static base::Vector<1>::Type sol( const VecDim& x,
const double radius, const double alpha1,
const double alpha2 )
{
VecDim dummy;
return (interface( x, radius, dummy ) ?
sol1( x, radius, alpha1, alpha2 ) :
sol2( x, radius, alpha1, alpha2 ) );
}
void sol3(double t) //计算Bezier曲线上点的坐标
{
double x=0,y=0,Ber;
int k;
for(k=0;k<n;k++)
{
Ber=sol2(n-1,k)*pow(t,k)*pow(1-t,n-1-k);
x+=point[k].x*Ber;
y+=point[k].y*Ber;
}
putpixel((int)x,(int)y,GREEN);
}
void TestSolver::circle4() {
const ExprSymbol& x=ExprSymbol::new_("x");
const ExprSymbol& y=ExprSymbol::new_("y");
const ExprSymbol& r2=ExprSymbol::new_("r2");
SystemFactory f;
f.add_var(x);
f.add_var(y);
f.add_var(r2);
f.add_ctr(sqr(x)+sqr(y)=r2);
f.add_ctr(sqr(x-1)+sqr(y)=r2);
double cospi6=0.5;
double sinpi6=::sqrt(3)/2;
double _sol1[]={cospi6,sinpi6,1};
double _sol2[]={cospi6,-sinpi6,1};
Vector sol1(3,_sol1);
Vector sol2(3,_sol2);
System sys(f);
RoundRobin rr(1e-3);
CellStack stack;
CtcHC4 hc4(sys);
VarSet params(sys.f_ctrs,sys.args[2],false);
Vector prec(3,1e-3);
Solver solver(sys,hc4,rr,stack,prec,prec);
solver.set_params(params);
IntervalVector box(3);
box[0]=Interval(-10,10);
box[1]=Interval(-10,10);
box[2]=Interval(1,1);
solver.start(box);
CovSolverData::BoxStatus status;
bool res=solver.next(status);
CPPUNIT_ASSERT(res);
CPPUNIT_ASSERT(status==CovSolverData::SOLUTION);
CPPUNIT_ASSERT(solver.get_data().nb_solution()==1);
CPPUNIT_ASSERT(solver.get_data().solution(0).is_superset(sol1));
res=solver.next(status);
CPPUNIT_ASSERT(status==CovSolverData::SOLUTION);
CPPUNIT_ASSERT(solver.get_data().nb_solution()==2);
CPPUNIT_ASSERT(solver.get_data().solution(1).is_superset(sol2));
res=solver.next(status);
CPPUNIT_ASSERT(!res);
}
void TestSolver::circle3() {
const ExprSymbol& x=ExprSymbol::new_("x");
const ExprSymbol& y=ExprSymbol::new_("y");
SystemFactory f;
f.add_var(x);
f.add_var(y);
f.add_ctr(sqr(x)+sqr(y)=1);
f.add_ctr(sqr(x-1)+sqr(y)=1);
double cospi6=0.5;
double sinpi6=(sqrt(Interval(3))/2).lb();
f.add_ctr(4*y*abs(y)<=3); // a rigorous way to impose y<=sin(pi/6).
double _sol1[]={cospi6,sinpi6};
double _sol2[]={cospi6,-sinpi6};
Vector sol1(2,_sol1);
Vector sol2(2,_sol2);
System sys(f);
RoundRobin rr(1e-3);
CellStack stack;
CtcHC4 hc4(sys);
Vector prec(2,1e-3);
Solver solver(sys,hc4,rr,stack,prec,prec);
solver.start(IntervalVector(2,Interval(-10,10)));
CovSolverData::BoxStatus status;
bool res=solver.next(status);
CPPUNIT_ASSERT(res);
CPPUNIT_ASSERT(status==CovSolverData::UNKNOWN);
CPPUNIT_ASSERT(solver.get_data().nb_unknown()==1);
CPPUNIT_ASSERT(solver.get_data().unknown(0).is_superset(sol1));
res=solver.next(status);
CPPUNIT_ASSERT(res);
CPPUNIT_ASSERT(status==CovSolverData::SOLUTION);
CPPUNIT_ASSERT(solver.get_data().nb_solution()==1);
CPPUNIT_ASSERT(solver.get_data().solution(0).is_superset(sol2));
res=solver.next(status);
CPPUNIT_ASSERT(!res);
}
int main()
{
eoPop<DualVector> pop;
// fixed test
DualVector sol1(2,-1);
DualVector sol2(2,-1);
DualVector sol3(2,1);
DualVector sol4(2,1);
pop.push_back( sol1 );
pop.push_back( sol2 );
pop.push_back( sol3 );
pop.push_back( sol4 );
// on the sphere function everyone has the same fitness of 1
if( test(pop, 0) != 0 ) {
exit(1);
}
pop.erase(pop.begin(),pop.end());
// fixed test
sol1 = DualVector(2,0);
sol2 = DualVector(2,0);
sol3 = DualVector(2,1);
sol4 = DualVector(2,1);
pop.push_back( sol1 );
pop.push_back( sol2 );
pop.push_back( sol3 );
pop.push_back( sol4 );
if( test(pop, 1) != 1 ) {
exit(1);
}
// test on a random normal distribution
eoNormalGenerator<double> normal(1,rng);
eoInitFixedLength<DualVector> init_N(2, normal);
pop = eoPop<DualVector>( 1000000, init_N );
double iqr = test(pop, 1.09);
if( iqr < 1.08 || iqr > 1.11 ) {
exit(1);
}
}
/**
* @return One or two intersection points between given entities.
