q-inter, CtcWrapper, colors, CtcUnion

examples/13_qinter/main.cpp

@@ -23,7 +23,7 @@ int main()
 
   DefaultFigure::set_axes(axis(0,{-6,6}), axis(1,{-6,6}));
 
-  int q = 2;
+  int q = 1;
   DefaultFigure::pave(
     {{-6,6},{-6,6}},
     SepQInter(q, s1,s2,s3),

examples/13_qinter/main.py

@@ -20,7 +20,7 @@ def create_sep(b, d):
 
 DefaultFigure.set_axes(axis(0, Interval(-6,6)), axis(1, Interval(-6,6)))
 
-q = 2
+q = 1
 DefaultFigure.pave(
   [[-6,6],[-6,6]],
   SepQInter(q, s1,s2,s3),

src/core/contractors/codac2_CtcInter.h

@@ -116,6 +116,7 @@ namespace codac2
       {
         for(const auto& ci : _ctcs)
         {
+          (void)ci;
           assert_release(ci->size() == this->size());
         }
       }

src/core/contractors/codac2_CtcQInter.cpp

@@ -21,7 +21,8 @@ namespace codac2
 
   void CtcQInter::contract(IntervalVector& x) const
   {
-    if(_q == 0)
+    // If all constraints may be violated, no contraction can be performed.
+    if(_q == _ctcs.size())
       return;
 
     std::list<IntervalVector> l;
@@ -35,4 +36,4 @@ namespace codac2
 
     x = qinter(_q, l);
   }
-}
+}

src/core/contractors/codac2_CtcQInter.h

@@ -21,11 +21,13 @@ namespace codac2
   {
     public:
 
+      // q is the maximum number of constraints that may be violated.
       CtcQInter(unsigned int q, const Collection<CtcBase<IntervalVector>>& c)
         : Ctc<CtcQInter,IntervalVector>([&c]() {
             assert_release(!c.empty());
             Index n = size_of(c.front());
             for(const auto& s : c) {
+              (void)s;
               assert_release(size_of(s) == n && "all contractors must be of same size");
             }
             return n;
@@ -34,6 +36,7 @@ namespace codac2
         assert_release(q <= c.size());
       }
 
+      // q is the maximum number of constraints that may be violated.
       explicit CtcQInter(unsigned int q, Index n, const Collection<CtcBase<IntervalVector>>& ctcs = {})
         : Ctc<CtcQInter,IntervalVector>(n), _q(q), _ctcs(ctcs)
       {
@@ -64,4 +67,4 @@ namespace codac2
       size_t _q;
       Collection<CtcBase<IntervalVector>> _ctcs;
   };
-}
+}

src/core/contractors/codac2_CtcUnion.h

@@ -48,6 +48,7 @@ namespace codac2
       {
         for(const auto& ci : _ctcs)
         {
+          (void)ci;
           assert_release(ci->size() == this->size());
         }
       }
@@ -65,7 +66,9 @@ namespace codac2
 
       void contract(X&... x) const
       {
-        auto result = std::tuple<X...>(x...);
+        const auto input = std::tuple<X...>(x...);
+
+        auto result = input;
         std::apply([](auto&... xi)
         {
           (xi.set_empty(), ...);
@@ -78,14 +81,20 @@ namespace codac2
 
         for(const auto& ci : _ctcs)
         {
-          auto saved = std::tuple<X...>(x...);
+          auto saved = input;
 
           std::apply([&](auto&... xi)
           {
             ci->contract(xi...);
           }, saved);
 
           accumulate_union(saved, std::index_sequence_for<X...>{});
+
+          // Each contractor is contractant, hence every remaining branch
+          // can only return a subset of input. Once the accumulated union
+          // has reached input, the final result is already known.
+          if(result == input)
+            return;
         }
 
         std::tie(x...) = result;

src/core/contractors/codac2_CtcWrapper.h

@@ -26,6 +26,10 @@ namespace codac2
         : Ctc<CtcWrapper<Y>,X>(y.size()), _y(y)
       { }
 
+      CtcWrapper(Y&& y)
+        : Ctc<CtcWrapper<Y>,X>(y.size()), _y(std::move(y))
+      { }
+
       void contract(X& x) const
       {
         assert_release(x.size() == this->size());

src/core/proj/codac2_qinter.cpp

@@ -20,9 +20,6 @@ namespace codac2
   {
     assert(!l.empty());
     Index n = l.begin()->size();
-
-    if(q > l.size())
-      return IntervalVector::empty(n);
 
     assert(([&l,n](){
       for(const auto& xi : l) {
@@ -33,18 +30,33 @@ namespace codac2
       return true;
     }()));
 
