source file of the GNU LilyPond music typesetter
- (c) 1996,1997 Han-Wen Nienhuys <hanwen@stack.nl>
+ (c) 1996, 1997--1998 Han-Wen Nienhuys <hanwen@stack.nl>
*/
#include "ineq-constrained-qp.hh"
#include "qlpsolve.hh"
#include "debug.hh"
#include "choleski.hh"
+#include "main.hh"
/*
- MAy be this also should go into a library
+ May be this also should go into a library
*/
const int MAXITER=100; // qlpsolve.hh
+
/*
assume x (idx) == value, and adjust constraints, lin and quad accordingly
void
Ineq_constrained_qp::eliminate_var (int idx, Real value)
{
- Vector row (quad.row (idx));
+ Vector row (quad_.row (idx));
row*= value;
- quad.delete_row (idx);
+ quad_.delete_row (idx);
- quad.delete_column (idx);
+ quad_.delete_column (idx);
- lin.del (idx);
+ lin_.del (idx);
row.del (idx);
- lin +=row ;
+ lin_ +=row ;
- for (int i=0; i < cons.size(); i++)
+ for (int i=0; i < cons_.size(); i++)
{
- consrhs[i] -= cons[i](idx) *value;
- cons[i].del (idx);
+ consrhs_[i] -= cons_[i](idx) *value;
+ cons_[i].del (idx);
}
}
void
Ineq_constrained_qp::add_inequality_cons (Vector c, double r)
{
- cons.push (c);
- consrhs.push (r);
+ cons_.push (c);
+ consrhs_.push (r);
}
Ineq_constrained_qp::Ineq_constrained_qp (int novars):
- quad (novars),
- lin (novars),
- const_term (0.0)
+ quad_ (novars),
+ lin_ (novars),
+ const_term_ (0.0)
{
}
Ineq_constrained_qp::OK() const
{
#if !defined (NDEBUG) && defined (PARANOID)
- assert (cons.size() == consrhs.size ());
- Matrix Qdif= quad - quad.transposed();
- assert (Qdif.norm()/quad.norm () < EPS);
-#endif
+ assert (cons_.size() == consrhs_.size ());
+ Matrix Qdif= quad_ - quad_.transposed();
+ assert (Qdif.norm()/quad_.norm () < EPS);
+#endif
}
-
+
Real
Ineq_constrained_qp::eval (Vector v)
{
- return v * quad * v + lin * v + const_term;
+ return v * quad_ * v + lin_ * v + const_term_;
}
int
min_elt_index (Vector v)
{
- Real m=infinity_f;
+ Real m=infinity_f;
int idx=-1;
for (int i = 0; i < v.dim(); i++)
{
- if (v (i) < m)
+ if (v (i) < m)
{
idx = i;
m = v (i);
*/
Vector
-Ineq_constrained_qp::constraint_solve (Vector start) const
-{
+Ineq_constrained_qp::constraint_solve (Vector start) const
+{
if (!dim())
return Vector (0);
-
- // experimental
- if (quad.dim() > 10)
- quad.try_set_band();
-
+
Active_constraints act (this);
- act.OK();
+ act.OK();
+
-
Vector x (start);
- Vector gradient=quad*x+lin;
- // Real fvalue = x*quad*x/2 + lin*x + const_term;
+ Vector gradient=quad_*x+lin_;
+ // Real fvalue = x*quad_*x/2 + lin*x + const_term;
// it's no use.
Vector last_gradient (gradient);
int iterations=0;
-
- while (iterations++ < MAXITER)
+
+ while (iterations++ < MAXITER)
{
+ //#ifdef PARANOID
+ if (experimental_features_global_b)
+ assert_solution (x);
+ //#endif
+
Vector direction= - act.find_active_optimum (gradient);
-
+
DOUT << "gradient "<< gradient<< "\ndirection " << direction<<"\n";
-
- if (direction.norm() > EPS)
+
+ if (direction.norm() > EPS)
{
DOUT << act.status() << '\n';
-
- Real minalf = infinity_f;
+
+ Real unbounded_alfa = 1.0;
+ Real minalf = unbounded_alfa;
Inactive_iter minidx (act);
we know the optimum on this "hyperplane". Check if we
bump into the edges of the simplex
*/
-
- for (Inactive_iter ia (act); ia.ok(); ia++)
- {
- if (ia.vec() * direction >= 0)
+ for (Inactive_iter ia (act); ia.ok(); ia++)
+ {
+ Real dot = ia.vec() * direction;
+ if (dot >= 0)
continue;
- Real alfa= - (ia.vec()*x - ia.rhs ())/
- (ia.vec()*direction);
-
- if (minalf > alfa)
+
+
+ Real numerator = ia.rhs () - ia.vec()*x;
+ if (numerator >= 0)
+ {
+ if (numerator > EPS)
+ warning (String ("Ineq_constrained_qp::solve (): Constraint off by ") + numerator);
+ minalf = -numerator;
+ minidx = ia;
+ break;
+ }
+
+ Real alfa = numerator / dot;
+
+
+ if (minalf > alfa)
{
minidx = ia;
minalf = alfa;
}
}
- Real unbounded_alfa = 1.0;
- Real optimal_step = min (minalf, unbounded_alfa);
+
+ Real optimal_step = minalf;
Vector deltax=direction * optimal_step;
- x += deltax;
- gradient += optimal_step * (quad * deltax);
-
+ x += deltax;
+ gradient += optimal_step * (quad_ * deltax);
+
DOUT << "step = " << optimal_step<< " (|dx| = " <<
- deltax.norm() << ")\n";
-
- if (minalf < unbounded_alfa)
+ deltax.norm() << ")\n";
+
+ if (minalf < unbounded_alfa)
{
/* bumped into an edge. try again, in smaller space. */
act.add (minidx.idx());
continue;
}
/*ASSERT: we are at optimal solution for this "plane"*/
-
-
+
+
}
-
- Vector lagrange_mult=act.get_lagrange (gradient);
+
+ Vector lagrange_mult=act.get_lagrange (gradient);
int m= min_elt_index (lagrange_mult);
-
- if (m>=0 && lagrange_mult (m) > 0)
+
+ if (m>=0 && lagrange_mult (m) > 0)
{
break; // optimal sol.
}
- else if (m<0)
+ else if (m<0)
{
assert (gradient.norm() < EPS) ;
-
+
break;
}
-
+
DOUT << "dropping cons " << m<<'\n';
act.drop (m);
}
if (iterations >= MAXITER)
- WARN<<"didn't converge!\n";
-
+ WARN<<_("didn't converge!\n");
+
DOUT << ": found " << x<<" in " << iterations <<" iterations\n";
assert_solution (x);
return x;
-}
+}
+
-
Vector
Ineq_constrained_qp::solve (Vector start) const
-{
+{
/* no hassle if no constraints*/
- if (! cons.size())
+ if (! cons_.size())
{
- Choleski_decomposition chol (quad);
- return - chol.solve (lin);
+ Choleski_decomposition chol (quad_);
+ return - chol.solve (lin_);
}
- else
+ else
{
return constraint_solve (start);
}
}
+
+int
+Ineq_constrained_qp::dim () const
+{
+ return lin_.dim();
+}
+
projects / lilypond.git / blobdiff