[SciPy-user] data fitting question

[Ryan Krauss]

I need to fit some data using the form:
Ydata = a[0]*vect1+a[1]*vect2+a[2]*vect3+.....

where Ydata might be the experimental data and vect1, vect2, and vect3
are known and constant (i.e. they aren't changing during the
optimization).  a is a vector of the unknown coefficients I am trying
to find.  The length of a and the number of constant vectors vectN
might change.  Is this a form that is already implemented using some
existing optimization or least squares function, or do I just need to
do something with fmin (for example) or optimize.leastsq?

I guess it could be reformulated as
Y=Ax
where A would be a matrix with vect1, vect2, vect3, ... as its columns
and x would be a column vector of the unknown a's.    I think this is
a very standard form and it is a linear set of equations.  So, I think
there is some simple way to do this, but it is eluding me at the
moment.  I don't think I can just use linalg.solve because A wouldn't
be square.  The matrix A might be 100x5 for example and Y would be
100x1 and x would be 5x1, so that I am trying to find a least squares
solution of the 5 unknowns for the 100 equations.


I think the more complicated way would be to do something like this:

fitfunc = lambda p, x: p[0]*cos(2*pi/p[1]*x+p[2]) + p[3]*x  # Target function
errfunc = lambda p, x, y: fitfunc(p,x) -y          # Distance to the
target function
p0 = [-15., 0.8, 0., -1.]                        # Initial guess for
the parameters
p1,success = optimize.leastsq(errfunc, p0[:], args = (Tx, tX))

from http://scipy.org/Cookbook/FittingData.  This could work and I
would just redefine fitfunc if the number of terms in my fit
increased.  But I don't think this is necessary because my system is
linear in the coefficients.

What is the easiest/best/cleanest way?

Thanks,

Ryan