void hex_unlineate (unsigned int l, signed int * x, signed int * y)
{
unsigned int
r = 0,
k = 0,
i = 0;
int
remainder;
if (l == 0)
{
*x = 0;
*y = 0;
return;
}
//printf ("%s: have %d\n", __FUNCTION__, l);
while (fx (r) <= l)
{
r++;
}
//printf ("%s: %d (fx (%d)) is smallest hex larger than l-val\n", __FUNCTION__, fx (r), r);
remainder = l - fx (r - 1);
//printf ("%s: %d remaining with r assigned as %d\n", __FUNCTION__, remainder, r);
assert (r != 0);
k = remainder / r;
i = remainder % r;
//printf ("got {%d %d %d} from %d\n", r, k, i, l);
hex_rki2xy (r, k, i, x, y);
return;
}
//------------------------------------------------------------
//
// Part I : Reachability Decision for Hyperbox
//
//------------------------------------------------------------
bool System::isReachable(Hyperbox* source, Hyperbox* sink){
//Four cases corresponding to 2D hyperbox.
//Case I : x-const, y varies, checking x' to be negative.
//Case II : y-const, x varies, checking y' to be positive.
//Case III: x-const, y varies, checking x' to be positive.
//Case IV : y-const, x varies, checking y' to be negative.
//Case I:
if(source->min[0]==sink->max[0]){
if(fx(source->min[0], source->min[1], source->max[1])!=positive){
return true;
}
}
//Case II:
if(source->max[1] == sink->min[1]){
if(fy(source->max[1], source->min[0], source->max[0]) != negative){
return true ;
}
}
//Case III:
if(source->max[0] == sink->min[0]){
if(fx(source->max[0], source->min[1], source->max[1]) != negative){
return true;
}
}
//Case IV:
if(source->min[1] == sink->max[1]){
if(fy(source->min[1], source->min[0], source->max[0]) != positive){
return true;
}
}
return false;
}
void Calculate()
{
int i;
double kx[4],kv[4];
kx[0] = fx(v)*dt;
kv[0] = fv(x)*dt;
kx[1] = fx(v+kv[0]/2.0)*dt;
kv[1] = fv(x+kx[0]/2.0)*dt;
kx[2] = fx(v+kv[1]/2.0)*dt;
kv[2] = fv(x+kx[1]/2.0)*dt;
kx[3] = fx(v+kv[2])*dt;
kv[3] = fv(x+kx[2])*dt;
t += dt;
x += (kx[0]+2.0*kx[1]+2.0*kx[2]+kx[3])/6.0;
v += (kv[0]+2.0*kv[1]+2.0*kv[2]+kv[3])/6.0;
T = m*pow((l*v),2.0)/2.0;
U = g/l*(1.0-cos(x));
E = T + U;
for(i=0;i<GN-1;i++){
graphT[i] = graphT[i+1];
graphU[i] = graphU[i+1];
}
graphT[GN-1] = T;
graphU[GN-1] = U;
}
void RomeoSimpleActuator::computeAllModelDeriv(double& dt, const stateVec_t& X,const stateVec_t& Xdes,const commandVec_t& U)
{
Xreal = X + Xdes;
fx = fxBase;
fx(1,3) += A13atan*(a/(1+a*a*Xreal(3,0)*Xreal(3,0)));
fx(3,3) -= A33atan*(a/(1+(a*a*Xreal(3,0)*Xreal(3,0))));
fxx[3](1,3) = -((2*dt*Jm*R)/(pi*Jl))*Cf0*((2*a*a*a*Xreal(3,0))/((1+(a*a*Xreal(3,0)*Xreal(3,0)))*(1+(a*a*Xreal(3,0)*Xreal(3,0)))));
fxx[3](3,3) = +((2*dt*Cf0)/(pi*Jl))*((2*a*a*a*Xreal(3,0))/((1+(a*a*Xreal(3,0)*Xreal(3,0)))*(1+(a*a*Xreal(3,0)*Xreal(3,0)))));
}
Real fy(Real y)
{
Real fx(Real x);
ysav = y;
return qsimp(fx,xmin,xmax);
}
void my_f(double *f, double *x, double *u, double time)// evaluate of f(x)
{
// double testtemp;
// testtemp = norm(u, nc);
fx(f, x, N, d); //What exactly is the vector x ??? Is it n*ns*nx+nx or just nx ???
