.applyOnTheRight(i, i+1, rot);
     }
   }
  
   if(totalIter <= maxIters)
     m_info = Success;
   else
     m_info = NoConvergence;
  
   m_isInitialized = true;
   m_matUisUptodate = computeU;
 }

◆ setMaxIterations()

template<typename MatrixType_ >

ComplexSchur& Eigen::ComplexSchur< MatrixType_ >::setMaxIterations ( Index maxIters )

inline

Sets the maximum number of iterations allowed.

If not specified by the user, the maximum number of iterations is m_maxIterationsPerRow times the size of the matrix.

Definition at line 230 of file ComplexSchur.h.

     {
       m_maxIters = maxIters;
       return *this;
     }

◆ subdiagonalEntryIsNeglegible()

template<typename MatrixType >

bool Eigen::ComplexSchur< MatrixType >::subdiagonalEntryIsNeglegible ( Index i )

inlineprivate

If m_matT(i+1,i) is negligible in floating point arithmetic compared to m_matT(i,i) and m_matT(j,j), then set it to zero and return true, else return false.

Definition at line 268 of file ComplexSchur.h.

 {
   RealScalar d = numext::norm1(m_matT.coeff(i,i)) + numext::norm1(m_matT.coeff(i+1,i+1));
   RealScalar sd = numext::norm1(m_matT.coeff(i+1,i));
   if (internal::isMuchSmallerThan(sd, d, NumTraits<RealScalar>::epsilon()))
   {
     m_matT.coeffRef(i+1,i) = ComplexScalar(0);
     return true;
   }
   return false;
 }

Member Data Documentation

◆ m_hess

template<typename MatrixType_ >

HessenbergDecomposition<MatrixType> Eigen::ComplexSchur< MatrixType_ >::m_hess

protected

Definition at line 251 of file ComplexSchur.h.

◆ m_info

template<typename MatrixType_ >

ComputationInfo Eigen::ComplexSchur< MatrixType_ >::m_info

protected

Definition at line 252 of file ComplexSchur.h.

◆ m_isInitialized

template<typename MatrixType_ >

bool Eigen::ComplexSchur< MatrixType_ >::m_isInitialized

protected

Definition at line 253 of file ComplexSchur.h.

◆ m_matT

template<typename MatrixType_ >

ComplexMatrixType Eigen::ComplexSchur< MatrixType_ >::m_matT

protected

Definition at line 250 of file ComplexSchur.h.

◆ m_matU

template<typename MatrixType_ >

ComplexMatrixType Eigen::ComplexSchur< MatrixType_ >::m_matU

protected

Definition at line 250 of file ComplexSchur.h.

◆ m_matUisUptodate

template<typename MatrixType_ >

bool Eigen::ComplexSchur< MatrixType_ >::m_matUisUptodate

protected

Definition at line 254 of file ComplexSchur.h.

◆ m_maxIterationsPerRow

template<typename MatrixType_ >

const int Eigen::ComplexSchur< MatrixType_ >::m_maxIterationsPerRow

static

Maximum number of iterations per row.

If not otherwise specified, the maximum number of iterations is this number times the size of the matrix. It is currently set to 30.

Definition at line 247 of file ComplexSchur.h.

◆ m_maxIters

template<typename MatrixType_ >

Index Eigen::ComplexSchur< MatrixType_ >::m_maxIters

protected

Definition at line 255 of file ComplexSchur.h.

The documentation for this class was generated from the following file:

ComplexSchur.h

Public Types

Public Member Functions

Static Public Attributes

Protected Attributes

Private Member Functions

Detailed Description

template<typename MatrixType_> class Eigen::ComplexSchur< MatrixType_ >

Member Typedef Documentation

◆ ComplexMatrixType

◆ ComplexScalar

◆ Index

◆ MatrixType

◆ RealScalar

◆ Scalar

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ ComplexSchur() [1/2]

◆ ComplexSchur() [2/2]

Member Function Documentation

◆ compute() [1/2]

◆ compute() [2/2]

◆ computeFromHessenberg() [1/2]

◆ computeFromHessenberg() [2/2]

◆ computeShift()

◆ getMaxIterations()

◆ info()

◆ matrixT()

◆ matrixU()

◆ reduceToTriangularForm()

◆ setMaxIterations()

◆ subdiagonalEntryIsNeglegible()

Member Data Documentation

◆ m_hess

◆ m_info

◆ m_isInitialized

◆ m_matT

◆ m_matU

◆ m_matUisUptodate

◆ m_maxIterationsPerRow

◆ m_maxIters

template<typename MatrixType_>
class Eigen::ComplexSchur< MatrixType_ >