Numpy Polyfit or any fitting to X and Y multidimensional arrays

Question

I have two large multidimensional arrays: Y carries three measurements of half a million objects (e.g. shape=(500000,3)) and X has same shape, but contains position of Y measurements.

At first, I would like for each row, containing an object, to fit a polynomial equation. I know that iterating over arrays are quite slow, but what I'm doing for the moment is:

fit = array([polyfit(X[i],Y[i],deg) for i in xrange(obs.shape[0])])

My question is: is there any possibility of fitting each row of both arrays without explicitly iterating over them?

Answer 1

It is possible to do so without iterate along the first axis. However, your second axis is rather short (being just 3), you can really fit no more than 2 coefficients.

In [67]:

import numpy as np
import scipy.optimize as so

In [68]:

def MD_ployError(p, x, y):
    '''if x has the shape of (n,m), y must be (n,m), p must be (n*p, ), where p is degree'''
    #d is no. of degree
    p_rshp=p.reshape((x.shape[0], -1))
    f=y*1.
    for i in range(p_rshp.shape[1]):
        f-=p_rshp[:,i][:,np.newaxis]*(x**i)
    return (f**2).sum()

In [69]:

X=np.random.random((100, 6))
Y=4+2*X+3*X*X
P=(np.zeros((100,3))+[1,1,1]).ravel()

In [70]:

MD_ployError(P, X, Y)

Out[70]:
11012.2067606684

In [71]:

R=so.fmin_slsqp(MD_ployError, P, args=(X, Y))
Iteration limit exceeded    (Exit mode 9) #you can increase iteration limit, but the result is already good enough.
            Current function value: 0.00243784856039
            Iterations: 101
            Function evaluations: 30590
            Gradient evaluations: 101

In [72]:

R.reshape((100, -1))

Out[72]:
array([[ 3.94488512,  2.25402422,  2.74773571],
       [ 4.00474864,  1.97966551,  3.02010015],
       [ 3.99919559,  2.0032741 ,  2.99753804],
..............................................)

Answer 2

Yes, if you use the new numpy polyfit from np.polynomial, not the old np.polyfit:

X = np.arange(3)
Y = np.random.rand(10000, 3)

fit = np.array([np.polyfit(X, y, 2) for y in Y])
fits = np.polynomial.polynomial.polyfit(X, Y.T, 2)

assert np.allclose(fit.T[::-1], fits)

Timing:

In [692]: timeit fit = np.array([np.polyfit(X, y, 2) for y in Y])
 1 loops, best of 3: 2.22 s per loop

In [693]:  timeit fits = np.polynomial.polynomial.polyfit(X, Y.T, 2)
100 loops, best of 3: 3.63 ms per loop