How to use the tensorly.dot function in tensorly

Parameters
    ----------
    matrix : ndarray
    threshold : float

    Returns
    -------
    ndarray
        matrix on which the operator has been applied

    See also
    --------
    procrustes : procrustes operator
    """
    U, s, V = tl.partial_svd(matrix, n_eigenvecs=min(matrix.shape))
    return tl.dot(U, tl.reshape(soft_thresholding(s, threshold), (-1, 1))*V)

# If a row is 0, we delete it.
        if any(rows_norms == 0):
            zero_idx = tl.argmin(rows_norms,axis=0)
            mask.pop(zero_idx)
            rest_of_rows = rest_of_rows[mask]
            A_new = A_new[mask,:]
            continue

        # Find the row of max norm
        max_row_idx = tl.argmax(rows_norms, axis=0)
        max_row = A[rest_of_rows[max_row_idx], :]

        # Compute the projection of max_row to other rows
        # projection a to b is computed as:  / sqrt(|a|*|b|)
        projection = tl.dot(A_new, tl.transpose(max_row))
        normalization = tl.sqrt(rows_norms[max_row_idx] * rows_norms)
        # make sure normalization vector is of the same shape of projection (causing bugs for MxNet)
        normalization = tl.reshape(normalization, tl.shape(projection))
        projection = projection/normalization

        # Subtract the projection from A_new:  b <- b - a * projection
        A_new = A_new - A_new * tl.reshape(projection, (tl.shape(A_new)[0], 1))

        # Delete the selected row
        mask.pop(max_row_idx)
        A_new = A_new[mask,:]

        # update the row_idx and rest_of_rows
        row_idx[i] = rest_of_rows[max_row_idx]
        rest_of_rows = rest_of_rows[mask]
        i = i + 1

weights = tl.ones(rank, **tl.context(tensor))
    for iteration in range(n_iter_max):
        for mode in range(n_dims):
            kr_prod, indices_list = sample_khatri_rao(factors, n_samples, skip_matrix=mode, random_state=rng)
            indices_list = [i.tolist() for i in indices_list]
            # Keep all the elements of the currently considered mode
            indices_list.insert(mode, slice(None, None, None))
            # MXNet will not be happy if this is a list insteaf of a tuple
            indices_list = tuple(indices_list)
            if mode:
                sampled_unfolding = tensor[indices_list]
            else:
                sampled_unfolding = tl.transpose(tensor[indices_list])

            pseudo_inverse = tl.dot(tl.transpose(kr_prod), kr_prod)
            factor = tl.dot(tl.transpose(kr_prod), sampled_unfolding)
            factor = tl.transpose(tl.solve(pseudo_inverse, factor))
            factors[mode] = factor

        if max_stagnation or tol:
            rec_error = tl.norm(tensor - kruskal_to_tensor((weights, factors)), 2) / norm_tensor
            if not min_error or rec_error < min_error:
                min_error = rec_error
                stagnation = -1
            stagnation += 1

            rec_errors.append(rec_error)

            if iteration > 1:
                if verbose:
                    print('reconstruction error={}, variation={}.'.format(

idx = tuple(idx)

    core = input_tensor[idx]
    # shape the core as a 3-tensor_order cube
    core = tl.reshape(core, (rank[k - 1], rank[k], tensor_shape[k - 1]))
    core = tl.transpose(core, (0, 2, 1))
    # merge n_{k-1} and r_k, get a matrix
    core = tl.reshape(core, (rank[k - 1], tensor_shape[k - 1] * rank[k]))
    core = tl.transpose(core)

    # Compute QR decomposition
    (Q, R) = tl.qr(core)
    # Maxvol
    (J, Q_inv) = maxvol(Q)
    Q_inv = tl.tensor(Q_inv)
    Q_skeleton = tl.dot(Q, Q_inv)

    # Retrive indices in folded tensor
    new_idx = [np.unravel_index(idx, [tensor_shape[k - 1], rank[k]]) for idx in J]  # First retrive idx in folded core
    next_col_idx = [(jc[0],) + col_idx[k - 1][jc[1]] for jc in new_idx]  # Then reconstruct the idx in the tensor

    return (next_col_idx, fibers_list, Q_skeleton)

----------
    factors: list of 3D-arrays
              MPS factors (known as core in TT terminology)

