Eigen::MatrixPower< MatrixType > Class Template Reference

#include <unsupported/Eigen/src/MatrixFunctions/MatrixPower.h>

Detailed Description

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

Class for computing matrix powers.

Template Parameters

MatrixType

type 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:

The matrix A is:
    (0.205189,0.696235)   (0.0722581,0.0241114)    (0.740165,-0.727247)    (-0.757623,-0.77815)
    (0.33421,-0.414795)    (-0.046008,0.432106)    (0.740565,-0.756752)   (-0.467268,-0.711254)
   (0.927654,-0.469531)    (-0.159573,0.134119)    (0.852317,-0.216464)   (0.220277,0.00720412)
   (-0.632501,0.445064) (-0.498144,-0.00985718)    (-0.833781,0.834695)    (-0.316277,0.858701)

A^3.1 is:
   (2.82147,0.617559)   (-1.48755,0.970963)    (2.78507,0.649057)   (0.194997,0.834121)
   (1.84394,0.119559)  (-0.630858,0.496335)     (2.3421,-1.29128) (-0.665452,-0.695366)
  (1.03594,-0.807657)   (0.497651,0.436822)    (2.25864,-2.05012)   (0.216299,-1.66751)
    (-1.9992,0.61037)  (0.188871,-0.368377)    (-2.65853,1.68493)   (-0.205445,1.32172)

A^3.3 is:
    (2.88197,1.03401)    (-1.71448,0.56892)    (2.77288,0.560704)  (-0.377224,0.528836)
   (1.86595,0.065641)  (-0.587984,0.349356)      (2.60795,-1.489)  (-0.645889,-1.14873)
   (1.30214,-1.04492)   (0.529013,0.724657)    (2.60152,-2.08115)    (0.563714,-1.5428)
  (-2.23995,0.600898) (0.0676424,-0.484104)     (-2.92631,1.7629)   (-0.408539,1.23203)

A^3.7 is:
    (2.72328,1.66936)  (-1.58303,-0.314641)    (3.03834,0.143548) (-0.930633,-0.690743)
  (2.08407,-0.171298)  (-0.262362,0.264476)    (3.33572,-1.82327) (-0.0983353,-1.85491)
      (2.038,-1.3345)    (0.272037,1.31458)    (3.17728,-2.04889)   (0.87513,-0.981768)
  (-2.69061,0.502821)  (0.0371093,-0.87408)    (-3.45106,1.93758)  (-0.441753,0.914223)

A^3.9 is:
     (2.5787,1.83411)  (-1.23803,-0.615574)   (3.36528,-0.108757)  (-0.808055,-1.38835)
  (2.30168,-0.305339) (-0.0687576,0.391672)    (3.76599,-1.92907)   (0.304986,-1.97759)
     (2.4526,-1.3626) (-0.00189484,1.52191)    (3.39393,-2.03868)  (0.781613,-0.684768)
  (-2.88289,0.447788)    (0.144684,-1.0595)    (-3.71845,2.06343)   (-0.26802,0.835181)

Public Member Functions
template<typename ResultType>
void	compute (ResultType &res, RealScalar p)
	Compute the matrix power.
	MatrixPower (const MatrixType &A)
	Constructor.
const MatrixPowerParenthesesReturnValue< MatrixType >	operator() (RealScalar p)
	Returns the matrix power.

Constructor & Destructor Documentation

MatrixPower()

template<typename MatrixType>

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

inlineexplicit

Constructor.

Parameters

[in]

A

the base of the matrix power.

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

Member Function Documentation

compute()

template<typename MatrixType>

template<typename ResultType>

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

Compute the matrix power.

Parameters

[in]	p	exponent, a real scalar.
[out]	res	\( A^p \) where A is specified in the constructor.

operator()()

template<typename MatrixType>

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

inline

Returns the matrix power.

Parameters

[in]

p

exponent, a real scalar.

Returns

The expression \( A^p \), where A is specified in the constructor.

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

• /builddir/build/BUILD/eigen3-5.0.1-build/eigen-5.0.1/unsupported/Eigen/src/MatrixFunctions/MatrixPower.h