*/
RS_VectorSolutions RS_Information::getIntersectionLineArc(RS_Line* line,
RS_Arc* arc) {
RS_VectorSolutions ret;
if (line==NULL || arc==NULL) {
return ret;
}
double dist=0.0;
RS_Vector nearest;
nearest = line->getNearestPointOnEntity(arc->getCenter(), false, &dist);
// special case: arc touches line (tangent):
if (fabs(dist - arc->getRadius()) < 1.0e-4) {
ret = RS_VectorSolutions(nearest);
ret.setTangent(true);
return ret;
}
RS_Vector p = line->getStartpoint();
RS_Vector d = line->getEndpoint() - line->getStartpoint();
if (d.magnitude()<1.0e-6) {
return ret;
}
RS_Vector c = arc->getCenter();
double r = arc->getRadius();
RS_Vector delta = p - c;
// root term:
double term = RS_Math::pow(RS_Vector::dotP(d, delta), 2.0)
- RS_Math::pow(d.magnitude(), 2.0)
* (RS_Math::pow(delta.magnitude(), 2.0) - RS_Math::pow(r, 2.0));
// no intersection:
if (term<0.0) {
RS_VectorSolutions s;
ret = s;
}
// one or two intersections:
else {
double t1 = (- RS_Vector::dotP(d, delta) + sqrt(term))
/ RS_Math::pow(d.magnitude(), 2.0);
double t2;
bool tangent = false;
// only one intersection:
if (fabs(term)<RS_TOLERANCE) {
t2 = t1;
tangent = true;
}
// two intersections
else {
t2 = (-RS_Vector::dotP(d, delta) - sqrt(term))
/ RS_Math::pow(d.magnitude(), 2.0);
}
RS_Vector sol1;
RS_Vector sol2(false);
sol1 = p + d * t1;
if (!tangent) {
sol2 = p + d * t2;
}
ret = RS_VectorSolutions(sol1, sol2);
ret.setTangent(tangent);
}
return ret;
}
int maxDepth(TreeNode* root) {
//return sol1(root);
return sol2(root);
}
bool isValidBST(TreeNode* root) {
/****** Sol 2. compare current node with the previous one ******/
TreeNode *prev = NULL;
return sol2(root, prev);
}
void PressureTable::ComputeDatabaseInputs_FromT( const double rho, const double Z, const double Zv, const double Yc, const double T,
double &P, double &Sz , double &C,
double P0, double C0) {
// Compute normalized variance
double eps = 1.0e-3;
Sz = ComputeNormalizedVariance(Z, Zv);
// Compute normalized progress variable
Z_newton = Z;
Zv_newton = Sz;
Yc_newton = Yc;
rho_newton = rho;
T_newton = T;
// I need to solve ( Yc(C,P) - Yc_target , rho(C,P) - rho_target) = (0 , 0)
C_newton = C0;
P_newton = P0/P_scale;// Pressure is rescaled
verbose_newton = false;
Bool check;
VecDoub_IO sol2(1, 0.0);
VecDoub_IO sol(2, 0.0);
int Newton_mode;
try {
// Get Approximation of Yceq from highest pressure
int nPress = GetDimension1();
double P_max = GetCoordinate1(nPress-1);
int nC = GetDimension4();
double C_max = GetCoordinate4(nC-2); // Maximum C value before one
double Yc_eq = Lookup(P_max,Z_newton,Zv_newton,1.0,"PROG");
double Yc_max = Lookup(P_max,Z_newton,Zv_newton,C_max,"PROG");
// If Yc_eq is small, C is set to 1 and we look for pressure only
if ((Yc_eq < eps)||(Yc > Yc_max)) {
Newton_mode = 1;
sol2[0] = P_newton;
C_newton = 1.0;
newt(sol2, check, usrfunc_wrapper4);
} else {
// usual
Newton_mode = 2;
sol[0] = C_newton;
sol[1] = P_newton;
try {newt(sol, check, usrfunc_wrapper3);}
catch (int e) {
cout << "relaunched with Newton_mode = 1" << endl;
Newton_mode = 1;
C_newton = sol[0];
sol2[0] = P0/P_scale;
newt(sol2, check, usrfunc_wrapper4);
}
}
}
catch (int e) {
int tol_failure = 0;
if (Newton_mode == 1) {
VecDoub out(1, 0.0);
out = DensityFromP(sol2);
if (abs(out[0]) > 1.0e-5) tol_failure = 1;
} else if (Newton_mode == 2) {
VecDoub out(2, 0.0);
out = YcAndDensityFromCP(sol);
if ((abs(out[0])>1.0e-4)||(abs(out[1]))>1.0e-5) tol_failure = 1;
}
