code: import contextlib
  import gc
  import sys
  import math
  import tempfile
  import time
  import threading
  import unittest
  import warnings
  from copy import deepcopy
  from collections import OrderedDict
  from itertools import product
  from operator import mul
  from functools import reduce
  import torch
  import json
  
  # TODO: remove this global setting
  # Autograd tests use double as the default dtype
  torch.set_default_dtype(torch.double)
  
  from torch import nn
  from torch._six import inf, nan, istuple
  from torch.autograd.gradcheck import gradgradcheck, gradcheck
  from torch.autograd.function import once_differentiable
  from torch.autograd.profiler import (profile, format_time, EventList,
                                       FunctionEvent, FunctionEventAvg,
                                       record_function, emit_nvtx)
  import torch.autograd.functional as autogradF
  from torch.utils.checkpoint import checkpoint
  from torch.testing._internal.common_utils import (TEST_MKL, TEST_WITH_ROCM, TestCase, run_tests, skipIfNoLapack,
                                                    suppress_warnings, slowTest,
                                                    load_tests, random_symmetric_pd_matrix, random_symmetric_matrix,
                                                    IS_WINDOWS, IS_MACOS, CudaMemoryLeakCheck)
  from torch.autograd import Variable, Function, detect_anomaly
  from torch.autograd.function import InplaceFunction
  from torch.testing import randn_like
  from torch.testing._internal.common_methods_invocations import (method_tests,
                                                                  create_input, unpack_variables,
                                                                  EXCLUDE_FUNCTIONAL, EXCLUDE_GRADCHECK,
                                                                  EXCLUDE_GRADGRADCHECK,
                                                                  EXCLUDE_GRADGRADCHECK_BY_TEST_NAME,
                                                                  exclude_tensor_method,
                                                                  mask_not_all_zeros,
                                                                  S)
  from torch.testing._internal.common_device_type import (instantiate_device_type_tests, skipCUDAIfRocm,
                                                          onlyCPU, onlyCUDA, dtypes, dtypesIfCUDA,
                                                          deviceCountAtLeast, skipCUDAIfCudnnVersionLessThan)
  
  # load_tests from common_utils is used to automatically filter tests for
  # sharding on sandcastle. This line silences flake warnings
  load_tests = load_tests
  
  if sys.version_info[0] == 2:
      import cPickle as pickle
  else:
      import pickle
  
  PRECISION = 1e-4
  
  
  @contextlib.contextmanager
  def backward_engine(engine):
      _prev_engine = Variable._execution_engine
      Variable._execution_engine = engine()
      try:
          yield
      finally:
          Variable._execution_engine = _prev_engine
  
  
  def graph_desc(fn):
      if fn is None:
          return 'None'
      result = type(fn).__name__ + '('
      next_functions = fn.next_functions
      for next_fn, _ in next_functions:
          result += graph_desc(next_fn)
          result += ', '
      if next_functions:
          result = result[:-2]
      return result + ')'
  
  
  class TestAutograd(TestCase):
  
      def _function_test(self, cls):
          x = torch.randn(5, 5, requires_grad=True)
          y = torch.randn(5, 5, requires_grad=True)
          result = cls.apply(x, 2, y)
          go = torch.ones((), requires_grad=True)
          result.sum().backward(go, create_graph=True)
  
          self.assertEqual(x.grad, y + torch.ones(5, 5))
          self.assertEqual(y.grad, x + torch.ones(5, 5) * 2)
          self.assertIsNotNone(x.grad.grad_fn)
          self.assertIsNotNone(y.grad.grad_fn)
  
          return x, y
  
      def test_function(self):
          class MyFunction(Function):
  
              @staticmethod
              def forward(ctx, tensor1, pyscalar, tensor2):
                  ctx.pyscalar = pyscalar
                  ctx.save_for_backward(tensor1, tensor2)
                  return tensor1 + pyscalar * tensor2 + tensor1 * tensor2
  
              @staticmethod
              def backward(ctx, grad_output):
                  var1, var2 = ctx.saved_tensors
                  # NOTE: self is the test case here
                  self.assertIsInstance(var1, torch.Tensor)
                  self.assertIsInstance(var2, torch.Tensor)
                  self.assertIsInstance(grad_output, torch.Tensor)
                  return (grad_output + grad_output * var2, None,
                          grad_output * ctx.pyscalar + grad_output * var1)
  
          x, y = self._function_test(MyFunction)
  
          x_grad_desc = graph_desc(x.grad.grad_fn)
          y_grad_desc = graph_desc(y.grad.grad_fn)
          self.assertExpected(x_grad_desc, "x_grad_desc")
          self.assertExpected(y_grad_desc, "y_grad_desc")
  
      def test_once_differentiable(self):
          class MyFunction(Function):
  
              @staticmethod
              def forward(ctx, tensor1, pyscalar, tensor2):
                  ctx.pyscalar = pyscalar
                  ctx.save_for_backward(tensor1, tensor2)
                  return tensor1 + pyscalar * tensor2 + tensor1 * tensor2
  
              @staticmethod
              @once_differentiable
              def backward(ctx, grad_output):
                  self.assertFalse(torch.is_grad_enabled())
                  t1, t2 = ctx.saved_tensors
                  return (grad_output + grad_output * t2, None,
                          grad_output * ctx.pyscalar + grad_output * t1)
  
          x, y = self._function_test(MyFunction)
          self.assertEqual(graph_desc(x.grad.grad_fn),
                           'CloneBackward(Error(AccumulateGrad(), None, AccumulateGrad()))')
          self.assertEqual(graph_desc(y.grad.grad_fn),
                           'CloneBackward(Error(AccumulateGrad(), None, AccumulateGrad()))')
  
      def test_function_returns_input(self):
          class MyFunction(Function):
              @staticmethod
              def forward(ctx, x):
                  return x
  
              @staticmethod
              def backward(ctx, grad):
                  return grad * 2
  
          for shape in [(1,), ()]:
              v = torch.ones(shape, requires_grad=True)
              MyFunction.apply(v).backward()
              self.assertEqual(v.grad, torch.full(shape, 2))
  
              with torch.no_grad():
                  v.grad.zero_()
              MyFunction.apply(v.clone()).backward()
              self.assertEqual(v.grad, torch.full(shape, 2))
  
      def test_legacy_function_deprecation_exception(self):
          # Trigger exception
          class MyFunction(Function):
              def forward(self, x):
                  return x
  
              def backward(self, grad_output):
                  return grad_output
  
          # Check exception occurs
          with self.assertRaisesRegex(
                  RuntimeError,
                  'Legacy autograd function with non-static forward method is deprecated'):
              MyFunction()(torch.randn(3, 4))
  
      class SimulateBackwardError(Function):
  
          @staticmethod
          def forward(ctx, input):
              return input.clone()
  
          @staticmethod
          @once_differentiable
          def backward(ctx, input):
              raise Exception("Simulate error on backward pass")
  
      def test_custom_function_exception(self):
  
          t1 = torch.rand((3, 3), requires_grad=True)
          t2 = torch.rand((3, 3), requires_grad=True)
  
          tmp = (t1 + t2) * (t1 + t2)
          t3 = TestAutograd.SimulateBackwardError.apply(tmp)
          with self.assertRaisesRegex(RuntimeError, "Simulate error on backward pass"):
              t3.sum().backward()
  
      def test_invalid_gradients(self):
          class MyFunction(Function):
              @staticmethod
              def forward(ctx, x):
                  return x * 2
  
              @staticmethod
              def backward(ctx, grad_output):
                  return torch.randn(10, dtype=torch.float)
  
          with self.assertRaisesRegex(RuntimeError, 'expected shape'):
              input = torch.randn(5, 5, dtype=torch.float, requires_grad=True)
              MyFunction.apply(input).sum().backward()
  
      def test_accumulate_grad(self):
          grad_output = torch.ones(5, 5)
  
          def compute_grad(create_graph):
              x = torch.randn(5, 5, requires_grad=True)
              y = x + 2
              y.backward(grad_output, retain_graph=True)
              x_grad = x.grad
              x_grad_clone = x.grad.clone()
              y.backward(grad_output, create_graph=create_graph)
              return x_grad, x_grad_clone
  
          # Accumulate in-place when create_graph is False
          x_grad, x_grad_clone = compute_grad(create_graph=False)
          self.assertEqual(x_grad, x_grad_clone * 2)
  
          # Accumulate out-of-place when create_graph is False
          x_grad, x_grad_clone = compute_grad(create_graph=True)
          self.assertEqual(x_grad, x_grad_clone)
  
      def test_accumulate_grad_tensor_reference(self):
          def _test_grad_tensor(params_grad_tensor, backward_grad_tensor, should_preserve_reference):
              params = torch.tensor([1.5, 1.5]).requires_grad_()
              params.grad = params_grad_tensor
              grad_saved = params.grad
              params.backward(backward_grad_tensor)
              self.assertEqual(id(grad_saved) == id(params.grad), should_preserve_reference)
  
          # Accumulate dense gradient to sparse gradient will change the `params.grad` reference
          _test_grad_tensor(
              torch.sparse_coo_tensor(torch.tensor([[1, 1]]).long(), torch.tensor([1., 1.])),
              torch.tensor([1.5, 1.5]),
              False)
  
          # Accumulate dense gradient to dense gradient will preserve the `params.grad` reference
          _test_grad_tensor(
              torch.tensor([1.5, 1.5]),
              torch.tensor([1.5, 1.5]),
              True)
  
          # Accumulate sparse gradient to sparse gradient will preserve the `params.grad` reference
          _test_grad_tensor(
              torch.sparse_coo_tensor(torch.tensor([[1, 1]]).long(), torch.tensor([1., 1.])),
              torch.sparse_coo_tensor(torch.tensor([[1, 1]]).long(), torch.tensor([1., 1.])),
              True)
  
      @skipIfNoLapack
      def test_slogdet_sign(self):
          a = torch.randn(3, 3, requires_grad=True)
          s, logdet = a.slogdet()
  
          # test that sign should not require grad
          self.assertFalse(s.requires_grad)
  
          # test that backward through computation involving sign works
          def sign_mul_logdet(mat):
              s, logdet = mat.slogdet()
              return s * logdet
  
          u, s, v = a.detach().svd()
          s.abs_().clamp_(0.0001)
          for sign in (-1, 1):
              s[-1] = sign
              mat = torch.chain_matmul(u, s.diag(), v.t()).requires_grad_()
              gradcheck(sign_mul_logdet, mat)
              gradgradcheck(sign_mul_logdet, mat)
  
      def test_sum_to_with_empty_dim_grad(self):
          a = torch.rand(4, 0, requires_grad=True)
          b = torch.rand(4, 1, requires_grad=True)
          c = a + b
          assert c.shape == (4, 0)
          c.sum().backward()
  
          self.assertEqual(b.grad, torch.zeros(4, 1))
          self.assertEqual(a.grad, torch.zeros(4, 0))
  
      def test_hessian_vector(self):
          x = torch.randn(2, 2, requires_grad=True)
          y = torch.randn(2, 2, requires_grad=True)
  
          z = x ** 2 + y * x + y ** 2
          z.backward(torch.ones(2, 2), create_graph=True)
  
          with torch.no_grad():
              x_grad = 2 * x + y
              y_grad = x + 2 * y
          self.assertEqual(x.grad, x_grad)
          self.assertEqual(y.grad, y_grad)
  
          grad_sum = 2 * x.grad + y.grad
          grad_sum.backward(torch.ones(2, 2))
          x_hv = torch.ones(2, 2) * 5
          y_hv = torch.ones(2, 2) * 4
          self.assertEqual(x.grad, x_grad + x_hv)
          self.assertEqual(y.grad, y_grad + y_hv)
  
      def test_grad(self):
          x = torch.randn(2, 2, requires_grad=True)
          y = torch.randn(2, 2, requires_grad=True)
          z = x ** 2 + y * x + y ** 2
          z.backward(torch.ones(2, 2), create_graph=True)
  
          x_grad = 2 * x + y
          y_grad = x + 2 * y
          self.assertEqual(x.grad, x_grad)
          self.assertEqual(y.grad, y_grad)
  
          grad_sum = 2 * x.grad + y.grad
          x_hv = torch.autograd.grad(
              outputs=[grad_sum], grad_outputs=[torch.ones(2, 2)],
              inputs=[x], create_graph=True)
          expected_x_hv = torch.ones(2, 2) * 5
          expected_y_hv = torch.ones(2, 2) * 4
  
          self.assertEqual(x_hv[0], expected_x_hv)
          self.assertEqual(x.grad, x_grad)
          self.assertEqual(y.grad, y_grad)
  
