SBasis toSBasis(SBasisOf<double> const &f){
SBasis result(f.size(), Linear());
for (unsigned i=0; i<f.size(); i++){
result[i] = Linear(f[i][0],f[i][1]);
}
return result;
}
OptInterval bounds_fast(const SBasisOf<double> &sb, int order) {
#else
OptInterval bounds_fast(const SBasis &sb, int order) {
#endif
Interval res(0,0); // an empty sbasis is 0.
for(int j = sb.size()-1; j>=order; j--) {
double a=sb[j][0];
double b=sb[j][1];
double v, t = 0;
v = res[0];
if (v<0) t = ((b-a)/v+1)*0.5;
if (v>=0 || t<0 || t>1) {
res[0] = std::min(a,b);
}else{
res[0]=lerp(t, a+v*t, b);
}
v = res[1];
if (v>0) t = ((b-a)/v+1)*0.5;
if (v<=0 || t<0 || t>1) {
res[1] = std::max(a,b);
}else{
res[1]=lerp(t, a+v*t, b);
}
}
if (order>0) res*=pow(.25,order);
return res;
}
OptInterval bounds_local(const SBasisOf<double> &sb, const OptInterval &i, int order) {
#else
OptInterval bounds_local(const SBasis &sb, const OptInterval &i, int order) {
#endif
double t0=i->min(), t1=i->max(), lo=0., hi=0.;
for(int j = sb.size()-1; j>=order; j--) {
double a=sb[j][0];
double b=sb[j][1];
double t = 0;
if (lo<0) t = ((b-a)/lo+1)*0.5;
if (lo>=0 || t<t0 || t>t1) {
lo = std::min(a*(1-t0)+b*t0+lo*t0*(1-t0),a*(1-t1)+b*t1+lo*t1*(1-t1));
}else{
lo = lerp(t, a+lo*t, b);
}
if (hi>0) t = ((b-a)/hi+1)*0.5;
if (hi<=0 || t<t0 || t>t1) {
hi = std::max(a*(1-t0)+b*t0+hi*t0*(1-t0),a*(1-t1)+b*t1+hi*t1*(1-t1));
}else{
hi = lerp(t, a+hi*t, b);
}
}
Interval res = Interval(lo,hi);
if (order>0) res*=pow(.25,order);
return res;
}
SBasisOf<T> integraaal(SBasisOf<T> const &c){
SBasisOf<T> a;
a.resize(c.size() + 1, LinearOf<T>(T(0.),T(0.)));
for(unsigned k = 1; k < c.size() + 1; k++) {
T ahat = (c[k-1][0]-c[k-1][1])/(2*k);
a[k] = LinearOf<T>(ahat);
}
T aTri = T(0.);
for(int k = c.size()-1; k >= 0; k--) {
aTri = (HatOf<T>(c[k]).d + (k+1)*aTri/2)/(2*k+1);
a[k][0] -= aTri/2;
a[k][1] += aTri/2;
}
//a.normalize();
return a;
}
SBasisOf<SBasisOf<double> > integral(SBasisOf<SBasisOf<double> > const &f, unsigned var){
//variable of f = 1, variable of f's coefficients = 0.
if (var == 1) return integraaal(f);
SBasisOf<SBasisOf<double> > result;
for(unsigned i = 0; i< f.size(); i++) {
//result.push_back(LinearOf<SBasisOf<double> >( integral(f[i][0]),integral(f[i][1])));
result.push_back(LinearOf<SBasisOf<double> >( integraaal(f[i][0]),integraaal(f[i][1])));
}
return result;
}
SBasisOf<double> compose(SBasisOf<SBasisOf<double> > const &f,
SBasisOf<double> const &x,
SBasisOf<double> const &y){
SBasisOf<double> y0 = -y + LinearOf<double>(1,1);
SBasisOf<double> s = multiply(y0,y);
SBasisOf<double> r;
for(int i = f.size()-1; i >= 0; i--) {
r = s*r + compose(f[i][0],x)*y0 + compose(f[i][1],x)*y;
}
return r;
}
SBasisOf<T> multi_compose(SBasisOf<double> const &f, SBasisOf<T> const &g ){
//assert( f.input_dim() <= g.size() );
SBasisOf<T> u1 = g;
SBasisOf<T> u0 = -g + LinearOf<SBasisOf<double> >(SBasisOf<double>(LinearOf<double>(1,1)));
SBasisOf<T> s = multiply(u0,u1);
SBasisOf<T> r;
for(int i = f.size()-1; i >= 0; i--) {
r = s*r + f[i][0]*u0 + f[i][1]*u1;
}
return r;
}