    Returns
    -------
    output_tensor: ndarray
                   tensor whose MPS/TT decomposition was given by 'factors'
    """
    full_shape = [f.shape[1] for f in factors]
    full_tensor = tl.reshape(factors[0], (full_shape[0], -1))

    for factor in factors[1:]:
        rank_prev, _, rank_next = factor.shape
        factor = tl.reshape(factor, (rank_prev, -1))
        full_tensor = tl.dot(full_tensor, factor)
        full_tensor = tl.reshape(full_tensor, (-1, rank_next))

    return tl.reshape(full_tensor, full_shape)

else:
                        accum = tl.dot(tl.transpose(factors[e]), factors[e])

            pseudo_inverse = tl.tensor(np.ones((rank, rank)), **tl.context(tensor))
            for i, factor in enumerate(factors):
                if i != mode:
                    pseudo_inverse = pseudo_inverse*tl.dot(tl.conj(tl.transpose(factor)), factor)

            if mask is not None:
                tensor = tensor*mask + tl.kruskal_to_tensor((None, factors), mask=1-mask)

            mttkrp = unfolding_dot_khatri_rao(tensor, (None, factors), mode)

            if non_negative:
                numerator = tl.clip(mttkrp, a_min=epsilon, a_max=None)
                denominator = tl.dot(factors[mode], accum)
                denominator = tl.clip(denominator, a_min=epsilon, a_max=None)
                factor = factors[mode] * numerator / denominator
            else:
                factor = tl.transpose(tl.solve(tl.conj(tl.transpose(pseudo_inverse)),
                                      tl.transpose(mttkrp)))
            
            if normalize_factors:
                weights = tl.norm(factor, order=2, axis=0)
                weights = tl.where(tl.abs(weights) <= tl.eps(tensor.dtype), 
                                   tl.ones(tl.shape(weights), **tl.context(factors[0])),
                                   weights)
                factor = factor/(tl.reshape(weights, (1, -1)))

            factors[mode] = factor

        if tol:

core = tl.tensor(rng.random_sample(rank) + 0.01, **tl.context(tensor))  # Check this
        factors = [tl.tensor(rng.random_sample(s), **tl.context(tensor)) for s in zip(tl.shape(tensor), rank)]
        nn_factors = [tl.abs(f) for f in factors]
        nn_core = tl.abs(core)

    norm_tensor = tl.norm(tensor, 2)
    rec_errors = []

    for iteration in range(n_iter_max):
        for mode in range(tl.ndim(tensor)):
            B = tucker_to_tensor((nn_core, nn_factors), skip_factor=mode)
            B = tl.transpose(unfold(B, mode))

            numerator = tl.dot(unfold(tensor, mode), B)
            numerator = tl.clip(numerator, a_min=epsilon, a_max=None)
            denominator = tl.dot(nn_factors[mode], tl.dot(tl.transpose(B), B))
            denominator = tl.clip(denominator, a_min=epsilon, a_max=None)
            nn_factors[mode] *= numerator / denominator

        numerator = tucker_to_tensor((tensor, nn_factors), transpose_factors=True)
        numerator = tl.clip(numerator, a_min=epsilon, a_max=None)
        for i, f in enumerate(nn_factors):
            if i:
                denominator = mode_dot(denominator, tl.dot(tl.transpose(f), f), i)
            else:
                denominator = mode_dot(nn_core, tl.dot(tl.transpose(f), f), i)
        denominator = tl.clip(denominator, a_min=epsilon, a_max=None)
        nn_core *= numerator / denominator

        rec_error = tl.norm(tensor - tucker_to_tensor((nn_core, nn_factors)), 2) / norm_tensor
        rec_errors.append(rec_error)
        if iteration > 1 and verbose:

if verbose > 1:
            print("Starting iteration", iteration + 1)
        for mode in range(tl.ndim(tensor)):
            if verbose > 1:
                print("Mode", mode, "of", tl.ndim(tensor))
            if non_negative:
                accum = 1
                # khatri_rao(factors).tl.dot(khatri_rao(factors))
                # simplifies to multiplications
                sub_indices = [i for i in range(len(factors)) if i != mode]
                for i, e in enumerate(sub_indices):
                    if i:
                        accum *= tl.dot(tl.transpose(factors[e]), factors[e])
                    else:
                        accum = tl.dot(tl.transpose(factors[e]), factors[e])

            pseudo_inverse = tl.tensor(np.ones((rank, rank)), **tl.context(tensor))
            for i, factor in enumerate(factors):
                if i != mode:
                    pseudo_inverse = pseudo_inverse*tl.dot(tl.conj(tl.transpose(factor)), factor)

            if mask is not None:
                tensor = tensor*mask + tl.kruskal_to_tensor((None, factors), mask=1-mask)

            mttkrp = unfolding_dot_khatri_rao(tensor, (None, factors), mode)

            if non_negative:
                numerator = tl.clip(mttkrp, a_min=epsilon, a_max=None)
                denominator = tl.dot(factors[mode], accum)
                denominator = tl.clip(denominator, a_min=epsilon, a_max=None)
                factor = factors[mode] * numerator / denominator