source file of the Flower Library
- (c) 1997 Han-Wen Nienhuys <hanwen@stack.nl>
+ (c) 1997--1998 Han-Wen Nienhuys <hanwen@cs.uu.nl>
*/
#include "choleski.hh"
// forward substitution
for (int i=0; i < n; i++)
{
- Real sum (0.0);
- for (int j=0; j < i; j++)
- sum += y (j) * L(i,j);
- y (i) = (rhs (i) - sum)/L(i,i);
+ Real sum (0.0);
+ for (int j=0; j < i; j++)
+ sum += y (j) * L(i,j);
+ y (i) = (rhs (i) - sum)/L(i,i);
}
for (int i=0; i < n; i++)
- y (i) /= D(i);
+ y (i) /= D(i);
// backward subst
Vector &x (out); // using input as return val.
for (int i=n-1; i >= 0; i--)
{
- Real sum (0.0);
- for (int j=i+1; j < n; j++)
- sum += L(j,i)*x (j);
- x (i) = (y (i) - sum)/L(i,i);
+ Real sum (0.0);
+ for (int j=i+1; j < n; j++)
+ sum += L(j,i)*x (j);
+ x (i) = (y (i) - sum)/L(i,i);
}
}
int b = L.band_i();
assert (n == L.dim());
- out.set_dim (n);
+ out.set_dim (n);
Vector y;
y.set_dim (n);
// forward substitution
for (int i=0; i < n; i++)
{
- Real sum (0.0);
- for (int j= 0 >? i - b; j < i; j++)
- sum += y (j) * L(i,j);
- y (i) = (rhs (i) - sum)/L(i,i);
+ Real sum (0.0);
+ for (int j= 0 >? i - b; j < i; j++)
+ sum += y (j) * L(i,j);
+ y (i) = (rhs (i) - sum)/L(i,i);
}
for (int i=0; i < n; i++)
- y (i) /= D(i);
+ y (i) /= D(i);
// backward subst
Vector &x (out); // using input as return val.
for (int i=n-1; i >= 0; i--)
{
- Real sum (0.0);
- for (int j=i+1; j <= i + b&&j < n ; j++)
- sum += L(j,i)*x (j);
- x (i) = (y (i) - sum)/L(i,i);
+ Real sum (0.0);
+ for (int j=i+1; j <= i + b&&j < n ; j++)
+ sum += L(j,i)*x (j);
+ x (i) = (y (i) - sum)/L(i,i);
}
}
void
Choleski_decomposition::solve (Vector &x, Vector const &rhs) const
{
- if (L.band_b())
+ if (band_b_)
{
- band_matrix_solve (x,rhs);
+ band_matrix_solve (x,rhs);
}
else
- full_matrix_solve (x,rhs);
+ full_matrix_solve (x,rhs);
}
Vector
Choleski_decomposition::full_matrix_decompose (Matrix const & P)
{
- int n = P.dim();
+ int n = P.dim();
L.unit();
for (int k= 0; k < n; k++)
{
- for (int j = 0; j < k; j++)
- {
- Real sum (0.0);
- for (int l=0; l < j; l++)
- sum += L(k,l)*L(j,l)*D(l);
- L(k,j) = (P(k,j) - sum)/D(j);
- }
- Real sum=0.0;
+ for (int j = 0; j < k; j++)
+ {
+ Real sum (0.0);
+ for (int l=0; l < j; l++)
+ sum += L(k,l)*L(j,l)*D(l);
+ L(k,j) = (P(k,j) - sum)/D(j);
+ }
+ Real sum=0.0;
- for (int l=0; l < k; l++)
- sum += sqr (L(k,l))*D(l);
- Real d = P(k,k) - sum;
- D(k) = d;
+ for (int l=0; l < k; l++)
+ sum += sqr (L(k,l))*D(l);
+ Real d = P(k,k) - sum;
+ D(k) = d;
}
}
for (int i= 0; i < n; i++)
{
- for (int j = 0 >? i - b; j < i; j++)
- {
- Real sum (0.0);
- for (int l=0 >? i - b; l < j; l++)
- sum += L(i,l)*L(j,l)*D(l);
- L(i,j) = (P(i,j) - sum)/D(j);
- }
- Real sum=0.0;
+ for (int j = 0 >? i - b; j < i; j++)
+ {
+ Real sum (0.0);
+ for (int l=0 >? i - b; l < j; l++)
+ sum += L(i,l)*L(j,l)*D(l);
+ L(i,j) = (P(i,j) - sum)/D(j);
+ }
+ Real sum=0.0;
- for (int l=0 >? i - b; l < i; l++)
- sum += sqr (L(i,l))*D(l);
- Real d = P(i,i) - sum;
- D(i) = d;
+ for (int l=0 >? i - b; l < i; l++)
+ sum += sqr (L(i,l))*D(l);
+ Real d = P(i,i) - sum;
+ D(i) = d;
}
- L.try_set_band();
- assert ( L.band_i() == P.band_i ());
+ L.set_band();
+ band_b_ = true;
}
*/
Choleski_decomposition::Choleski_decomposition (Matrix const & P)
- : L(P.dim()), D(P.dim ())
+ : L(P.dim()), D(P.dim ())
{
#ifdef PARANOID
assert ((P-P.transposed()).norm ()/P.norm () < EPS);
#endif
- if (P.band_b())
- band_matrix_decompose (P);
+ band_b_ = false;
+
+ int b = P.calc_band_i ();
+
+ if (b <= P.dim ()/2)
+ band_matrix_decompose (P);
else
- full_matrix_decompose (P);
-
+ full_matrix_decompose (P);
#ifdef PARANOID
assert ((original()-P).norm () / P.norm () < EPS);
Vector inv (n);
for (int i = 0; i < n; i++)
{
- e_i.set_unit (i);
- solve (inv, e_i);
- for (int j = 0 ; j<n; j++)
- invm (i,j) = inv (j);
+ e_i.set_unit (i);
+ solve (inv, e_i);
+ for (int j = 0 ; j<n; j++)
+ invm (i,j) = inv (j);
}
#ifdef PARANOID