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"""
Source: http://scikit-learn.org/stable/auto_examples/linear_model/plot_polynomial_interpolation.html
"""

import numpy as np
import matplotlib.pyplot as plt

from sklearn.preprocessing import PolynomialFeatures
from sklearn.linear_model import LinearRegression
from sklearn.pipeline import make_pipeline

# 1. Simple polynomial with weird shape over [0, 10]
def f(x):
    """ function to approximate by polynomial interpolation"""
    return (x ** 0.8) * np.sin(x + 12)

# generate points used to plot
x_plot = np.linspace(0, 10, 100)

# create matrix versions of these arrays
X_plot = x_plot[:, np.newaxis]

# plot
plt.plot(x_plot, f(x_plot), color='cornflowerblue', linewidth=2,
         label="ground truth")
plt.legend(loc='lower left')
plt.show()


# 2. Create a random polynomial
def make_data(N=30, err=0.8, rseed=None):
    # randomly sample the data
    rng = np.random.RandomState(rseed)
    X = rng.rand(N, 1) ** 2
    y = 10 - 1. / (X.ravel() + 0.1)
    if err > 0:
        y += err * rng.randn(N)
    return X, y

def PolynomialRegression(degree=2, **kwargs):
    
    return make_pipeline(PolynomialFeatures(degree),
                         LinearRegression(**kwargs))

def custom_poly(degree):
    """Returns a polynomial function over [-0.1, 1] by fitting 
    a polynomial to a randomly generated datast"""
    X, y = make_data()
    xfit = np.linspace(-0.1, 1.0, 1000)[:, None]
    model = PolynomialRegression(20).fit(X, y)

    poly_func = lambda x: model.predict(x)

    return poly_func

my_poly = custom_poly(15)

# plot
plt.plot(xfit.ravel(), my_poly(xfit), color='gray')
plt.axis([0, 1.0, -10, 20])
plt.show()