Gaussian Accelerated Billiard Walk (#323)

* New gaussian accelerated billiard walk * minor changes for PR * add space * Fix indentation, simplify equation * minor optimizations * added normalized flag, made indentation consistent, changed file name * remove line * add copyright comments * added is_normalized function to all types of bodies * remove old file * fix outdated example
GeomScale · Jul 22, 2024 · 9d2eb4c · 9d2eb4c
1 parent c2504a5
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Showing 16 changed files with 274 additions and 115 deletions.
diff --git a/examples/sampling-hpolytope-with-billiard-walks/sampler.cpp b/examples/sampling-hpolytope-with-billiard-walks/sampler.cpp
@@ -7,6 +7,7 @@
 #include "sampling/random_point_generators.hpp"
 #include "random_walks/random_walks.hpp"
 #include "preprocess/max_inscribed_ellipsoid.hpp"
+#include "preprocess/inscribed_ellipsoid_rounding.hpp"
 #include "convex_bodies/ellipsoid.h"
 #include "convex_bodies/hpolytope.h"
 
@@ -69,23 +70,18 @@ void sample_using_gaussian_billiard_walk(HPOLYTOPE& HP, RNGType& rng, unsigned i
     Point q(HP.dimension()); // origin
 
     // ----------- Get inscribed ellipsoid --------------------------------
-    typedef Ellipsoid<Point> EllipsoidType;
     unsigned int max_iter = 150;
     NT tol = std::pow(10, -6.0), reg = std::pow(10, -4.0);
     VT x0 = q.getCoefficients();
-    MT E;
     VT center;
     bool converged;
-    std::tie(E, center, converged) = max_inscribed_ellipsoid<MT>(HP.get_mat(),
-        HP.get_vec(), x0, max_iter, tol, reg);
-
-    if (!converged) // not converged
-        throw std::runtime_error("max_inscribed_ellipsoid not converged");
-
-    EllipsoidType inscribed_ellipsoid(E);
+    std::tuple<MT, VT, NT> ellipsoid = compute_inscribed_ellipsoid<MT, EllipsoidType::VOLUMETRIC_BARRIER>
+    (HP.get_mat(), HP.get_vec(), x0, max_iter, tol, reg);
+
+    const MT E = get<0>(ellipsoid);
     // --------------------------------------------------------------------
 
-    Generator::apply(HP, q, inscribed_ellipsoid, num_points, walk_len,
+    Generator::apply(HP, q, E, num_points, walk_len,
                      randPoints, push_back_policy, rng);
     write_to_file(filename, randPoints);
 }

diff --git a/include/convex_bodies/ballintersectconvex.h b/include/convex_bodies/ballintersectconvex.h
@@ -50,6 +50,12 @@ class BallIntersectPolytope {
         return P.get_vec();
     }
 
+    bool is_normalized () {
+        return true;
+    }
+
+    void normalize() {}
+
     int is_in(PointType const& p) const
     {
         if (B.is_in(p)==-1)

diff --git a/include/convex_bodies/correlation_matrices/correlation_spectrahedron.hpp b/include/convex_bodies/correlation_matrices/correlation_spectrahedron.hpp
@@ -261,6 +261,12 @@ class CorrelationSpectrahedron : public Spectrahedron<Point>{
     MT get_mat() const {
         return MT::Identity(this->d, this->d);
     }
+
+    bool is_normalized () {
+        return true;
+    }
+
+    void normalize() {}
 };
 
 #endif //VOLESTI_CONVEX_BODIES_CORRELATION_MATRICES_VOLESTI_CORRELATION_SPECTRAHEDRON_HPP
diff --git a/include/convex_bodies/hpolytope.h b/include/convex_bodies/hpolytope.h
@@ -6,6 +6,7 @@
 //Contributed and/or modified by Apostolos Chalkis, as part of Google Summer of Code 2018-19 programs.
 //Contributed and/or modified by Repouskos Panagiotis, as part of Google Summer of Code 2019 program.
 //Contributed and/or modified by Alexandros Manochis, as part of Google Summer of Code 2020 program.
+//Contributed and/or modified by Luca Perju, as part of Google Summer of Code 2024 program.
 