          # Test that grad_outputs and outputs have the same shape
          grad_out = torch.ones(2)
          try:
              torch.autograd.grad(
                  outputs=[grad_sum], grad_outputs=[grad_out],
                  inputs=[x], create_graph=True)
              self.assertFail()
          except RuntimeError as error:
              self.assertEqual(str(error), "Mismatch in shape: grad_output[0] has a shape of "
                               + str(grad_out.shape) + " and output[0] has a shape of "
                               + str(grad_sum.shape) + ".")
  
      def test_grad_nonleaf(self):
          x_init = torch.randn(2, 2, requires_grad=True)
          x = x_init
          y = torch.randn(2, 2, requires_grad=True)
          grad_output = torch.ones(2, 2)
  
          def fn(x):
              return x ** 2 + y * x + y ** 2
  
          for _ in range(5):
              grad_x, = torch.autograd.grad(
                  fn(x), x, grad_outputs=grad_output, create_graph=True)
  
              grad_x_expected = 2 * x + y
              self.assertIsNone(y.grad)
              self.assertIsNone(x.grad)
              self.assertEqual(grad_x, grad_x_expected)
  
              x = x + 0.05 * grad_x
  
          val_init = fn(x_init).sum()
          val_final = fn(x).sum()
          self.assertGreater(val_final, val_init)
  
          x.backward(grad_output)
          self.assertIsNotNone(y.grad)
          self.assertIsNotNone(x_init.grad)
  
      def test_grad_nonleaf_many_outputs(self):
          # This checks an edge case for function callbacks
          # We want to capture two grads of a function, but can only
          # register a single callback.
          x = torch.randn(4, 2, requires_grad=True)
          a, b = x.chunk(2)
  
          def hook(*grads):
              hook_called[0] = True
          hook_called = [False]
          x.register_hook(hook)
  
          go = torch.randn(2, 2)
          grad_a, grad_b = torch.autograd.grad(
              (a + 2 * b), [a, b], grad_outputs=go, create_graph=True)
  
          self.assertEqual(grad_a, go)
          self.assertEqual(grad_b, go * 2)
          self.assertFalse(hook_called[0])
          self.assertIsNone(x.grad)
  
      def test_grad_nonleaf_register_hook(self):
          # This checks an edge case for register_hook.
          # We want to capture grad of a nonleaf tensor,
          # but avoid segfault during backward of other nonleaf tensors
          x = torch.randn(5, requires_grad=True)
          x_list = x.unbind()
  
          x0 = x_list[0]
          hook_results = [None]
  
          def hook(grad):
              hook_results[0] = grad
          x0.register_hook(hook)
  
          x_list[0].backward()
          self.assertEqual(hook_results[0], torch.tensor(1.))
          expected_grad = torch.tensor([1., 0, 0, 0, 0])
          self.assertEqual(x.grad, expected_grad)
          self.assertIsNone(x_list[0].grad)
  
          for i in range(1, 5, 1):
              x_list[i].backward()
              self.assertEqual(hook_results[0], None)
              expected_grad[i] = 1.0
              self.assertEqual(x.grad, expected_grad)
              self.assertIsNone(x_list[i].grad)
  
      def test_sharded_grad(self):
          leaves = [torch.zeros(5, 5, requires_grad=True) for _ in range(10)]
          intermediates = [l * i + l * l for i, l in enumerate(leaves)]
          loss = sum(v * i for i, v in enumerate(intermediates)).sum()
  
          # define a helper for dividing intermediates into groups
          def group(l, group_size):
              return (l[i:i + group_size] for i in range(0, len(l), group_size))
  
          # Compute the d loss / d intermediates in chunks of shard_size
          shard_size = 2
          d_intermediates = [d_i for intermediates_batch in group(intermediates, shard_size)
                             for d_i in torch.autograd.grad(loss, intermediates_batch)]
          # Compute rest of backward pass
          torch.autograd.backward(intermediates, d_intermediates)
  
          for i, l in enumerate(leaves):
              self.assertEqual(l.grad, i * i * (1 + l))
  
      def test_backward_badcalls(self):
          x = torch.ones(1)
          with self.assertRaisesRegex(RuntimeError, 'does not require grad'):
              x.backward()
  
      def test_grad_badcalls(self):
          x = torch.ones(1)
          y = x ** 2
          with self.assertRaisesRegex(RuntimeError, 'does not require grad'):
              torch.autograd.grad(x, y)
          with self.assertRaisesRegex(RuntimeError, 'does not require grad'):
              torch.autograd.grad(y, x)
  
          x = torch.ones(1, requires_grad=True)
          y = x ** 2
          torch.autograd.grad(y, x)  # this should succeed now
  
      def test_grad_fn_badcalls(self):
          error_regex = 'expected .* arguments, got .* instead'
          x = torch.ones(1, requires_grad=True)
          y = x ** 2
          with self.assertRaisesRegex(TypeError, error_regex):
              y.grad_fn(x.detach(), x.detach())  # too many
          with self.assertRaisesRegex(TypeError, error_regex):
              y.grad_fn()  # too few
  
          y.grad_fn(x.detach())  # this should succeed
  
      def test_grad_unreachable(self):
          x = torch.ones(1, requires_grad=True)
          y = torch.ones(1, requires_grad=True)
          # Make sure x and y have grad accumulators allocated
          z = x * 2
          w = y * 2
  
          grad_x, grad_y = torch.autograd.grad(x * 2, [x, y], allow_unused=True)
          self.assertEqual(grad_x, x * 2)
          self.assertIsNone(grad_y)
  
          # This is slightly different than the case above, because z doesn't even
          # have a grad accumulator allocated.
          z = torch.ones(1, requires_grad=True)
          grad_x, grad_z = torch.autograd.grad(x * 2, [x, z], allow_unused=True)
          self.assertEqual(grad_x, x * 2)
          self.assertIsNone(grad_z)
  
          # allow_unused=False, but grads contains None inside, should throw
          with self.assertRaisesRegex(RuntimeError,
                                      "Set allow_unused=True"):
              grad_x, grad_y = torch.autograd.grad(x * 2, [x, y], allow_unused=False)
  
      def test_hooks(self):
          x = torch.ones(5, 5, requires_grad=True)
          y = torch.ones(5, 5) * 4
          y.requires_grad_(True)
  
          counter = [0]
  
          def bw_hook(inc, grad):
              self.assertIsInstance(grad, torch.Tensor)
              counter[0] += inc
  
          z = x ** 2 + x * 2 + x * y + y
          x.register_hook(lambda *args: bw_hook(0, *args))
          test = z.register_hook(lambda *args: bw_hook(1, *args))
          z.backward(torch.ones(5, 5), retain_graph=True)
          self.assertEqual(counter[0], 1)
  
          test2 = z.register_hook(lambda *args: bw_hook(2, *args))
          z.backward(torch.ones(5, 5), retain_graph=True)
          self.assertEqual(counter[0], 4)
  
          test2.remove()
          z.backward(torch.ones(5, 5), retain_graph=True)
          self.assertEqual(counter[0], 5)
  
          def bw_hook_modify(grad):
              return grad.mul(2)
  
          test.remove()
          z.register_hook(bw_hook_modify)
          with torch.no_grad():
              y.grad.zero_()
          z.backward(torch.ones(5, 5), retain_graph=True)
          self.assertEqual(y.grad, (x + 1) * 2)
  
          y.register_hook(bw_hook_modify)
          with torch.no_grad():
              y.grad.zero_()
          z.backward(torch.ones(5, 5))
          self.assertEqual(y.grad, (x + 1) * 4)
  
      def test_hooks_cpp(self):
          # Tests hooks for autograd function implemented in C++
          bn = torch.nn.BatchNorm1d(5, affine=False)
          bn.eval()
  
          counter = [0]
  
          def bw_hook(grad):
              counter[0] += 1
              return grad * 2
  
          x = torch.ones(5, 5, requires_grad=True)
          z = bn(x)
          z.register_hook(bw_hook)
          z.sum().backward()
  
          self.assertEqual(counter[0], 1, 'bw_hook not called')
          self.assertEqual(x.grad, torch.ones(5, 5) * 2)
  
      def test_hook_none(self):
          # WARNING: this is a test for autograd internals.
          # You should never have to use such things in your code.
          class NoneGradientFunction(Function):
              @staticmethod
              def forward(ctx, x, y):
                  assert ctx.needs_input_grad[0]
                  assert not ctx.needs_input_grad[1]
                  return x, y
  
              @staticmethod
              def backward(ctx, grad_x, grad_y):
                  return grad_x, None
  
          was_called = [False]
  
          def hook(grad):
              self.assertIsNotNone(grad)
              was_called[0] = True
  
          x = torch.randn(5, 5, requires_grad=True)
          y = torch.randn(5, 5)
          rx, ry = NoneGradientFunction.apply(x, y)
          rx.register_hook(hook)
          ry.register_hook(hook)
          sum(rx, ry).sum().backward()
          self.assertTrue(was_called[0])
  
      def test_retain_grad(self):
          input = torch.rand(1, 3, requires_grad=True)
          h1 = input * 3
          out = (h1 * h1).sum()
  
          # It should be possible to call retain_grad() multiple times
          h1.retain_grad()
          h1.retain_grad()
  
          # Gradient should be accumulated
          out.backward(retain_graph=True)
          self.assertEqual(h1 * 2, h1.grad)
          out.backward(retain_graph=True)
          self.assertEqual(h1 * 4, h1.grad)
  
          with torch.no_grad():
              input.grad.zero_()
          # It should be a no-op for leaves
          input.retain_grad()
          input.retain_grad()
          out.backward()
          self.assertEqual(input * 18, input.grad)
  
      def test_retain_grad_cycle(self):
          import gc
          import weakref
          counter = [0]
          refs = [None]
  
          x = torch.ones(5, 5, requires_grad=True)
  
          def run_test():
              y = x * 2
              y.retain_grad()
  
              def inc(*args):
                  counter[0] += 1
              refs[0] = weakref.ref(y, inc)
              return y / 2
  
          z = run_test()
          gc.collect()
          self.assertIsNone(refs[0]())
          self.assertEqual(counter[0], 1)
          z.sum().backward()
  
      def test_backward(self):
          v = torch.randn(5, 5, requires_grad=True)
          x = torch.randn(5, 5, requires_grad=True)
          y = (torch.rand(5, 5) + 0.1).requires_grad_(True)
          z = torch.randn(5, 5, requires_grad=True)
          grad_output = torch.randn(5, 5)
  
          v.backward(grad_output)
          self.assertEqual(v.grad, grad_output)
  
          a = x + (y * z) + 4 * z ** 2 * x / y
          a.backward(grad_output)
          x_grad = 4 * z.pow(2) / y + 1
          y_grad = z - 4 * x * z.pow(2) / y.pow(2)
          z_grad = 8 * x * z / y + y
          self.assertEqual(x.grad, x_grad * grad_output)
          self.assertEqual(y.grad, y_grad * grad_output)
          self.assertEqual(z.grad, z_grad * grad_output)
  
      def test_sparse_backward(self):
          class FixedGradientFunction(Function):
              @staticmethod
              def forward(ctx, x, grad_x):
                  ctx.save_for_backward(grad_x)
                  return x
  
              @staticmethod
              def backward(ctx, grad_x):
                  saved_grad_x, = ctx.saved_tensors
                  return saved_grad_x, None
  
          size = torch.Size([6, 3, 2])
          i1 = torch.LongTensor([
              [0, 3, 4],
              [0, 2, 2],
          ])
          v1 = torch.DoubleTensor([[1, 2], [4, 5], [7, 8]])
          sparse_grad1 = torch.sparse.DoubleTensor(i1, v1, size)
          i2 = torch.LongTensor([
              [0, 1, 3, 4],
              [0, 1, 2, 2],
          ])
          v2 = torch.DoubleTensor([[1, 2], [4, 3], [4, 5], [7, 8]])
          sparse_grad2 = torch.sparse.DoubleTensor(i2, v2, size)
          dense_grad = torch.rand(size).double()
          fn = FixedGradientFunction
  
