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

A^3.1 is:
   (-0.16858,-2.88335)     (-1.19171,1.31734)   (-0.205385,-2.85231)  (-0.793347,-0.323082)
   (0.170369,-1.83994)   (-0.588912,0.545447)     (1.64177,-2.11127)    (0.582705,0.766038)
   (0.95977,-0.896837)  (-0.353594,-0.559858)     (2.37821,-1.91013)    (1.68082,0.0472203)
    (-0.915598,1.8791)   (0.393388,-0.128919)     (-2.08007,2.36222) (-1.33759,-0.00384762)

A^3.3 is:
  (0.387072,-3.03728)    (-1.28527,1.26933)   (0.759272,-2.72521) (-0.642452,0.0960228)
  (0.788638,-1.69238)  (-0.578217,0.365293)     (2.51069,-1.6477)    (0.730302,1.09701)
  (1.52219,-0.685834) (-0.405507,-0.800341)    (3.03538,-1.37315)    (1.63056,0.198142)
   (-1.55232,1.72301)   (0.462049,0.159509)    (-2.89927,1.80702)  (-1.28322,-0.195319)

A^3.7 is:
   (1.66859,-2.72375)   (-1.26765,0.999027)    (2.64201,-1.50728)   (-0.515609,1.03796)
  (1.93469,-0.793522)  (-0.353836,-0.11654)     (3.7999,0.110159)    (0.754493,1.69738)
   (2.42172,0.263819)   (-0.354422,-1.2948)    (3.76115,0.383115)    (1.22546,0.477461)
  (-2.62563,0.773497)   (0.429889,0.761964)  (-3.95456,-0.159646) (-0.808653,-0.614027)

A^3.9 is:
   (2.26004,-2.21492)   (-1.12649,0.801666)   (3.34086,-0.419028)    (-0.58092,1.49767)
 (2.32111,-0.0584826) (-0.129182,-0.376093)      (4.0214,1.31619)    (0.610594,1.90553)
   (2.63556,0.962157)  (-0.239951,-1.50288)     (3.67106,1.48265)   (0.879111,0.554066)
(-2.91745,0.00870841)    (0.308645,1.02382)   (-3.99547,-1.45633) (-0.395371,-0.782971)

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:

• /builds/libeigen/eigen/unsupported/Eigen/src/MatrixFunctions/MatrixPower.h