cout << "Newton error. Test tol = " << tol_failure << endl;
if (tol_failure == 1) {
cout << "Newton inputs : " << Z_newton << " "
<< Zv_newton << " "
<< Yc_newton << " "
<< rho_newton << " "
<< C_newton << " "
<< P_newton*P_scale << endl;
cout << "C0 : " << C0 << " P0 : " << P0 << endl;
cout << " Check : " << check << endl;
if (Newton_mode == 2) {
cout << " sol : C = " << sol[0] << " , P = " << sol[1]*P_scale << endl;
} else if (Newton_mode == 1) {
cout << " sol : P = " << sol2[0]*P_scale << endl;
}
}
}
if (Newton_mode == 2) {
C_newton = sol[0];
P_newton = sol[1];
} else if (Newton_mode == 1) {
P_newton = sol2[0];
}
C = C_newton;
P = P_newton*P_scale;
}
void PressureTable::ComputeDatabaseInputs( const double rho, const double Z, const double Zv, const double Yc,
double &P, double &Sz , double &C,
double P0, double C0) {
// Compute normalized variance
double eps = 1.0e-3;
if ((Z <= 1-eps)||(Z >= eps)) {
Sz = Zv/(Z*(1.0-Z));
} else {
Sz = 0.0;
}
Sz = max(0.0, min(1.0, Sz));
// Compute normalized progress variable
Z_newton = Z;
Zv_newton = Sz;
Yc_newton = Yc;
rho_newton = rho;
// I need to solve ( Yc(C,P) - Yc_target , rho(C,P) - rho_target) = (0 , 0)
C_newton = C0;
P_newton = P0/P_scale;// Pressure is rescaled
verbose_newton = false;
Bool check;
VecDoub_IO sol2(1, 0.0);
VecDoub_IO sol(2, 0.0);
int Newton_mode;
try {
//Newton : newt(sol, check, usrfunc_wrapper);
//Broyden : broydn(sol, check, usrfunc_wrapper);
// Get Approximation of Yceq from highest pressure
int nPress = GetDimension1();
double P_max = GetCoordinate1(nPress-1);
int nC = GetDimension4();
double C_max = GetCoordinate4(nC-2); // Maximum C value before one
double Yc_eq = Lookup(P_max,Z_newton,Zv_newton,1.0,"PROG");
double Yc_max = Lookup(P_max,Z_newton,Zv_newton,C_max,"PROG");
// If Yc_eq is small, C is set to 1 and we look for pressure only
if ((Yc_eq < eps)||(Yc > Yc_max)) {
Newton_mode = 1;
sol2[0] = P_newton;
C_newton = 1.0;
newt(sol2, check, usrfunc_wrapper2);
} else {
// usual
Newton_mode = 2;
sol[0] = C_newton;
sol[1] = P_newton;
try {newt(sol, check, usrfunc_wrapper);}
catch (int e) {
cout << "relaunched with Newton_mode = 1" << endl;
Newton_mode = 1;
C_newton = sol[0];
sol2[0] = P0/P_scale;
newt(sol2, check, usrfunc_wrapper2);
}
}
}
catch (int e) {
int tol_failure = 0;
if (Newton_mode == 1) {
VecDoub out(1, 0.0);
out = DensityFromP(sol2);
if (abs(out[0]) > 1.0e-5) tol_failure = 1;
} else if (Newton_mode == 2) {
VecDoub out(2, 0.0);
out = YcAndDensityFromCP(sol);
if ((abs(out[0])>1.0e-4)||(abs(out[1]))>1.0e-5) tol_failure = 1;
}
cout << "Newton error. Test tol = " << tol_failure << endl;
if (tol_failure == 1) {
cout << "Newton inputs : " << Z_newton << " "
<< Zv_newton << " "
<< Yc_newton << " "
<< rho_newton << " "
<< C_newton << " "
<< P_newton*P_scale << endl;
cout << "C0 : " << C0 << " P0 : " << P0 << endl;
cout << " Check : " << check << endl;
if (Newton_mode == 2) {
cout << " sol : C = " << sol[0] << " , P = " << sol[1]*P_scale << endl;
} else if (Newton_mode == 1) {
cout << " sol : P = " << sol2[0]*P_scale << endl;
}
// Relaunch with verbose
verbose_newton = true;
try {
Int MaxIter = 200;
if (Newton_mode == 1) {
sol2[0] = P_newton;
C_newton = 1.0;
cout << "Reinit with " << sol2[0] << " " << MaxIter << endl;
newt(sol2, check, usrfunc_wrapper2, MaxIter);
} else if (Newton_mode == 2) {
// usual
sol[0] = C_newton;
sol[1] = P_newton;
cout << "Reinit with " << sol[0] << " " << sol[1] << " " << MaxIter << endl;
