Printing Curve Fit Function

Question

I have been struggling to find a way to get the determined parameters for the curve fit function below to print. The graph properly matches my data, but I can't figure out how to get the equation it produced. Any help would be appreciated!

import matplotlib.pyplot as plt
import numpy as np
from scipy.optimize import curve_fit

x_data = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31]
y_data = [.99, 1, .98, .93, .85, .77, .67, .56, .46, .36, .27, .19, .12, .07, .03, .01, 0, .01, .05, .09, .16, .24, .33, .44, .55, .65, .76, .85, .93, .98, 1]
x_val = np.array(x_data)
y_val = np.array(y_data)

def fitFunc(x, a, b, c, d):
    return a * np.sin((2* np.pi / b) * x - c) + d
    print(a, b, c, d)

plt.plot(x_val, y_val, marker='.', markersize=0, linewidth='0.5', color='green')
popt, pcov = curve_fit(fitFunc, x_val, y_val)
plt.plot(x_val, fitFunc(x_val, *popt), color='orange', linestyle='--')

You have already implemented the equation in `fitFunc`. The tuple `popt` contains `(a, b, c, d)`. — Warren Weckesser, Oct 09 '18 at 03:28
Remove the "print(a, b, c, d)" in fitFunc and add "print(popt)" after the call to curve_fit. — James Phillips, Oct 09 '18 at 13:28

score 0 · Answer 1 · answered Oct 09 '18 at 14:14

Here is a graphing example that uses your data, note the equation. This example uses initial parameter estimates that were manually estimated from a scatterplot of the data, the default curve_fit estimates are all 1.0 by default and those do not work well in this case.

import numpy as np
import scipy, matplotlib
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit

xData = np.array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 16.0, 17.0, 18.0, 19.0, 20.0, 21.0, 22.0, 23.0, 24.0, 25.0, 26.0, 27.0, 28.0, 29.0, 30.0, 31.0])
yData = np.array([.99, 1.0, 0.98, 0.93, 0.85, 0.77, 0.67, 0.56, 0.46, 0.36, 0.27, 0.19, 0.12, 0.07, 0.03, 0.01, 0, 0.01, 0.05, 0.09, 0.16, 0.24, 0.33, 0.44, 0.55, 0.65, 0.76, 0.85, 0.93, 0.98, 1.0])


def fitFunc(x, amplitude, center, width, offset):
    return amplitude * np.sin(np.pi * (x - center) / width) + offset

# these are the curve_fit default parameter estimates, and
# do not work well for this data and equation - manually estimate below
#initialParameters = np.array([1.0, 1.0, 1.0, 1.0])

# eyeball the scatterplot for some better, simple, initial parameter estimates
initialParameters = np.array([0.5, 1.0, 16.0, 0.5])

# curve fit the test data using initial parameters
fittedParameters, pcov = curve_fit(fitFunc, xData, yData, initialParameters)
print(fittedParameters)

modelPredictions = fitFunc(xData, *fittedParameters) 

absError = modelPredictions - yData

SE = np.square(absError) # squared errors
MSE = np.mean(SE) # mean squared errors
RMSE = np.sqrt(MSE) # Root Mean Squared Error, RMSE
Rsquared = 1.0 - (np.var(absError) / np.var(yData))
print('RMSE:', RMSE)
print('R-squared:', Rsquared)

print()


##########################################################
# graphics output section
def ModelAndScatterPlot(graphWidth, graphHeight):
    f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
    axes = f.add_subplot(111)

    # first the raw data as a scatter plot
    axes.plot(xData, yData,  'D')

    # create data for the fitted equation plot
    xModel = np.linspace(min(xData), max(xData))
    yModel = fitFunc(xModel, *fittedParameters)

    # now the model as a line plot
    axes.plot(xModel, yModel)

    axes.set_xlabel('X Data') # X axis data label
    axes.set_ylabel('Y Data') # Y axis data label

    plt.show()
    plt.close('all') # clean up after using pyplot

graphWidth = 800
graphHeight = 600
ModelAndScatterPlot(graphWidth, graphHeight)

Printing Curve Fit Function

1 Answers1