Logarithmic and Exponential Curve Fit in Python - Numpy

With numpy function "polyfit":

X,y : data to be fitted

import numpy as np

1. Exponential fit

cf = np.polyfit(X, np.log(y), 1)

will return two coefficients, who will compose the equation:

exp(cf[1])*exp(cf[0]*X)


2. Logarithm fit:

cf = np.polyfit(np.log(X), y, 1)

will return two coefficients, who will compose the equation:

cf[0]*log(X)+cf[1]

Polynomial Curve Fitting

The code below shows how easily you can do a Polynomial Curve Fitting with Python and Numpy.

import numpy as np

# sample x and y data - example
x = [7.76,10.11,11.89,14.81,15.49]
y = [1.851,1.971,1.953,1.842,1.805]

# the polyfit functions does the nth degree polynomial best fit on the data, 
# returning the polynomial coefficients

n = 4   # 4th degree polynomial, you can change for whatever degree you want
coefs = np.polyfit(x,y,n)

# The poly1d function applies the polynomial function to our calculated coefficients
polyf = np.poly1d(coefs)

#if we want to apply our polynomial function to a range of x values
xf = np.linspace(0,20)
yf = polyf(xf)

Exponential curve fit in numpy

With numpy function "polyfit" we can easily fit diferent kind of curves, not only polynomial curves.

According to the users manual, the numpy.polyfit does:

"
Least squares polynomial fit.

Fit a polynomial p(x) = p[0] * x**deg + ... + p[deg] of degree deg to points (x, y). Returns a vector of coefficients p that minimises the squared error.
"

If we use X and y as arrays with our data, the code:

coef = np.polyfit(X, np.log(y), 1)

will return two coefficients, who will compose the equation:

exp(coef[1])*exp(coef[0]*X)

Giving you the exponential curve that better fits our data - X and y.
The polyfit function can receive weight values, which we can use in case of giving less importance to very small values, for example. We can use a weight function as following:

coef = np.polyfit(X, np.log(y), 1, w=np.sqrt(y))

Giving more weight to higher values.

To retrieve the R-squared index of our exponenctial curve, we can use de scikit r2_score, as following:
y_pred = np.exp(coefs[1])*np.exp(coefs[0]*X)

from sklearn.metrics import r2_score

r2s = r2_score(y, y_pred, sample_weight=None, multioutput=None)