/**
* Compute the matrix R with the method Gram Schmidt
* @attribute n, number of rows and columns of Q, A and R.
* @attribute Q, matrix Q.
* @attribute A, matrix A.
* @attribute R, matrix R.
*/
void matrixR(int n, double **Q, double **A, double **R) {
double **QTrans;
createMatrix(&QTrans, n, n);
transposedMatrix(n, n, Q, QTrans);
multiplicationMatrix(n, n, QTrans, A, R);
destroyMatrix(&QTrans, n, n);
}
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;
}