Behavior of scipy's splrep
python, scipy, splines
Solution
You need to define what you mean by "satisfying". Clearly, your cubic spline is not interpolating through the points, whereas the `splrep` result does (and is perfectly satisfactory in that sense). Note also that your 'cubicspline' is actually just a single polynomial rather than a spline (which are polynomials with breakpoints).
You need to explicitly tell `splrep` that the spline doesn't need to go through the points --- pass in a nonzero `s` smoothing parameter. How to choose this properly, see this question: scipy.interpolate.UnivariateSpline not smoothing regardless of parameters
Problem
I have a set of data points and would like to approximate them with a spline function. I used two different functions: - splrep from scipy - and a cubic spline function that I found here. The results look like this. The code is as follows: ``` from matplotlib.pyplot import * from numpy import * from scipy import interpolate #---------------------------------------------- s = arange(257)/256.0 z = s[::-1] b = transpose(array((z*z*z, 3*z*z*s, 3*z*s*s, s*s*s))) def cubicspline(c,t): return dot(b[t],c) #---------------------------------------------- A = array([ [ -126.041 , 246.867004], [ -113.745003, 92.083 ], [ 208.518997, -183.796997], [ 278.859009, -190.552994]]) a1 = A[:,0] a2 = A[:,1] cs = reshape(A, (-1, 4, 2)) X = [] Y = [] #spline with cubicspline() for (x,y) in [cubicspline(c,16*t) for c in cs for t in arange(17)]: X.append(x) Y.append(y) # spline with splrep tck = interpolate.splrep( a1, a2) xnew = np.arange( min(a1), max(a1), 5) ynew = interpolate.splev(xnew, tck) plot(a1, a2, "--ob", ms = 9, label = "points") plot(X, Y, "r", lw=2, label = "cubicspline") plot(xnew, ynew, "g", lw=2, label = "splrep") legend(); savefig("image.png"); show() ``` As you may see the results of splrep are far from being satisfying. Can someone please explain this behavior and how to get reasonable approximation from splrep?