import matplotlib.pyplot as plt
import numpy as np

resolutions = [10,20,40,80,100,160,200,320]
resolutions2 = []
for resolution in resolutions:
    resolutions2.append(resolution**2)
    
numericTimes = [0.515,2.018,7.828,30.030,46.033,116.879,177.527,464.059]
monte10 = [0.012,0.024,0.084,0.314,0.0483,1.205,1.862,4.710]
monte50 = [0.021,0.063,0.250,1.007,1.578,3.915,6.267,15.407]
monte200 = [0.063,0.232,0.932,3.697,5.506,14.197,22.452,56.731]
monte800 = [0.231,0.904,3.559,14.420,22.403,56.611,88.400,227.990]
monte1600 = [0.466,1.808,7.245,28.605,44.723,114.017,179.114,455.755]
monte2400 = [0.696,2.762,10.894,42.909,66.179,177.273,274.045,693.686]

m, b = np.polyfit(resolutions2, numericTimes, 1)
numericTimesFit = []
for resolution in resolutions2:
    numericTimesFit.append(resolution*m)

m, b = np.polyfit(resolutions2, monte10, 1)
monte10Fit = []
for resolution in resolutions2:
    monte10Fit.append(resolution*m)

m, b = np.polyfit(resolutions2, monte50, 1)
monte50Fit = []
for resolution in resolutions2:
    monte50Fit.append(resolution*m)

m, b = np.polyfit(resolutions2, monte200, 1)
monte200Fit = []
for resolution in resolutions2:
    monte200Fit.append(resolution*m)

m, b = np.polyfit(resolutions2, monte800, 1)
monte800Fit = []
for resolution in resolutions2:
    monte800Fit.append(resolution*m)

m, b = np.polyfit(resolutions2, monte1600, 1)
monte1600Fit = []
for resolution in resolutions2:
    monte1600Fit.append(resolution*m)

m, b = np.polyfit(resolutions2, monte2400, 1)
monte2400Fit = []
for resolution in resolutions2:
    monte2400Fit.append(resolution*m)

ax = plt.axes()
plt.scatter(resolutions2, numericTimes, color="red")
plt.plot(resolutions2, numericTimesFit, color="red", label="Numeric method")
plt.scatter(resolutions2, monte10, color="orange")
plt.plot(resolutions2, monte10Fit, color="orange", label="Monte method with 10 samples")
plt.scatter(resolutions2, monte50, color="yellow")
plt.plot(resolutions2, monte50Fit, color="yellow", label="Monte method with 50 samples")
plt.scatter(resolutions2, monte200, color="green")
plt.plot(resolutions2, monte200Fit, color="green", label="Monte method with 200 samples")
plt.scatter(resolutions2, monte800, color="blue")
plt.plot(resolutions2, monte800Fit, color="blue", label="Monte method with 800 samples")
plt.scatter(resolutions2, monte1600, color="purple")
plt.plot(resolutions2, monte1600Fit, color="purple", label="Monte method with 1600 samples")
plt.scatter(resolutions2, monte2400, color="pink")
plt.plot(resolutions2, monte2400Fit, color="pink", label="Monte method with 2400 samples")
plt.xlabel("Resolution^2 (Pixels^2)")
plt.ylabel("Time (s)") 
plt.legend()
plt.show()