unsigned long int MultiIndex<I, DIMENSION>::number()
{
unsigned long int num;
unsigned int level,a,b;
switch (DIMENSION)
{
case 1:
num = (FixedArray1D<I, DIMENSION>::operator [] (0));
break;
case 2:
level = multi_degree(*this);
num = (level*(level+1)/2 + (FixedArray1D<I, DIMENSION>::operator [] (0)) );
break;
case 3:
//lambda = (a,b,c)
level = multi_degree(*this);
a = FixedArray1D<I, DIMENSION>::operator [] (0);
b = FixedArray1D<I, DIMENSION>::operator [] (1);
num = level*(level+1)*(level+2)/6 + a*(2*level-a+3)/2 + b;
break;
default:
// much slower, but works in every dimension
MultiIndex temp;
num = 0;
while ((temp) < (*this))
{
++temp;
num++;
}
break;
}
return num;
};
void plot_indices(const TENSORBASIS* basis,
const InfiniteVector<double, typename TENSORBASIS::Index>& coeffs,
const int maxrange,
std::ostream& os,
const char* colormap = "cool",
bool boxed = false,
bool colorbar = true,
const double aa = -6)
{
typedef typename TENSORBASIS::Index Index;
typedef typename TENSORBASIS::IntervalBasis Basis1D;
typedef typename Index::level_type level_type;
typedef typename Index::type_type type_type;
typedef typename Index::translation_type translation_type;
const int DIM = 2;
/*
// we dont want to be limited to the 2 dimensional case!
const Basis1D* xbasis = basis->bases()[0];
const Basis1D* ybasis = basis->bases()[1];
*/
const level_type j0 = basis->j0();
const double maxnorm = linfty_norm(coeffs);
// determine number of sublevels on each level
// this gives the number of rows in the multiplot
//FixedArray1D<int, maxrange+1> number_of_rows;
Array1D<int> number_of_rows;
number_of_rows.resize(maxrange+1);
number_of_rows[0]=2;
for (int i=1; i<=maxrange; i++)
{
number_of_rows[i]=1;
}
for (int d=1; d<DIM; d++)
{
Array1D<int> temp_nor;
temp_nor.resize(maxrange+1);
temp_nor[0]= 1<<(d+1);
for (int i=1; i<=maxrange; i++)
{
temp_nor[i]=0;
for (int j=0; j<i; j++)
{
temp_nor[i]+=number_of_rows[j];
}
temp_nor[i]+=2*number_of_rows[i];
}
for (int i=0; i<=maxrange; i++)
number_of_rows[i]=temp_nor[i];
}
const double threshold = 1e-15;
cout << "linfinity norm of coefficients = " << maxnorm << endl;
cout << "number of coefficients" << coeffs.size() << endl;
// initialize m-file
os << "colormap(" << colormap << ");" << endl;
os << "X=" << colormap << ";" << endl;
// iterate over all coeffs.
// if ++lambda leads to an increased sublevel we need to plot a new row
// if ++lambda leads to an increased level we need to start a new column
MathTL::FixedArray1D<std::map<int, int>,DIM> sizes;
level_type currentlevel;
type_type currenttype;
translation_type current_k;
for (int i=0; i < DIM; i++)
{
currentlevel[i]=j0[i];
currenttype[i]=0;
current_k[i]=basis->bases()[i]->DeltaLmin();
sizes[i][0] = basis->bases()[i]->Deltasize(j0[i]); // Number of generators on level j0
sizes[i][1] = basis->bases()[i]->Nablasize(j0[i]); // Number of Wavelets on level j0
}
int row(1),column(1);
bool atmaxrange = false;
int range(0); // determines wether a new entry has to be computed in "sizes"
while (!atmaxrange)
{
// start a new box
//os << "subplot("<< number_of_rows[maxrange]<<"," << (maxrange +1) << ","<< (((boxstep-1)% number_of_rows[maxrange])*(maxrange+1)+ ((boxstep-1)/ number_of_rows[maxrange]) +1)<<");" << endl;
os << "subplot("<< number_of_rows[maxrange]<<"," << (maxrange +1) << ","<< ((row-1)*(maxrange+1)+column)<<");" << endl;
os << "box on" << endl;
os << "set(gca,'Layer','top')" << endl;
// turn off x ticks
os << "set(gca,'XTick',[])" << endl;
// turn off y ticks
os << "set(gca,'YTick',[])" << endl;
os << "ylabel('"<<currentlevel<<", "<<currenttype << ": ','rotation',0)" << endl;
os << "title 'level " << multi_degree(currentlevel) << "'" << endl;
os << "axis([0,1,0,1]);" << endl;
// based on tbasis_index :: operator ++
FixedArray1D<double,DIM> pos;
bool jplusplus = false;
while (!jplusplus)
{
// determine current position
for (int i=0; i<DIM; i++)
pos[i] = (current_k[i]-((currenttype[i] == 0) ? basis->bases()[i]->DeltaLmin() : basis->bases()[i]->Nablamin()))
