# [SciPy-User] a routine for fitting a straight line to data

David Pine djpine@gmail....
Sun Mar 24 18:53:35 CDT 2013

```I would like to submit a routine to scipy for performing least squares fitting of a straight line f(x) = ax + b to an (x,y) data set.  There are a number of ways of doing this currently using scipy or numpy but all have serious drawbacks.  Here is what is currently available, as far as I can tell, and what seem to me to be their drawbacks.

1. numpy.polyfit :
a.  It is slower than it needs to be.  polyfit uses matrix methods that are needed to find best fits to general polynomials (quadratic, cubic, quartic, and higher orders), but matrix methods are overkill when you just want to fit a straight line f(x)= ax + b to data set.  A direct approach can yield fits significantly faster.
b.  polyfit currently does not allow using absolute error estimates for weighting the data; only relative error estimates are currently possible.  This can be fixed, but for the moment it's a problem.
c.  New or inexperienced uses are unlikely to look for a routine to fit straight lines in a routine that is advertised as being for polynomials.  This is a more important point than it may seem.  Fitting data to a straight line is probably the most common curve fitting task performed, and the only one that many users will ever use.  It makes sense to cater to such users by providing them with a routine that does what they want in as clear and straightforward a manner as possible.  I am a physics professor and have seen the confusion first hand with a wide spectrum of students who are new to Python.  It should not be this hard for them.

2. scipy.linalg.lstsq
a.  Using linalg.lstsq to fit a straight line is clunky and very slow (on the order of 10 times slower than polyfit, which is already slower than it needs to be).
b.  While linalg.lstsq can be used to fit data with error estimates (i.e. using weighting), how to do this is far from obvious.  It's unlikely that anyone but an expert would figure out how to do it.
c.  linalg.lstsq requires the use of matrices, which will be unfamiliar to some users.  Moreover, it should not be necessary to use matrices when the task at hand only involves one-dimensional arrays.

3. scipy.curve_fit
a.  This is a nonlinear fitting routine.  As such, it searches for the global minimum in the objective function (chi-squared) rather than just calculating where the global minimum is using the analytical expressions for the best fits.  It's the wrong method for the problem, although it will work.

Questions:  What do others in the scientific Python community think about the need for such a routine?   Where should routine to fit data to a straight line go?  It would seem to me that it should go in the scipy.optimize package, but I wonder what others think.

David Pine
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