/*
* Compute power basis coefficients from B-spline basis coefficients
*/
DenseMatrix getPowerBasisCoefficients(DenseVector c, std::vector<unsigned int> degrees, std::vector<double> lb, std::vector<double> ub)
{
// Calculate tensor product transformation matrix T*lambda = c
DenseMatrix T = getTransformationMatrix(degrees, lb, ub);
// Compute power basis coefficients from B-spline basis coefficients
DenseMatrix L = T.colPivHouseholderQr().solve(c);
return L;
}
/*
* Transformation matrix taking a power basis to a B-spline basis
*/
DenseMatrix getTransformationMatrix(std::vector<unsigned int> degrees, std::vector<double> lb, std::vector<double> ub)
{
unsigned int dim = degrees.size();
assert(dim >= 1); // At least one variable
assert(dim == lb.size());
assert(dim == ub.size());
// Calculate tensor product transformation matrix T
SparseMatrix T(1,1);
T.insert(0,0) = 1;
for (unsigned int i = 0; i < dim; i++)
{
SparseMatrix temp(T);
unsigned int deg = degrees.at(i);
DenseMatrix Mi = getBSplineToPowerBasisMatrix1D(deg);
DenseMatrix Ri = getReparameterizationMatrix1D(deg, lb.at(i), ub.at(i));
DenseMatrix Ti = Mi.colPivHouseholderQr().solve(Ri);
T = kroneckerProduct(temp, Ti);
}
return T;
}