S(f, x, N, d);
M(f, x, N, d);
L(f, x, N, d);
int i;
for(i=0; i<d; i++)
{
*(f + (N+1)*d + i) += u[i];
}
*(f+nx-1) = 0.5*nu*norm(u, nc)*norm(u, nc) + l1(x, N, d); //What exactly is the vector u ??? Is it n*ns*nc or just nc ???
return;
}
void
polyfill(int n, vec2 points[])
{
int i;
int xoff, yoff;
MWPOINT pv[MAXPOLY];
if(!hdc)
return;
/* calc window offset*/
xoff = hdc->hwnd->clirect.left;
yoff = hdc->hwnd->clirect.top;
/* only plot non-trivial polygons*/
if(n > 2) {
for(i=0; i<n; ++i) {
pv[i].x = fx(points[i].x) + xoff;
pv[i].y = fy(points[i].y) + yoff;
/* fix: floating round error, y intercept difference
* with GdLine
*/
/*pv[i].x = fx(points[i].x + xoff);*/
/*pv[i].y = fy(points[i].y + yoff);*/
}
GdSetForegroundColor(hdc->psd, hdc->pen->color);
GdFillPoly(hdc->psd, n, pv);
}
}
void createSampleGrid(SGPP::base::Grid& grid, size_t l, SGPP::optimization::VectorFunction& f,
SGPP::base::DataMatrix& functionValues) {
SGPP::base::GridStorage& gridStorage = *grid.getStorage();
const size_t d = f.getNumberOfParameters();
const size_t m = f.getNumberOfComponents();
// generate regular sparse grid
gridStorage.emptyStorage();
std::unique_ptr<SGPP::base::GridGenerator>(grid.createGridGenerator())->regular(l);
const size_t n = gridStorage.size();
SGPP::base::DataVector x(d);
SGPP::base::DataVector fx(m);
functionValues.resize(n, m);
for (size_t i = 0; i < n; i++) {
SGPP::base::GridIndex& gp = *gridStorage[i];
// don't forget to set the point distribution to Clenshaw-Curtis
// if necessary (currently not done automatically)
if (grid.getType() == SGPP::base::GridType::BsplineClenshawCurtis ||
grid.getType() == SGPP::base::GridType::ModBsplineClenshawCurtis ||
grid.getType() == SGPP::base::GridType::LinearClenshawCurtis) {
gp.setPointDistribution(
SGPP::base::GridIndex::PointDistribution::ClenshawCurtis);
}
for (size_t t = 0; t < d; t++) {
x[t] = gp.getCoord(t);
}
f.eval(x, fx);
functionValues.setRow(i, fx);
}
}
Array<double,2> NumericalJacobian<F>::Jacobian(Array<double,1>& x)
{
int i,j;
Array<double,2> result(f.retdim(),f.argdim());
Array<double,1> fx(f(x).copy());
Array<double,1> dx(f.argdim());
dx = 0.0;
for (j=0; j<f.argdim(); j++) {
dx(j) = d;
Array<double,1> xdx(x + dx);
Array<double,1> fxdx(f(xdx).copy());
for (i=0; i<f.retdim(); i++) result(i,j) = (fxdx(i)-fx(i))/d;
dx(j) = 0.0;
}
return result;
}
void
Permittivity<EvalT, Traits>::
init_KL_RF(std::string &type, Teuchos::ParameterList& sublist, Teuchos::ParameterList& p){
is_constant = false;
if (type == "Truncated KL Expansion")
randField = UNIFORM;
else if (type == "Log Normal RF")
randField = LOGNORMAL;
Teuchos::RCP<PHX::DataLayout> scalar_dl =
p.get< Teuchos::RCP<PHX::DataLayout> >("QP Scalar Data Layout");
Teuchos::RCP<PHX::DataLayout> vector_dl =
p.get< Teuchos::RCP<PHX::DataLayout> >("QP Vector Data Layout");
PHX::MDField<MeshScalarT,Cell,QuadPoint,Dim>
fx(p.get<std::string>("QP Coordinate Vector Name"), vector_dl);
coordVec = fx;
this->addDependentField(coordVec);
exp_rf_kl =
Teuchos::rcp(new Stokhos::KL::ExponentialRandomField<MeshScalarT>(sublist));
int num_KL = exp_rf_kl->stochasticDimension();
// Add KL random variables as Sacado-ized parameters
rv.resize(num_KL);
Teuchos::RCP<ParamLib> paramLib =