* (1. / sizes[i][currentlevel[i]-j0[i]+currenttype[i]]);
const double c = coeffs.get_coefficient(Index(currentlevel, currenttype, current_k, basis));
if (fabs(c) < threshold) {
} else
{
double col = (std::max(log10(fabs(c)/maxnorm),aa)+(-aa))/(-aa);
// this part is for 2 space dimensions
os << "Y=ceil(" << col << " * length(colormap));" << endl;
os << "if Y==0" << endl << "Y=Y+1;" << endl << "end;" << endl;
os << "patch(" << "[" << pos[0] << ";" << pos[0] + (1. / sizes[0][currentlevel[0]-j0[0]+currenttype[0]]) << ";" << pos[0] + (1. / sizes[0][currentlevel[0]-j0[0]+currenttype[0]]) << ";" << pos[0] << "],"
<< "[" << pos[1] << ";" << pos[1] << ";" << pos[1] + (1. / sizes[1][currentlevel[1]-j0[1]+currenttype[1]]) << ";" << pos[1] + (1. / sizes[1][currentlevel[1]-j0[1]+currenttype[1]]) << "],"
<< "X(Y,:)";
if (!boxed)
os << ",'EdgeColor','none'";
os
// << ",'LineStyle','none'"
// << ",'LineWidth',0.125"
<< ")" << endl;
}
// determine next translation index
for (int i = DIM-1; i >= 0; i--) {
const int last_index = (currenttype[i] == 0 ? basis->bases()[i]->DeltaRmax(currentlevel[i])
: basis->bases()[i]->Nablamax(currentlevel[i]));
if (current_k[i] == last_index)
{
current_k[i] = (currenttype[i] == 0 ? basis->bases()[i]->DeltaLmin()
: basis->bases()[i]->Nablamin());
jplusplus = (i == 0);
} else
{
++current_k[i];
break;
}
}
} // end of while (!jplusplus)
// current sublevel has been drawn. Increase sublevel or level if needed
// determine next (sub)level index
// "small loop" "currenttype++" (currentlevel is fixed)
// iterate over all combinations of generators/wavelets for all dimensions with currentlevel[i]=j0[i]
// this looks like binary addition: (in 3 Dim:) gwg is followed by gww (g=0,w=1)
bool done = true;
for (int i(DIM-1); i >= 0; i--)
{
// find first position on level j0
if (currentlevel[i] == j0[i])
{
if (currenttype[i] == 1)
{
currenttype[i]=0;
current_k[i]=basis->bases()[i]->DeltaLmin();
} else
{
currenttype[i]=1;
current_k[i]=basis->bases()[i]->Nablamin();
row++;
done = false;
break;
}
}
}
// done == true bedeutet, dass alle Komponenten auf level j0() wavelets waren.
// "big loop" "currentlevel++"
if (done == true)
{
for (int i(DIM-1); i >= 0; i--)
{
if (i != 0)
{ // try to increase sublevel
if (currentlevel[i] != j0[i])
{
// increase left neighbor
currentlevel[i-1]=currentlevel[i-1]+1;
if (currentlevel[i-1]-j0[i] == range) sizes[i-1][range+1]=basis ->bases()[i]->Nablasize(currentlevel[i-1]); // if needed compute and store new size information
currenttype[i-1]=1;
current_k[i-1]=basis->bases()[i-1]->Nablamin();
int temp = currentlevel[i]-j0[i];
currentlevel[i]=j0[i];
currenttype[i]=0;
current_k[i]=basis->bases()[i]->DeltaLmin();
currentlevel[DIM-1]=j0[DIM-1]+temp-1;
currenttype[DIM-1]= (temp == 1?0:1);
current_k[DIM-1]= (temp == 1?basis->bases()[i]->DeltaLmin():basis->bases()[i]->Nablamin());
row++;
break;
}
} else // i == 0. "big loop" arrived at the last index. We have to increase the level!
{
range = range +1;
row=1;
column++;
if (DIM == 1)
{
currenttype[i] = 1; // diese Zeile erfüllt nur in der allerersten Iteration einen Zweck
current_k[i]=basis->bases()[i]->Nablamin(); // diese Zeile erfüllt nur in der allerersten Iteration einen Zweck
currentlevel[i]=currentlevel[i]+1;
sizes[0][range]=basis->bases()[0]->Nablasize(currentlevel[0]); // if needed compute and store new size information
}
else
{
currentlevel[DIM-1]=j0[DIM-1]+currentlevel[0]-j0[0]+1;
currenttype[DIM-1]=1;
current_k[DIM-1]=basis->bases()[i]->Nablamin();
currentlevel[0]=j0[0];
currenttype[0]=0;
current_k[0]=basis->bases()[i]->DeltaLmin();
sizes[DIM-1][range+1]=basis ->bases()[DIM-1]->Nablasize(currentlevel[DIM-1]); // if needed compute and store new size information
}
atmaxrange = (range > maxrange);
break; // unnoetig, da i==0 gilt.
}
}
} // end of "big loop"
} // end of while(!atmaxrange)
}
bool is_non_manifold() const { return multi_degree() > 0; }