foreword

Env

import torch

var

tensor([0., 1., 2., 3.])

tensor([[ 0,  1,  2,  3],
        [ 4,  5,  6,  7],
        [ 8,  9, 10, 11],
        [12, 13, 14, 15],
        [16, 17, 18, 19]])

sum

x.sum()

Output

tensor(6.)

\( \sum_{i=1}^{d} x_i \)

A.sum()

Output

tensor(190.)

\( \sum_{i=1}^{m}\sum_{j=1}^{n} a_{ij} \)

A.sum(axis=0)

Output

tensor([40., 45., 50., 55.])

A.sum(axis=[0, 1])

Output

tensor(190.)

mean

x.mean()
// x.sum() / x.numel()

Output

tensor(1.5000)

\( \frac{1}{d} \sum_{i=1}^{d} x_i \)

A.mean()
// A.sum() / A.numel()

Output

tensor(9.5000)

\( \frac{1}{mn} \sum_{i=1}^{m}\sum_{j=1}^{n} a_{ij} \)

A.mean(axis=0)
// A.sum(axis=0) / A.shape[0]

Output

tensor([ 8.,  9., 10., 11.])

A.mean(axis=[0,1])

Output

tensor(9.5000)

Non-dimensionality reduction summation

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

Output

tensor([[ 6.],
        [22.],
        [38.],
        [54.],
        [70.]])