          # sparse first
          x = torch.randn(size, requires_grad=True)
          (fn.apply(x, sparse_grad1) + fn.apply(x, dense_grad) + fn.apply(x, sparse_grad2)).sum().backward()
          self.assertEqual(x.grad, dense_grad + sparse_grad1 + sparse_grad2)
          # dense first
          x = torch.randn(size, requires_grad=True)
          (fn.apply(x, dense_grad) + fn.apply(x, sparse_grad1) + fn.apply(x, sparse_grad2)).sum().backward()
          self.assertEqual(x.grad, dense_grad + sparse_grad1 + sparse_grad2)
          # sparse only
          x = torch.randn(size, requires_grad=True)
          (fn.apply(x, sparse_grad1) + fn.apply(x, sparse_grad2)).sum().backward()
          self.assertEqual(x.grad, sparse_grad1 + sparse_grad2)
  
      def test_sparse_mm_backward(self):
          size = (3, 3)
          sparse = torch.sparse_coo_tensor(size, requires_grad=True)
          dense = torch.randn(size, requires_grad=True)
  
          z = sparse.mm(dense)
          with self.assertRaisesRegex(RuntimeError,
                                      "calculating the gradient of a sparse Tensor argument to mm is not supported."):
              z.sum().backward()
  
          z = dense.addmm(sparse, dense)
          with self.assertRaisesRegex(RuntimeError,
                                      "calculating the gradient of a sparse Tensor argument to mm is not supported."):
              z.sum().backward()
  
  
      def test_multi_backward(self):
          x = torch.randn(5, 5, requires_grad=True)
          y = torch.randn(5, 5, requires_grad=True)
  
          q = torch.randn(5, 5, requires_grad=True)
  
          a = torch.randn(5, 5, requires_grad=True)
          b = torch.randn(5, 5, requires_grad=True)
  
          q2 = q * 2
          z = x + y + q2
          c = a * b + q2
          grad_z = torch.randn(5, 5)
          grad_c = torch.randn(5, 5)
          torch.autograd.backward([z, c], [grad_z, grad_c])
  
          self.assertEqual(x.grad, grad_z)
          self.assertEqual(y.grad, grad_z)
          self.assertEqual(a.grad, grad_c * b)
          self.assertEqual(b.grad, grad_c * a)
          self.assertEqual(q.grad, (grad_c + grad_z) * 2)
  
      def test_multi_backward_no_grad(self):
          x = torch.randn(5, 5, requires_grad=True)
          y = torch.randn(5, 5, requires_grad=False)
  
          z = x + y
          q = y * 2
  
          # NB: we currently raise an exception if any arguments to backwards
          # have requires_grad=False and don't have a grad_fn. We may want to
          # relax that check to a warning.
          def call_backwards():
              torch.autograd.backward([z, q], [torch.ones(5, 5), torch.ones(5, 5)])
          self.assertRaises(RuntimeError, call_backwards)
  
      def test_dependent_backward(self):
          x = torch.randn(10, requires_grad=True)
          y = x ** 2
          z = y ** 3
  
          go_y = torch.randn(10)
          go_z = torch.randn(10)
          torch.autograd.backward([y, z], [go_y, go_z])
  
          xd = x
          self.assertEqual(x.grad, 2 * xd * go_y + 6 * xd.pow(5) * go_z)
  
      def test_save_output_nr(self):
          x = torch.randn(10, requires_grad=True)
  
          class MultiOutputFn(Function):
              @staticmethod
              def forward(ctx, x):
                  return x[:5], x[5:]
  
              @staticmethod
              def backward(ctx, *grad):
                  return torch.cat(grad)
  
          a, b = MultiOutputFn.apply(x)
          self.assertEqual(b.output_nr, 1)
  
          class TestFn(Function):
              @staticmethod
              def forward(ctx, b):
                  ctx.save_for_backward(b)
                  return b * 2
  
              @staticmethod
              def backward(ctx, grad_b):
                  b, = ctx.saved_tensors
                  self.assertEqual(b.output_nr, 1)
  
          TestFn.apply(b).sum().backward()
  
      def test_free_deep_graph(self):
          def scope():
              depth = 150000
              x = torch.randn(1, requires_grad=True)
              y = x.clone()
  
              # build a "chain" computation graph
              for _ in range(depth):
                  y = y + y * 0.000001
  
              # graph deletion occurs when the above locals go out of scope.
              # In this case `del y` will trigger it but it's easier to leave
              # it to Python to delete the locals.
  
          # Should not stack overflow
          scope()
  
      def test_free_deep_graph_complicated(self):
          def scope():
              depth = 100000
              randchoice = torch.randint(2, [depth, 2])
              x = torch.randn(1, requires_grad=True)
              y = x.clone()
  
              # Hold the two previous values
              prev_values = [None, None]
  
              # Build a "chain with skip connections" graph
              for _ in range(depth):
                  prev_tensors = [tensor for tensor in prev_values[:-1]
                                  if tensor is not None]
                  prev_values.append(y)
                  prev_values.pop(0)
  
                  # Definitely pick one tensor to add
                  y += y * 0.000001
  
                  # Possibly add other tensors
                  nprev = len(prev_tensors)
                  if nprev == 2:
                      y += randchoice[depth].mul(torch.cat(prev_tensors)).sum()
  
              # graph deletion occurs when the above locals go out of scope.
  
          # Should not stack overflow
          scope()
  
      def test_free_deep_graph_pyfunction(self):
          class MyOp(Function):
              @staticmethod
              def forward(ctx, tensor1, tensor2):
                  return tensor1 + tensor2
  
              @staticmethod
              def backward(ctx, grad_output):
                  return grad_output, grad_output
  
          def scope():
              depth = 150000
              x = torch.randn(1, requires_grad=True)
              y = x.clone()
  
              # build deeply nested computation graph
              for _ in range(depth):
                  y = MyOp.apply(y, y)
  
              # graph deletion occurs when the above locals go out of scope.
  
          # Should not stack overflow
          scope()
  
      def test_no_unnecessary_save(self):
          # If we kept x in the derivative Function of x * 2 we would
          # get an error in the backward that would complain that we've
          # modified x, which was needed for gradient computation.
          # Since we should elide unnecessary saves, this test should pass.
          mu = torch.ones(1, requires_grad=True)
          x = torch.empty(1)
          loss = 0
          for i in range(3):
              x.detach_()
              x.copy_(mu + i)
              ft = torch.tensor([float(i)])
              multiplied = x * ft
              s = multiplied.sum()
              loss += s
          loss.backward()
  
      def test_no_grad(self):
          x = torch.ones(5, 5, requires_grad=True)
          y = torch.ones(5, 5) * 4
          with torch.no_grad():
              w = x + y
  
          @torch.no_grad()
          def adder(x, y):
              return x + y
  
          z = adder(x, y)
  
          self.assertFalse(w.requires_grad)
          self.assertRaises(RuntimeError, lambda: w.backward(torch.ones(5, 5)))
          self.assertIsNone(w.grad_fn)
          self.assertFalse(z.requires_grad)
          self.assertRaises(RuntimeError, lambda: z.backward(torch.ones(5, 5)))
          self.assertIsNone(z.grad_fn)
  
          # test nested decorator and with-statement on no_grad
          with torch.no_grad():
              self.assertFalse(torch.is_grad_enabled())
              w = adder(x, y)
              self.assertFalse(torch.is_grad_enabled())
  
      def test_set_grad_generator_functions(self):
          @torch.no_grad()
          def gen_no_grad():
              for i in range(10):
                  self.assertEqual(torch.is_grad_enabled(), False)
                  yield i
  
          with torch.enable_grad():
              for _ in gen_no_grad():
                  self.assertEqual(torch.is_grad_enabled(), True)
  
          @torch.enable_grad()
          def gen_enable_grad():
              for i in range(10):
                  self.assertEqual(torch.is_grad_enabled(), True)
                  yield i
  
          with torch.no_grad():
              for _ in gen_enable_grad():
                  self.assertEqual(torch.is_grad_enabled(), False)
  
      def test_no_grad_python_function(self):
          """Python Functions should respect grad mode."""
          x = torch.ones(5, 5, requires_grad=True)
  
          class MyOp(Function):
              @staticmethod
              def forward(self, x):
                  return x + 1
  
              @staticmethod
              def backward(self, dy):
                  return dy
  
          with torch.no_grad():
              y = MyOp.apply(x)
          self.assertFalse(y.requires_grad)
  
      def test_indexing(self):
          x = torch.arange(1., 17).view(4, 4)
          y = Variable(x, requires_grad=True)
  
          def compare(x, y, idx, indexed_tensor, indexed_var):
              indexed_var_t = indexed_var.data
              if not isinstance(indexed_tensor, torch.Tensor):
                  indexed_var_t = indexed_var_t[0]
              self.assertEqual(indexed_tensor, indexed_var_t)
  
              indexed_var.sum().backward()
              expected_grad = torch.Tensor(x.size()).fill_(0)
              expected_grad[idx] = 1
              self.assertEqual(y.grad, expected_grad)
  
          def check_index(x, y, idx):
              if y.grad is not None:
                  with torch.no_grad():
                      y.grad.zero_()
              indexed_tensor = x[idx]
              indexed_var = y[idx]
              compare(x, y, idx, indexed_tensor, indexed_var)
  
          check_index(x, y, 1)
          check_index(x, y, (1, 1))
          check_index(x, y, slice(1, None))
          check_index(x, y, slice(None, 2))
          check_index(x, y, (slice(None, 2), 2))
          check_index(x, y, (slice(1, 2), 2))
          check_index(x, y, (1, slice(2, None)))
          check_index(x, y, (slice(None, None), slice(2, None)))
          check_index(x, y, torch.LongTensor([0, 2]))
          check_index(x, y, torch.rand(4, 4).bernoulli().bool())
          check_index(x, y, (Ellipsis, slice(2, None)))
          check_index(x, y, ([0], [0]))
          check_index(x, y, ([1, 2, 3], [0]))
          check_index(x, y, ([1, 2], [2, 1]))
          check_index(x, y, ([[1, 2], [3, 0]], [[0, 1], [2, 3]]))
          check_index(x, y, ([slice(None), [2, 3]]))
          check_index(x, y, ([[2, 3], slice(None)]))
  
          # advanced indexing, with less dim, or ellipsis
          check_index(x, y, ([0]))
          check_index(x, y, ([0], ))
  
          x = torch.arange(1., 49).view(4, 3, 4)
          y = Variable(x, requires_grad=True)
  
          check_index(x, y, (slice(None), [0], [0]))
          check_index(x, y, ([0], [0], slice(None)))
          check_index(x, y, (slice(None), [0, 1, 2], [0]))
          check_index(x, y, ([0, 1, 2], [0], slice(None)))
          check_index(x, y, (slice(None), [1, 2], [2, 1]))
          check_index(x, y, ([1, 2], [2, 1], slice(None)))
          check_index(x, y, (slice(None), [[1, 2], [2, 0]], [[0, 1], [2, 3]]))
          check_index(x, y, ([[1, 2], [3, 0]], [[0, 1], [2, 2]], slice(None)))
          check_index(x, y, (slice(None), slice(None), [2, 1]))
          check_index(x, y, (slice(None), [2, 1], slice(None)))
          check_index(x, y, ([2, 1], slice(None), slice(None)))
  
          # advanced indexing, with less dim, or ellipsis
          check_index(x, y, ([0], ))
          check_index(x, y, ([0], slice(None)))
          check_index(x, y, ([0], Ellipsis))
          check_index(x, y, ([1, 2], [0, 1]))
          check_index(x, y, ([1, 2], [0, 1], Ellipsis))
          check_index(x, y, (Ellipsis, [1, 2], [0, 1]))
  
          # advanced indexing, with a tensor wrapped in a variable
          z = torch.LongTensor([0, 1])
          zv = Variable(z, requires_grad=False)
          seq = [z, Ellipsis]
          seqv = [zv, Ellipsis]
  
          if y.grad is not None:
              with torch.no_grad():
                  y.grad.zero_()
          indexed_tensor = x[seq]
          indexed_var = y[seqv]
          compare(x, y, seq, indexed_tensor, indexed_var)
  
      def test_indexing_duplicates(self):
          x = torch.arange(1., 17).view(4, 4)
          y = Variable(x, requires_grad=True)
  
          idx = torch.LongTensor([1, 1, 3, 2, 1, 2])
          y[idx].sum().backward()
          expected_grad = torch.zeros(4, 4)
          for i in idx:
              expected_grad[i] += 1
          self.assertEqual(y.grad, expected_grad)
  
