Exemplo n.º 1
0
/*
 * 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;
}
Exemplo n.º 2
0
/*
 * 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;
}