- This package implements bspline and linear interpolation in julia
- For most purposes, Interpolations.jl will be preferrable to this package.
- However, there are some features which are available here, and not there.
is a valid knot vector.
- the method
getTensorCoefis a very efficient algorithm to compute approximating coefficients from a tensor product of basis matrices. it is efficient because it never forms the tensor product.
- the package allows low-level access to objects such as spline knot vectors. Suppose you want to have a knot vector with a knot multiplicity in the interior knot span to approximate a kink. For example,
knots = vcat(lb,-0.5,0,0,0.5,ub)
- the method
- Documentation is non-existent. Please look at the tests. Sorry.
using ApproXD f(x) = abs.(x).^0.5 lb,ub = (-1.0,1.0) nknots = 13 deg = 3 # standard case: equally spaced knots params1 = BSpline(nknots,deg,lb,ub) nevals = 5 * params1.numKnots # get nBasis < nEvalpoints # myknots with knot multiplicity at 0 myknots = vcat(range(-1,stop = -0.1,length = 5),0,0,0, range(0.1,stop = 1,length =5)) params2 = BSpline(myknots,deg) # 0: no derivative # get coefficients for each case eval_points = collect(range(lb,stop = ub,length = nevals)) c1 = getBasis(eval_points,params1) \ f(eval_points) c2 = getBasis(eval_points,params2) \ f(eval_points) # look at errors over entire interval test_points = collect(range(lb,stop = ub,length = 1000)); truth = f(test_points); p1 = getBasis(test_points,params1) * c1; p2 = getBasis(test_points,params2) * c2; e1 = p1 - truth; e2 = p2 - truth;