bool least_solve(double * const A,//m*n
double * const B,//m*z
double *X,//n*z unknown
double *AA,//A'A n*n temp
double *TAA,//(A'A)^1 n*n temp
double *AB,//A'B n*z temp
int m,int n,int z) {
//A'A
mata(A,AA,m,n);
//A'B
matb(A,B,AB,m,n,z);
//(A'A)^-1
if(!gauss_elim(AA,TAA,n)) {
return false;
}
//X
mul(TAA,AB,X,n,n,z);
return true;
}
// t = independent value, y = response value (dependent value)
int CCurveFitting::exponential_fitting(double* x, int t_len, double* y, double* a_out, double* c_out)
{
//determine how many points used
int n = t_len;
// Solve a first order linear curve fit Ax=b
//[n sum(X) [B = [sum(Y)
// sum(X) sum(X^2)] A] sum(X*Y)]
// where: Y=ln(y), X=x, and finally C=exp(B)
Mat matA(2, 2, CV_64F);
Mat matx(2, 1, CV_64F);
Mat matb(2, 1, CV_64F);
double sumX=0.0, sumX2=0.0, sumY=0.0, sumXY=0.0, B;
bool bNonSingular;
for (int i = 0; i < n; i++)
{
sumX += (x[i]);
sumX2 += (pow(x[i], 2.0));
sumY += (log(y[i]));
sumXY += (x[i] * log(y[i]));
}
matA.ptr<double>(0, 0)[0] = (double)n;
matA.ptr<double>(0, 1)[0] = sumX;
matA.ptr<double>(1, 0)[0] = sumX;
matA.ptr<double>(1, 1)[0] = sumX2;
matb.ptr<double>(0, 0)[0] = sumY;
matb.ptr<double>(1, 0)[0] = sumXY;
bNonSingular = solve(matA, matb, matx, DECOMP_LU);
*a_out = matx.ptr<double>(1, 0)[0];
B = matx.ptr<double>(0, 0)[0];
*c_out = exp(B);
return 0;
}
void mata(double * const A,double *AA,int m,int n) {
matb(A,A,AA,m,n,n);
}
