Curve fit libraries?

[VenusInBlueJeans]

Hello,

I have two arrays, X[] and Y[] in Visual C++, and am looking for a library, a function or a way to use excel curve fitting in order to find the coefficients appropriate.

The curve is a Y(X)=A+B*X+C*X*X and I need the coefficients A, B and C!

Does anyone have any clues about these things?

Thx,
M

 

[jfmclemore]

I would use a least squares algorithm like the following that accepts vectors x and y (allows sample size variability).
Assuming inputs std::vector<double> x, y:

.....
if(x.size()!=y.size())
return;
int i, j, k, l, exp, sz = x.size();
double tot, tot2, res, X[3][3], scratch[3][3], Y[3], soln[3];

//create the matrices for the normal equations
for(i = 0; i < 3; ++i){
for(j = 0; j < 3; ++j){
tot = tot2 = 0.0;
for(k = 0; k < sz; ++k){
exp = j+i;
res = 1.0;
for(l = 0; l <exp 3; ++l)
res *= x[k];
tot +=res;
if(j ==2)
tot2 += (x[k]*y[k]);
}
X[j] = tot;
}
Y = tot2;
}

//Then using Cramer's rule
double detX = det(X);
if(detX == 0){
AfxMessageBox(&quot;Can't solve&quot;
return;
}
for(i = 0; i < 3; ++i){
for(j = 0; j < 3; ++j){
for(k = 0; k < sz; ++k){
if(i == k)
scratch[j][k] = Y[j];
else
scratch[j][k] = X[j][k];
}
}
soln = (det(scratch))/detX;
}
.....

//function for calculating the determinant of 3x3 matrix
double det(double *matrix){
double retVal = posVal = negVal = 0.0;
int i, j = 0;
for(i = 0; i < 3; ++i){
double prod1 = prod2 = 1;
for(j = 0; j < 3; ++j){
int l = 2 - j;
int k = (i+j)%3;
prod1 *= matrix[j][k];
k = (i+l)%3;
prod2 *= matrix[j][k];
}
posVal += prod1;
negVal += prod2;
}
retVal = posVal - negVal;
return retVal;
}

I haven't tested the above code - I just did it off the top of my head so use it with caution. Most of this is pretty standard linear algebra stuff though so if there is an error you should be able to hunt it down using a reference book - topics: Least Squares curve fit for Polynomial and Cramer's Rule.

Good luck,

John