CODEWITHSUNDEEP
pythonscipyinterpolationspline
lqbweb
lqbweb

Reputation: 1708

Spline lineal continuation on borders

I have code interpolating a spline from a CDF that seems valid between the range x=40 and x=110. Below 40, I want a flat line at 0, and after 110, a flat line at 1 towards infinite.

I have come up with this code:

def _find_spline(x_orig: np.ndarray, cdf: np.ndarray) -> BSpline:

    # Find the smoothing factor
    smoothing_factor, iters = _find_highest_smoothing_factor(x_orig, cdf, 1e-5)

    # Fit a linear spline to the first segment
    t_begin, c_begin, k_begin = splrep([0, x_orig[0]], [0, cdf[0]], k=1)

    # Fit the middle segment with the specified smoothing factor
    t_middle, c_middle, k_middle = splrep(x_orig, cdf, s=smoothing_factor)

    # Explicitly construct the final segment
    t_end = np.array([x_orig[-1], x_orig[-1], 300, 300])  # Linear knots
    c_end = np.array([cdf[-1], 1.0])  # Start from the evaluated value

    # Combine the knots and coefficients
    t_combined = np.concatenate([t_begin[:-1], t_middle[1:-1], t_end])
    c_combined = np.concatenate([c_begin[:-1], c_middle[1:-1], c_end])

    return BSpline(t_combined, c_combined, k_middle, extrapolate=True)

I have uploaded a full reproducible example here.

however, this generates something like in:

enter image description here

so, the first segment until 40 seems fine and evaluates to 0... but I don't know why the spline goes down to 0 at the end at 110, I want it just to continue straight...

What is wrong?

Upvotes: 0

Views: 46

Answers (1)

ev-br
ev-br

Reputation: 26040

You cannot just have a constant extrapolation to fall out of the spline construction by itself, and you'll have to implement it yourselves (unless linear interpolation is OK in which case you just use np.interp).

There are several ways to implement it:

  • you can construct a spline and manually extend the knots and coefficients to make all derivatives at edges equal zero
  • you can use a small wrapper which contains a BSpline (or any other interpolator) and fills in the desired constants.

In fact, I would recommend the latter approach. This scipy page has a several examples (it starts with an interp1d example, which is very much not recommended anymore; the other ones are relevant):

https://docs.scipy.org/doc/scipy/tutorial/interpolate/extrapolation_examples.html

Upvotes: 2

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