/* computes a conjugate gradient optimisation */
int methodedugradient(double*w,double *G,double *lambda,double *tirages,double spot, double r,int N )
{
int i;
double pas;
double test;
double t;
double *Grad=malloc((N+1)*sizeof(double));
double *grad=malloc((N+1)*sizeof(double));
double *mult=malloc((N+1)*sizeof(double));
double *add=malloc((N+1)*sizeof(double));
double *Mult=malloc((N+1)*sizeof(double));
double *lambda0=malloc((N+1)*sizeof(double));
double*zero=malloc((N+1)*sizeof(double));
double *direction=malloc((N+1)*sizeof(double));
for(i=0;i<N;i++)
{
lambda0[i]=1;
zero[i]=0;
}
multiplication(lambda,0,lambda0,spot,r,N);
gradient(w,G,Grad,tirages,lambda ,spot,r,N);
gradient(w,G,direction,tirages,lambda ,spot,r,N);
test=normeinfinie(Grad,lambda,spot,r,N);
while ((normeinfinie(lambda0,lambda,spot,r,N)>1E-10)&&(normeinfinie(zero,Grad,spot,r,N)/test>1E-5)){
printf("W\n");
t=1;
pas=RegledeWolfe(w,lambda,direction,t,G,tirages,spot,r,N);
for(i=0;i<N;i++){
lambda0[i]=lambda[i];
}
multiplication(Mult,- pas,direction,spot,r,N);
addition(lambda,lambda0,Mult,spot,r,N);
gradient(w,G,Grad,tirages,lambda ,spot,r,N);
gradient(w,G,grad,tirages,lambda0 ,spot,r,N);
multiplication(mult,produitscalaire(Grad,Grad,spot,r,N)/produitscalaire(grad,grad,spot,r,N),Grad,spot,r,N);
addition(direction,direction,mult,spot,r,N);
printf("%g\n",fonctionnelle(w,G,tirages, lambda, spot,r,N));
}
free(Grad);
free(lambda0);
free(add);
free(mult);
free(Mult);
free(zero);
free(direction);
free(grad);
return 0;
}
myVecteur2D::myVecteur2D(myVecteur2D* v1, myVecteur2D* v2){ // créer un rebond : premier vecteur sur le deuxième
vertex originrebond;
originrebond.x = 0;
originrebond.y = 0;
int sens;
sens = intersectionDroites(v1, v2, originrebond);
if (sens > 0)
{
v1->normalise();
v2->normalise();
//std::cout << "V1 : " << v1->getNorme() << " v2 : " << v2->getNorme() << " v1x : " << v1->getxdir() << " v1y : " << v1->getydir() << " v2x : " << v2->getxdir() << " v2y : " << v2->getydir() << std::endl;
vertex dirOrtho;
dirOrtho.x = v2->getydir();
dirOrtho.y = - v2->getxdir();
float psv12 = produitscalaire(v1,v2); //produit scalaire de v1 sur v2
float psv12ortho = v1->getxdir() * dirOrtho.x + v1->getydir() * dirOrtho.y;
xdir = psv12*v2->getxdir() - psv12ortho * dirOrtho.x;
ydir = psv12*v2->getydir() - psv12ortho * dirOrtho.y;
origin = originrebond;
//std::cout << "psv12 : " << psv12 << " ortho " << psv12ortho << "xdir : " << xdir << "direct " << psv12*v2->getxdir() + psv12ortho * dirOrtho.x<< std::endl;
normalise();
}
else
{
//on ne crée rien
}
}
int methodedugradient2(double *w,double *G,double *lambda,double *tirages,double spot, double r,int N )
{
int i;
double pas;
double test;
double pasapriori=0.0001;
int max=floor(((1.3*spot)-(0.7*spot))/5);
double *Grad=malloc((N+1)*sizeof(double));
double *mult=malloc((N+1)*sizeof(double));
double *add=malloc((N+1)*sizeof(double));
double *Mult=malloc((N+1)*sizeof(double));
double *lambda0=malloc((N+1)*sizeof(double));
double*zero=malloc((N+1)*sizeof(double));
for(i=0;i<N;i++)
{
lambda0[i]=1;
zero[i]=0;
}
