Public Member Functions | Private Types | Private Member Functions | Static Private Member Functions | Private Attributes | List of all members
Eigen::MatrixPower< MatrixType > Class Template Reference

Class for computing matrix powers. More...

#include <MatrixPower.h>

Inheritance diagram for Eigen::MatrixPower< MatrixType >:
Inheritance graph
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Public Member Functions

Index cols () const
 
template<typename ResultType >
void compute (ResultType &res, RealScalar p)
 Compute the matrix power. More...
 
 MatrixPower (const MatrixType &A)
 Constructor. More...
 
const MatrixPowerParenthesesReturnValue< MatrixType > operator() (RealScalar p)
 Returns the matrix power. More...
 
Index rows () const
 

Private Types

typedef Matrix< ComplexScalar, Dynamic, Dynamic, 0, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime > ComplexMatrix
 
typedef std::complex< RealScalar > ComplexScalar
 
typedef MatrixType::Index Index
 
typedef MatrixType::RealScalar RealScalar
 
typedef MatrixType::Scalar Scalar
 

Private Member Functions

template<typename ResultType >
void computeFracPower (ResultType &res, RealScalar p)
 
template<typename ResultType >
void computeIntPower (ResultType &res, RealScalar p)
 
void initialize ()
 Perform Schur decomposition for fractional power. More...
 
void split (RealScalar &p, RealScalar &intpart)
 Split p into integral part and fractional part. More...
 
- Private Member Functions inherited from Eigen::internal::noncopyable
EIGEN_DEVICE_FUNC noncopyable ()
 
EIGEN_DEVICE_FUNC ~noncopyable ()
 

Static Private Member Functions

template<int Rows, int Cols, int Options, int MaxRows, int MaxCols>
static void revertSchur (Matrix< ComplexScalar, Rows, Cols, Options, MaxRows, MaxCols > &res, const ComplexMatrix &T, const ComplexMatrix &U)
 
template<int Rows, int Cols, int Options, int MaxRows, int MaxCols>
static void revertSchur (Matrix< RealScalar, Rows, Cols, Options, MaxRows, MaxCols > &res, const ComplexMatrix &T, const ComplexMatrix &U)
 

Private Attributes

MatrixType::Nested m_A
 Reference to the base of matrix power. More...
 
RealScalar m_conditionNumber
 Condition number of m_A. More...
 
ComplexMatrix m_fT
 Store fractional power of m_T. More...
 
Index m_nulls
 Rank deficiency of m_A. More...
 
Index m_rank
 Rank of m_A. More...
 
ComplexMatrix m_T
 Store the result of Schur decomposition. More...
 
MatrixType m_tmp
 Temporary storage. More...
 
ComplexMatrix m_U
 

Detailed Description

template<typename MatrixType>
class Eigen::MatrixPower< MatrixType >

Class for computing matrix powers.

Template Parameters
MatrixTypetype of the base, expected to be an instantiation of the Matrix class template.

This class is capable of computing real/complex matrices raised to an arbitrary real power. Meanwhile, it saves the result of Schur decomposition if an non-integral power has even been calculated. Therefore, if you want to compute multiple (>= 2) matrix powers for the same matrix, using the class directly is more efficient than calling MatrixBase::pow().

Example:

#include <unsupported/Eigen/MatrixFunctions>
#include <iostream>
using namespace Eigen;
int main()
{
Matrix4cd A = Matrix4cd::Random();
MatrixPower<Matrix4cd> Apow(A);
std::cout << "The matrix A is:\n" << A << "\n\n"
"A^3.1 is:\n" << Apow(3.1) << "\n\n"
"A^3.3 is:\n" << Apow(3.3) << "\n\n"
"A^3.7 is:\n" << Apow(3.7) << "\n\n"
"A^3.9 is:\n" << Apow(3.9) << std::endl;
return 0;
}

Output: 

 

Definition at line 15 of file MatrixPower.h.


