Second Example - Comparison With/Without Constraint

This example compares a cubic spline without constraints and a cubic spline with a monotonicity constraint.

Complete Code

examples/quick_start2.py

    import numpy as np
    from BsplineQuantRegpy import SplineCubicQuant
    import matplotlib.pyplot as plt
    
    print("test_basic_fit")
    x = np.linspace(0, 1, 30)
    #y = x + 0.5*np.sin(10*np.pi*x) + 0.05*np.random.randn(30)
    y = x*(1-x) + 0.05*np.random.randn(30)

    x_eval = np.linspace(0, 1, 100)

    knots = np.quantile(x, np.linspace(0, 1, 6))
    result = SplineCubicQuant(x, y, knots, tau=0.5)
    y_eval = result(x_eval)


    print(" test_monotonicity")

    knots = np.quantile(x, np.linspace(0, 1, 6))
    result_m = SplineCubicQuant(x, y, knots, tau=0.5, monot=1)

    y_eval_m = result_m(x_eval)


    plt.plot(x,y,"*r")
    plt.plot(x_eval,y_eval,color='grey')
    plt.plot(x_eval,y_eval_m,color='black')
    plt.show()

Explanation

Data: - 30 points on the interval [0, 1] - The target function is \(x(1-x)\) with added noise
Two fits: - Unconstrained: Standard cubic spline (SplineCubicQuant without constraint parameter) - Constrained: Cubic spline with monot=1 (increasing)
Visual comparison: - Data points in red - Unconstrained spline in gray - Constrained spline in black

Result

The graph illustrates how the monotonicity constraint forces the curve to remain increasing, unlike the unconstrained spline which may exhibit oscillations.

Possible Modification

You can test other constraints by modifying the monot parameter: - monot=-1: decreasing - convex=1: convex - convex=-1: concave