p.get< Teuchos::RCP<ParamLib> >("Parameter Library", Teuchos::null);
for (int i=0; i<num_KL; i++) {
std::string ss = Albany::strint("Permittivity KL Random Variable",i);
new Sacado::ParameterRegistration<EvalT, SPL_Traits>(ss, this, paramLib);
rv[i] = sublist.get(ss, 0.0);
}
} // (type == "Truncated KL Expansion" || type == "Log Normal RF")
haskell_range<T> operator| ( TFx&& fx, const haskell_range<T>& set ) {
std::vector<T> comprehension;
comprehension.reserve( set.items.size() );
for ( auto& item : set ) {
comprehension.emplace_back( fx( item ) );
}
return haskell_range<T>( std::move( comprehension ) );
}
//计算f(x)
int fx(int x)
{
if(x = 1)
return 1;
else{
return fx(x-1)*x;
}
}
void CameraCalibration::set4Params(float _fx, float _fy, float _cx, float _cy){
m_intrinsic = cv::Matx33f::zeros();
fx() = _fx;
fy() = _fy;
cx() = _cx;
cy() = _cy;
}
A jtfxeachv(J jt,I r,A w){A*wv,x,z,*zv;I n,wd;
RZ(w);
n=AN(w); wv=AAV(w); wd=(I)w*ARELATIVE(w);
ASSERT(r>=AR(w),EVRANK);
ASSERT(n,EVLENGTH);
ASSERT(BOX&AT(w),EVDOMAIN);
GA(z,BOX,n,AR(w),AS(w)); zv=AAV(z);
DO(n, RZ(zv[i]=x=fx(WVR(i))); ASSERT(VERB&AT(x),EVDOMAIN););
set_build<T> operator| ( const set_build<T>& set, TFx&& fx ) {
std::vector<T> comprehension;
comprehension.reserve( set.items.size() );
for ( auto& item : set ) {
comprehension.emplace_back( fx( item ) );
}
return set_build<T>( std::move( comprehension ) );
}
Absorption<EvalT, Traits>::
Absorption(Teuchos::ParameterList& p) :
absorption(p.get<std::string>("QP Variable Name"),
p.get<Teuchos::RCP<PHX::DataLayout> >("QP Scalar Data Layout"))
{
Teuchos::ParameterList* cond_list =
p.get<Teuchos::ParameterList*>("Parameter List");
Teuchos::RCP<PHX::DataLayout> vector_dl =
p.get< Teuchos::RCP<PHX::DataLayout> >("QP Vector Data Layout");
std::vector<PHX::DataLayout::size_type> dims;
vector_dl->dimensions(dims);
numQPs = dims[1];
numDims = dims[2];
std::string type = cond_list->get("Absorption Type", "Constant");
if (type == "Constant") {
is_constant = true;
constant_value = cond_list->get("Value", 1.0);
// Add absorption as a Sacado-ized parameter
Teuchos::RCP<ParamLib> paramLib =
p.get< Teuchos::RCP<ParamLib> >("Parameter Library", Teuchos::null);
this->registerSacadoParameter("Absorption", paramLib);
}
#ifdef ALBANY_STOKHOS
else if (type == "Truncated KL Expansion") {
is_constant = false;
Teuchos::RCP<PHX::DataLayout> scalar_dl =
p.get< Teuchos::RCP<PHX::DataLayout> >("QP Scalar Data Layout");
PHX::MDField<MeshScalarT,Cell,QuadPoint,Dim>
fx(p.get<std::string>("QP Coordinate Vector Name"), vector_dl);
coordVec = fx;
this->addDependentField(coordVec);
exp_rf_kl =
Teuchos::rcp(new Stokhos::KL::ExponentialRandomField<RealType>(*cond_list));
int num_KL = exp_rf_kl->stochasticDimension();
// Add KL random variables as Sacado-ized parameters
rv.resize(num_KL);
Teuchos::RCP<ParamLib> paramLib =
p.get< Teuchos::RCP<ParamLib> >("Parameter Library", Teuchos::null);
for (int i=0; i<num_KL; i++) {
std::string ss = Albany::strint("Absorption KL Random Variable",i);
this->registerSacadoParameter(ss, paramLib);
rv[i] = cond_list->get(ss, 0.0);
}
}
#endif
else {
TEUCHOS_TEST_FOR_EXCEPTION(true, Teuchos::Exceptions::InvalidParameter,