+    if(q > l.size())
+      return IntervalVector::empty(n);
+
+    // q is the maximum number of boxes that may be violated.
+    // Hence, at least l.size()-q boxes must contain the point.
+    const size_t min_satisfied = l.size()-q;
+
+    if(min_satisfied == 0)
+      return IntervalVector(n);
+
     unsigned int p = 0;
     for(const auto& li : l)
       if(!li.is_empty())
         p++;
 
+    // Empty boxes cannot be satisfied.
+    if(min_satisfied > p)
+      return IntervalVector::empty(n);
+
     IntervalVector res(n);
     std::vector<std::pair<double,ProjBound>> b(2*p);
 
-    // Main loop: solve the q-inter independently on each dimension, and return the Cartesian product
+    // Main loop: solve the q-relaxed intersection independently on each dimension,
+    // and return the Cartesian product
     for(Index i = 0 ; i < n ; i++)
     {
-      // Solve the q-inter for dimension i
+      // Solve the q-relaxed intersection for dimension i
 
       int j = 0;
       for(const auto& xj : l)
@@ -64,7 +76,7 @@ namespace codac2
       for(unsigned int k = 0 ; k < 2*p ; k++)
       {
         (b[k].second == ProjBound::LEFT) ? c++ : c--;
-        if(c == (int)q)
+        if(c == static_cast<int>(min_satisfied))
         {
           lb0 = b[k].first;
           break;
@@ -82,7 +94,7 @@ namespace codac2
       for(int k = 2*p-1 ; k >= 0 ; k--)
       {
         (b[k].second == ProjBound::RIGHT) ? c++ : c--;
-        if(c == (int)q)
+        if(c == static_cast<int>(min_satisfied))
         {
           rb0 = b[k].first;
           break;
@@ -94,4 +106,4 @@ namespace codac2
 
     return res;
   }
-}
+}

src/core/proj/codac2_qinter.h

@@ -14,9 +14,9 @@
 
 namespace codac2
 {
-  // Approximate Q-intersection, using Luc Jaulin's algorithm
+  // Approximate q-relaxed intersection, using Luc Jaulin's algorithm
   // Author: Clement Carbonnel, Benoit Desrochers, Simon Rohou
-  // The q-intersection of n boxes corresponds to the set of all elements
-  // which belong to at least q of these boxes.
+  // The q-relaxed intersection of n boxes corresponds to the set of all elements
+  // which belong to at least n-q of these boxes, i.e. which violate at most q boxes.
   IntervalVector qinter(unsigned int q, const std::list<IntervalVector>& l);
-}
+}

src/core/separators/codac2_SepQInter.cpp

@@ -22,7 +22,8 @@ namespace codac2
 
   BoxPair SepQInter::separate(const IntervalVector& x) const
   {
-    if(_q == 0)
+    // If all constraints may be violated, the represented set is the whole space.
+    if(_q == _seps.size())
       return { IntervalVector::empty(x.size()), x };
 
     std::list<IntervalVector> l_inner, l_outer;
@@ -34,11 +35,11 @@ namespace codac2
     }
 
     BoxPair x_sep {
-      qinter(_seps.size()-_q+1, l_inner),
+      qinter(_seps.size()-_q-1, l_inner),
       qinter(_q, l_outer)
     };
 
     assert((x_sep.inner | x_sep.outer) == x);
     return x_sep;
   }
-}
+}

src/core/separators/codac2_SepQInter.h

@@ -20,11 +20,13 @@ namespace codac2
   {
     public:
 
+      // q is the maximum number of constraints that may be violated.
       SepQInter(unsigned int q, const Collection<SepBase>& c)
         : Sep<SepQInter>([&c]() {
             assert_release(!c.empty());
             Index n = size_of(c.front());
             for(const auto& s : c) {
+              (void)s;
               assert_release(size_of(s) == n && "all separators must be of same size");
             }
             return n;
@@ -33,6 +35,7 @@ namespace codac2
         assert_release(q <= c.size());
       }
 
+      // q is the maximum number of constraints that may be violated.
       explicit SepQInter(unsigned int q, Index n, const Collection<SepBase>& sep = {})
         : Sep<SepQInter>(n), _q(q), _seps(sep)
       {
@@ -62,4 +65,4 @@ namespace codac2
       size_t _q;
       Collection<SepBase> _seps;
   };
-}
+}

src/graphics/styles/codac2_Color.h

@@ -162,7 +162,7 @@ namespace codac2
        */
       static Color random(float alpha = 1.)
       {
-        return Color({(float)Interval(0,360).rand(),100,100, (float)(alpha * 255.)}, Model::HSV);
+        return Color({(float)Interval(0,360).rand(),100,100, (float)(alpha * 100.)}, Model::HSV);
       };
 
       #define DEFINE_COLOR(NAME, R, G, B) \