Orthogonal regression fitting in scipy least squares method

Question

The leastsq method in scipy lib fits a curve to some data. And this method implies that in this data Y values depends on some X argument. And calculates the minimal distance bet

Answer 1

If/when you are able to invert the function described by p you may just include x-pinverted(y) in mFunc, I guess as sqrt(a^2+b^2), so (pseudo code)

return sqrt( (y - (p[0]*x**p[1]))^2 + (x - (pinverted(y))^2)

for example for

y=kx+m   p=[m,k]    
pinv=[-m/k,1/k]

return sqrt( (y - (p[0]+x*p[1]))^2 + (x - (pinv[0]+y*pinv[1]))^2)

But what you ask for is in some cases problematic. For example, if a polynomial (or your x^j) curve has a minimum ym at y(m) and you have a point x,y lower than ym, what kind of value do you want to return? There's not always a solution.