Arithmetics

Basic Arithmetics

The most basic tensor operations (addition +, subtraction -, and product * with either a scalar or with another tensor) can be accomplished via direct manipulation of tensor cores (see e.g. the original tensor train paper).

import tntorch as tn
import torch
import numpy as np

t1 = tn.ones([32]*4)
t2 = tn.ones([32]*4)

t = tn.round((t1+t2)*(t2-2))
print(t)

4D TT tensor:

 32  32  32  32
  |   |   |   |
 (0) (1) (2) (3)
 / \ / \ / \ / \
1   1   1   1   1

You can also assign values to parts of a tensor:

t = tn.ones(5, 5)
t[:3, :] = 2
t[:, :2] *= 3
print(t.torch())

tensor([[6., 6., 2., 2., 2.],
        [6., 6., 2., 2., 2.],
        [6., 6., 2., 2., 2.],
        [3., 3., 1., 1., 1.],
        [3., 3., 1., 1., 1.]])

Advanced Operations

Thanks to cross-approximation, tntorch supports many other more advanced operations on tensors, including element-wise division /, exp(), log(), sin(), etc.

domain = [torch.linspace(0, np.pi, 32)]*4
x, y, z, w = tn.meshgrid(domain)

t = tn.round(1 / (1+x+y+z+w))
print(t)

4D TT-Tucker tensor:

 32  32  32  32
  |   |   |   |
  7  13  13   7
 (0) (1) (2) (3)
 / \ / \ / \ / \
1   7   7   7   1

We will now try the trigonometric identity \(\sin^2(x) + \cos^2(x) = 1\):

t = tn.round(tn.sin(t)**2 + tn.cos(t)**2)
print(t)

4D TT tensor:

 32  32  32  32
  |   |   |   |
 (0) (1) (2) (3)
 / \ / \ / \ / \
1   13  17  13  1

The tensor t should be \(1\) everywhere. Indeed:

print(tn.mean(t))
print(tn.var(t))

tensor(1.0000)
tensor(1.8159e-15)