          # with advanced indexing
          x = torch.arange(1., 17).view(4, 4)
          y = Variable(x, requires_grad=True)
  
          idx = [[1, 1, 3, 2, 1, 2], [0]]
          y[idx].sum().backward()
          expected_grad = torch.zeros(4, 4)
          for i in idx[0]:
              for j in idx[1]:
                  expected_grad[i][j] += 1
  
          self.assertEqual(y.grad, expected_grad)
  
          x = torch.arange(1., 17).view(4, 4)
          y = Variable(x, requires_grad=True)
          idx = [[[1, 2], [0, 0]], [[0, 1], [1, 1]]]
          y[idx].sum().backward()
          expected_grad = torch.Tensor([[0, 2, 0, 0],
                                        [1, 0, 0, 0],
                                        [0, 1, 0, 0],
                                        [0, 0, 0, 0]])
          self.assertEqual(y.grad, expected_grad)
  
          x = torch.arange(1., 65).view(4, 4, 4)
          y = Variable(x, requires_grad=True)
  
          idx = [[1, 1, 1], slice(None), slice(None)]
          y[idx].sum().backward()
          expected_grad = torch.Tensor(4, 4, 4).zero_()
          expected_grad[1].fill_(3)
          self.assertEqual(y.grad, expected_grad)
  
      def test_index_backward_does_not_save_tensor(self):
          # Example from https://github.com/pytorch/pytorch/issues/24853.
          # if `index(tensor, indices)` saves `tensor` for backwards, then it will
          # trigger a version check on `tensor` during the backward pass, which
          # will cause the following code to error because `tensor` gets modified
          # by the indexing line.
          a = torch.tensor([1., 0, 0])
          b = torch.zeros(3, requires_grad=True)
          tensor = b + 0
          tensor[a != 0] = tensor[a != 0]
          tensor.backward(torch.zeros_like(tensor))
  
      def test_volatile_deprecated(self):
          v = torch.autograd.torch.randn(3, 3)
          with warnings.catch_warnings(record=True) as w:
              self.assertFalse(v.volatile)
          self.assertIn('volatile', str(w[0].message))
  
      def test_saved_variables_deprecated(self):
          class MyFunction(Function):
              @staticmethod
              def forward(ctx, tensor1, tensor2):
                  ctx.save_for_backward(tensor1, tensor2)
                  return tensor1 + tensor2
  
              @staticmethod
              def backward(ctx, grad_output):
                  var1, var2 = ctx.saved_variables
                  return (grad_output, grad_output)
  
          with warnings.catch_warnings(record=True) as warns:
              warnings.simplefilter("always")
              x = torch.randn((3, 3), requires_grad=True)
              y = torch.randn((3, 3), requires_grad=True)
              model = MyFunction()
              model.apply(x, y).sum().backward()
  
              has_deprecated = map(lambda warn:
                                   'deprecated' in str(warn) and
                                   'saved_variables' in str(warn),
                                   warns)
              has_deprecated = reduce(lambda x, y: x or y, has_deprecated)
              self.assertTrue(has_deprecated)
  
      def test_requires_grad(self):
          x = torch.randn(5, 5)
          y = torch.randn(5, 5)
          z = torch.randn(5, 5, requires_grad=True)
          a = x + y
          self.assertFalse(a.requires_grad)
          b = a + z
          self.assertTrue(b.requires_grad)
  
          def error():
              raise RuntimeError
          # Make sure backward isn't called on these
          a._backward_hooks = OrderedDict()
          x._backward_hooks = OrderedDict()
          y._backward_hooks = OrderedDict()
          a._backward_hooks['test'] = error
          x._backward_hooks['test'] = error
          y._backward_hooks['test'] = error
          b.backward(torch.ones(5, 5))
  
      def test_requires_grad_(self):
          x = torch.randn(5, 5)
          y = torch.randn(5, 5, requires_grad=True)
          self.assertIs(x, x.requires_grad_())
          self.assertTrue(x.requires_grad)
          self.assertIs(y, y.requires_grad_())
          self.assertTrue(y.requires_grad)
          self.assertIs(x, x.requires_grad_(True))
          self.assertTrue(x.requires_grad)
          self.assertIs(y, y.requires_grad_(True))
          self.assertTrue(y.requires_grad)
          z = x * y
          self.assertRaises(RuntimeError, lambda: z.requires_grad_(False))
          self.assertIs(z, z.requires_grad_())
          self.assertTrue(z.requires_grad)
          self.assertIs(z, z.requires_grad_(True))
          self.assertTrue(z.requires_grad)
  
          self.assertIs(x, x.requires_grad_(False))
          self.assertFalse(x.requires_grad)
          self.assertIs(y, y.requires_grad_(False))
          self.assertFalse(y.requires_grad)
  
      def test_requires_grad_inplace(self):
          a = torch.randn(5, 5)
          b = torch.randn(5, 5, requires_grad=True)
          a += b
          self.assertTrue(a.requires_grad)
  
          # non-leaf
          a = torch.randn(5, 5) + 0
          b = torch.randn(5, 5, requires_grad=True)
          a += b
          self.assertTrue(a.requires_grad)
  
      def test_no_requires_grad_inplace(self):
          # basic case, should be able to modify inplace while requires_grad is False
          a = torch.randn(2, 3)
          a.add_(5)
          a.requires_grad = True
          a.sum().backward()
          self.assertEqual(a.grad, torch.ones(2, 3))
  
          # same but with a view
          a = torch.randn(2, 3)
          b = a[:]
          b.add_(5)
          a.requires_grad = True
          a.sum().backward()
          self.assertEqual(a.grad, torch.ones(2, 3))
  
          # should fail if requires_grad = True when we modify inplace
          a = torch.randn(2, 3)
          b = a[:]
          a.requires_grad = True
          with self.assertRaises(RuntimeError):
              a.add_(5)
          with self.assertRaises(RuntimeError):
              b.add_(5)
  
      def test_attribute_deletion(self):
          x = torch.randn((5, 5), requires_grad=True)
          del x.grad
          self.assertIsNone(x.grad)
          with self.assertRaises(RuntimeError):
              del x.data
          with self.assertRaises(TypeError):
              x.data = None
          with self.assertRaises(RuntimeError):
              del x.requires_grad
          with self.assertRaises(RuntimeError):
              del x._grad_fn
          with self.assertRaises(RuntimeError):
              del x._backward_hooks
  
      def test_duplicate_backward_root(self):
          a = torch.randn(5, 5, requires_grad=True)
          b = torch.randn(5, 5, requires_grad=True)
  
          x = a * b
          grad_output = torch.randn_like(x)
          torch.autograd.backward([x, x], [grad_output, grad_output])
  
          self.assertEqual(a.grad, b * grad_output * 2)
          self.assertEqual(b.grad, a * grad_output * 2)
  
      def test_backward_no_grad(self):
          a = torch.randn(5, 5, requires_grad=True)
          b = a + 2
          with self.assertRaises(RuntimeError):
              torch.autograd.backward([b], [None])
  
      def test_backward_twice_with_saved_values(self):
          b = torch.randn(3, requires_grad=True, dtype=torch.double)
          c = torch.zeros(3, dtype=torch.double)
          c[[1, 2]] = b[[1, 1]]
          c.backward(torch.tensor([1, 1, 1], dtype=torch.double))
          self.assertRaisesRegex(RuntimeError, 'Specify retain_graph=True',
                                 lambda: c.backward(torch.tensor([1, 1, 1], dtype=torch.double)))
  
      def test_backward_twice_retained_graph_with_saved_values(self):
          b = torch.randn(3, requires_grad=True, dtype=torch.double)
          c = torch.zeros(3, dtype=torch.double)
          c[[1, 2]] = b[[1, 1]]
          c.backward(torch.tensor([1, 1, 1], dtype=torch.double), retain_graph=True)
          c.backward(torch.tensor([1, 1, 1], dtype=torch.double))
  
      def test_backward_twice_without_saved_values(self):
          b = torch.randn(3, requires_grad=True, dtype=torch.double)
          c = b + 1
          c.backward(torch.tensor([1, 1, 1], dtype=torch.double))
          c.backward(torch.tensor([1, 1, 1], dtype=torch.double))
  
      def test_backward_twice_retained_graph_without_saved_values(self):
          b = torch.randn(3, requires_grad=True, dtype=torch.double)
          c = torch.zeros(3, dtype=torch.double)
          c[[1, 2]] = b[[1, 1]]
          c.backward(torch.tensor([1, 1, 1], dtype=torch.double), retain_graph=True)
          c.backward(torch.tensor([1, 1, 1], dtype=torch.double))
  
      def test_next_functions(self):
          x = torch.randn(5, 5, requires_grad=True)
          y = torch.randn(5, 5, requires_grad=True)
  
          a = x + y
          self.assertIsNotNone(a.grad_fn)
          next_functions = a.grad_fn.next_functions
          self.assertEqual(len(next_functions), 2)
          self.assertIsInstance(next_functions[0][0], torch._C._functions.AccumulateGrad)
          self.assertEqual(next_functions[0][1], 0)
          self.assertIsInstance(next_functions[1][0], torch._C._functions.AccumulateGrad)
          self.assertEqual(next_functions[1][1], 0)
  
          b = a + 5
          next_functions = b.grad_fn.next_functions
          self.assertEqual(len(next_functions), 2)
          self.assertIs(next_functions[0][0], a.grad_fn)
          self.assertIs(next_functions[1][0], None)
  
      def test_inplace(self):
          x = torch.ones(5, 5, requires_grad=True)
          y = Variable(torch.ones(5, 5) * 4, requires_grad=True)
  
          z = x * y
          q = z + y
          w = z * y
          z.add_(2)
          # Add doesn't need it's inputs to do backward, so it shouldn't raise
          q.backward(torch.ones(5, 5), retain_graph=True)
          # Mul saves both inputs in forward, so it should raise
          self.assertRaises(RuntimeError, lambda: w.backward(torch.ones(5, 5)))
  
          z = x * y
          q = z * y
          r = z + y
          w = z.add_(y)
          # w is a the last expression, so this should succeed
          w.backward(torch.ones(5, 5), retain_graph=True)
          # r doesn't use the modified value in backward, so it should succeed
          r.backward(torch.ones(5, 5), retain_graph=True)
          # q uses dirty z, so it should raise
          self.assertRaises(RuntimeError, lambda: q.backward(torch.ones(5, 5)))
  
          with torch.no_grad():
              x.grad.zero_()
          m = x / 2
          z = m + y / 8
          q = z * y
          r = z + y
          prev_version = z._version
          w = z.exp_()
          self.assertNotEqual(z._version, prev_version)
          r.backward(torch.ones(5, 5), retain_graph=True)
          self.assertEqual(x.grad, torch.ones(5, 5) / 2)
          w.backward(torch.ones(5, 5), retain_graph=True)
          self.assertEqual(x.grad, torch.Tensor(5, 5).fill_((1 + math.e) / 2))
          self.assertRaises(RuntimeError, lambda: q.backward(torch.ones(5, 5)))
  
          leaf = torch.ones(5, 5, requires_grad=True)
          x = leaf.clone()
          x.add_(10)
          self.assertEqual(x, torch.ones(5, 5) * 11)
          # x should be still usable
          y = x + 2
          y.backward(torch.ones(5, 5))
          self.assertEqual(leaf.grad, torch.ones(5, 5))
          z = x * y
          x.add_(2)
          self.assertRaises(RuntimeError, lambda: z.backward(torch.ones(5, 5)))
  
      def test_mark_non_differentiable(self):
          class MyFunction(Function):
              @staticmethod
              def forward(ctx, input):
                  output = input > 0
                  ctx.mark_non_differentiable(output)
                  return output
  
              @staticmethod
              def backward(ctx, grad_output):
                  return (grad_output * 0).type(torch.DoubleTensor)
  
          x = torch.randn(5, 5, requires_grad=True)
          mask = MyFunction.apply(x)
          self.assertFalse(mask.requires_grad)
          y = x.masked_fill(mask, 0)
          y.sum().backward()
  
      def test_mark_non_differentiable_mixed(self):
          class MyFunction(Function):
              @staticmethod
              def forward(ctx, input):
                  a = input + 1
                  b = input + 2
                  ctx.mark_non_differentiable(a)
                  return a, b
  
