Travaux Pratiques » Polytech Ge SP4abc 2021

void Add_Mat_Mat(int Ligne_MatA, int Colonne_MatA, double A[Ligne_MatA][Colonne_MatA],int Ligne_MatB, int Colonne_MatB, double B[Ligne_MatB][Colonne_MatB], double Res[Ligne_MatA][Colonne_MatA])

{

for (int i = 0; i < Ligne_MatA; i++)

{

for (int j = 0; j < Colonne_MatA; j++)

{

Res[i][j] = A[i][j]+B[i][j];

}

}

}

void Sub_Mat_Mat(int Ligne_MatA, int Colonne_MatA, double A[Ligne_MatA][Colonne_MatA],int Ligne_MatB, int Colonne_MatB, double B[Ligne_MatB][Colonne_MatB], double Res[Ligne_MatA][Colonne_MatA])

{

for (int i = 0; i < Ligne_MatA; i++)

{

for (int j = 0; j < Colonne_MatA; j++)

{

Res[i][j] = A[i][j]-B[i][j];

}

}

}

void Mul_Mat_Mat(int Ligne_MatA, int Colonne_MatA, double A[Ligne_MatA][Colonne_MatA],int Ligne_MatB, int Colonne_MatB, double B[Ligne_MatB][Colonne_MatB], double Res[Ligne_MatA][Colonne_MatB])

{

for (int i = 0; i < Ligne_MatA; i++)

{

for (int j = 0; j < Colonne_MatB; j++)

{

Res[i][j]=0;

for(int k=0; k < Ligne_MatB; k++)

{

Res[i][j] += A[i][k]*B[k][j];

}

}

}

}

void Inverse_Mat_Mat(int Ligne_MatA, int Colonne_MatA, double A[Ligne_MatA][Colonne_MatA],double Res[Ligne_MatA][Colonne_MatA])

//OBLIGATOIREMENT POUR DES MATRICES DE TAILLES 2x2

{

double unSurDet;

unSurDet = 1/(A[0][0]*A[1][1]-A[0][1]*A[1][0]);

Res[0][0] = A[1][1]*unSurDet;

Res[0][1] = -unSurDet*A[0][1];

Res[1][0] = -unSurDet*A[1][0];

Res[1][1] = A[0][0]*unSurDet;

}

void Transpose_Mat(int Ligne_MatA, int Colonne_MatA, double A[Ligne_MatA][Colonne_MatA],double Res[Colonne_MatA][Ligne_MatA])

{

int i,j;

for (i=0;i<Colonne_MatA;i++)

{

for (j=0;j<Ligne_MatA;j++)

{

Res[i][j]=A[j][i];

}

}

}

void tests_unitaires(void){

//Matrices d'entrée

double T21a[2][1]={{7},{-5}};

double T21b[2][1]={{-3},{46}};

double T22a[2][2]={{12,78},{-5,13}};

double T22b[2][2]={{-25,36},{7,42}};

double T24[2][4]={{7,-71,-12,3},{41,123,-5,10}};

double T41a[4][1]={{45},{-123},{-78},{-410}};

double T41b[4][1]={{-10},{45},{27},{-9}};

double T42a[4][2]={{-73,45},{10,12},{-41,-35},{8,-23}};

double T44a[4][4]={{1,2,7,4},{6,5,7,8},{9,8,7,6},{5,4,3,2}};

double T44b[4][4]={{12,13,14,15},{21,22,23,40},{78,45,12,3},{54,10,12,47}};

//Matrices résultat

double R21[2][1],R22[2][2],R24[2][4],R41[4][1],R42[4][2],R44[4][4];

//Matrices de validation

double RST21[2][1]={{10},{-51}};

double RInvT22[2][2]={{0.02380952380952381,-0.1428571428571428},{0.009157509157509158,0.02197802197802198}};

double RAT22[2][2]={{-13,114},{2,55}};

double RTT24[4][2]={{7,41},{-71,123},{-12,-5},{3,10}};

double RMT24T41[2][1]={{8754},{-16994}};

double RMT24T42[2][2]={{-705,-186},{-1478,3266}};

double RMT24T44[2][4]={{-512,-425,-523,-606},{784,697,1143,1138}};

double RAT41[4][1]={{35},{-78},{-51},{-419}};

double RMT42T21[4][1]={{-736},{10},{-112},{171}};

double RMT42T22[4][2]={{-1101,-5109},{60,936},{-317,-3653},{211,325}};

double RMT42T24[4][4]={{1334,10718,651,231},{562,766,-180,150},{-1722,-1394,667,-473},{-887,-3397,19,-206}};

double RTT44[4][4]={{1,6,9,5},{2,5,8,4},{7,7,7,3},{4,8,6,2}};

double RMT44T41[4][1]={{-2387},{-4171},{-3585},{-1321}};

double RMT44T42[4][2]={{-308,-268},{-611,-99},{-816,118},{-432,122}};

double RAT44[4][4]={{13,15,21,19},{27,27,30,48},{87,53,19,9},{59,14,15,49}};

double RST44[4][4]={{-11,-11,-7,-11},{-15,-17,-16,-32},{-69,-37,-5,3},{-49,-6,-9,-45}};

double RMT44T44[4][4]={{816,412,192,304},{1155,583,379,687},{1146,668,466,758},{486,308,222,338}};

printf("Execution des tests unitaires.\n");

