[update 2014-02-19: fix error in polyfitBM, add root and select-terms tools]
This submission contains four convenience polynomial fitting functions similar to POLYFIT.
1. POLYFITZERO - fit polynomial to data, forcing y-intercept to zero.
2. POLYFITB - force y-intercept to "b".
3. POLYFITB0 - force y-intercept to "b" and slope at (0,b) to zero.
4. POLYFITBM - force y-intercept to "b" and slope at x=0 to "m", e.g.: dy/dx = m.
5. POLYFITBROOT - force intercept and root
6. POLYFITBMROOT - force intercept, slope and root
7. POLYFITBMROOTTERMS - force intercept, slope, root and terms
If you get to POLYFITBMROOTTERMS please just use POLYFITN by John D'Errico:
Forcing the y-intercept to zero is accomplished by noting for polynomial p = [aN, ..., a3, a2, a1, a0],
IE: y = aN*y^N + ... + a3*y^3 + a2*y^2 + a1*y + a0
when x is zero, then y is the constant term, "a0". Therefore a0 = 0, or in the general case when forcing the y-intercept to an arbitrary value, a0 = b.
Forcing the slope at x=0, is accomplished by noticing that the derivative of p
IE: dy/dx = N*aN*y^(N-1) + ... + 3*a3*y^2 + 2*a2*y + a1
evaluated at x = 0 yields "a1". Therefore a1 = 0 for zero slope, or in the general case when forcing the slope to an arbitrary value, a1 = m.