##### https://github.com/tensorly/tensorly
Tip revision: 247917c
test_mps_decomposition.py
``````import tensorly as tl
import numpy as np

from ..mps_decomposition import matrix_product_state
from ...mps_tensor import mps_to_tensor
from ...random import check_random_state

def test_matrix_product_state():
""" Test for matrix_product_state """
rng = check_random_state(1234)

## Test 1

# Create tensor with random elements
tensor = tl.tensor(rng.random_sample([3, 4, 5, 6, 2, 10]))
tensor_shape = tensor.shape

# Find MPS decomposition of the tensor
rank = [1, 3, 3, 4, 2, 2, 1]
factors = matrix_product_state(tensor, rank)

assert(len(factors) == 6), "Number of factors should be 6, currently has " + str(len(factors))

# Check that the ranks are correct and that the second mode of each factor
# has the correct number of elements
r_prev_iteration = 1
for k in range(6):
(r_prev_k, n_k, r_k) = factors[k].shape
assert(tensor_shape[k] == n_k), "Mode 1 of factor " + str(k) + "needs " + str(tensor_shape[k]) + " dimensions, currently has " + str(n_k)
assert(r_prev_k == r_prev_iteration), " Incorrect ranks of factors "
r_prev_iteration = r_k

## Test 2
# Create tensor with random elements
tensor = tl.tensor(rng.random_sample([3, 4, 5, 6, 2, 10]))
tensor_shape = tensor.shape

# Find MPS decomposition of the tensor
rank = [1, 5, 4, 3, 8, 10, 1]
factors = matrix_product_state(tensor, rank)

for k in range(6):
(r_prev, n_k, r_k) = factors[k].shape

first_error_message = "MPS rank " + str(k) + " is greater than the maximum allowed "
first_error_message += str(r_prev) + " > " + str(rank[k])
assert(r_prev<=rank[k]), first_error_message

first_error_message = "MPS rank " + str(k+1) + " is greater than the maximum allowed "
first_error_message += str(r_k) + " > " + str(rank[k+1])
assert(r_k<=rank[k+1]), first_error_message

## Test 3
tol = 10e-5
tensor = tl.tensor(rng.random_sample([3, 3, 3]))
factors = matrix_product_state(tensor, (1, 3, 3, 1))
reconstructed_tensor = mps_to_tensor(factors)
error = tl.norm(reconstructed_tensor - tensor, 2)
error /= tl.norm(tensor, 2)
tl.assert_(error < tol,
'norm 2 of reconstruction higher than tol')

``````