 // Licensed under GNU LGPL.3, see LICENCE file
 
@@ -56,6 +57,7 @@ class HPolytope {
     MT                   A; //matrix A
     VT                   b; // vector b, s.t.: Ax<=b
     std::pair<Point, NT> _inner_ball;
+    bool                 normalized = false; // true if the polytope is normalized
 
 public:
     //TODO: the default implementation of the Big3 should be ok. Recheck.
@@ -68,7 +70,7 @@ class HPolytope {
 
     // Copy constructor
     HPolytope(HPolytope<Point> const& p) :
-            _d{p._d}, A{p.A}, b{p.b}, _inner_ball{p._inner_ball}
+            _d{p._d}, A{p.A}, b{p.b}, _inner_ball{p._inner_ball}, normalized{p.normalized}
     {
     }
 
@@ -172,11 +174,17 @@ class HPolytope {
         return b;
     }
 
+    bool is_normalized ()
+    {
+        return normalized;
+    }
+
 
     // change the matrix A
     void set_mat(MT const& A2)
     {
         A = A2;
+        normalized = false;
     }
 
 
@@ -541,7 +549,6 @@ class HPolytope {
 
         NT lamda = 0;
         VT sum_nom;
-        unsigned int j;
         int m = num_of_hyperplanes(), facet;
 
         Ar.noalias() += lambda_prev*Av;
@@ -822,6 +829,7 @@ class HPolytope {
     void linear_transformIt(MT const& T)
     {
         A = A * T;
+        normalized = false;
     }
 
 
@@ -866,6 +874,7 @@ class HPolytope {
             A.row(i) = A.row(i) / row_norm;
             b(i) = b(i) / row_norm;
         }
+        normalized = true;
     }
 
     void compute_reflection(Point& v, Point const&, int const& facet) const
@@ -909,6 +918,18 @@ class HPolytope {
             v += a;
     }
 
+    template <typename update_parameters>
+    NT compute_reflection(Point &v, const Point &, MT const &AE, VT const &AEA, NT const &vEv, update_parameters const &params) const {
+
+            Point a((-2.0 * params.inner_vi_ak) * A.row(params.facet_prev));
+            VT x = v.getCoefficients();
+            NT new_vEv = vEv - (4.0 * params.inner_vi_ak) * (AE.row(params.facet_prev).dot(x) - params.inner_vi_ak * AEA(params.facet_prev));
+            v += a;
+            NT coeff = std::sqrt(vEv / new_vEv);
+            v = v * coeff;
+            return coeff;
+    }
+
     void update_position_internal(NT&){}
 
     template <class bfunc, class NonLinearOracle>

diff --git a/include/convex_bodies/orderpolytope.h b/include/convex_bodies/orderpolytope.h
@@ -100,6 +100,10 @@ class OrderPolytope {
         return b;
     }
 
+    bool is_normalized ()
+    {
+        return _normalized;
+    }
 
     // print polytope in Ax <= b format
     void print() const

diff --git a/include/convex_bodies/spectrahedra/spectrahedron.h b/include/convex_bodies/spectrahedra/spectrahedron.h
@@ -341,6 +341,13 @@ class Spectrahedron {
     {
         return MT::Identity(lmi.dimension(), lmi.dimension());
     }
+
+    bool is_normalized ()
+    {
+        return true;
+    }
+
+    void normalize() {}
 
     void resetFlags()
     {

diff --git a/include/convex_bodies/vpolyintersectvpoly.h b/include/convex_bodies/vpolyintersectvpoly.h
@@ -92,6 +92,10 @@ class IntersectionOfVpoly {
         return P1.get_vec();
     }
 
+    bool is_normalized () {
+        return true;
+    }
+
     MT get_T() const {
         return P1.get_mat();
     }

diff --git a/include/convex_bodies/vpolytope.h b/include/convex_bodies/vpolytope.h
@@ -213,6 +213,10 @@ class VPolytope {
         return b;
     }
 
+    bool is_normalized () {
+        return true;
+    }
+
     // change the matrix V
     void set_mat(const MT &V2) {
         V = V2;

diff --git a/include/convex_bodies/zonoIntersecthpoly.h b/include/convex_bodies/zonoIntersecthpoly.h
@@ -65,6 +65,12 @@ class ZonoIntersectHPoly {
         return HP.get_vec();
     }
 
+    bool is_normalized () {
+        return true;
+    }
+
+    void normalize() {}
+
     std::pair<PointType,NT> InnerBall() const
     {
         return Z.InnerBall();

diff --git a/include/convex_bodies/zpolytope.h b/include/convex_bodies/zpolytope.h
@@ -299,6 +299,11 @@ class Zonotope {
         return b;
     }
 
+    bool is_normalized ()
+    {
+        return true;
+    }
+
     // change the matrix V
     void set_mat(MT const& V2)
     {