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"
const Real EPS = 1e-7; // so sue me. Hard coded
-Vector
-Choleski_decomposition::solve(Vector rhs)const
+// for testing new Matrix_storage.
+//#define PARANOID
+
+void
+Choleski_decomposition::full_matrix_solve (Vector &out, Vector const &rhs) const
{
- int n= rhs.dim();
- assert(n == L.dim());
- Vector y(n);
-
- // 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);
+ int n= rhs.dim();
+ assert (n == L.dim());
+ Vector y;
+ y.set_dim (n);
+ out.set_dim (n);
+
+ // 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);
}
- for (int i=0; i < n; i++)
- y(i) /= D(i);
-
- // backward subst
- Vector &x(rhs); // 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);
+
+ for (int i=0; i < n; 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);
}
- return x;
}
-/*
- Standard matrix algorithm.
- Should add support for banded matrices
- */
+void
+Choleski_decomposition::band_matrix_solve (Vector &out, Vector const &rhs) const
+{
+ int n= rhs.dim();
+ int b = L.band_i();
+ assert (n == L.dim());
+
+ 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);
+ }
+ for (int i=0; i < n; 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);
+ }
+}
-Choleski_decomposition::Choleski_decomposition(Matrix P)
- : L(P.dim()), D(P.dim())
+void
+Choleski_decomposition::solve (Vector &x, Vector const &rhs) const
{
- int n = P.dim();
+ if (band_b_)
+ {
+ band_matrix_solve (x,rhs);
+ }
+ else
+ full_matrix_solve (x,rhs);
+}
-#ifdef PARANOID
- assert((P-P.transposed()).norm()/P.norm() < EPS);
-#endif
-
- 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);
+Vector
+Choleski_decomposition::solve (Vector rhs) const
+{
+ Vector r;
+ solve (r, rhs);
+ return r;
+}
+
+void
+Choleski_decomposition::full_matrix_decompose (Matrix const & P)
+{
+
+ 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;
+ 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;
}
+}
+
+void
+Choleski_decomposition::band_matrix_decompose (Matrix const &P)
+{
+ int n = P.dim();
+ int b = P.band_i();
+ L.unit();
+
+ 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 l=0 >? i - b; l < i; l++)
+ sum += sqr (L(i,l))*D(l);
+ Real d = P(i,i) - sum;
+ D(i) = d;
+ }
+ L.set_band();
+ band_b_ = true;
+}
+
+
+
+
+/*
+ Standard matrix algorithm.
+ */
+
+Choleski_decomposition::Choleski_decomposition (Matrix const & P)
+ : L(P.dim()), D(P.dim ())
+{
+#ifdef PARANOID
+ assert ((P-P.transposed()).norm ()/P.norm () < EPS);
+#endif
+ band_b_ = false;
+
+ int b = P.calc_band_i ();
+
+ if (b <= P.dim ()/2)
+ band_matrix_decompose (P);
+ else
+ full_matrix_decompose (P);
+
#ifdef PARANOID
- assert((original()-P).norm() / P.norm() < EPS);
+ assert ((original()-P).norm () / P.norm () < EPS);
#endif
}
Matrix
Choleski_decomposition::original() const
{
- Matrix T(L.dim());
- T.set_diag(D);
- return L*T*L.transposed();
+ Matrix T(L.dim());
+ T.set_diag (D);
+ return L*T*L.transposed();
}
Matrix
Choleski_decomposition::inverse() const
{
- int n=L.dim();
- Matrix invm(n);
- Vector e_i(n);
- for (int i = 0; i < n; i++) {
- e_i.set_unit(i);
- Vector inv(solve(e_i));
- for (int j = 0 ; j<n; j++)
- invm(i,j) = inv(j);
+ int n=L.dim();
+ Matrix invm (n);
+ Vector e_i (n);
+ 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);
}
-
+
#ifdef PARANOID
- Matrix I1(n), I2(original());
- I1.unit();
- assert((I1-I2*invm).norm()/I2.norm() < EPS);
+ Matrix I1(n), I2(original());
+ I1.unit();
+ assert ((I1-I2*invm).norm()/I2.norm () < EPS);
#endif
-
- return invm;
+
+ return invm;
}
projects / lilypond.git / blobdiff