code: def test_cholesky_grad():
      if not imported_scipy:
          raise SkipTest("Scipy needed for the Cholesky op.")
      rng = np.random.RandomState(utt.fetch_seed())
      r = rng.randn(5, 5).astype(config.floatX)
  
      # The dots are inside the graph since Cholesky needs separable matrices
  
      # Check the default.
      yield (
          lambda: utt.verify_grad(
              lambda r: cholesky(r.dot(r.T)), [r], 3, rng
          )
      )
      # Explicit lower-triangular.
      yield (
          lambda: utt.verify_grad(
              lambda r: Cholesky(lower=True)(r.dot(r.T)), [r], 3, rng
          )
      )
      # Explicit upper-triangular.
      yield (
          lambda: utt.verify_grad(
              lambda r: Cholesky(lower=False)(r.dot(r.T)), [r], 3, rng
          )
      )
  
imports: from __future__ import absolute_import, print_function, division
  import unittest
  import numpy
  import numpy.linalg
  from numpy.testing import assert_array_almost_equal
  from numpy.testing import dec, assert_array_equal, assert_allclose
  from numpy import inf
  import itertools
  import theano
  from theano import tensor, function, grad
  from theano.tensor.basic import _allclose
  from theano.tests.test_rop import break_op
  from theano.tests import unittest_tools
  from theano import config
  from theano.tensor.slinalg import Cholesky, cholesky, CholeskyGrad, Solve, solve, Eigvalsh, EigvalshGrad, eigvalsh, expm, kron
  from theano.tests.unittest_tools import attr
  from nose.plugins.skip import SkipTest
  from nose.tools import assert_raises
label_desc: Use image node_id 5 for calling a global function with example usage: test_cholesky_grad() without return types