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:
 (-0.211234,0.680375)   (0.10794,-0.444451)   (0.434594,0.271423) (-0.198111,-0.686642)
   (0.59688,0.566198) (0.257742,-0.0452059)  (0.213938,-0.716795) (-0.782382,-0.740419)
 (-0.604897,0.823295) (0.0268018,-0.270431) (-0.514226,-0.967399)  (-0.563486,0.997849)
 (0.536459,-0.329554)    (0.83239,0.904459)  (0.608354,-0.725537)  (0.678224,0.0258648)

A^3.1 is:
   (2.80575,-0.607662) (-1.16847,-0.00660555)    (-0.760385,1.01461)   (-0.38073,-0.106512)
     (1.4041,-3.61891)     (1.00481,0.186263)   (-0.163888,0.449419)   (-0.388981,-1.22629)
   (-2.07957,-1.58136)     (0.825866,2.25962)     (5.09383,0.155736)    (0.394308,-1.63034)
  (-0.818997,0.671026)  (2.11069,-0.00768024)    (-1.37876,0.140165)    (2.50512,-0.854429)

A^3.3 is:
  (2.83571,-0.238717) (-1.48174,-0.0615217)  (-0.0544396,1.68092) (-0.292699,-0.621726)
    (2.0521,-3.58316)    (0.87894,0.400548)  (0.738072,-0.121242)   (-1.07957,-1.63492)
  (-3.00106,-1.10558)     (1.52205,1.92407)    (5.29759,-1.83562)  (-0.532038,-1.50253)
  (-0.491353,-0.4145)     (2.5761,0.481286)  (-1.21994,0.0367069)    (2.67112,-1.06331)

A^3.7 is:
     (1.42126,0.33362)   (-1.39486,-0.560486)      (1.44968,2.47066)   (-0.324079,-1.75879)
    (2.65301,-1.82427)   (0.357333,-0.192429)      (2.01017,-1.4791)    (-2.71518,-2.35892)
   (-3.98544,0.964861)     (2.26033,0.554254)     (3.18211,-5.94352)    (-2.22888,0.128951)
   (0.944969,-2.14683)      (3.31345,1.66075) (-0.0623743,-0.848324)        (2.3897,-1.863)

A^3.9 is:
 (0.0720766,0.378685) (-0.931961,-0.978624)      (1.9855,2.34105)  (-0.530547,-2.17664)
  (2.40934,-0.265286)  (0.0299975,-1.08827)    (1.98974,-2.05886)   (-3.45767,-2.50235)
    (-3.71666,2.3874)        (2.054,-0.303)   (0.844348,-7.29588)    (-2.59136,1.57689)
   (1.87645,-2.38798)     (3.52111,2.10508)    (0.799055,-1.6122)    (1.93452,-2.44408)