How to calculate error between 2 curves ?

Hello,

I want to calculate and plot the percentage of error between two curves: (one is interpolated from the other with the function interp1).

The first (experimental) curve is drawn from 3357 points (xi, yi), the interpolated curve is drawn from 274 (xq, yq).

How do I calculate and plot the error?

here is the program:

dataset =xlsread('Ecrouissage-na.xlsx','Sheet1','A5:B3361');
T=dataset(:,1);
H=dataset(:,2);
xi= T.'
yi=H.'
xq  = 0 : 0.001 : 0.2732;
yq  = interp1(xi,yi,xq,'linear');
plot(xi,yi,'--', xq,yq,'m')
legend('reel','interpolation')

[rubindan]

What do you mean by "percentage of error"? Can root-mean-sqaure (RMS) error be of help?

[Nawfel Salha]

Hi,

i'm talking about the relative error, i know the formula but how i can calculate it when i have matrices of different diensions ?

[Alex]

Hello how can you compute the real error?

i.e. Taking a symbolic function and substracting to the interpolation? Then I would integrate in the interval of the interpolation.

The problem is I cannot operate the interpolation (double array) with the symbolic function.

Is there any method in MATLAB to do that?

[Km Shraddha]

I am facing the same challenge. Did you find any solution?

Answer 1

[KSSV]

If y0 is original value and y1 is obtained value. You can get the error using :

dy = y0-y1 ; % error 
abs_dy = abs(y0-y1) ;   % absolute error 
relerr = abs(y0-y1)./y0 ;  % relative error 
pererr = abs(y0-y1)./y0*100 ;   % percentage error 
mean_err = mean(abs(y0-y1)) ;    % mean absolute error 
MSE = mean((y0-y1).^2) ;        % Mean square error 
RMSE = sqrt(mean((y0-y1).^2)) ; % Root mean square error 

[Nawfel Salha]

Thank you for your answer, but I cannot apply these functions because I don't have the same dimension of the matrices. The problem is that The first (experimental) curve is drawn from 3357 points (xi, yi), the interpolated curve is drawn from 274 (xq, yq).

how i fix this problem?

[KSSV]

That is not a problem. Use interp1 and convert them to same dimensions.

[Hugo Keck]

Hi, I tried this but what happens when one of y0 values is equal to 0 ?

[KSSV]

You skip that value ..

Answer 2

[Muhammad Bilal Ahmad]

import numpy as np
import matplotlib.pyplot as plt

# Function definition
def f(x):
    return 1/x

# Quadratic polynomial definition
def P2(x):
    return 1 - 0.25*(x - 1) + 0.0208*(x - 1)*(x - 2)

# Error bound calculation
h = 4 - 1
M = 0.0208  # Assuming M is an upper bound for the third derivative, derived from the divided difference table
error_bound = (M / 8) * h**2

# Generate x values for plotting
x_values = np.linspace(1, 4, 100)

# Calculate y values for the original function and the quadratic polynomial
y_original = f(x_values)
y_interpolation = P2(x_values)

# Plot the graphs
plt.plot(x_values, y_original, label='f(x) = 1/x', color='blue')
plt.plot(x_values, y_interpolation, label='P2(x)', linestyle='dashed', color='red')

# Mark the interpolation points
plt.scatter([1, 2, 4], [f(1), f(2), f(4)], color='black', marker='o', label='Interpolation Points')

# Highlight the largest real error point
max_error_index = np.argmax(np.abs(y_original - y_interpolation))
plt.scatter(x_values[max_error_index], y_interpolation[max_error_index], color='green', marker='x', label='Max Real Error')

# Add legend and labels
plt.legend()
plt.xlabel('x')
plt.ylabel('y')
plt.title('Interpolation and Original Function')

# Display the plot
plt.show()

# Compare real error with error bound
print(f"Error Bound: {error_bound}")
print(f"Real Error at Max Point: {np.abs(y_original[max_error_index] - y_interpolation[max_error_index])}")