Linear Algebra with scipy

linear.py

import numpy as np
from itertools import combinations
import scipy.linalg

x = [1.2, 1.3, 1.6, 2.5, 2.3, 2.8]
y = [167.0, 180.3, 177.8, 160.4, 179.6, 154.3]
z = [-0.3, -0.8, -0.75, -1.21, -1.65, -0.68]
f = np.array([0.1, 0.2, 0.3, 0.4, 0.5, 0.6]).transpose()

G = np.c_[x, y, z]

A = np.concatenate((G, np.ones((G.shape[0],1))), axis=1)
C, _, _, _ = scipy.linalg.lstsq(A, f)
# C will have now the coefficients for:
# f(x, y, z) = ax + by + cz + d
def linear(x, y, z):
    return C[0] * x + C[1] * y + C[2] * z + C[3]



# quadratic eq.
dim = G.shape[1]
A = np.concatenate((G**2, np.array([np.prod(G[:, k], axis=1) for k in combinations(range(dim), dim-1)]).transpose(), G, np.ones((G.shape[0], 1))), axis=1)
D, _, _, _ = scipy.linalg.lstsq(A, f)
# C will have now the coefficients for:
# f(x, y, z) = ax**2 + by**2 + cz**2 + dxy+ exz + fyz + gx + hy + iz + j

def quadratic(a):
    # a is for example a numpy.array([x, y, z])
    dim = a.shape[0]
    A = np.concatenate((a**2, np.array([np.prod(a[k,]) for k in combinations(range(dim), dim-1)]), a, [1]))
    return np.sum(np.dot(A, D))

for i in range(G.shape[0]):
    print(quadratic(G[i,:]), f[i])