codac-team
Error in gates result of contraction by Lohner Contractor
Le contracteur CtcLohner perd les portes initiales et finales ponctuelles du premier tube d'un tube vector de dimension 2 (BVP) pendant la contraction. la porte initiale [1,1] devient [-92.35, 94.85] la porte finale [0,0] devient [-93.6, 93.6]
code
#include
using namespace std; using namespace ibex; using namespace codac;
int main(){
IntervalVector bounds (2);
bounds[0]=Interval(-100,100);
bounds[1]=Interval(-100,100);
Interval domain(0.,1);
TubeVector x(domain,0.5,bounds);
Function f("x1", "x2" ,"(x2;x1)");
IntervalVector v(2);
v[0]=Interval(1.,1.);
v[1]=Interval(-100,100);
x.set(v, 0.); // ini
v[0]=Interval(0.,0.);
v[1]=Interval(-100,100);
x.set(v, 1.); // ini
cout << " x avant " << x << endl;
CtcLohner ctclohner(f);
cout << " x before Lohner " << x << endl;
for (int k=0; k< x.size(); k++){
const Slice *slice = x[k].first_slice();
while(slice != NULL){
cout << " slice " << k << *slice << endl;
slice = slice->next_slice();
}
} ctclohner.contract(x); cout << " x after Lohner " << x << endl; for (int k=0; k< x.size(); k++){
const Slice *slice = x[k].first_slice();
while(slice != NULL){
cout << " slice " << k << *slice << endl;
slice = slice->next_slice();
}
} cout << " x " << x << endl; return 0; }
voici les résultats x avant TubeVector (dim 2) [0, 1]↦([-100, 100] ; [-100, 100]), 2 slices x before Lohner TubeVector (dim 2) [0, 1]↦([-100, 100] ; [-100, 100]), 2 slices slice 0Slice [0, 0.5]↦([1, 1])[-100, 100]([-100, 100]) slice 0Slice [0.5, 1]↦([-100, 100])[-100, 100]([0, 0]) slice 1Slice [0, 0.5]↦([-100, 100])[-100, 100]([-100, 100]) slice 1Slice [0.5, 1]↦([-100, 100])[-100, 100]([-100, 100]) x after Lohner TubeVector (dim 2) [0, 1]↦([-93.6, 94.85] ; [-100, 100]), 2 slices slice 0Slice [0, 0.5]↦([-92.35, 94.85])[-92.35, 94.85]([-92.35, 93.6]) slice 0Slice [0.5, 1]↦([-92.35, 93.6])[-93.6, 93.6]([-93.6, 93.6]) slice 1Slice [0, 0.5]↦([-100, 100])[-100, 100]([-100, 100]) slice 1Slice [0.5, 1]↦([-100, 100])[-100, 100]([-100, 100]) x TubeVector (dim 2) [0, 1]↦([-93.6, 94.85] ; [-100, 100]), 2 slices
This should correct the bug: 044535fcf63c5bb506ef63458d2c50a960b1ff46
I add @AugusteBourgois (main developer of the Lohner) to this conversation.
OK for this correction; I have now another problem where the solution of the BVP is lost when the Lohner Contractor is applied in a fixed-point loop. the firrst tube becomes empty. The code of the is the following :
int main(){
Interval domain(0.,1);
TubeVector x(domain,0.03125,2);
Function f("x1", "x2" ,"(x2;x1)");
IntervalVector v(2);
v[0]=Interval(1.,1.);
v[1]=Interval(-100,100);
x.set(v, 0.); // ini
v[0]=Interval(0.,0.);
v[1]=Interval(-100,100);
x.set(v, 1.); // ini
for (int i=0; i<10;i++){
cout << " x avant " << x << endl;
CtcLohner ctclohner(f);
cout << " x before Lohner " << x << endl;
for (int k=0; k< x.size(); k++){
const Slice *slice = x[k].first_slice();
while(slice != NULL){
cout << " slice " << k << *slice << endl;
slice = slice->next_slice();
}
}
ctclohner.contract(x);
cout <<" i " << i << " x after Lohner " << x << endl;
for (int k=0; k< x.size(); k++){
const Slice *slice = x[k].first_slice();
while(slice != NULL){
cout << " slice " << k << *slice << endl;
slice = slice->next_slice();
}
}
}
return 0;
}
