Tensor in NumPy and what may be useful to know about tensor shapes

NumPy is the fundamental package for scientific computing with Python. It contains among other things: a powerful N-dimensional array object;

import numpy as np
    T = np.array([
  [[1,2,3],    [4,5,6],    [7,8,9]],
  [[11,12,13], [14,15,16], [17,18,19]],
  [[21,22,23], [24,25,26], [27,28,29]],
])
print(T.shape) # (3,3,3)
print(T.ndim) # 3
print(T.size) # 27
print(T)

Each array has attributes ndim (the number of dimensions), shape (the size of each dimension), and size (the total size of the array):

When you need to randomly set the tensor with some default values you may use this:

import numpy as np
np.random.seed(0)  # we used seed to reproduce this again

# x1, x2, x3 are tensors
x1 = np.random.randint(10, size=3)  # 1D
x2 = np.random.randint(10, size=(3, 4))  # 2D
x3 = np.random.randint(10, size=(3, 4, 5))  # 3D

Operation we can do on tensors is dot product:

c = np.tensordot(x1, x2, axes=0)
print(c)

For tensor addition and tensor subtraction operations the tensors need to have the same shape. These are element wise operations.

import numpy as np
np.random.seed(0) 
x21 = np.random.randint(10, size=(3, 4))  # 2D
x22 = np.random.randint(10, size=(3, 4))  # 2D
c = x21 + x22

This would not work because the tensors need to be with the same shape

x21 = np.random.randint(10, size=(4, 4))  # 2D
    x22 = np.random.randint(10, size=(3, 4))  # 2D
c = x21 + x22

The following error ValueError: operands could not be broadcast together with shapes (4,4) (3,4) would occure.

The same shape principle need to be also for the element vise multiplication and element vise division.

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