code: def test_factorize(use_native, use_gpu, use_cg, dtype):
      if use_gpu and (
          not use_cg or dtype != np.float32 or not use_native
      ):
          return
  
      counts = csr_matrix(
          [
              [1, 1, 0, 1, 0, 0],
              [0, 1, 1, 1, 0, 0],
              [1, 0, 1, 0, 0, 0],
              [1, 1, 0, 0, 0, 0],
              [0, 0, 1, 1, 0, 1],
              [0, 1, 0, 0, 0, 1],
              [0, 0, 0, 0, 1, 1],
          ],
          dtype=np.float64,
      )
  
      model = AlternatingLeastSquares(
          factors=6,
          regularization=0,
          alpha=2.0,
          dtype=dtype,
          use_native=use_native,
          use_cg=use_cg,
          use_gpu=use_gpu,
          random_state=42,
      )
      model.fit(counts, show_progress=False)
      rows, cols = model.user_factors, model.item_factors
  
      if use_gpu:
          rows, cols = rows.to_numpy(), cols.to_numpy()
  
      reconstructed = rows.dot(cols.T)
      for i in range(counts.shape[0]):
          for j in range(counts.shape[1]):
              assert (
                  pytest.approx(counts[i, j], abs=1e-3)
                  == reconstructed[i, j]
              ), (
                  "failed to reconstruct row=%s, col=%s,"
                  " value=%.5f, dtype=%s, cg=%s, native=%s gpu=%s"
                  % (
                      i,
                      j,
                      reconstructed[i, j],
                      dtype,
                      use_cg,
                      use_native,
                      use_gpu,
                  )
              )
  
imports: import pickle
  import unittest
  import numpy
  import pytest
  from numpy.testing import assert_array_equal
  from recommender_base_test import RecommenderBaseTestMixin, get_checker_board
  from scipy.sparse import coo_matrix, csr_matrix, random
  import implicit
  from implicit.als import AlternatingLeastSquares
  from implicit.gpu import HAS_CUDA
label_desc: Use image node_id 6 for calling a global function with example usage: test_factorize(use_native, use_gpu, use_cg, dtype) without return types