"Invalid absorption type " << type);
}
this->addEvaluatedField(absorption);
this->setName("Absorption" );
}
int main()
{double x1=5,x2,y1,y2,x,y=APPROX;
unsigned iterations=0;
y1=fx(x1);x2=x1-1;y2=fx(x2);clrscr();
clrscr();
while(fabs(y)>=APPROX)
{x=x1-y1/(y1-y2)*(x1-x2);
y=fx(x);
x2=x1,y2=y1;
x1=x,y1=y;
iterations++;
printf("Iteration%d: x=%f\n",iterations,x);
}
printf("\nThe Root of the Equation is :\
%f\nTotal Iterations=%u",x,iterations);
getch();
return 0;
}
int main(void)
{
int i,nb=NBMAX;
float *xb1,*xb2;
xb1=vector(1,NBMAX);
xb2=vector(1,NBMAX);
zbrak(fx,X1,X2,N,xb1,xb2,&nb);
printf("\nbrackets for roots of bessj0:\n");
printf("%21s %10s %16s %10s\n","lower","upper","f(lower)","f(upper)");
for (i=1;i<=nb;i++)
printf("%s %2d %10.4f %10.4f %3s %10.4f %10.4f\n",
" root ",i,xb1[i],xb2[i]," ",
fx(xb1[i]),fx(xb2[i]));
free_vector(xb2,1,NBMAX);
free_vector(xb1,1,NBMAX);
return 0;
}
void BehaviorFunction::update(float dt)
{
timeAlive += dt;
if(fx){
var->x = fx(timeAlive);
}
if(fy){
var->y = this->fy(timeAlive);
}
}
haskell_range<T> operator% ( TFx&& fx ) {
std::vector<T> filtered;
filtered.reserve( items.size() );
for ( auto&& item : items ) {
if ( fx( item ) )
filtered.emplace_back( item );
}
items = std::move( filtered );
return *this;
}
cv::Point3d PinholeCameraModel::projectPixelTo3dRay(const cv::Point2d& uv_rect) const
{
assert( initialized() );
cv::Point3d ray;
ray.x = (uv_rect.x - cx() - Tx()) / fx();
ray.y = (uv_rect.y - cy() - Ty()) / fy();
ray.z = 1.0;
return ray;
}
/***定义求解搜索方向函数Sk*********/
void solveS(double x,double y,double *s) //在(x,y)处求解，s为存放搜索向量
{
double a[2],A;
a[0]=fx(x,y); //偏x值
a[1]=fy(x,y); //偏y值
A=sqrt(a[0]*a[0]+a[1]*a[1]);
s[0]=-a[0]/A; //归一化
s[1]=-a[1]/A;
}
//fx Declaration
//PURPOSE: Recursive function to process f(x) = f(x-1) + 2
//AUTHOR: Brodie Davis
//DATE CREATED: 12/12/2015
//Function's Dictionary of Variables
///x is input
///result is used to return the result of the calculations
//Function's Inputs
///input value from main function
int fx(int x){
int result=0;
//printf("\nfx round %d",++counter); //debugging statement, shows number of times function calls itself
if(x<=0)
result = 0;
else
result = fx(x-1)+2;
return result;
}
void
TruncatedKL<EvalT,Traits>::
DependentFields(Source<EvalT,Traits> &source, Teuchos::ParameterList& p) {
Teuchos::RCP<PHX::DataLayout> vector_dl =
p.get< Teuchos::RCP<PHX::DataLayout> >("QP Vector Data Layout");
PHX::MDField<MeshScalarT,Cell,Point,Dim>
fx(p.get<std::string>("QP Coordinate Vector Name"), vector_dl);
m_coordVec = fx;
source.addDependentField(m_coordVec);
}
set_build<T>& operator, ( TFx&& fx ) {
std::vector<T> filtered;
filtered.reserve( items.size() );
for ( auto&& item : items ) {
if ( fx( item ) )
filtered.emplace_back( item );
}
items = std::move( filtered );
return *this;
}
static T__ fxy(const T__ &y, const T__ &x, const size_t &nx, const size_t &ny)
{
switch(nx)
{
case(0):
{
switch(ny)
{
case(0):
{
return f(y,x);
break;
}
case(1):
{
return fy(y,x);
break;
}
default:
{
// TODO: NEED TO IMPLEMENT THIS
assert(false);
return 0;
break;
}
}
}
case(1):
{
switch(ny)
{
case(0):
{
return fx(y,x);
break;
}
default:
{
// TODO: NEED TO IMPLEMENT THIS
assert(false);
return 0;
break;