/* multiplication(lambda,0,lambda0,spot,r,N);*/
methodedugradient(w,G,lambda,tirages,spot,r,N);
gradient(w,G,Grad,tirages,lambda ,spot,r,N);
multiplication(mult,- pasapriori,Grad,spot,r,N);
addition(add,lambda,mult,spot,r,N);
test=normeinfinie(Grad,lambda,spot,r,N);
while ((normeinfinie(lambda0,lambda,spot,r,N)>1E-10)&&(normeinfinie(zero,Grad,spot,r,N)/test>1E-5)){
printf("W2\n");
if((fonctionnelle(w,G,tirages,lambda,spot,r,N)>fonctionnelle(w,G,tirages,lambda0,spot,r,N))){
lambda=lambda0;
pasapriori=0.001*pasapriori;}
else {if(fabs(fonctionnelle(w,G,tirages,lambda,spot,r,N)-fonctionnelle(w,G,tirages,lambda0,spot,r,N))<1E-5){
pasapriori=0.001*pasapriori;
} else {
pasapriori=1;
}
}
pas=pasapriori*produitscalaire(Grad,Grad,spot,r,N)/(2*(pasapriori*produitscalaire(Grad,Grad,spot,r,N)-fonctionnelle(w,G,tirages,lambda,spot,r,N)+fonctionnelle(w,G,tirages,add,spot,r,N)));
for(i=0;i<N*max;i++){
lambda0[i]=lambda[i];
}
if(pas>=0){
if((fonctionnelle(w,G,tirages,add,spot,r,N)-fonctionnelle(w,G,tirages,lambda,spot,r,N))<-0.5*pasapriori*produitscalaire(Grad,Grad,spot,r,N)){
pas=1;
multiplication(Mult,- pas*pasapriori,Grad,spot,r,N);
addition(lambda,lambda0,Mult,spot,r,N);
} else {
multiplication(Mult,-pas*pasapriori,Grad,spot,r,N);
printf("ok\n");
addition(lambda,lambda0,Mult,spot,r,N);
}
} else {
printf("non!\n");
pas=1;
multiplication(Mult,- pas*pasapriori,Grad,spot,r,N);
addition(lambda,lambda0,Mult,spot,r,N);
}
gradient(w,G,Grad,tirages,lambda ,spot,r,N);
multiplication(mult,- pasapriori,Grad,spot,r,N);
addition(add,lambda,mult,spot,r,N);
printf("%g\n",fonctionnelle(w,G,tirages, lambda, spot,r,N));
}
free(Grad);
free(lambda0);
free(add);
free(mult);
free(Mult);
free(zero);
return 0;
}
/* computes the "Regle de Wolfe" */
double RegledeWolfe(double*w,double *x,double*d,double t,double*G,double *tirages,double spot,double r,int N)
{ double m1=0.4;
double m2=0.8;
double td=0;
double tg=0;
double a=2;
double *Grad=malloc((N+1)*sizeof(double));
double *grad=malloc((N+1)*sizeof(double));
double *add=malloc((N+1)*sizeof(double));
double *mult=malloc((N+1)*sizeof(double));
multiplication(mult,-t,d,spot,r,N);
addition(add,x,mult,spot,r,N);
gradient(w,G,Grad,tirages,x ,spot,r,N);
gradient(w,G,grad,tirages,add ,spot,r,N);
while((fonctiondemerite(w,x,t,d,G,tirages,spot,r,N)>fonctiondemerite(w,x,0,d,G,tirages,spot,r,N)-m1*t*produitscalaire(Grad,Grad,spot,r,N))||(produitscalaire(Grad,grad,spot,r,N)>m2*produitscalaire(Grad,Grad,spot,r,N))){printf("no\n");printf("%f %f\n",tg,td);
while (td==0){
printf("ok\n");
if (fonctiondemerite(w,x,t,d,G,tirages,spot,r,N)>fonctiondemerite(w,x,0,d,G,tirages,spot,r,N)-m1*t*produitscalaire(Grad,Grad,spot,r,N)){td=t;
} else {
t=a*t;
}
}
t=0.5*(td+tg);
if(fonctiondemerite(w,x,t,d,G,tirages,spot,r,N)>fonctiondemerite(w,x,0,d,G,tirages,spot,r,N)-m1*t* produitscalaire(Grad,Grad,spot,r,N)){
td=t;
} else {
tg=t;
}
if(fabs(td-tg)<1E-6){
return tg;
} else {
t=0.5*(td+tg);
}
multiplication(mult,-t,d,spot,r,N);
addition(add,x,mult,spot,r,N);
gradient(w,G,grad,tirages,add ,spot,r,N);
}
free(Grad);
free(grad);
free(add);
free(mult);
return t;}