newt(sol, check, usrfunc_wrapper, MaxIter);
} else {cerr << "Impossible value of Newton_mode: " << Newton_mode << endl;}
}
catch (int e2) {
cout << "Bis Newton inputs : " << Z_newton << " "
<< Zv_newton << " "
<< Yc_newton << " "
<< rho_newton << " "
<< C_newton << " "
<< P_newton*P_scale << endl;
cout << "Bis Check : " << check << endl;
if (Newton_mode == 2) {
cout << "Bis sol : C = " << sol[0] << " , P = " << sol[1]*P_scale << endl;
} else if (Newton_mode == 1) {
cout << "Bis sol : P = " << sol2[0]*P_scale << endl;
}
throw(-1);
}
throw(-1);
}
}
if (Newton_mode == 2) {
C_newton = sol[0];
P_newton = sol[1];
} else if (Newton_mode == 1) {
P_newton = sol2[0];
}
C = C_newton;
P = P_newton*P_scale;
}
bool SIMoutput::dumpResults (const Vector& psol, double time,
utl::LogStream& os, const ResPointVec& gPoints,
bool formatted, std::streamsize precision) const
{
if (gPoints.empty())
return true;
size_t i, j, k;
Matrix sol1, sol2;
Vector reactionFS;
const Vector* reactionForces = myEqSys->getReactions();
for (i = 0; i < myModel.size(); i++)
{
if (myModel[i]->empty()) continue; // skip empty patches
ResPointVec::const_iterator p;
std::array<RealArray,3> params;
IntVec points;
// Find all evaluation points within this patch, if any
for (j = 0, p = gPoints.begin(); p != gPoints.end(); j++, p++)
if (this->getLocalPatchIndex(p->patch) == (int)(i+1))
if (opt.discretization >= ASM::Spline)
{
points.push_back(p->inod > 0 ? p->inod : -(j+1));
for (k = 0; k < myModel[i]->getNoParamDim(); k++)
params[k].push_back(p->u[k]);
}
else if (p->inod > 0)
points.push_back(p->inod);
if (points.empty()) continue; // no points in this patch
myModel[i]->extractNodeVec(psol,myProblem->getSolution());
if (opt.discretization >= ASM::Spline)
{
// Evaluate the primary solution variables
if (!myModel[i]->evalSolution(sol1,myProblem->getSolution(),
params.data(),false))
return false;
// Evaluate the secondary solution variables
LocalSystem::patch = i;
if (myProblem->getNoFields(2) > 0)
{
const_cast<SIMoutput*>(this)->setPatchMaterial(i+1);
if (!myModel[i]->evalSolution(sol2,*myProblem,params.data(),false))
return false;
}
}
else
// Extract nodal primary solution variables
if (!myModel[i]->getSolution(sol1,myProblem->getSolution(),points))
return false;
// Formatted output, use scientific notation with fixed field width
std::streamsize flWidth = 8 + precision;
std::streamsize oldPrec = os.precision(precision);
std::ios::fmtflags oldF = os.flags(std::ios::scientific | std::ios::right);
for (j = 0; j < points.size(); j++)
{
if (!formatted)
os << time <<" ";
else if (points[j] < 0)
os <<" Point #"<< -points[j] <<":\tsol1 =";
else
{
points[j] = myModel[i]->getNodeID(points[j]);
os <<" Node #"<< points[j] <<":\tsol1 =";
}
for (k = 1; k <= sol1.rows(); k++)
os << std::setw(flWidth) << utl::trunc(sol1(k,j+1));
if (opt.discretization >= ASM::Spline)
{
if (formatted && sol2.rows() > 0)
os <<"\n\t\tsol2 =";
for (k = 1; k <= sol2.rows(); k++)
os << std::setw(flWidth) << utl::trunc(sol2(k,j+1));
}
if (reactionForces && points[j] > 0)
// Print nodal reaction forces for nodes with prescribed DOFs
if (mySam->getNodalReactions(points[j],*reactionForces,reactionFS))
{
if (formatted)
os <<"\n\t\treac =";
for (k = 0; k < reactionFS.size(); k++)
os << std::setw(flWidth) << utl::trunc(reactionFS[k]);
}
os << std::endl;
}
os.precision(oldPrec);
os.flags(oldF);
}
return true;
}