Polynomial Fit force first degree to zero - c++

Question

i found good code to do some polynomial least squares fitting based on GSL.
i am using it with 3 degrees: y = Cx² + Bx + A.
In my application i know that A must be zero. Is it possible to change the algorithm so that A alway will be zero?
bool polynomialfit(int obs, int degree,
double *dx, double *dy, double *store) /* n, p */
{
gsl_multifit_linear_workspace *ws;
gsl_matrix *cov, *X;
gsl_vector *y, *c;
double chisq;
int i, j;
X = gsl_matrix_alloc(obs, degree);
y = gsl_vector_alloc(obs);
c = gsl_vector_alloc(degree);
cov = gsl_matrix_alloc(degree, degree);
for(i=0; i < obs; i++) {
gsl_matrix_set(X, i, 0, 1.0);
for(j=0; j < degree; j++) {
gsl_matrix_set(X, i, j, pow(dx[i], j));
}
gsl_vector_set(y, i, dy[i]);
}
ws = gsl_multifit_linear_alloc(obs, degree);
gsl_multifit_linear(X, y, c, cov, &chisq, ws);
/* store result ... */
for(i=0; i < degree; i++)
{
store[i] = gsl_vector_get(c, i);
}
gsl_multifit_linear_free(ws);
gsl_matrix_free(X);
gsl_matrix_free(cov);
gsl_vector_free(y);
gsl_vector_free(c);
return true; /* we do not "analyse" the result (cov matrix mainly)
to know if the fit is "good" */
}

Answer 1

You can replace y by y' = y/x and then perform fitting of a 1. degree polynomial y'= Cx + B?
(if point x = 0 is present in your data set you have to remove it but this point does not improve fit in case you want to apply the A = 0 constraint, you can still use it to re-compute goodness of fit)

Answer 2

In the code you posted there is this loop:
for(j=0; j < degree; j++) {
gsl_matrix_set(X, i, j, pow(dx[i], j));
}
and the function pow computes the x^j terms, you have to "ignore" the term where j==0.
I have no access to GSL and so the following is just off the top of my head and it is untested:
bool polynomialfit(int obs, int polynom_degree,
double *dx, double *dy, double *store) /* n, p */
{
gsl_multifit_linear_workspace *ws;
gsl_matrix *cov, *X;
gsl_vector *y, *c;
double chisq;
int i, j;
int degree = polynom_degree - 1;
X = gsl_matrix_alloc(obs, degree);
y = gsl_vector_alloc(obs);
c = gsl_vector_alloc(degree);
cov = gsl_matrix_alloc(degree, degree);
for(i=0; i < obs; i++) {
gsl_matrix_set(X, i, 0, 1.0);
for(j=0; j < degree; j++) {
gsl_matrix_set(X, i, j, pow(dx[i], j+1));
}
gsl_vector_set(y, i, dy[i]);
}
ws = gsl_multifit_linear_alloc(obs, degree);
gsl_multifit_linear(X, y, c, cov, &chisq, ws);
/* store result ... */
for(i=0; i < degree; i++)
{
store[i] = gsl_vector_get(c, i);
}
gsl_multifit_linear_free(ws);
gsl_matrix_free(X);
gsl_matrix_free(cov);
gsl_vector_free(y);
gsl_vector_free(c);
return true; /* we do not "analyse" the result (cov matrix mainly)
to know if the fit is "good" */
}
In order to fit to y=c*x*x+b*x you have to call it with polynom_degree set to 3.
You also may have a look at the theory:
Weisstein, Eric W. "Least Squares Fitting--Polynomial." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/LeastSquaresFittingPolynomial.html