Curve Fitting y = ax^b Python Program
This Python program implements least square method to fit curve of type y = axb.
We first read n data points from user and then we implement curve fitting for y = axb using least square approach in Python programming language as follow:
Python Source Code: Fitting y = axb
# This is naive approach, there are shortcut methods for doing it! # Least square method # Fitting y = ax^b to given n data points import numpy as np # Reading value of n n = int(input("How many data points? ")) # Creating numpy array x & y to store n data points x = np.zeros(n) y = np.zeros(n) # Reading data print("Enter data:") for i in range(n): x[i] = float(input("x["+str(i)+"]= ")) y[i] = float(input("y["+str(i)+"]= ")) # Finding required sum for least square methods sumX,sumX2,sumY,sumXY = 0,0,0,0 for i in range(n): sumX = sumX + np.log(x[i]) sumX2 = sumX2 +np.log(x[i])*np.log(x[i]) sumY = sumY + np.log(y[i]) sumXY = sumXY + np.log(x[i])*np.log(y[i]) # Finding coefficients A and B b = (n*sumXY-sumX*sumY)/(n*sumX2-sumX*sumX) A = (sumY - b*sumX)/n # Obtaining a and b a = np.exp(A) # Displaying coefficients a, b & equation print("\nCoefficients are:") print("a: ", a) print("b: ", b)
How many data points? 4 Enter data: x= 61 y= 350 x= 26 y= 400 x= 7 y= 500 x= 2.6 y= 600 Coefficients are: a: 701.9919475945616 b: -0.1708554336187208