polynomial2d provides polyfit2d(), a 2-dim polynomial fitting routine. It determines 2-dim polynomial coefficients of a given degree n, using a least square fit to given data values z at given points (x, y). It assumes a polynomial in a form of

z(x,y) = \\sum_{i,j} c_{i,j} * x^i * y^j

with a constraint of i + j <= n. The coefficients are returned in a 2-dim array in a form that allows to work with relevant polynomial functions in numpy.polynomial.polynomial.

polynomial2d also provides, for consistency, polyval2d() and polygrid1d(), wrapper functions of those in numpy.polynomial.polynomial.

>>> import numpy as np
>>> from polynomial2d import polyfit2d

>>> x = np.random.rand(20)
>>> y = np.random.rand(20)
>>> z = 2.0 + 3.0 * x - y + 0.1 * x**2 - 0.01 * x * y - 0.2 * y**2
>>> c = polyfit2d(x, y, z, deg=2)
>>> print(c)
[[ 2.   -1.   -0.2 ]
 [ 3.   -0.01  0.  ]
 [ 0.1   0.    0.  ]]

Note that the coefficients are returned in an array with a shape of (3, 3). The coefficients are arranged so that the returned array nicely work with 2-dim polynomial functions in numpy.polynomial.polynomial.

>>> import numpy.polynomial.polynomial import polyval2d
>>> np.allclose(polyval2d(x, y, c), z)
True

Most of code in the polynomial fitting routine were borrowed from polyfit() in numpy.polynomial.polynomial.