Numpy et tableau de contingence#

Un exercice classique : écrire le calcul du $\chi_2$ d’un tableau de contingence sans écrire explicitement une boucle. numpy s’en chargera. A suivre jusqu’à ce que vous n’en ayez plus besoin.

[46]:

import numpy as np

A = np.array([[0, 1, 2, 3], [4, 5, 6, 7]], dtype=float)
A

[46]:

array([[0., 1., 2., 3.],
       [4., 5., 6., 7.]])

[48]:

A.sum(axis=1, keepdims=1)

[48]:

array([[ 6.],
       [22.]])

[49]:

A + A.sum(axis=1, keepdims=1)

[49]:

array([[ 6.,  7.,  8.,  9.],
       [26., 27., 28., 29.]])

[45]:

A.sum(axis=0, keepdims=1)

[45]:

array([[ 4,  6,  8, 10]])

[54]:

B = np.zeros(A.shape, dtype=A.dtype)
N2 = A.sum() ** 2
L = A.sum(axis=1)
C = A.sum(axis=0)
for i in range(A.shape[0]):
    for j in range(A.shape[1]):
        B[i, j] = A[i, j] - L[i] * C[j] / N2
B

[54]:

array([[-0.03061224,  0.95408163,  1.93877551,  2.92346939],
       [ 3.8877551 ,  4.83163265,  5.7755102 ,  6.71938776]])

[56]:

A - A.sum(axis=1, keepdims=1) * A.sum(axis=0, keepdims=1) / A.sum() ** 2

[56]:

array([[-0.03061224,  0.95408163,  1.93877551,  2.92346939],
       [ 3.8877551 ,  4.83163265,  5.7755102 ,  6.71938776]])

[57]:

L = A.sum(axis=1, keepdims=1)
C = A.sum(axis=0, keepdims=1)
L.shape, C.shape

[57]:

((2, 1), (1, 4))

[58]:

L * C

[58]:

array([[ 24.,  36.,  48.,  60.],
       [ 88., 132., 176., 220.]])

[59]:

C * L

[59]:

array([[ 24.,  36.,  48.,  60.],
       [ 88., 132., 176., 220.]])

[61]:

L @ C

[61]:

array([[ 24.,  36.,  48.,  60.],
       [ 88., 132., 176., 220.]])

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