              @staticmethod
              def backward(ctx, grad_a, grad_b):
                  self.assertTrue((grad_a == 0).all())
                  self.assertTrue((grad_b == 1).all())
                  return grad_b
  
          x = torch.randn(5, 5, requires_grad=True)
          a, b = MyFunction.apply(x)
          self.assertFalse(a.requires_grad)
          self.assertTrue(b.requires_grad)
          b.sum().backward()
          self.assertEqual(x.grad, torch.ones(5, 5))
  
      def test_mark_non_differentiable_none(self):
          # This used to segfault because MyFunction would send back null
          # gradients to MulBackward, which is implemented in C++. C++
          # implemented functions expect incoming  grad_ouptuts to be non-null.
          class MyFunction(Function):
              @staticmethod
              def forward(ctx, input):
                  output = input.clone()
                  ctx.mark_non_differentiable(output)
                  return output
  
              @staticmethod
              def backward(ctx, grad_output):
                  return None
  
          x = torch.randn(5, 5, requires_grad=True)
          r = MyFunction.apply(x * x)
          (r * x).sum().backward()
  
      def test_return_duplicate(self):
          class DoubleDuplicate(Function):
              @staticmethod
              def forward(ctx, x):
                  output = x * 2
                  return output, output
  
              @staticmethod
              def backward(ctx, grad1, grad2):
                  return grad1 * 2 + grad2 * 2
  
          def fn(x):
              a, b = DoubleDuplicate.apply(x)
              self.assertIs(a, b)
              return a + b
  
          x = torch.randn(5, 5, requires_grad=True)
          gradcheck(fn, [x])
          gradgradcheck(fn, [x])
  
      def test_return_duplicate_inplace(self):
          class DoubleInplace(Function):
              @staticmethod
              def forward(ctx, x):
                  x.mul_(2)
                  ctx.mark_dirty(x)
                  return x, x
  
              @staticmethod
              def backward(ctx, grad1, grad2):
                  return grad1 * 2 + grad2 * 2
  
          def inplace_fn(x):
              a, b = DoubleInplace.apply(x.clone())
              self.assertIs(a, b)
              return a + b
  
          x = torch.randn(5, 5, requires_grad=True)
          gradcheck(inplace_fn, [x])
          gradgradcheck(inplace_fn, [x])
  
          # Can't modify leaf variables in-place
          self.assertRaises(RuntimeError, lambda: InplaceFunction.apply(x))
          # Functions which modify views in-place must return only one output
          self.assertRaises(RuntimeError, lambda: InplaceFunction.apply(x.clone()[0]))
  
      @suppress_warnings
      def test_resize(self):
          x = torch.ones(2, 3)
          self.assertTrue(x.resize(3, 2).size() == (3, 2))
  
      def _test_setitem(self, size, index):
          x = torch.ones(*size, requires_grad=True)
          y = x + 2
          y_version = y._version
          y[index] = 2
          self.assertNotEqual(y._version, y_version)
          y.backward(torch.ones(*size))
          expected_grad = torch.ones(*size)
          expected_grad[index] = 0
          self.assertEqual(x.grad, expected_grad)
  
      def _test_setitem_tensor(self, size, index):
          x = torch.ones(*size, requires_grad=True)
          y = x + 2
          y_version = y._version
          value = x.new(x[index].size()).fill_(7)
          value.requires_grad = True
          y[index] = value
          self.assertNotEqual(y._version, y_version)
          y.backward(torch.ones(*size))
          expected_grad_input = torch.ones(*size)
          expected_grad_input[index] = 0
          self.assertEqual(x.grad, expected_grad_input)
          self.assertEqual(value.grad, torch.ones_like(value))
  
          # case when x broadcasts to as y[1]
          x = torch.randn(4, requires_grad=True)
          y = torch.zeros(2, 3, 4)
          y[1] = x
          y.backward(torch.randn(2, 3, 4))
          self.assertEqual(x.size(), x.grad.size())
  
      def test_setitem(self):
          self._test_setitem((5, 5), 1)
          self._test_setitem((5,), 1)
          self._test_setitem((1,), 0)
          self._test_setitem((10,), [[0, 4, 2]])
          self._test_setitem((5, 5), [[0, 4], [2, 2]])
          self._test_setitem((5, 5, 5), [slice(None), slice(None), [1, 3]])
          self._test_setitem((5, 5, 5), [slice(None), [1, 3], slice(None)])
          self._test_setitem((5, 5, 5), [[1, 3], slice(None), slice(None)])
          self._test_setitem((5, 5, 5), [slice(None), [2, 4], [1, 3]])
          self._test_setitem((5, 5, 5), [[1, 3], [2, 4], slice(None)])
          self._test_setitem_tensor((5, 5), 3)
          self._test_setitem_tensor((5, 5), [[0, 1], [1, 0]])
          self._test_setitem_tensor((5,), 3)
          self._test_setitem_tensor((5,), Variable(torch.LongTensor([3]), requires_grad=False).sum())
          self._test_setitem_tensor((5,), [[0, 1, 2, 3]])
          self._test_setitem_tensor((5, 5, 5), [slice(None), slice(None), [1, 3]])
          self._test_setitem_tensor((5, 5, 5), [slice(None), [1, 3], slice(None)])
          self._test_setitem_tensor((5, 5, 5), [[1, 3], slice(None), slice(None)])
          self._test_setitem_tensor((5, 5, 5), [slice(None), [2, 4], [1, 3]])
          self._test_setitem_tensor((5, 5, 5), [[1, 3], [2, 4], slice(None)])
          self._test_setitem_tensor((5, 5, 5), [Variable(torch.LongTensor([1,
                                                3]), requires_grad=False), [2, 4], slice(None)])
  
      def test_setitem_mask(self):
          mask = torch.BoolTensor(5, 5).bernoulli_()
          self._test_setitem((5, 5), Variable(mask))
          self._test_setitem((5,), Variable(mask[0]))
          self._test_setitem((1,), Variable(mask[0, 0:1]))
          self._test_setitem_tensor((5, 5), Variable(mask))
          self._test_setitem_tensor((5,), Variable(mask[0]))
  
      def test_select_sum(self):
          # both select and sum return Scalars in ATen; ensure they work together.
          x = torch.randn(10, requires_grad=True)
  
          def func(x):
              return x.select(0, 1).sum()
  
          gradcheck(func, [x])
          gradgradcheck(func, [x])
  
      def test_stack(self):
          x = torch.randn(10, 10, requires_grad=True)
          y = torch.randn(10, 10, requires_grad=True)
          z = torch.randn(10, 10, requires_grad=True)
          stacked = torch.stack([x, y, z], 0)
          grad = torch.randn(3, 10, 10)
          stacked.backward(grad)
          self.assertEqual(x.grad, grad[0])
          self.assertEqual(y.grad, grad[1])
          self.assertEqual(z.grad, grad[2])
  
      def test_unbind(self):
          stacked = torch.randn(3, 10, 10, requires_grad=True)
          x, y, z = stacked.unbind()
          grad = torch.randn(3, 10, 10)
          torch.autograd.backward([x, y, z], grad.unbind())
          self.assertEqual(stacked.grad, grad)
          # check that it works with only one gradient provided (#9977)
          for i in range(3):
              stacked = torch.randn(3, 10, 10, requires_grad=True)
              outs = stacked.unbind()
              gi = grad.unbind()[i]
              g, = torch.autograd.grad(outs[i], stacked, gi)
              g_expected = torch.stack([gi if j == i else torch.zeros_like(gi)
                                        for j in range(3)], dim=0)
              self.assertEqual(g, g_expected)
  
      def test_put(self):
          root = torch.randn(4, 5, requires_grad=True)
          values = torch.randn(6, requires_grad=True)
          idx = Variable(torch.LongTensor([1, 2, 3, -1, -2, -3]))
  
          def func(root, values):
              x = root.clone()
              x.put_(idx, values)
              return x
  
          gradcheck(func, [root, values])
          gradgradcheck(func, [root, values])
  
      def test_put_accumulate(self):
          root = torch.randn(4, 5, requires_grad=True)
          values = torch.randn(6, requires_grad=True)
          idx = Variable(torch.LongTensor([1, 2, 3, 1, 2, 3]))
  
          def func(root, values):
              x = root.clone()
              x.put_(idx, values, accumulate=True)
              return x
  
          gradcheck(func, [root, values])
          gradgradcheck(func, [root, values])
  
      def test_fill(self):
          root = torch.randn(4, 5, requires_grad=True)
  
          def func(root):
              x = root.clone()
              x.fill_(2)
              return x
  
          gradcheck(func, [root])
          gradgradcheck(func, [root])
  
      def test_unused_output(self):
          x = torch.randn(10, 10, requires_grad=True)
          outputs = x.chunk(5)
          o = outputs[2]
          o = o * 4 + 2
          o.sum().backward()
          expected_grad = torch.zeros(10, 10)
          expected_grad[4:6] = 4
          self.assertEqual(x.grad, expected_grad)
  
          with torch.no_grad():
              x.grad.zero_()
          grad_output = torch.randn(2, 10)
          outputs = x.chunk(5)
          outputs[0].backward(grad_output)
          expected_grad = torch.zeros(10, 10)
          expected_grad[:2] = grad_output
          self.assertEqual(x.grad, expected_grad)
  
      def _test_sparse_gather(self, size_x, size_ind, dim):
          x = torch.randn(size_x, requires_grad=True)
          if len(size_ind) > 0 and len(size_x) > 0:
              ind = torch.randint(x.size(dim), size_ind)
          else:
              ind = torch.zeros(size_ind, dtype=torch.int64)
          out = torch.gather(x, dim, ind, sparse_grad=False)
          grad = torch.rand_like(out)
          out.backward(grad)
          grad_dense = x.grad.clone()
          x.grad = None
          out = torch.gather(x, dim, ind, sparse_grad=True)
          out.backward(grad)
          self.assertEqual(grad_dense, x.grad.to_dense())
  
      def test_sparse_gather_dim0(self):
          self._test_sparse_gather((10, 10), (5, 10), 0)
  
      def test_sparse_gather_dim1(self):
          self._test_sparse_gather((10, 10, 5), (10, 5, 5), 1)
  
      def test_sparse_gather_dim_neg(self):
          self._test_sparse_gather((10, 10, 5), (10, 10, 2), -1)
  
      def test_sparse_gather_ind_scalar(self):
          self._test_sparse_gather((10,), (), 0)
  
      def test_sparse_gather_x_scalar(self):
          self._test_sparse_gather((), (2,), 0)
  
      def test_sparse_gather_both_scalar(self):
          self._test_sparse_gather((), (), 0)
  
      def test_gc_in_destructor(self):
          """
          Previously, if a Function destructor triggered a garbage collection,
          the Variable's tp_dealloc handler would get called twice leading to a
          segfault.
          """
          class CollectOnDelete(Function):
              def forward(self, x):
                  return x
  
              def backward(self, grad_output):
                  return grad_output
  
              def __del__(self):
                  gc.collect()
  
          for _ in range(10):
              CollectOnDelete().forward(torch.randn(1, requires_grad=True)).backward()
  
      # Delete this test when legacy custom autograd functions are deleted.
      def test_naughty_legacy_variable_grad_fn(self):
          class Id(Function):
              def forward(self, x):
                  return x
  
              def backward(self, grad_x):
                  return grad_x
  
          self.assertRaises(RuntimeError, lambda: Variable(torch.zeros(1), _grad_fn=Id()))
  
      # Delete this test when legacy custom autograd functions are deleted.
      def test_naughty_legacy_function_backward_before_forward(self):
          class Id(Function):
              def forward(self, x):
                  return x
  
              def backward(self, grad_x):
                  return grad_x
  
          f = Id()
          self.assertRaises(RuntimeError, lambda: f._do_backward((torch.zeros(0), ), False))
  
