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sampling_increment = 9
sparse_input = in_array[::sampling_increment]
sparse_data =     curve[::sampling_increment]

title_suffix = ' sparse data' +   ' - with B-Spline (sampling increment = 9)'

x_interp = np.linspace(x_min, x_max, 100)
BSpline = scipy.interpolate.make_interp_spline(sparse_input, sparse_data, 2)
y_BSpline = BSpline(x_interp)

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title_suffix = 'smooth data (assumed ground truth)'
graph(in_array, curve, title_suffix , scatter=True, solid_line=False)

title_suffix = '  –  sparse data' +   ' - with B-Spline'
import scipy

x_interp = np.linspace(x_min, x_max, 100)
BSpline = scipy.interpolate.make_interp_spline(sparse_input, sparse_data, 2)
y_BSpline = BSpline(x_interp)

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title_suffix = ' - noisy data'
graph(in_array, noisy_data, title_suffix, scatter=True, solid_line=False)

import pandas as pd
noisy_data_series = pd.Series(noisy_data)

# Use pandas's rolling method to generate a list of moving average series based on different bin sizes
bin_sizes = [3, 5, 7, 10]
mvg_avg_list = [ (in_array, noisy_data_series.rolling(bin_size).mean()) for bin_size in bin_sizes ]
title_suffix = ' - noisy data'+ ' - moving average'

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title_suffix = ' - noisy data'
graph(in_array, noisy_data, title_suffix, scatter=True, solid_line=False)

z = np.polyfit(in_array, noisy_data, 20)
p = np.poly1d(z)
xp = np.linspace(x_min, x_max, 100)

title_suffix = ' - noisy data'+ ' - 20th dgr polynomial regression'
graph(in_array, noisy_data,  ' - noisy data'+ ' - 20th dgr polynomial regression', scatter=True, solid_line=False, line_viz = [(xp, p(xp))])

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title_suffix = ' - noisy data'
graph(in_array, noisy_data, title_suffix, scatter=True, solid_line=False)

x_min, x_max = -3.3, 4.3
from numpy.polynomial import polynomial as P
z = np.polyfit(in_array, noisy_data, 3)
p = np.poly1d(z)
xp = np.linspace(x_min, x_max, 100)

title_suffix = ' - noisy data'+ ' - 3rd dgr polynomial regression'

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title_suffix = ' - noisy data'
graph(in_array, noisy_data, title_suffix, scatter=True, solid_line=False)

m, b = np.polyfit(in_array, noisy_data, 1)

title_suffix =  ' - noisy data'+ ' - with linear regression'
graph(in_array, noisy_data,  title_suffix, scatter=True, solid_line=False, line_viz = [(in_array, m*x+b)])

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title_suffix = ' - noisy data'
graph(in_array, noisy_data, title_suffix, scatter=True, solid_line=False)

title_suffix =  ' - noisy data'+ ' - with linear interpolation'
graph(in_array, noisy_data,  title_suffix, scatter=True, solid_line=True)

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title_suffix = 'smooth data (assumed ground truth)'
graph(in_array, curve, title_suffix , scatter=True, solid_line=False)

title_suffix = ' - noisy data'
graph(in_array, noisy_data, title_suffix, scatter=True, solid_line=False)

title_suffix = ' -  sparse data'
graph(sparse_input, sparse_data, title_suffix, scatter=True, solid_line=False, line_viz = None)

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title_suffix = 'smooth data (assumed ground truth)'
graph(in_array, curve, title_suffix , scatter=True, solid_line=False)

title_suffix = 'smooth data' + ' with linear interpolation'
graph(in_array, curve, title_suffix, scatter=True, solid_line=True)

title_suffix = 'smooth data' + ' - linear interpolation only'
graph(in_array, curve, title_suffix, scatter=False, solid_line=True)

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def graph(x_array, y_array, custom_title, scatter=True, solid_line=False, line_viz = None):
    ''' This function can accept basic x and y arrays for a basic 
    scatter plot or line plot (or both), but it can also accept, 
    in its line_viz parameter, a list of x, y array pairs.
    Its configuration for coloring, line weight, and dot size are 
    tailored specifically for the smoothing examples presented in 
    this blog.'''
    
    # Set up the plotting
    figure_proportions = (10, 5)