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 \([-1, 1]\).
construct.K.1d(basis)A matrix. Rows of the matrix are taken as the degree of the Legendre polynomial.
A matrix where each entry is \(<f, g>\) with $$<f, g> = \int_X \frac{d^2f}{dx^2}\frac{d^2g}{dx^2} dx,$$ with \(f, g\) being the Legendre polynomials described by the appropriate exponent vectors.