Module act_one: single HT-tensor operations

teneva_ht_jax.act_one: single HT-tensor operations.

This module contains the basic operations with one HT-tensor (Y), including “get”, etc.

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teneva_ht_jax.act_one.get(Y, k)

Compute the element of the HT-tensor.

Parameters:

• Y (list) – d-dimensional HT-tensor.

• k (np.ndarray) – the multi-index for the tensor of the length d.

Returns:

the element of the HT-tensor.

Return type:

float

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)

# Select some tensor element and compute the value:
k = np.array([0, 1, 2, 3, 4, 5, 6, 7])
y = tnv.get(Y, k)
print(y)

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

# 0.11423279171264825
#

Let multiply the HT-tensor by 2, and check the change of the value in the same multi-index:

Y[-1] = Y[-1] * 2
y = tnv.get(Y, k)
print(y)

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

# 0.2284655834252965
#

We may transform the HT-tensor into full format and check the result:

# TODO!

# Y_full = tnv.full(Y) # This function is not ready!

# y_full = Y_full[tuple(k)]
# print(y_full)

# Let compare values:
# e = np.abs(y - y_full)
# print(f'Error : {e:7.1e}')