This function constructs the K matrix for a given multivariate basis assuming the basis is a Legendre polynomial basis and the smoothing criterion is the Frobenius norm of the Hessian integrated over \([-1, 1]^d\).
construct.K(basis)A matrix. Rows of the matrix are taken as the exponent vectors of the leading terms of a Legendre polynomial basis.
A matrix where each entry is \(<f, g>\) with $$<f, g> = \int_X \sum_{i,j}\frac{d^2f}{dx_idx_j}\frac{d^2g}{dx_idx_j} dx,$$ with \(f, g\) being the Legendre polynomials described by the appropriate exponent vectors.