"""
interpolation.py
creates and displays interpolation functions
"""
from scipy.interpolate import interp1d
import numpy as np
import matplotlib.pyplot as plotlib

# Define parameters.
x_sample_start = 0
x_sample_end = 15
x_sample_number = 16
x_sample_endpoint = True
x_new_sample_number = 60
y_exponent = 2
y_divisor = 15.0

# Create an array of x sample data points.
x = np.linspace(
    x_sample_start,
    x_sample_end,
    num=x_sample_number,
    endpoint=x_sample_endpoint)
print("x array values:")
print(x)

# Create an array of y sample data points as a sine function of x.
y = np.sin(-x**y_exponent/y_divisor)
print("y array values:")
print(y)

# Create interpolation functions to generate new y data points.
linear_interpolation_function = interp1d(x, y, kind='linear')
cubic_interpolation_function = interp1d(x, y, kind='cubic')
quadratic_interpolation_function = interp1d(x, y, kind='quadratic')

# Define an array of new x data points.
x_new = np.linspace(
    x_sample_start,
    x_sample_end,
    num=x_new_sample_number,
    endpoint=x_sample_endpoint)

# Plot the functions.
plotlib.plot(
    x, y, 'o',
    x_new, linear_interpolation_function(x_new), '-',
    x_new, cubic_interpolation_function(x_new), '--',
    x_new, quadratic_interpolation_function(x_new), ':'
)

# Plot the legend.
plotlib.legend(['data', 'linear', 'cubic', 'quadratic'], loc='best')

# Display the plot.
plotlib.show()