4 Choleski_decomposition::solve(Vector rhs)const
10 // forward substitution
11 for (int i=0; i < n; i++) {
13 for (int j=0; j < i; j++)
15 y(i) = (rhs(i) - sum)/L(i,i);
17 for (int i=0; i < n; i++) {
24 for (int i=n-1; i >= 0; i--) {
26 for (int j=i+1; j < n; j++)
28 x(i) = (y(i) - sum)/L(i,i);
34 Standard matrix algorithm.
37 Choleski_decomposition::Choleski_decomposition(Matrix P)
38 : L(P.dim()), D(P.dim())
41 assert((P-P.transposed()).norm() < EPS);
43 for (int k= 0; k < n; k++) {
44 for (int j = 0; j < k; j++){
46 for (int l=0; l < j; l++)
47 sum += L(k,l)*L(j,l)*D(l);
48 L(k,j) = (P(k,j) - sum)/D(j);
52 for (int l=0; l < k; l++)
53 sum += sqr(L(k,l))*D(l);
54 Real d = P(k,k) - sum;
59 assert((original()-P).norm() < EPS);
64 Choleski_decomposition::original() const
68 return L*T*L.transposed();
72 Choleski_decomposition::inverse() const
77 for (int i = 0; i < n; i++) {
79 Vector inv(solve(e_i));
80 for (int j = 0 ; j<n; j++)
85 Matrix I1(n), I2(original());
87 assert((I1-original()*invm).norm() < EPS);