// A = Q * R QR Decomposition
void QRDecomp(MAT &A,MAT &Q, MAT &R){
int n=A.dim();
MAT AT(A.tpose());
MAT QT(Q.tpose());
VEC S(n); //sum vector
R[0][0]=sqrt(AT[0]*AT[0]); //initial R
QT[0]=AT[0]/R[0][0]; //initial Q
for(int j=1;j<n;j++){
for(int i=0;i<n;i++){
S[i] = 0;
} //initialization of sum vector
for(int i=0;i<=j;i++){
R[i][j] = QT[i]*AT[j];
}
for(int i=0;i<=j-1;i++){
S = S + R[i][j]*QT[i]; //do the summation
}
S = AT[j] - S;
R[j][j]=sqrt(S*S);
QT[j] = S/R[j][j];
}
Q=QT.tpose();
}
VEC choSolve(MAT &L, VEC b){
VEC y(b);
y = fwdSubs1(L,b); //do the forward substitution to solve y
L = L.tpose(); //compute the transpose of L
VEC x(y);
x = bckSubs(L,y); //do the backward substitution to solve x
return x;
}