      # Delete this test when legacy custom autograd functions are deleted.
      def test_naughty_legacy_function_early_access(self):
          class Id(Function):
              def forward(self, x):
                  return x
  
              def backward(self, grad_x):
                  return grad_x
  
          f = Id()
          # A legacy autograd function is not fully initialized until you actually
          # apply it.  That means a lot of accessors on them don't actually work.
          # Test that we properly error in this case.
          self.assertRaises(RuntimeError, lambda: f.register_hook(lambda x, y: None))
          self.assertRaises(RuntimeError, lambda: f.next_functions)
          self.assertRaises(RuntimeError, lambda: f.metadata)
  
      @unittest.expectedFailure
      def test_naughty_anomaly_access(self):
          class MyFunction(Function):
              @staticmethod
              def forward(ctx, x):
                  return x
  
              @staticmethod
              def backward(ctx, g):
                  return g
  
          x = torch.zeros(1, requires_grad=True)
          y = MyFunction.apply(x)
          y.backward()
          y.grad_fn.metadata
          g = y.grad_fn
          del y
          g.metadata  # this currently fails, but shouldn't
  
      def test_naughty_autograd_function_stashing_ctx(self):
          saved_ctx = []
  
          class Id(Function):
              @staticmethod
              def forward(ctx, x):
                  ctx.save_for_backward(x)
                  return x
  
              @staticmethod
              def backward(ctx, grad_x):
                  saved_ctx.append(ctx)
                  return ctx.saved_tensors
  
          p = torch.zeros(1, requires_grad=True)
          loss = Id.apply(p)
          loss.backward(retain_graph=True)
          del loss
          # At this point in time, it complains that the graph has been freed
          # (which indeed true, although a somewhat indirect way of stating the
          # problem).
          self.assertRaises(RuntimeError, lambda: saved_ctx[0].saved_tensors)
  
      def test_custom_autograd_repeated_grad_grad(self):
          # This test failed the equality check in PR #22983; it's an interesting
          # and different test case worth enshrining.  mult1 is not testing
          # anything that interesting, but mult2 is the interesting case.
  
          def mult1(x):
              return x.prod(dim=-1).prod(dim=-1)
  
          class Mult(torch.autograd.Function):
              @staticmethod
              def forward(ctx, x):
                  y = mult1(x)
                  ctx.save_for_backward(x, y)
                  return y
  
              @staticmethod
              def backward(ctx, grad_output):
                  x, y = ctx.saved_tensors
                  return (grad_output * y)[:, None, None] / x
  
          mult2 = Mult.apply
  
          def check_gradgrad_repeated(x, y):
              gy, = torch.autograd.grad(y[0], x, create_graph=True)
              ggy_1, = torch.autograd.grad(gy[0, 0, 0], x, retain_graph=True)
              gy, = torch.autograd.grad(y[0], x, create_graph=True)
              ggy_2, = torch.autograd.grad(gy[0, 0, 0], x, retain_graph=True)
              self.assertEqual(ggy_1[0, 0, 1], ggy_2[0, 0, 1])
  
          x = torch.ones(2, 4, 4).requires_grad_()
          check_gradgrad_repeated(x, mult1(x))
          check_gradgrad_repeated(x, mult2(x))
  
      def test_custom_autograd_no_early_free(self):
          # This test failed complaining that buffers had already been freed
          # prior to #22983.  Also pretty interesting test case.
          class Double(torch.autograd.Function):
              @staticmethod
              def forward(ctx, x):
                  y = x ** 2
                  ctx.save_for_backward(x, y)
                  return y
  
              @staticmethod
              def backward(ctx, grad_output):
                  x, _ = ctx.saved_tensors
                  return grad_output * 2 * x
  
          # this is equivalent, but uses the output of .forward() in .backward()
          class Double2(Double):
              @staticmethod
              def backward(ctx, grad_output):
                  x, y = ctx.saved_tensors
                  return grad_output * 2 * y / x
  
          double = Double.apply
          double2 = Double2.apply
  
          x = torch.tensor(2).double().requires_grad_()
  
          self.assertTrue(torch.autograd.gradcheck(double, x))
          self.assertTrue(torch.autograd.gradgradcheck(double, x))
          self.assertTrue(torch.autograd.gradcheck(double2, x))
          self.assertTrue(torch.autograd.gradgradcheck(double2, x))
  
          y = double(x)
          torch.autograd.grad(y, x, create_graph=True)
          torch.autograd.grad(y, x)
  
          y = double2(x)
          torch.autograd.grad(y, x, create_graph=True)
          torch.autograd.grad(y, x)  # should not error!
  
      def test_detach(self):
          x = torch.randn(10, 10, requires_grad=True)
          y = x + 2
          y = y.detach()
          z = y * 4 + 2
          self.assertFalse(y.requires_grad)
          self.assertFalse(z.requires_grad)
  
          x = torch.randn(10, 10, requires_grad=True)
          y = x * 2
          y = y.detach()
          self.assertFalse(y.requires_grad)
          self.assertIsNone(y.grad_fn)
          z = x + y
          z.sum().backward()
          # This is an incorrect gradient, but we assume that's what the user
          # wanted. detach() is an advanced option.
          self.assertEqual(x.grad, torch.ones(10, 10))
  
          # in-place detach
          x = torch.randn(10, 10, requires_grad=True)
          y = torch.randn(10, 10, requires_grad=True)
          a = x * 2
          (y + a).sum().backward(retain_graph=True)
          a.detach_()
          self.assertFalse(a.requires_grad)
          (y + a).sum().backward()  # this won't backprop to x
          self.assertEqual(x.grad, torch.ones(10, 10) * 2)
          self.assertEqual(y.grad, torch.ones(10, 10) * 2)
  
          # in-place deatch on a view raises an exception
          view = x.narrow(0, 1, 4)
          self.assertRaisesRegex(RuntimeError, 'view', lambda: view.detach_())
  
      def test_detach_base(self):
          "detaching base does not detach view"
          x = torch.randn(10, 10, requires_grad=True)
          view = x.narrow(0, 1, 4)
          x.detach_()
          self.assertFalse(x.requires_grad)
          self.assertTrue(view.requires_grad)
          self.assertIsNotNone(view.grad_fn)
          self.assertIs(view._base, x)
  
      def _test_type_conversion_backward(self, t, ):
          fvar = Variable(t(torch.randn(5, 5).float()), requires_grad=True)
          fvar.double().sum().backward()
          self.assertEqual(fvar.grad, torch.ones_like(fvar))
          self.assertEqual(type(fvar.grad), type(fvar))
          dvar = Variable(t(torch.randn(5, 5).double()), requires_grad=True)
          dvar.float().sum().backward()
          self.assertEqual(dvar.grad, torch.ones_like(dvar))
          self.assertEqual(type(dvar.grad), type(dvar))
  
      def test_type_conversions(self):
          x = torch.randn(5, 5)
          self.assertIsInstance(x.float(), torch.FloatTensor)
          self.assertIsInstance(x.int(), torch.IntTensor)
          if torch.cuda.is_available():
              self.assertIsInstance(x.float().cuda(), torch.cuda.FloatTensor)
              self.assertIsInstance(x.int().cuda(), torch.cuda.IntTensor)
              self.assertIsInstance(x.int().cuda().cpu(), torch.IntTensor)
              if torch.cuda.device_count() >= 2:
                  x2 = x.float().cuda(1)
                  self.assertIsInstance(x2, torch.cuda.FloatTensor)
                  self.assertIs(x2.get_device(), 1)
                  x2 = x.float().cuda()
                  self.assertIsInstance(x2, torch.cuda.FloatTensor)
                  self.assertIs(x2.get_device(), 0)
                  x2 = x2.cuda(1)
                  self.assertIsInstance(x2, torch.cuda.FloatTensor)
                  self.assertIs(x2.get_device(), 1)
                  y = Variable(torch.randn(5).cuda(1), requires_grad=True)
                  y.cpu().sum().backward()
                  self.assertIs(y.grad.get_device(), 1)
                  self.assertIs(y.long().get_device(), 1)
  
          for t in [torch.DoubleTensor, torch.FloatTensor, torch.IntTensor, torch.ByteTensor]:
              for y_var in (True, False):
                  y = torch.randint(5, (5, 5), dtype=t.dtype)
                  y = Variable(y) if y_var else y
                  self.assertIsInstance(x.type(t), t)
                  self.assertIsInstance(x.type_as(y), t)
                  # TODO: t.dtype should work
                  t_dtype = t().dtype
                  self.assertIsInstance(x.type(t_dtype), t)
                  self.assertIs(t_dtype, x.type(t_dtype).dtype)
                  self.assertEqual(y.data_ptr(), y.type(t).data_ptr())
                  if torch.cuda.is_available():
                      for x_cuda in (True, False):
                          for y_cuda in (True, False):
                              x_c = x.cuda() if x_cuda else x
                              y_c = y.cuda() if y_cuda else y
                              _, y_type = y_c.type().rsplit('.', 1)
                              y_typestr = ('torch.cuda.' if y_cuda else 'torch.') + y_type
                              self.assertEqual(y_c.type(), x_c.type(y_typestr).type())
                              self.assertIs(y_c.dtype, x_c.type(y_c.dtype).dtype)
                              self.assertEqual(y_c.data_ptr(), y_c.cuda().data_ptr() if y_cuda else y_c.data_ptr())
  
          self._test_type_conversion_backward(lambda x: x)
          if torch.cuda.is_available():
              self._test_type_conversion_backward(lambda x: x.cuda())
              if torch.cuda.device_count() >= 2:
                  # one of these has to be the non-default device
                  self._test_type_conversion_backward(lambda x: x.cuda(0))
                  self._test_type_conversion_backward(lambda x: x.cuda(1))
  
      def test_isolated_node(self):
          x = torch.randn(5, 5, requires_grad=True)
          y = torch.randn(5, 5, requires_grad=True)
  
          a = x + y
          b = torch.max(a, 1, True)[1].repeat(1, 5).double()
          o = (b + a).sum()
          o.backward()
  
      def test_shape(self):
          x = torch.randn(3, 4)
          self.assertEqual(2, len(x.shape))
          self.assertEqual(x.shape[0], 3)
          self.assertEqual(x.shape[1], 4)
  
      def test_numpy_requires_grad(self):
          x = torch.randn(2, 2, requires_grad=True)
          self.assertRaisesRegex(RuntimeError, 'requires grad', lambda: x.numpy())
  
      def test_return_leaf(self):
          class Identity(Function):
              @staticmethod
              def forward(ctx, a, b):
                  return a, a + b
  
              @staticmethod
              def backward(ctx, grad_a, grad_b):
                  return grad_a + grad_b, grad_b
  
          hook_called = [False]
          x = torch.randn(5, 5, requires_grad=True)
          y = torch.randn(5, 5, requires_grad=True)
  
          q, p = Identity.apply(x, y)
  
          # Make sure hooks only receive grad from usage of q, not x.
          def hook(grad):
              hook_called[0] = True
              self.assertEqual(grad, torch.ones(5, 5))
  
          q.register_hook(hook)
          (q + p + x).sum().backward()
          self.assertEqual(x.grad, torch.ones(5, 5) * 3)
          self.assertEqual(y.grad, torch.ones(5, 5))
          self.assertTrue(hook_called[0])
  
      def test_return_leaf_inplace(self):
          class Inplace(InplaceFunction):
              @staticmethod
              def forward(ctx, a, b):
                  ctx.mark_dirty(a)
                  return a.add_(b), b + 2
  
              @staticmethod
              def backward(ctx, grad_a, grad_b):
                  return grad_a, grad_a + grad_b
  
          x = torch.randn(5, 5)
          y = torch.randn(5, 5, requires_grad=True)
  
          fn = Inplace(True)
          q, p = fn.apply(x, y)
          self.assertIs(q, x)
          self.assertIs(q.grad_fn.__class__, fn._backward_cls)
          self.assertTrue(q.requires_grad)
          q.sum().backward()
          self.assertEqual(y.grad, torch.ones(5, 5))
  
      def test_leaf_assignment(self):
          x = torch.randn(5, 5)
          y = torch.randn(5, requires_grad=True)
          z = torch.randn(5, requires_grad=True)
  
          x[0] = y
          x[1] = 2 * z
          self.assertTrue(x.requires_grad)
          self.assertIsNot(x.grad_fn, None)
          x.sum().backward()
          self.assertEqual(y.grad, torch.ones(5))
          self.assertEqual(z.grad, torch.ones(5) * 2)
  
      def test_no_grad_assignment(self):
          x = torch.randn(5, 5, requires_grad=True)
          y = torch.randn(5)
          with torch.no_grad():
              x[0] = y
  
          self.assertTrue(x.requires_grad)
          self.assertIsNone(x.grad_fn)
  
      def test_no_grad_modifies_version(self):
          x = torch.randn(5, requires_grad=True)
          y = torch.randn(5, requires_grad=True)
          z = (x * y).sum()
          with torch.no_grad():
              x *= 2
          self.assertRaisesRegex(RuntimeError, 'modified by an inplace operation',
                                 lambda: z.backward())
  
      def test_no_grad_input(self):
          class MyFunction(Function):
              @staticmethod
              def forward(self, x):
                  return x
  
