double* mat_power(double mat[5][5], double *vec, int rows, int cols, int power) {
if (power == 0) {
return vec;
} else {
double *solution = matrix_vector_mult(mat, vec, rows, cols);
double *solution2 = mat_power (mat, solution, rows, cols, (power - 1));
return solution2;
}
}
double* mat_power(double mat[5][5], double *vec, int rows, int cols, int power) {
if (power == 0) {
return vec;
} else {
double *solution = matrix_vector_mult(mat, vec, rows, cols);
double *solution2 = vec_add (mat_power (mat, solution, rows, cols, (power - 1)), solution) ;
/* for (int i = 0; i < 5; i++) {
solution2[i] = solution2[i] + solution[i];
if (solution2[i] < 0) {
solution2[i] = 0;
}
if (solution2[i] > 10) {
solution2[i] = 10;
}
}*/
return solution2;
}
}
Table_quadruplet least_squares_approximation(Table_triplet points,
Booleen uniformConf) {
int i, j;
Table_quadruplet res;
res.nb = points.nb;
ALLOUER(res.table, points.nb);
Table_flottant steps = steps_computation(points, uniformConf);
double ** B;
ALLOUER(B, points.nb);
for(i = 0; i < points.nb; i++)
ALLOUER(B[i], points.nb);
B[0][0] = B[points.nb - 1][points.nb - 1] = 1;
for(i = 1; i < points.nb; i++)
B[0][i] = 0;
for(i = 0; i < points.nb; i++) {
for(j = 1; j < points.nb - 1; j++) {
B[j][i] = bernsteinPolynomial(i, points.nb - 1, steps.table[j]);
}
}
for(i = 0; i < points.nb - 1; i++)
B[points.nb - 1][i] = 0;
double ** BT = transposedMatrix(B, points.nb);
Grille_flottant Aprime;
Aprime.nb_lignes = Aprime.nb_colonnes = points.nb;
Aprime.grille = matrix_matrix_mult(B, BT, points.nb);
for(i = 0; i < points.nb; i++)
free(BT[i]);
free(BT);
double * pointsX, * pointsY, * pointsZ;
ALLOUER(pointsX, points.nb);
ALLOUER(pointsY, points.nb);
ALLOUER(pointsZ, points.nb);
split_x_y_z(points, pointsX, pointsY, pointsZ);
Table_flottant BprimeX, BprimeY, BprimeZ;
BprimeX.nb = BprimeY.nb = BprimeZ.nb = points.nb;
BprimeX.table = matrix_vector_mult(B, pointsX, points.nb);
BprimeY.table = matrix_vector_mult(B, pointsY, points.nb);
BprimeZ.table = matrix_vector_mult(B, pointsZ, points.nb);
free(pointsX); free(pointsY); free(pointsZ);
for(i = 0; i < points.nb; i++)
free(B[i]);
free(B);
Table_flottant resX, resY, resZ;
resX.nb = resY.nb = resZ.nb = points.nb;
ALLOUER(resX.table, points.nb);
ALLOUER(resY.table, points.nb);
ALLOUER(resZ.table, points.nb);
resolution_systeme_lineaire(&Aprime, &BprimeX, &resX);
resolution_systeme_lineaire(&Aprime, &BprimeY, &resY);
resolution_systeme_lineaire(&Aprime, &BprimeZ, &resZ);
for(i = 0; i < points.nb; i++) {
res.table[i].x = resX.table[i];
res.table[i].y = resY.table[i];
res.table[i].z = resZ.table[i];
res.table[i].h = 1;
}
free(BprimeX.table); free(BprimeY.table); free(BprimeZ.table);
free(resX.table); free(resY.table); free(resZ.table);
for(i = 0; i < Aprime.nb_lignes; i++)
free(Aprime.grille[i]);
free(Aprime.grille);
return res;
}
