print(values)
P = pb1.newton_interpolation(values, cheb_zeros)
X = cheb_zeros
print("This gives the following interpolation polynomial:")
pb1.print_polynomial(P, X)
max_diff = 0
max_x = 0
poly_values = zeros(1001)
x = linspace(interval[0], interval[1], 1001)
for i in range(1001):
x_coord = x[i]
y_coord = pb1.get_value_of_polynomial(P, X, x_coord)
fx = f(x_coord)
if abs(fx - y_coord) > max_diff:
max_diff = abs(fx - y_coord)
max_x = x_coord
poly_values[i] = y_coord
print("The maximum error found on the test points was:",
max_diff) # max difference
print("This maximum error was found at the x value:", max_x)
print("Plotting the graph...")
figure(1)
plot(x, poly_values, 'b-', x, f(x), 'g-', cheb_zeros, values, 'or')
xlabel("Abscissas", fontsize=20)
# Newton with Chebyshev zeros:
cheb_zeros = pb2.chebyshev(-5, 5, N) # Retrieves the Chebyshev zeros
cheb_values = [f(x) for x in cheb_zeros] # Retrieves the ordinates for the Chebyshev zeros
cheb_newton_poly = pb1.newton_interpolation(cheb_values, cheb_zeros) # Generates polynomial
spline_coeff = pb3.SplineCoefficients(points, values) # Returns our spline interpolation coefficients
x = linspace(interval[0], interval[1], 1001)
for i in range(1001): # We loop through the 1001 points
x_coord = x[i]
# We evaluate all of the approximations at the iteration absica and store it in an array
y = [pb1.get_value_of_polynomial(newton_poly, points, x_coord),
pb1.get_value_of_polynomial(cheb_newton_poly, cheb_zeros, x_coord),
pb3.evaluate_spline(spline_coeff, points, x_coord)]
for j in range(len(y)): # We check if the current error of each approximation is bigger than the last error
y_coord = y[j]
fx = f(x_coord)
if abs(fx - y_coord) > max_error[j]:
max_error[j] = abs(fx - y_coord) # If yes, we record the new biggest error
max_x[j] = x_coord # We also record the x value at which the biggest error occurred.
for k in range(len(max_errors)):
max_errors[k][N - 3] = max_error[k]
# For personal observation, I stored each of the errors in a separate file for easier inspection.