Member Typedef Documentation








template<typename MatrixType> 



  

  
      

        

          typedef Matrix<ComplexScalar, Dynamic, Dynamic, 0, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime> Eigen::MatrixPower< MatrixType >::ComplexMatrix
        

      

  		
  
private  
  







Definition at line 387 of file MatrixPower.h.













template<typename MatrixType> 



  

  
      

        

          typedef std::complex<RealScalar> Eigen::MatrixPower< MatrixType >::ComplexScalar
        

      

  		
  
private  
  







Definition at line 385 of file MatrixPower.h.













template<typename MatrixType> 



  

  
      

        

          typedef MatrixType::Index Eigen::MatrixPower< MatrixType >::Index
        

      

  		
  
private  
  







Definition at line 343 of file MatrixPower.h.













template<typename MatrixType> 



  

  
      

        

          typedef MatrixType::RealScalar Eigen::MatrixPower< MatrixType >::RealScalar
        

      

  		
  
private  
  







Definition at line 342 of file MatrixPower.h.













template<typename MatrixType> 



  

  
      

        

          typedef MatrixType::Scalar Eigen::MatrixPower< MatrixType >::Scalar
        

      

  		
  
private  
  







Definition at line 341 of file MatrixPower.h.







Constructor & Destructor Documentation








template<typename MatrixType> 



  

  
      

        

          Eigen::MatrixPower< MatrixType >::MatrixPower 
          (
          const MatrixType & 
          A)
          
        

      

  		
  
inlineexplicit  
  







Constructor. 


Parameters

  

    
[in]Athe base of the matrix power.

  

  




The class stores a reference to A, so it should not be changed (or destroyed) before evaluation. 



Definition at line 354 of file MatrixPower.h.







Member Function Documentation








template<typename MatrixType> 



  

  
      

        

          Index Eigen::MatrixPower< MatrixType >::cols 
          (
          void 
          )
           const
        

      

  		
  
inline  
  







Definition at line 382 of file MatrixPower.h.













template<typename MatrixType > 



template<typename ResultType > 

      

        

          void Eigen::MatrixPower< MatrixType >::compute 
          (
          ResultType & 
          res, 
        

        

          
          
          RealScalar 
          p 
        

        

          
          )
          
        

      





Compute the matrix power. 


Parameters

  

    
[in]pexponent, a real scalar. 

    
[out]res$ A^p $ where A is specified in the constructor. 

  

  





Definition at line 450 of file MatrixPower.h.













template<typename MatrixType > 



template<typename ResultType > 



  

  
      

        

          void Eigen::MatrixPower< MatrixType >::computeFracPower 
          (
          ResultType & 
          res, 
        

        

          
          
          RealScalar 
          p 
        

        

          
          )
          
        

      

  		
  
private  
  







Definition at line 553 of file MatrixPower.h.













template<typename MatrixType > 



template<typename ResultType > 



  

  
      

        

          void Eigen::MatrixPower< MatrixType >::computeIntPower 
          (
          ResultType & 
          res, 
        

        

          
          
          RealScalar 
          p 
        

        

          
          )
          
        

      

  		
  
private  
  







Definition at line 530 of file MatrixPower.h.













template<typename MatrixType > 



  

  
      

        

          void Eigen::MatrixPower< MatrixType >::initialize 
          (
          void 
          )
          
        

      

  		
  
private  
  







Perform Schur decomposition for fractional power. 



Definition at line 491 of file MatrixPower.h.













template<typename MatrixType> 



  

  
      

        

          const MatrixPowerParenthesesReturnValue<MatrixType> Eigen::MatrixPower< MatrixType >::operator() 
          (
          RealScalar 
          p)
          
        

      

  		
  
inline  
  







Returns the matrix power. 


Parameters

  

    
[in]pexponent, a real scalar. 

  

  




Returns
The expression $ A^p $, where A is specified in the constructor. 



