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>

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 MatrixPowerRetval< MatrixType > operator() (RealScalar p)
 Returns the matrix power. More...
 
Index rows () const
 

Private Types

enum  { RowsAtCompileTime = MatrixType::RowsAtCompileTime, ColsAtCompileTime = MatrixType::ColsAtCompileTime, MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime }
 
typedef Matrix< ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, MatrixType::Options, MaxRowsAtCompileTime, MaxColsAtCompileTime > 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 &, RealScalar)
 
template<typename ResultType >
void computeIntPower (ResultType &, RealScalar)
 
RealScalar modfAndInit (RealScalar, RealScalar *)
 

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
 
RealScalar m_conditionNumber
 
ComplexMatrix m_fT
 
ComplexMatrix m_T
 
MatrixType m_tmp
 
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:

Output: 

 

Definition at line 15 of file MatrixPower.h.


Member Typedef Documentation



◆ ComplexMatrix








template<typename MatrixType> 



  

  
      

        

          typedef Matrix<ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, MatrixType::Options, MaxRowsAtCompileTime, MaxColsAtCompileTime> Eigen::MatrixPower< MatrixType >::ComplexMatrix
        

      

  		
  
private  
  







Definition at line 326 of file MatrixPower.h.








◆ ComplexScalar








template<typename MatrixType> 



  

  
      

        

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

      

  		
  
private  
  







Definition at line 324 of file MatrixPower.h.








◆ Index








template<typename MatrixType> 



  

  
      

        

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

      

  		
  
private  
  







Definition at line 286 of file MatrixPower.h.








◆ RealScalar








template<typename MatrixType> 



  

  
      

        

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

      

  		
  
private  
  







Definition at line 285 of file MatrixPower.h.








◆ Scalar








template<typename MatrixType> 



  

  
      

        

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

      

  		
  
private  
  







Definition at line 284 of file MatrixPower.h.







Member Enumeration Documentation



◆ anonymous enum








template<typename MatrixType> 



  

  
      

        

          anonymous enum
        

      

  		
  
private  
  








Enumerator
RowsAtCompileTime 


ColsAtCompileTime 


MaxRowsAtCompileTime 


MaxColsAtCompileTime 





Definition at line 278 of file MatrixPower.h.







Constructor & Destructor Documentation



◆ MatrixPower()








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 297 of file MatrixPower.h.







Member Function Documentation



◆ cols()








template<typename MatrixType> 



  

  
      

        

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

      

  		
  
inline  
  







Definition at line 321 of file MatrixPower.h.








◆ compute()








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 356 of file MatrixPower.h.








◆ computeFracPower()








template<typename MatrixType > 



template<typename ResultType > 



  

  
      

        

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

        

          
          
          RealScalar 
          p 
        

        

          
          )
          
        

      

  		
  
private  
  







Definition at line 416 of file MatrixPower.h.








◆ computeIntPower()








template<typename MatrixType > 



template<typename ResultType > 



  

  
      

        

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

        

          
          
          RealScalar 
          p 
        

        

          
          )
          
        

      

  		
  
private  
  







Definition at line 398 of file MatrixPower.h.








◆ modfAndInit()








template<typename MatrixType > 



  

  
      

        

          MatrixPower< MatrixType >::RealScalar Eigen::MatrixPower< MatrixType >::modfAndInit 
          (
          RealScalar 
          x, 
        

        

          
          
          RealScalar * 
          intpart 
        

        

          
          )
          
        

      

  		
  
private  
  







Definition at line 373 of file MatrixPower.h.








◆ operator()()








template<typename MatrixType> 



  

  
      

        

          const MatrixPowerRetval<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 307 of file MatrixPower.h.








◆ revertSchur() [1/2]








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 428 of file MatrixPower.h.








◆ revertSchur() [2/2]








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 436 of file MatrixPower.h.








◆ rows()








template<typename MatrixType> 



  

  
      

        

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

      

  		
  
inline  
  







Definition at line 320 of file MatrixPower.h.







Member Data Documentation



◆ m_A








template<typename MatrixType> 



  

  
      

        

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

      

  		
  
private  
  







Definition at line 328 of file MatrixPower.h.








◆ m_conditionNumber








template<typename MatrixType> 



  

  
      

        

          RealScalar Eigen::MatrixPower< MatrixType >::m_conditionNumber
        

      

  		
  
private  
  







Definition at line 331 of file MatrixPower.h.








◆ m_fT








template<typename MatrixType> 



  

  
      

        

          ComplexMatrix Eigen::MatrixPower< MatrixType >::m_fT
        

      

  		
  
private  
  







Definition at line 330 of file MatrixPower.h.








◆ m_T








template<typename MatrixType> 



  

  
      

        

          ComplexMatrix Eigen::MatrixPower< MatrixType >::m_T
        

      

  		
  
private  
  







Definition at line 330 of file MatrixPower.h.








◆ m_tmp








template<typename MatrixType> 



  

  
      

        

          MatrixType Eigen::MatrixPower< MatrixType >::m_tmp
        

      

  		
  
private  
  







Definition at line 329 of file MatrixPower.h.








◆ m_U








template<typename MatrixType> 



  

  
      

        

          ComplexMatrix Eigen::MatrixPower< MatrixType >::m_U
        

      

  		
  
private  
  







Definition at line 330 of file MatrixPower.h.







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







acado

Author(s): Milan Vukov, Rien Quirynen

autogenerated on Mon Feb 28 2022 21:32:31