}
}
}
default:
case(2):
{
// TODO: IMPLEMENT THIS
assert(false);
return 0;
break;
}
}
}
void NR::zbrak(DP fx(const DP), const DP x1, const DP x2, const int n,
Vec_O_DP &xb1, Vec_O_DP &xb2, int &nroot)
{
int i;
DP x,fp,fc,dx;
int nb=xb1.size();
nroot=0;
dx=(x2-x1)/n;
fp=fx(x=x1);
for (i=0;i<n;i++) {
fc=fx(x += dx);
if (fc*fp <= 0.0) {
xb1[nroot]=x-dx;
xb2[nroot++]=x;
if(nroot == nb) return;
}
fp=fc;
}
}
void ConstitutiveModelParameters<EvalT, Traits>::
parseParameters(const std::string &n,
Teuchos::ParameterList &p,
Teuchos::RCP<ParamLib> paramLib)
{
Teuchos::ParameterList pl =
p.get<Teuchos::ParameterList*>("Material Parameters")->sublist(n);
std::string type_name(n + " Type");
std::string type = pl.get(type_name, "Constant");
if (type == "Constant") {
is_constant_map_.insert(std::make_pair(n, true));
constant_value_map_.insert(std::make_pair(n, pl.get("Value", 1.0)));
new Sacado::ParameterRegistration<EvalT, SPL_Traits>(n, this, paramLib);
if (have_temperature_) {
if (pl.get<std::string>("Temperature Dependence Type", "Linear")
== "Linear") {
temp_type_map_.insert(std::make_pair(n,"Linear"));
dparam_dtemp_map_.insert
(std::make_pair(n,
pl.get<RealType>("Linear Temperature Coefficient", 0.0)));
ref_temp_map_.insert
(std::make_pair(n, pl.get<RealType>("Reference Temperature", -1)));
} else if (pl.get<std::string>("Temperature Dependence Type", "Linear")
== "Arrhenius") {
temp_type_map_.insert(std::make_pair(n,"Arrhenius"));
pre_exp_map_.insert(
std::make_pair(n, pl.get<RealType>("Pre Exponential", 0.0)));
exp_param_map_.insert(
std::make_pair(n, pl.get<RealType>("Exponential Parameter", 0.0)));
}
}
} else if (type == "Truncated KL Expansion") {
is_constant_map_.insert(std::make_pair(n, false));
PHX::MDField<MeshScalarT, Cell, QuadPoint, Dim>
fx(p.get<std::string>("QP Coordinate Vector Name"), dl_->qp_vector);
coord_vec_ = fx;
this->addDependentField(coord_vec_);
exp_rf_kl_map_.
insert(
std::make_pair(n,
Teuchos::rcp(
new Stokhos::KL::ExponentialRandomField<MeshScalarT>(pl))));
int num_KL = exp_rf_kl_map_[n]->stochasticDimension();
// Add KL random variables as Sacado-ized parameters
rv_map_.insert(std::make_pair(n, Teuchos::Array<ScalarT>(num_KL)));
for (int i(0); i < num_KL; ++i) {
std::string ss = Albany::strint(n + " KL Random Variable", i);
new Sacado::ParameterRegistration<EvalT, SPL_Traits>(ss, this, paramLib);
rv_map_[n][i] = pl.get(ss, 0.0);
}
}
}
int main(){
int n,i,j;
char s[100];
char c;
fx(4);
int y = fx(5);
strcpy(s,"000123456");
strcpy(s,"0001'''3456");
printf("%s_\n",s);
c = '0';
c = '\"';
c = '"';
//putchar(c);
n=100;
for (i=2;i<=n;i++){
for (j=2;j*j<=i;j++)
if (i%j==0) break;
if (j*j>i) printf("%d\n",i);
}
return 0;
}
double max_euler_error(size_t k, Vector const *euler_ys_half_h)
{
double max_f = 0;
double max_fx = 0;
double max_fy = 0;
for (size_t i = 0; i < euler_ys_half_h->size; ++i) {
max_f = max(max_f, fabs(f(get_x(i, 0.5 * h), euler_ys_half_h->values[i])));
max_fx = max(max_fx, fabs(fx(get_x(i, 0.5 * h), euler_ys_half_h->values[i])));
max_fy = max(max_fy, fabs(fy(get_x(i, 0.5 * h), euler_ys_half_h->values[i])));
}
return 0.5 * (max_fx + max_f * max_fy) / max_fy * h * exp(max_fy * (get_x(k, h) - get_x(0, h)));
}