results at the iteration 9 i 9 x after Lohner TubeVector (dim 2) [0, 1]↦([-3.60482, 0.0271986] ; [5.82926, 9.75906]), 32 slices slice 0Slice [0, 0.03125]↦([ empty ])[ empty ]([ empty ]) slice 0Slice [0.03125, 0.0625]↦([ empty ])[ empty ]([ empty ]) slice 0Slice [0.0625, 0.09375]↦([ empty ])[ empty ]([ empty ]) slice 0Slice [0.09375, 0.125]↦([ empty ])[ empty ]([ empty ]) slice 0Slice [0.125, 0.15625]↦([ empty ])[ empty ]([ empty ]) slice 0Slice [0.15625, 0.1875]↦([ empty ])[ empty ]([ empty ]) slice 0Slice [0.1875, 0.21875]↦([ empty ])[ empty ]([ empty ]) slice 0Slice [0.21875, 0.25]↦([ empty ])[ empty ]([ empty ]) slice 0Slice [0.25, 0.28125]↦([ empty ])[ empty ]([ empty ]) slice 0Slice [0.28125, 0.3125]↦([ empty ])[ empty ]([ empty ]) slice 0Slice [0.3125, 0.34375]↦([ empty ])[ empty ]([ empty ]) slice 0Slice [0.34375, 0.375]↦([ empty ])[ empty ]([ empty ]) slice 0Slice [0.375, 0.40625]↦([ empty ])[ empty ]([ empty ]) slice 0Slice [0.40625, 0.4375]↦([ empty ])[ empty ]([ empty ]) slice 0Slice [0.4375, 0.46875]↦([ empty ])[ empty ]([ empty ]) slice 0Slice [0.46875, 0.5]↦([ empty ])[ empty ]([ empty ]) slice 0Slice [0.5, 0.53125]↦([ empty ])[-0.302171, -0.199592]([ empty ]) slice 0Slice [0.53125, 0.5625]↦([ empty ])[-1.25698, -0.338892]([-1.25698, -0.863086]) slice 0Slice [0.5625, 0.59375]↦([-1.25698, -0.863086])[-2.25302, -0.863086]([-2.25302, -1.13284]) slice 0Slice [0.59375, 0.625]↦([-2.25302, -1.13284])[-2.93505, -1.13284]([-2.93505, -1.13284]) slice 0Slice [0.625, 0.65625]↦([-2.93505, -1.13284])[-3.3586, -1.13169]([-3.3586, -1.13169]) slice 0Slice [0.65625, 0.6875]↦([-3.3586, -1.13169])[-3.53808, -0.954964]([-3.53808, -0.954964]) slice 0Slice [0.6875, 0.71875]↦([-3.53808, -0.954964])[-3.60482, -0.82612]([-3.24533, -0.82612]) slice 0Slice [0.71875, 0.75]↦([-3.24533, -0.82612])[-3.24533, -0.705014]([-2.88235, -0.705014]) slice 0Slice [0.75, 0.78125]↦([-2.88235, -0.705014])[-2.88235, -0.591248]([-2.51596, -0.591248]) slice 0Slice [0.78125, 0.8125]↦([-2.51596, -0.591248])[-2.51596, -0.484293]([-2.14636, -0.484293]) slice 0Slice [0.8125, 0.84375]↦([-2.14636, -0.484293])[-2.14636, -0.383486]([-1.77387, -0.383486]) slice 0Slice [0.84375, 0.875]↦([-1.77387, -0.383486])[-1.77387, -0.288028]([-1.39898, -0.288028]) slice 0Slice [0.875, 0.90625]↦([-1.39898, -0.288028])[-1.39898, -0.196996]([-1.01103, -0.196996]) slice 0Slice [0.90625, 0.9375]↦([-1.01103, -0.196996])[-1.01103, -0.12059]([-0.625276, -0.12059]) slice 0Slice [0.9375, 0.96875]↦([-0.625276, -0.12059])[-0.625276, -0.0618176]([-0.299184, -0.0618176]) slice 0Slice [0.96875, 1]↦([-0.299184, -0.0618176])[-0.299184, 0.0271986]([0, 0])
the solution of this problem is found using capd in the solver
nb sol 1 TubeVector (dim 2) [0, 1]↦([-5.18293e-20, 1] ; [-1.31807, -0.850177]), 40000 slices ti-> ([1, 1] ; [-1.31807, -1.31189]) tf -> ([0, 0] ; [-0.858027, -0.850177]) max diam : 1, 0.467892 volume : 1.46789 ti (diam) -> (0 ; 0.00617769) tf (diam) -> (0 ; 0.00784996)
Does this problem appears before 044535fcf63c5bb506ef63458d2c50a960b1ff46? Or this commit was already necessary for allowing propagations in your solver?
Without this commit, the problem does not appear, but the propagation stops after a few steps and does not reach the solution, the initial and final gates have been enlarged.