Transpose_Mat(2,4,T24,R42); if (!Equal_Mat_Mat(RTT24,R42)) error("Erreur calcul Transposition 2x4");

Transpose_Mat(4,4,T44a,R44); if (!Equal_Mat_Mat(RTT44,R44)) error("Erreur calcul Transposition 4x4");

Inverse_Mat_Mat(2,2,T22a,R22); if (!Equal_Mat_Mat(RInvT22,R22)) error("Erreur calcul Inversion 2x2");

Add_Mat_Mat(2,2,T22a,2,2,T22b,R22); if (!Equal_Mat_Mat(RAT22,R22)) error("Erreur calcul Addition 2x2");

Add_Mat_Mat(4,4,T44a,4,4,T44b,R44); if (!Equal_Mat_Mat(RAT44,R44)) error("Erreur calcul Addition 4x4");

Add_Mat_Mat(4,1,T41a,4,1,T41b,R41); if (!Equal_Mat_Mat(RAT41,R41)) error("Erreur calcul Addition 4x1");

Sub_Mat_Mat(2,1,T21a,2,1,T21b,R21); if (!Equal_Mat_Mat(RST21,R21)) error("Erreur calcul Soustraction 2x1");

Sub_Mat_Mat(4,4,T44a,4,4,T44b,R44); if (!Equal_Mat_Mat(RST44,R44)) error("Erreur calcul Soustraction 4x4");

Mul_Mat_Mat(4,4,T44a,4,4,T44b,R44); if (!Equal_Mat_Mat(RMT44T44,R44)) error("Erreur calcul Multiplication 4x4 4x4");

Mul_Mat_Mat(4,4,T44a,4,1,T41a,R41); if (!Equal_Mat_Mat(RMT44T41,R41)) error("Erreur calcul Multiplication 4x4 4x1");

Mul_Mat_Mat(4,4,T44a,4,2,T42a,R42); if (!Equal_Mat_Mat(RMT44T42,R42)) error("Erreur calcul Multiplication 4x4 4x2");

Mul_Mat_Mat(4,2,T42a,2,1,T21a,R41); if (!Equal_Mat_Mat(RMT42T21,R41)) error("Erreur calcul Multiplication 4x2 2x1");

Mul_Mat_Mat(4,2,T42a,2,2,T22a,R42); if (!Equal_Mat_Mat(RMT42T22,R42)) error("Erreur calcul Multiplication 4x2 2x2");

Mul_Mat_Mat(4,2,T42a,2,4,T24,R44); if (!Equal_Mat_Mat(RMT42T24,R44)) error("Erreur calcul Multiplication 4x2 2x4");

Mul_Mat_Mat(2,4,T24,4,1,T41a,R21); if (!Equal_Mat_Mat(RMT24T41,R21)) error("Erreur calcul Multiplication 2x4 4x1");

Mul_Mat_Mat(2,4,T24,4,2,T42a,R22); if (!Equal_Mat_Mat(RMT24T42,R22)) error("Erreur calcul Multiplication 2x4 4x2");

Mul_Mat_Mat(2,4,T24,4,4,T44a,R24); if (!Equal_Mat_Mat(RMT24T44,R24)) error("Erreur calcul Multiplication 2x4 4x4");

printf("Test unitaires OK.\n");

int main(int argc,char **argv){

tests_unitaires();

debug=1; ///Mettre à 1 pour afficher les matrices.

// Kalmans

// X = F*X

Mul_Mat_Mat(4,4,F,4,1,X,X);

//P = F*P*F'+Q;

double A[4][4];

double B[4][4];

// A = F*P

Mul_Mat_Mat(4,4,F,4,4,P,A);

// B = A*FT

double FT[4][4];

Transpose_Mat(4,4,F,FT);

Mul_Mat_Mat(4,4,A,4,4,FT,B);

// P = B+Q

Add_Mat_Mat(4,4,B,4,4,Q,P);

// K = P*H' / ( H*P*H' + R);

// K = C /E

double C[4][2];

double HT[4][2];

Transpose_Mat(2,4,H,HT);

Mul_Mat_Mat(4,4,P,4,2,HT,C);

double D[2][4];

Mul_Mat_Mat(2,4,H,4,4,P,D);

double E[2][2];

Mul_Mat_Mat(2,4,D,4,2,HT,E);

Add_Mat_Mat(2,2,E,2,2,R,E);

double E_inv[2][2];

Inverse_Mat_Mat(2,2,E,E_inv);

Mul_Mat_Mat(4,2,C,2,2,E,K);

Plot_Mat(K,"K = ");

// DELTA = obs - H*X

double DELTA[2][1];

double obs[2][1]={{x},{y}};

double Z[2][1];

Mul_Mat_Mat(2,4,H,4,1,X,Z);

Sub_Mat_Mat(2,1,obs,2,1,Z,DELTA);

Plot_Mat(DELTA,"DELTA = Obs - H.X(k+1|k)");

// X = X + K*DELTA

double KD[4][1];

Mul_Mat_Mat(4,2,K,2,1,DELTA,KD);

Add_Mat_Mat(4,1,X,4,1,KD,X);

// P = P - K*H*P;

// W = H*P

double W[2][4];

Mul_Mat_Mat(2,4,H,4,4,P,W);

// Y = K*W

double Y[4][4];

Mul_Mat_Mat(4,2,K,2,4,W,Y);

// P = P-Y

Sub_Mat_Mat(4,4,P,4,4,Y,P);