Scipy curve_fit fails when fitting a curve with large values
I am trying to tie some horizontal wind data to a cosine curve to estimate the direction and speed of the winds at different heights (displaying the azimuth of speed), however, it seems that whenever I try to do this with values> ~ 1, the curve seems too flat and yield less than expected fit.
import numpy as np
import scipy.optimize as sc
azimuth = np.full((8), 60) #All values = 60 deg.
velocity = [5.6261001,6.6962662,3.9316666,-0.88413334,-5.4323335,-6.5153003,-3.2538002,1.0269333]
#Function that defines curve that data will be fitted to
def cos_Wave(x,a, b, c):
return a * np.cos(x-b) + c
azimuthData = np.deg2rad(azimuth)
coeffs, matcov = sc.curve_fit(cos_Wave, azimuthData, velocity, p0 = (1,0,0)
plt.scatter(azimuthData, velocity)
plt.plot(azimuthData, cos_Wave(azimuthData, *coeffs))
plt.show()
print(coeffs)
With output coeffs: [1., 0., 0.13705066] and attached graph:
Python CurveFit
I made a similar curve using the built-in IDL curve function and got more realistic values giving [7.0348234, 0.59962606, 0.079354301] and providing a proper fit. Is there a reason why this is so? I guess it probably has something to do with the initial estimate (P0), however using the initial initial estimate in the IDL implementation still provides much more reasonable results.
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There are a few things you need to fix:
import numpy as np
import scipy.optimize as sc
import matplotlib.pyplot as plt
azimuth = np.linspace(0, 360, 8) # deg values from 0 to 360
velocity = [5.6261001, 6.6962662, 3.9316666, -0.88413334, -5.4323335,
-6.5153003, -3.2538002, 1.0269333]
def cos_Wave(x, a, b, c):
"""Function that defines curve that data will be fitted to"""
return a * np.cos(x-b) + c
azimuthData = np.deg2rad(azimuth)
coeffs, matcov = sc.curve_fit(cos_Wave, azimuthData, velocity, p0=[1, 0, 0])
plt.scatter(azimuthData, velocity)
nx = np.linspace(0, 2 * np.pi, 100)
plt.plot(nx, cos_Wave(nx, *coeffs))
plt.savefig("plot.png")
print(coeffs)
[6.63878549 1.03148322 -0.27674095]
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