Finished Exercise 2 with pyTest

week1/ex2.py

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+#!/usr/bin/env python3
+
+# Lagrange Polynomial Interpolation
+#----------------------------------
+
+import numpy as np
+
+def my_lagrange(data_x, data_y, x):
+    """
+    Lagrange Interpolation
+
+    param @data_x   : array: x values to be interpolated
+    param @data_y   : array: y values to be interpolated
+    param @x        : array_like: x part of the interpolation set
+
+    returns @p      : array: y part of the interpolation set
+    """
+    # make sure data_x is a numpy array with nd >= 1
+    x = np.array(x, ndmin=1)
+    p = np.zeros(np.size(x), dtype=np.float64)
+
+
+    for i, x_i in enumerate( x ):
+        p[i] = np.sum( data_y * my_lagrange_polynomials(data_x, x_i) )
+
+    return p
+
+
+def my_lagrange_polynomials(data_x, x_i):
+    """ 
+    Determine Lagrange Polynomials
+    
+    param @data_x   : array_like : various data parts
+    param @x_i      : float : interpolating x value
+
+    returns @L      : array : lagrange polynomial terms for each x_i
+    """
+
+    # make sure data_x is a numpy array with nd >= 1
+    data_x = np.array(data_x, ndmin=1)
+
+    L = np.zeros(np.size(data_x), dtype=np.float64)
+
+    L_fixed = np.prod( x_i - data_x )
+
+    for k, x_k in enumerate( data_x ):
+        if x_k != x_i:
+            L[k] = L_fixed / ( x_i - x_k )
+        else:
+            # Avoid dividing by zero if x_i and x_k are equal
+            L[k] = np.prod( x_i - np.delete(data_x, k) )
+
+        L[k] *=  1 / np.prod( x_k - np.delete(data_x,k) )
+
+    return L
+
+
+def main(x_values = None, y_values = None, x = None, x_min = None, x_max = None, x_step = None, x_N = None):
+    """
+    Example implementation of my_lagrange[_polynomials]()
+    """
+
+    if x_values is None or y_values is None:
+        x_values = [2,3,4,5,6]
+        y_values = [2,5,5,5,6]
+
+    if x is None:
+        x_min = x_min if x_min is not None else min(x_values)
+        x_max = x_max if x_max is not None else max(y_values)
+        
+        x_N = x_N if x_N is not None else (int(abs((x_max - x_min ) / x_step)) if x_step is not None else 1e3)
+        
+        x = np.linspace(x_min, x_max, x_N, endpoint=True)
+    
+    import matplotlib.pyplot as plt
+
+    fig, ax = plt.subplots()
+
+    ax.set_title("Lagrange Interpolations")
+    ax.grid()
+    ax.set_xlabel("x")
+    ax.set_ylabel("y")
+
+    # Plot my Lagrange Interpolation
+    ax.plot(x, my_lagrange(x_values, y_values, x), '.', label="My Lagrange Interpolation")
+
+    # Plot Scipy's Lagrange Interpolation
+    from scipy.interpolate import lagrange as scipy_lagrange
+    ax.plot(x, scipy_lagrange(x_values, y_values)(x), '--', label="Scipy Interpolation")
+
+
+    # Plot the data
+    ax.plot(x_values, y_values, 'gd', label="Data")
+    ax.legend()
+
+    plt.show()
+
+
+if __name__ == "__main__":
+    main()

week1/test_ex2.py

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+#!/usr/bin/env python3
+
+# Test Lagrange Polynomial Interpolation Implementation
+#------------------------------------------------------
+
+from ex2 import my_lagrange, my_lagrange_polynomials
+import numpy as np
+
+def test_import():
+    """
+    Test the import
+    """
+    assert my_lagrange is not None
+    assert my_lagrange_polynomials is not None
+
+def test_my_lagrange_polynomials():
+    """
+    Test the my_lagrange_polynomials function
+    """
+    # Take Numpy Array
+    assert (my_lagrange_polynomials(np.array([0,1]), 1) == np.array([0, 1])).all()
+    # Take Python List
+    assert (my_lagrange_polynomials([0,1], 1) == np.array([0, 1])).all()
+
+
+    # Changing the order of x_values changes the order of the returned values
+    assert (my_lagrange_polynomials([2,4,6,8], 5)  == np.array([-0.0625, 0.5625, 0.5625, -0.0625])).all()
+    assert (my_lagrange_polynomials([6,8,2,4], 5)  == np.array([0.5625, -0.0625, -0.0625, 0.5625])).all()
+
+def test_my_lagrange():
+    """
+    Test the my_lagrange function
+    """
+    # Take x_i as a single number
+    assert (my_lagrange([1, 2], [1, 2], 1) == np.array([1])).all()
+
+
+    assert (my_lagrange([1, 2], [1, 2], [1, 1.5, 2]) == np.array([1, 1.5, 2])).all()
+
+
+if __name__ == "__main__":
+    import pytest
+    print("pyTesting ", __file__)
+    pytest.main([__file__])