Fitting a monotonically increasing spline function using Scipy

Question

I want to fit a monotonically increasing smooth spline function for a dataset

Code:

from scipy.interpolate import interp1d
import matplotlib.pyplot as plt

x = [0., 0.75, 1.8, 2.25, 3.75, 4.5, 6.45, 6.75, 7.5, 8.325, 10.875, 11.25, 12.525, 12.75, 15., 20.85, 21.]
    y = [2.83811035, 2.81541896, 3.14311655, 3.22373554, 3.43033456, 3.50433385, 3.66794514, 3.462296, 3.59480959,
         3.56250726, 3.6209845,  3.63034523, 3.68238915, 3.69096892, 3.75560395, 3.83545191, 3.90419498]

    plt.plot(x, y, '*')
    plt.show()
    f = interp1d(x, y, kind='cubic')
    yinp = f(x)
    plt.plot(x, yinp)
    plt.show()

The current fit looks like the above. I would like to know how to fit a monotonically increasing spline function.

I found an example in r posted here How to make monotonic (increasing) smooth spline with smooth.spline() function?. I am not sure what's the appropriate function in the scipy library.

Suggestions will be really helpful.

EDIT: I'm looking for something like the below (ref.)

EDIT 2:

I'm now using a smoothing spline function scipy.interpolate.UnivariateSpline

import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import UnivariateSpline

x = np.array([0., 0.75, 1.8, 2.25, 3.75, 4.5, 6.45, 6.75, 
              7.5, 8.325, 10.875, 11.25, 12.525, 12.75, 15., 
              20.85, 21.])
y = np.array([2.83811035, 2.81541896, 3.14311655, 
              3.22373554, 3.43033456, 3.50433385, 
              3.66794514, 3.462296,   3.59480959, 
              3.56250726, 3.6209845,  3.63034523, 
              3.68238915, 3.69096892, 3.75560395, 
              3.83545191, 3.90419498])
              

spl = UnivariateSpline(x, y, s=0.05)
xs  = np.linspace(x.min(), x.max(), 100)
plt.plot(x, y, 'ro', ms=5)
plt.plot(xs, spl(xs), 'cyan', lw=1)
plt.show()

gives the following result

I could get the coeffs and knots of the spline using

    print(spl.get_coeffs())
    print(spl.get_knots())

    k = 3
    tck = splrep(xmean, ymean, k=k, s=0.09)
    knots = tck[0]
    coeffs = tck[1]
    print('knot points=', knots)
    print('coefficients=', coeffs)

But I am not sure how to use the coefficients and manually generate the function of the spline curve. Could someone please add a bit more detail to this?

For example, when we have 4 data points

x = [0., 0.75, 1.8, 2.25]
y = [2.83811035, 2.81541896, 3.14311655, 3.22373554]

I would like to print the piecewise polynomial function to understand how the spline function looks like.

how do you expect to fit monotonically increasing splines if your data isn't monotonically increasing? — Nin17, Sep 05 '22 at 08:05

ev-br · Answer 1 · 2022-09-09T13:22:40.970

1

Use splrep from scipy.interpolate and manually tweak its s parameter which controls the amount of smoothing.

EDIT: The definition of the spline function that splrep returns, in terms of knots and coefficients, is equivalent to scipy.interpolate.BSpline, https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.BSpline.html

edited Sep 09 '22 at 13:22

answered Sep 07 '22 at 04:43

ev-br

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Thank you, could you please check my edit? – Natasha Sep 07 '22 at 15:23
The splin function is defined like this: https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.BSpline.html – ev-br Sep 08 '22 at 16:18

Fitting a monotonically increasing spline function using Scipy

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