              @staticmethod
              def backward(self, grad_output):
                  return grad_output
  
          x = torch.randn(5, requires_grad=True)
          with torch.no_grad():
              y = MyFunction.apply(x)
  
          self.assertTrue(x.requires_grad)
          self.assertIsNone(y.grad_fn)
  
      def test_backward_copy(self):
          # This tests checks backward engine for a very subtle bug that appreared
          # in one of the initial versions of autograd. Gradients tensors were
          # simply stored in lists while the function waited for all its gradients
          # to be computed. However, sometimes an output was used multiple times,
          # so the gradients needed to be summed. Engine used to keep a need_copy
          # set of tensors that will need a clone upon next addition and removed
          # them from the set as soon as the clone was performed. However, this
          # could lead to incorrect results if the same gradient tensor was
          # buffered in three places in the graph:
          # 1. When accumulating gradients in one of these places it was cloned
          #    and removed from need_copy set.
          # 2. When accumulating in second place, it wasn't in the need_copy set,
          #    so the gradients were simply accumulated in-place (which already
          #    modified the grad in 3rd place)
          # 3. When accumulating in the third place, it wasn't in the need_copy set
          #    as well, so the incoming gradient was summed in-place, yielding
          #    incorrect results in all functions, except the first one.
          x = torch.ones(5, 5, requires_grad=True)
          y = torch.ones(5, 5, requires_grad=True)
          # Simulate that we're in the middle of the graph
          a = x + 2
          b = y + 2
          c = x + 2
          # This op will just return grad_output two times in backward
          add1 = a + b
          add2 = add1 + c
          # Simulate a long branch, so grad_output will get buffered.
          for _ in range(4):
              a = a * 2
              b = b * 2
              c = c * 2
          branch = a + b + c
          out = add2 + branch
          # expected gradients are:
          # for x: 34 (16 from final a, 16 from final c, 2 from add2)
          # for y: 17 (16 from final b, 1 from add2)
          grad_output = torch.ones(5, 5)
          out.backward(grad_output)
          self.assertEqual(x.grad, torch.ones(5, 5) * 34)
          self.assertEqual(y.grad, torch.ones(5, 5) * 17)
  
      def test_save_none_for_backward(self):
          test_case = self
  
          class MyFn(Function):
              @staticmethod
              def forward(ctx, input):
                  ctx.save_for_backward(None, input, None)
                  return input * input
  
              @staticmethod
              def backward(ctx, grad_output):
                  n1, input, n2 = ctx.saved_tensors
                  test_case.assertIsNone(n1)
                  test_case.assertIsNone(n2)
                  return 2 * input * grad_output
  
          x = torch.randn(5, 5, requires_grad=True)
          y = MyFn.apply(x)
          y.sum().backward()
          self.assertEqual(x.grad, 2 * x)
  
      def test_too_many_grads(self):
          class MyFn(Function):
              @staticmethod
              def forward(ctx, input):
                  return input
  
              @staticmethod
              def backward(ctx, grad_output):
                  return grad_output, None, None
  
          x = torch.randn(5, 5, requires_grad=True)
          y = MyFn.apply(x)
          y.sum().backward()
          self.assertEqual(x.grad, torch.ones_like(x))
  
      def test_pickle(self):
          x = torch.randn(10, 10, requires_grad=True)
          y = torch.randn(10, 10, requires_grad=False)
  
          def assert_strict_equal(var1, var2):
              self.assertEqual(var1, var2)
              self.assertEqual(var1.requires_grad, var2.requires_grad)
  
          serialized = [pickle.dumps([x, y], protocol=p) for p in range(3)]
          for dump in serialized:
              xc, yc = pickle.loads(dump)
              assert_strict_equal(xc, x)
              assert_strict_equal(yc, y)
  
      def test_dep_nograd(self):
          class F1(Function):
              @staticmethod
              def forward(ctx, input):
                  out = torch.randn(input.size())
                  ctx.mark_non_differentiable(out)
                  return input, out
  
              @staticmethod
              def backward(ctx, grad_output, ignored):
                  return grad_output
  
          class F2(Function):
              @staticmethod
              def forward(ctx, input, ignored):
                  return input
  
              @staticmethod
              def backward(ctx, grad_output):
                  return grad_output, None
  
          x = torch.randn(5, requires_grad=True)
          a, b = F1.apply(x)
          b = b + 1  # separate F1 from F2 by another op
          self.assertTrue(a.requires_grad)
          self.assertFalse(b.requires_grad)
          c = F2.apply(a, b)
          c.backward(torch.ones(c.size()))
          self.assertEqual(x.grad, torch.ones(x.size()))
  
      def test_set_grad_enabled(self):
          x = torch.tensor([1.], requires_grad=True)
          with torch.set_grad_enabled(False):
              y = x * 2
          self.assertFalse(y.requires_grad)
          with torch.set_grad_enabled(True):
              y = x * 2
          self.assertTrue(y.requires_grad)
          with torch.set_grad_enabled(False):
              torch.set_grad_enabled(True)
              y = x * 2
          self.assertTrue(y.requires_grad)
  
      def test_simple_reentrant(self):
          y_data = torch.randn(2, 2)
  
          class Reenter(Function):
              @staticmethod
              def forward(ctx, x):
                  with torch.enable_grad():
                      ctx.x = Variable(x, requires_grad=True)
                      ctx.y = Variable(y_data, requires_grad=True)
                      ctx.output_var = ctx.x * ctx.y
                  return ctx.output_var.detach()
  
              @staticmethod
              def backward(ctx, grad_output):
                  with torch.enable_grad():
                      ctx.output_var.sum().backward()
                  return ctx.x.grad * grad_output
  
          # Reentrant starts on CPU thread, finishs on GPU thread
          x = torch.randn(2, 2, requires_grad=True)
          out = Reenter.apply(x)
          out.sum().backward()
          self.assertEqual(x.grad, y_data)
  
      def test_reentrant_child_error(self):
          # Parent graph.
          a = torch.rand(3, 3, requires_grad=True)
          c = a * a
  
          # Reentrant child graph.
          b = torch.rand(3, 3, requires_grad=True)
          e = b * b
          f = TestAutograd.SimulateBackwardError.apply(e)
          reentrant_root = f.sum()
  
          class ReentrantFunc(Function):
  
              @staticmethod
              def forward(ctx, inp):
                  return inp.clone()
  
              @staticmethod
              def backward(ctx, grad):
                  # Reentrant backward in child will throw an error.
                  reentrant_root.backward()
                  return grad
  
          d = ReentrantFunc.apply(c)
          with self.assertRaisesRegex(RuntimeError, 'Simulate error'):
              d.sum().backward()
  
      def test_broadcast_tensors(self):
          f_args_variable = (torch.randn(3, requires_grad=True),
                             torch.randn(1, 2, 1, requires_grad=True),
                             torch.randn(1, 1, requires_grad=True),
                             torch.randn(5, 1, 1, requires_grad=True))
          f_args_tensor = deepcopy(unpack_variables(f_args_variable))
          run_functional_checks(self, "test_broadcast_tensors", "broadcast",
                                lambda a, b, c, d: torch.broadcast_tensors(a, b, c, d),
                                True, f_args_variable, f_args_tensor)
  
      def test_cat(self):
          f_args_variable = (torch.randn(1, S, S, requires_grad=True),
                             torch.randn(2, S, S, requires_grad=True),
                             torch.randn(3, S, S, requires_grad=True),
                             0)
          f_args_tensor = deepcopy(unpack_variables(f_args_variable))
          run_functional_checks(self, "test_cat", "cat",
                                lambda a, b, c, dim: torch.cat((a, b, c), dim),
                                True, f_args_variable, f_args_tensor)
  
      def test_cat_negdim_1(self):
          f_args_variable = (torch.randn(S, S, 1, requires_grad=True),
                             torch.randn(S, S, 2, requires_grad=True),
                             torch.randn(S, S, 3, requires_grad=True),
                             -1)
          f_args_tensor = deepcopy(unpack_variables(f_args_variable))
          run_functional_checks(self, "test_cat_negdim_1", "cat",
                                lambda a, b, c, dim: torch.cat((a, b, c), dim),
                                True, f_args_variable, f_args_tensor)
  
      def test_cat_negdim_2(self):
          f_args_variable = (torch.randn(S, 1, S, requires_grad=True),
                             torch.randn(S, 2, S, requires_grad=True),
                             torch.randn(S, 3, S, requires_grad=True),
                             -2)
          f_args_tensor = deepcopy(unpack_variables(f_args_variable))
          run_functional_checks(self, "test_cat_negdim_2", "cat",
                                lambda a, b, c, dim: torch.cat((a, b, c), dim),
                                True, f_args_variable, f_args_tensor)
  
      def test_cat_empty_legacy(self):
          f_args_variable = (torch.randn(0, requires_grad=True),
                             torch.randn(S, S, requires_grad=True))
          # gradgradcheck doesn't work, probably because legacy size tracking is wrong somewhere,
          # hence False passed below, but gradcheck checked explicitly.
          f_args_tensor = deepcopy(unpack_variables(f_args_variable))
          run_functional_checks(self, "test_cat_empty_legacy", "cat",
                                lambda a, b: torch.cat((a, b)),
                                False, f_args_variable, f_args_tensor)
          self.assertTrue(gradcheck(lambda a, b: torch.cat((a, b)), f_args_variable, eps=1e-6, atol=PRECISION))
  
      def test_cat_empty(self):
          f_args_variable = (torch.randn(0, S, requires_grad=True),
                             torch.randn(S, S, requires_grad=True))
          f_args_tensor = deepcopy(unpack_variables(f_args_variable))
          run_functional_checks(self, "test_cat_empty", "cat",
                                lambda a, b: torch.cat((a, b)),
                                True, f_args_variable, f_args_tensor)
  
      def test_trapz(self):
          f_args_variable = (torch.randn(2, 3, requires_grad=True),
                             torch.tensor([[1.0, 2.0, 5.5], [2.3, 0.5, 6.2]], requires_grad=True))
          f_args_tensor = deepcopy(unpack_variables(f_args_variable))
          run_functional_checks(self, "test_trapz", "trapz",
                                lambda y, x: torch.trapz(y, x),
                                True, f_args_variable, f_args_tensor)
  
  
      def test_var_mean_differentiable(self):
          dim = [2, 4]
          keepdim = False
          input1 = torch.randn(3, 4, 5, 6, 2, 3, requires_grad=True)
          input2 = deepcopy(input1)
          var1, mean1 = torch.var_mean(input1, dim=dim, keepdim=keepdim)
          var2 = input2.var(dim=dim, keepdim=keepdim)
          mean2 = input2.mean(dim=dim, keepdim=keepdim)
          grad = torch.randn(3, 4, 6, 3, requires_grad=True)
  
          r1 = var1 * var1 * mean1 * mean1
          r2 = var2 * var2 * mean2 * mean2
          self.assertTrue(torch.allclose(r1, r2, rtol=0.01, atol=0.0))
  
          torch.autograd.backward(r1, grad)
          torch.autograd.backward(r2, grad)
          self.assertTrue(torch.allclose(input1.grad, input2.grad, rtol=0.01, atol=0.0))
  
      @skipIfNoLapack
      def test_cholesky(self):
          def func(root, upper):
              x = torch.matmul(root, root.transpose(-1, -2)) + 1e-05
              return torch.cholesky(x, upper)
  
          def run_test(upper, dims):
              root = torch.rand(*dims, requires_grad=True)
  
              gradcheck(func, [root, upper])
              gradgradcheck(func, [root, upper])
  
              root = random_symmetric_pd_matrix(dims[-1], *dims[:-2]).requires_grad_()
              chol = root.cholesky().sum().backward()
              self.assertEqual(root.grad, root.grad.transpose(-1, -2))  # Check the gradient is symmetric
  
          for upper, dims in product([True, False], [(3, 3), (4, 3, 2, 2)]):
              run_test(upper, dims)
              run_test(upper, dims)
  
