# 使用特征库时“从这里需要”“required from here” when using Eigen library

``````#include <iostream>
#include "System.h"
#include "ControllerCode2.h"

using namespace std;

int main(){

int n = 3;   // # of states
int m = 1;   // # of inputs
int l = 1;   // # of outputs

MatrixXd A(n, n), B(n,m), C(l,n), D(l,m), Q(n,n), R(m,m), Qe(n,n), Re(m,m);

A << 0,  1,  0,
0,  0,  1,
0, -2, -3;

B << 0,
0,
1;

C << 1, 0, 0;

D << 0;

MatrixXd C_trans = C.transpose();
Q = C_trans * C;
R =  MatrixXd::Identity(m, m); // initially

MatrixXd B_trans = B.transpose();
Qe = B * B_trans;
Re =  MatrixXd::Identity(m, m); // initially

System sys = System(A, B, C, D);

sys.set_covariance_matrices(R, Q);
sys.set_noise_covariance_matrices(Re, Qe);
schur_eigen_test(sys);

return 5;
}
``````

``````#include "ControllerCode2.h"

MatrixXd U11;
MatrixXd U21;

void schur_eigen_test( System G ){
/****** Constructing the Hamiltonian Matrix ******/
int n = G.A.rows();
MatrixXd H(2*n, 2*n);          // the Hamiltonian matrix has the dimensions of 2n*2n where n is the number of states
H.block(0,0,n,n)      = G.A;
H.block(0,n,n,n)      = -1 * G.B * G.R.inverse() * G.B.transpose();
H.block(n,0,n,n)      = -1 * G.Q;
H.block(n,n,n,n)      = -1 * G.A.transpose();

/****** Performing a real Schur decomposition on the square Hamiltonian matrix ******/
RealSchur<MatrixXd> schur(H);
MatrixXd U = schur.matrixU(); //The orthogonal matrix U
MatrixXd T = schur.matrixT(); //The quasi-triangular matrix T

/****** Find the eigenvalues and eigenvectors of the Hamiltonian matrix ******/
EigenSolver<MatrixXd> H_eigen;        // create an EigenSolver Matrix
H_eigen.compute(H, false);            // compute the eigenvalues ./and eigenvectors of matrix H
MatrixXd H_eigenval = H_eigen.eigenvalues();
//              //MatrixXd H_eigenvec = H_eigen.eigenvectors();

/****** Select the eigenvectors (U11, U21) corresponding to the stable (with -ve real part) eigenvalues ******/
U11 = U.block(0,0,n,n);
U21 = U.block(n,0,n,n);

/****** Calculate F ******/
MatrixXd F = -1 * G.R.inverse() * G.B.transpose() * U21 * U11.inverse(); // transposeInPlace or transpose??

//////// Extra: for output
cout << endl << "H = " << endl << H << endl;
cout << endl << "U schur(H) " << endl << U << endl;
cout << endl << "T schur(H) " << endl << T << endl;
cout << endl << "U*T*U.transpose() " << endl << U * T * U.transpose();

//      cout << endl << "U.transpose() - U.inverse() " << endl << U.transpose() - U.inverse(); // = which proves that U is orthogonal, i.e. U.transpose() = U.inverse()
//      EigenSolver<MatrixXd> H_eigen;        // create an EigenSolver Matrix
//      H_eigen.compute(H, false);            // compute the eigenvalues and eigenvectors of matrix H
//      MatrixXd H_eigenval = H_eigen.eigenvalues();
//      cout << endl << "eigenvalues of H = " << endl << H_eigenval << endl;
}
``````

``````MatrixXd H_eigenval = H_eigen.eigenvalues();
``````

``````#ifndef CONTROLLERCODE_H_
#define CONTROLLERCODE_H_

#include "System.h"

void schur_eigen_test( System );

//};

#endif /* CONTROLLERCODE_H_ */
``````

System.h代码：

``````// include guard
#ifndef SYSTEM_H_
#define SYSTEM_H_

#include <Eigen/Dense>
#include <iostream>
#include <Eigen/Eigenvalues>
#include <iostream>

using namespace Eigen;
using namespace std;
using Eigen::MatrixXd;

class System {

public:

MatrixXd A;
MatrixXd B;
MatrixXd C;
MatrixXd D;
MatrixXd Q;
MatrixXd R;
MatrixXd Re;
MatrixXd Qe;

System(MatrixXd a, MatrixXd b, MatrixXd c, MatrixXd d){
A = a;
B = b;
C = c;
D = d;
//cout << A << endl << B << endl << C << endl;
};

void set_covariance_matrices(MatrixXd r, MatrixXd q){
R = r;
Q = q;
//cout << R << endl << Q << endl;
}

void set_noise_covariance_matrices(MatrixXd re, MatrixXd qe){
Re = re;
Qe = qe;
//cout << Re << endl << Qe << endl;
}

virtual ~System();

// this function receives the 4 state space matrices and returns one plant matrix G
MatrixXd setContSys(MatrixXd a, MatrixXd b, MatrixXd c, MatrixXd d);

};

#endif /* SYSTEM_H_ */
``````

``````15:12:51 **** Incremental Build of configuration Debug for project Controller ****
Info: Internal Builder is used for build
g++ "-IC:\\Users\\Alsharif\\eigen" -O0 -g3 -Wall -c -fmessage-length=0 -o ControllerCode2.o "..\\ControllerCode2.cpp"
In file included from C:\Users\Alsharif\eigen/Eigen/Core:285:0,
from C:\Users\Alsharif\eigen/Eigen/Dense:1,
from ..\System.h:12,
from ..\ControllerCode2.h:11,
from ..\ControllerCode2.cpp:8:
C:\Users\Alsharif\eigen/Eigen/src/Core/Matrix.h: In instantiation of 'Eigen::Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>::Matrix(const Eigen::MatrixBase<OtherDerived>&) [with OtherDerived = Eigen::Matrix<std::complex<double>, -1, 1>; _Scalar = double; int _Rows = -1; int _Cols = -1; int _Options = 0; int _MaxRows = -1; int _MaxCols = -1]':
..\ControllerCode2.cpp:220:45:   required from here
C:\Users\Alsharif\eigen/Eigen/src/Core/util/StaticAssert.h:115:9: error: 'YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY' is not a member of 'Eigen::internal::static_assertion<false>'
if (Eigen::internal::static_assertion<static_cast<bool>(CONDITION)>::MSG) {}
^
C:\Users\Alsharif\eigen/Eigen/src/Core/Matrix.h:326:7: note: in expansion of macro 'EIGEN_STATIC_ASSERT'
EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
^

15:12:55 Build Finished (took 4s.567ms)
``````

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