Definition at line 368 of file MatrixPower.h.













template<typename MatrixType > 



template<int Rows, int Cols, int Options, int MaxRows, int MaxCols> 



  

  
      

        

          void Eigen::MatrixPower< MatrixType >::revertSchur 
          (
          Matrix< ComplexScalar, Rows, Cols, Options, MaxRows, MaxCols > & 
          res, 
        

        

          
          
          const ComplexMatrix & 
          T, 
        

        

          
          
          const ComplexMatrix & 
          U 
        

        

          
          )
          
        

      

  		
  
inlinestaticprivate  
  







Definition at line 570 of file MatrixPower.h.













template<typename MatrixType > 



template<int Rows, int Cols, int Options, int MaxRows, int MaxCols> 



  

  
      

        

          void Eigen::MatrixPower< MatrixType >::revertSchur 
          (
          Matrix< RealScalar, Rows, Cols, Options, MaxRows, MaxCols > & 
          res, 
        

        

          
          
          const ComplexMatrix & 
          T, 
        

        

          
          
          const ComplexMatrix & 
          U 
        

        

          
          )
          
        

      

  		
  
inlinestaticprivate  
  







Definition at line 578 of file MatrixPower.h.













template<typename MatrixType> 



  

  
      

        

          Index Eigen::MatrixPower< MatrixType >::rows 
          (
          void 
          )
           const
        

      

  		
  
inline  
  







Definition at line 381 of file MatrixPower.h.













template<typename MatrixType > 



  

  
      

        

          void Eigen::MatrixPower< MatrixType >::split 
          (
          RealScalar & 
          p, 
        

        

          
          
          RealScalar & 
          intpart 
        

        

          
          )
          
        

      

  		
  
private  
  







Split p into integral part and fractional part. 


Parameters

  

    
[in]pThe exponent. 

    
[out]pThe fractional part ranging in $ (-1, 1) $. 

    
[out]intpartThe integral part.

  

  




Only if the fractional part is nonzero, it calls initialize(). 



Definition at line 470 of file MatrixPower.h.







Member Data Documentation








template<typename MatrixType> 



  

  
      

        

          MatrixType::Nested Eigen::MatrixPower< MatrixType >::m_A
        

      

  		
  
private  
  







Reference to the base of matrix power. 



Definition at line 390 of file MatrixPower.h.













template<typename MatrixType> 



  

  
      

        

          RealScalar Eigen::MatrixPower< MatrixType >::m_conditionNumber
        

      

  		
  
private  
  







Condition number of m_A. 


It is initialized as 0 to avoid performing unnecessary Schur decomposition, which is the bottleneck. 



Definition at line 407 of file MatrixPower.h.













template<typename MatrixType> 



  

  
      

        

          ComplexMatrix Eigen::MatrixPower< MatrixType >::m_fT
        

      

  		
  
private  
  







Store fractional power of m_T. 



Definition at line 399 of file MatrixPower.h.













template<typename MatrixType> 



  

  
      

        

          Index Eigen::MatrixPower< MatrixType >::m_nulls
        

      

  		
  
private  
  







Rank deficiency of m_A. 



Definition at line 413 of file MatrixPower.h.













template<typename MatrixType> 



  

  
      

        

          Index Eigen::MatrixPower< MatrixType >::m_rank
        

      

  		
  
private  
  







Rank of m_A. 



Definition at line 410 of file MatrixPower.h.













template<typename MatrixType> 



  

  
      

        

          ComplexMatrix Eigen::MatrixPower< MatrixType >::m_T
        

      

  		
  
private  
  







Store the result of Schur decomposition. 



Definition at line 396 of file MatrixPower.h.













template<typename MatrixType> 



  

  
      

        

          MatrixType Eigen::MatrixPower< MatrixType >::m_tmp
        

      

  		
  
private  
  







Temporary storage. 



Definition at line 393 of file MatrixPower.h.













template<typename MatrixType> 



  

  
      

        

          ComplexMatrix Eigen::MatrixPower< MatrixType >::m_U
        

      

  		
  
private  
  







Definition at line 396 of file MatrixPower.h.







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







gtsam

Author(s): 

autogenerated on Sat May 8 2021 02:53:14