Module tensors: collection of explicit useful HT-tensors

teneva_ht_jax.tensors: various useful HT-tensors.

This module contains the collection of functions for explicit construction of various useful HT-tensors (only random tensor for now).

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teneva_ht_jax.tensors.rand(d, n, r, key, a=-1.0, b=1.0)

Construct a random HT-tensor from the uniform distribution.

Parameters:

• d (int) – number of tensor dimensions.

• n (int) – mode size of the tensor.

• r (int) – TT-ranks of the tensor. It should be a number (if all ranks are equal) or list of the length q-1, where q is a number of levels.

• key (jax.random.PRNGKey) – jax random key.

• a (float) – minimum value for random items of the HT-cores.

• b (float) – maximum value for random items of the HT-cores.

Returns:

HT-tensor.

Return type:

list

Examples:

d = 8         # Dimension of the tensor
n = 10        # Mode size for the tensor
r = [3, 4, 5] # Ranks for tree layers

# Build the random HT-tensor:
rng, key = jax.random.split(rng)
Y = tnv.rand(d, n, r, key)

# Print the resulting HT-tensor:
tnv.show(Y)

# >>> ----------------------------------------
# >>> Output:

# HT-tensor  | d=  8
# Level:   1 | Shape: (8, 10, 3)
# Level:   2 | Shape: (4, 3, 4, 3)
# Level:   3 | Shape: (2, 4, 5, 4)
# Level:   4 | Shape: (5, 5)
#

If all ranks are equal, we may set it is a number:

d = 8   # Dimension of the tensor
n = 10  # Mode size for the tensor
r = 4   # Ranks for tree layers

# Build the random HT-tensor:
rng, key = jax.random.split(rng)
Y = tnv.rand(d, n, r, key)

# Print the resulting HT-tensor:
tnv.show(Y)

# >>> ----------------------------------------
# >>> Output:

# HT-tensor  | d=  8
# Level:   1 | Shape: (8, 10, 4)
# Level:   2 | Shape: (4, 4, 4, 4)
# Level:   3 | Shape: (2, 4, 4, 4)
# Level:   4 | Shape: (4, 4)
#

We may also use custom limits for the uniform destribution:

a = 0.99  # Minimum value
b = 1.    # Maximum value

# Build the random HT-tensor:
rng, key = jax.random.split(rng)
Y = tnv.rand(d, n, r, key, a, b)

# Print the first HT-core of first level (leafs):
print(Y[0][0])

# >>> ----------------------------------------
# >>> Output:

# [[0.99490545 0.99509254 0.99896936 0.9990159 ]
#  [0.99463993 0.99899983 0.99047322 0.99053174]
#  [0.99541567 0.99509018 0.99153423 0.99793196]
#  [0.99355632 0.99384485 0.9993778  0.99203122]
#  [0.99295211 0.99767601 0.990772   0.99722857]
#  [0.99141873 0.99057659 0.99087454 0.99856481]
#  [0.99690017 0.99883118 0.99864542 0.99090145]
#  [0.99295839 0.99265914 0.99846659 0.99330255]
#  [0.99348785 0.9949604  0.99655398 0.99307878]
#  [0.99094869 0.99198819 0.99494987 0.9941452 ]]
#