Method buildBasisMatrix

src/bsplinebasis1d.cpp:160–216

Used to evaluate basis functions - alternative to the recursive deBoorCox

// Used to evaluate basis functions - alternative to the recursive deBoorCox
SparseMatrix BSplineBasis1D::buildBasisMatrix(double x, unsigned int u, unsigned int k, bool diff) const
{
    /* Build B-spline Matrix
     * R_k in R^(k,k+1)
     * or, if diff = true, the differentiated basis matrix
     * DR_k in R^(k,k+1)
     */

    if (!(k >= 1 && k <= getBasisDegree()))
    {
        throw Exception("BSplineBasis1D::buildBasisMatrix: Incorrect input paramaters!");
    }

//    assert(u >= basisDegree + 1);
//    assert(u < ks.size() - basisDegree);

    unsigned int rows = k;
    unsigned int cols = k+1;
    SparseMatrix R(rows, cols);
    R.reserve(Eigen::VectorXi::Constant(cols, 2));

    for (unsigned int i = 0; i < rows; i++)
    {
        double dk = knots.at(u+1+i) - knots.at(u+1+i-k);
        if (dk == 0)
        {
            continue;
        }
        else
        {
            if (diff)
            {
                // Insert diagonal element
                R.insert(i,i) = -1/dk;

                // Insert super-diagonal element
                R.insert(i,i+1) = 1/dk;
            }
            else
            {
                // Insert diagonal element
                double a = (knots.at(u+1+i) - x)/dk;
                if (a != 0)
                    R.insert(i,i) = a;

                // Insert super-diagonal element
                double b = (x - knots.at(u+1+i-k))/dk;
                if (b != 0)
                    R.insert(i,i+1) = b;
            }
        }
    }

    R.makeCompressed();

    return R;
}