Curve Fitting of Type y=ax^b Using C++ with Output


C++ Program for fitting curve y=axb using least square method with output.


#include<iostream>
#include<math.h>

#define S 50

using namespace std;

int main()
{
 int n, i;
 float x[S], y[S], sumX=0, sumX2=0, sumY=0, sumXY=0, a, b, A;


 /* Input */
 cout<<"How many data points? " << endl;
 cin >> n;

 for(i=1;i<=n;i++)
 {
  cout << "x["<< i <<"] = ";
  cin >> x[i];
  cout << "y["<< i <<"] = ";
  cin >> y[i];
 }

 /* Calculating Required Sum */
 for(i=1;i<=n;i++)
 {
  sumX = sumX + log(x[i]);
  sumX2 = sumX2 + log(x[i])*log(x[i]);
  sumY = sumY + log(y[i]);
  sumXY = sumXY + log(x[i])*log(y[i]);
 }

 /* Calculating A and b */
 b = (n*sumXY-sumX*sumY)/(n*sumX2-sumX*sumX);
 A = (sumY - b*sumX)/n;

 /* Transformation of A to a */
 a = exp(A);

 /* Displaying value of a and b */
 cout << "Values are: a = " << a << " and b = " << b;

 return(0);
}

Output

How many data points?
4
x[1] = 1
y[1] = 4.9
x[2] = 2
y[2] = 40.1
x[3] = 3
y[3] = 134.9
x[4] = 4
y[4] = 320.1
Values are: a = 4.92024 and b = 3.01453

Recommended Readings

  1. Algorithm for fitting Curve y = axb
  2. Pseudocode for fitting y = axb
  3. C Program for fitting curve y = axb
  4. C++ Program for fitting curve y = axb
  5. Algorithm for fitting Curve y = abx
  6. Pseudocode for fitting y = abx
  7. C Program for fitting curve y = abx
  8. C++ Program for fitting curve y = abx