      @skipIfNoLapack
      def test_cholesky_solve(self):
          def _test_with_size(A_dims, B_dims, upper):
              root = torch.rand(*A_dims).requires_grad_()
              b = torch.rand(*B_dims).requires_grad_()
  
              def func(root, b, upper):
                  if upper:
                      A = root.triu()
                  else:
                      A = root.tril()
                  return torch.cholesky_solve(b, A, upper)
  
              gradcheck(func, [root, b, upper])
              gradgradcheck(func, [root, b, upper])
  
          for (a_size, b_size), upper in product([((3, 3), (3, 4)), ((3, 3), (3, 2)),
                                                  ((2, 3, 3), (2, 3, 4)), ((2, 3, 3), (2, 3, 2))],
                                                 [True, False]):
              _test_with_size(a_size, b_size, upper)
  
      @skipIfNoLapack
      def test_eig(self):
          def func(B):
              return torch.eig(B, eigenvectors=True)
  
          def func_eigvals(B):
              return torch.eig(B, eigenvectors=True)[0]
  
          def func_eigvecs(B):
              return torch.eig(B, eigenvectors=True)[1]
  
          def run_test(dims):
              # The backward operation for eig only works for real eigenvalues,
              # so the matrix should be B = U^{-1}*A*U where A is a random
              # symmetric matrix and U is a random full-rank matrix.
              # Slight change to the matrix should not make the eigenvalues
              # complex, so we apply requires_grad_ to B, not A and U
  
              A = random_symmetric_matrix(dims[-1], *dims[:-2])
              U = torch.rand(*dims)
              Uinv = torch.inverse(U)
              B = torch.matmul(Uinv, torch.matmul(A, U)).requires_grad_()
  
              gradcheck(func, [B])
              gradgradcheck(func, [B])
              gradcheck(func_eigvals, [B])
              gradgradcheck(func_eigvals, [B])
              gradcheck(func_eigvecs, [B])
              gradgradcheck(func_eigvecs, [B])
  
          for dims in [(3, 3), (5, 5)]:
              run_test(dims)
  
      @skipIfNoLapack
      def test_symeig(self):
          def func(root, upper):
              x = 0.5 * (root + root.transpose(-2, -1))
              return torch.symeig(x, eigenvectors=True, upper=upper)
  
          def run_test(upper, dims):
              root = torch.rand(*dims, requires_grad=True)
  
              gradcheck(func, [root, upper])
              gradgradcheck(func, [root, upper])
  
              root = random_symmetric_matrix(dims[-1], *dims[:-2]).requires_grad_()
              w, v = root.symeig(eigenvectors=True)
              (w.sum() + v.sum()).backward()
              self.assertEqual(root.grad, root.grad.transpose(-1, -2))  # Check the gradient is symmetric
  
          for upper, dims in product([True, False], [(3, 3), (5, 3, 3), (4, 3, 2, 2)]):
              run_test(upper, dims)
  
      @skipIfNoLapack
      def test_cholesky_inverse(self):
          def _test_with_size(upper, dims):
              # We require to create a Cholesky factor which requires that the diagonal elements are positive.
              # Initializing too small values for the diagonal elements could cause issues when being perturbed
              # to obtain the numerical Jacobian, thereby leading to inconsistent gradcheck
              A = torch.randn(*dims)
              A.diagonal().uniform_(0.1, 5.0)
              A.requires_grad_()
  
              def func(A, upper):
                  if upper:
                      root = A.triu()
                  else:
                      root = A.tril()
                  return torch.cholesky_inverse(root, upper)
  
              gradcheck(func, [A, upper])
              gradgradcheck(func, [A, upper])
  
          for upper, dims in product([True, False], [(3, 3), (5, 5)]):
              _test_with_size(upper, dims)
  
      @skipIfNoLapack
      def test_triangular_solve(self):
          def _test_with_size(A_dims, B_dims):
              A = torch.rand(*A_dims).requires_grad_()
              b = torch.rand(*B_dims).requires_grad_()
  
              for upper, transpose, unitriangular in product((True, False), repeat=3):
                  def func(A, b):
                      return torch.triangular_solve(b, A, upper, transpose, unitriangular)
  
                  gradcheck(func, [A, b])
                  gradgradcheck(func, [A, b])
  
          _test_with_size((3, 3), (3, 4))
          _test_with_size((3, 3), (3, 2))
          _test_with_size((2, 3, 3), (2, 3, 4))
          _test_with_size((2, 3, 3), (2, 3, 2))
  
      @unittest.skipIf(not TEST_MKL, "PyTorch is built without MKL support")
      def test_fft_ifft_rfft_irfft(self):
          def _test_complex(sizes, signal_ndim):
              x = torch.randn(sizes, requires_grad=True, dtype=torch.double)
  
              for normalized in (True, False):
                  def fft(x):
                      return x.fft(signal_ndim, normalized=normalized)
  
                  gradcheck(fft, [x])
                  gradgradcheck(fft, [x], gen_non_contig_grad_outputs=True)
  
                  def ifft(fx):
                      return fx.ifft(signal_ndim, normalized=normalized)
  
                  # Use output of fft(x) for inverse fft, due to symmetry requirements
                  fx = fft(x).detach()
                  fx.requires_grad = True
                  gradcheck(ifft, [fx])
                  gradgradcheck(ifft, [fx], gen_non_contig_grad_outputs=True)
  
          def _test_real(sizes, signal_ndim):
              x = torch.randn(sizes, requires_grad=True, dtype=torch.double)
              if x.dim() == signal_ndim:
                  start_dim = 0
              else:
                  start_dim = 1
              signal_sizes = x.size()[start_dim:start_dim + signal_ndim]
  
              for normalized, onesided in product((True, False), repeat=2):
                  def rfft(x):
                      return x.rfft(signal_ndim, normalized=normalized, onesided=onesided)
  
                  gradcheck(rfft, [x])
                  gradgradcheck(rfft, [x], gen_non_contig_grad_outputs=True)
  
                  # Generally speaking, irfft itself won't and can't pass the
                  # current gradcheck as it assumes the input follows conjugate
                  # symmetry, an requirement that is never true with our point
                  # numerical Jacobian estimate. Without input symmtry, irfft's
                  # behavior is undefined.
                  #
                  # Even onesided results can't remove all redundancy. For
                  # example, consider the .select(last_signal_dim, 0) slice.
                  # It is entirely represented in the onesided results (except
                  # for 1D), and will be reflected onto itself!
                  #
                  # So only 1D onesided irfft should pass grad check as it is
                  # guaranteed that the input has no symmetrical values.
                  #
                  # In other cases, we test a function that first uses rfft to
                  # generate a tensor that follows the conjugate symmetry irfft
                  # expects, and then feeds it into irfft. Since rfft is already
                  # tested above, we thereby verify the correctness of irfft.
                  if signal_ndim == 1 and onesided:
                      def irfft(fx):
                          return fx.irfft(signal_ndim, normalized=normalized,
                                          onesided=onesided, signal_sizes=signal_sizes)
  
                      # Use output of rfft(x) for inverse rfft, due to symmetry requirements
                      fx = rfft(x).detach()
                      fx.requires_grad = True
                      gradcheck(irfft, [fx])
                      gradgradcheck(irfft, [fx], gen_non_contig_grad_outputs=True)
                  else:
                      # Test this function: f(x) = ifft(rfft(x) + rfft(z)), where
                      # z is some fixed tensor of same size as x. rfft(z) term is
                      # needed because otherwise f becomes identity.
                      z = torch.randn(sizes, dtype=torch.double)
                      fz = z.rfft(signal_ndim, normalized=normalized, onesided=onesided)
  
                      def rfft_irfft(x):
                          fx = x.rfft(signal_ndim, normalized=normalized, onesided=onesided)
                          y = fx + fz
                          return y.irfft(signal_ndim, normalized=normalized,
                                         onesided=onesided, signal_sizes=signal_sizes)
  
                      gradcheck(rfft_irfft, [x])
                      gradgradcheck(rfft_irfft, [x], gen_non_contig_grad_outputs=True)
  
          _test_real((2, 10), 1)
          _test_real((2, 3, 4), 2)
          _test_real((2, 3, 4, 3), 3)
  
          _test_complex((2, 2, 10, 2), 1)
          _test_complex((1, 2, 3, 4, 2), 2)
          _test_complex((2, 1, 3, 4, 3, 2), 3)
  
      def test_gradcheck_fail_when_no_differentiable_outputs_and_num_grad_not_zero(self):
          def autograd_fn(input):
              output = torch.detach(input)
              self.assertFalse(output.requires_grad)
              return output
  
          f_args_variable = torch.ones(S, S, requires_grad=True)
          self.assertRaisesRegex(RuntimeError, 'Numerical gradient for function expected to be zero',
                                 lambda: gradcheck(autograd_fn, f_args_variable, eps=1e-6, atol=PRECISION))
  
      def test_variable_traverse(self):
          def get_out_and_unrefed_cycle():
              inp = torch.randn(10, requires_grad=True)
              tmp = inp.view(10, 1)
              out = tmp.view(10)
  
              # Create a reference cycle that contains an
              # intermediary Variable in the graph
              my_list = []
              my_list.append(tmp)
              my_list.append(my_list)
  
              return out
  
          out = get_out_and_unrefed_cycle()
          gc.collect()
          # This will segfault if things have been erroneously released
          out.backward(torch.randn(out.size()))
  
      def test_norm_subgradient(self):
          def run_test(input_size, norm_deg):
              input = torch.zeros(*input_size, requires_grad=True)
              input.norm(norm_deg).backward()
              self.assertEqual(input.grad.abs().sum(), 0)
  
          run_test((10,), 2)
          run_test((10, 10), 2)
          run_test((10,), 3)
          run_test((10,), 1)
          run_test((10,), 1.5)
  
      def test_pow_zero_tensor_gradient(self):
          def run_test(input_size, exponent):
              input = torch.zeros(*input_size, requires_grad=True)
              input.pow(exponent).sum().backward()
              self.assertEqual(input.grad.abs().sum(), 0)
  
          run_test((10,), torch.zeros(10))
          run_test((10, 10), torch.zeros(10, 10))
          run_test((10,), 0)
  
      def test_pow_scalar_base(self):
          a = torch.arange(1, 13, dtype=torch.double).view(3, 4).requires_grad_()
          gradcheck(lambda a: torch.pow(2, a), (a,))
  
      @skipIfNoLapack
      def test_pinverse(self):
          # Why is pinverse tested this way, and not ordinarily as other linear algebra methods?
          # 1. Pseudo-inverses are not generally continuous, which means that they are not differentiable
          # 2. Derivatives for pseudo-inverses exist typically for constant rank (Golub et al, 1973)
          # 3. This method creates two orthogonal matrices, and a constructs a test case with large
          #    singular values (given by x to the function).
          # 4. This will ensure that small perturbations don't affect the rank of matrix, in which case
          #    a derivative exists.
          # 5. This test exists since pinverse is implemented using SVD, and is hence a backpropable method
          m, n = 5, 10
          U = torch.randn(n, m).qr()[0].t()  # Orthogonal with dimensions m x n
          V = torch.randn(n, m).qr()[0].t()  # Orthogonal with dimensions m x n
  
          def func(x):
              S = torch.cat([x, torch.zeros(n - m)], 0)
              M = U.mm(torch.diag(S)).mm(V.t())
              return M.pinverse()
  
          gradcheck(func, [torch.rand(m).add_(1).requires_grad_()])
          gradcheck(func, [torch.rand(m).add_(10).requires_grad_()])
          gradgradcheck(func, [torch.rand(m).add_(1).requires_grad_()])
          gradgradcheck(func, [torch.rand(m).add_(10).requires_grad_()])
  
      def test_chain_matmul(self):
          def gen_matrices(p):
              matrices = []
              for (pi, pi_1) in zip(p[:-1], p[1:]):
                  matrices.append(torch.randn(pi, pi_1).requires_grad_())
              return matrices
  
          gradcheck(torch.chain_matmul, gen_matrices([5, 10, 15, 5]))
          gradcheck(torch.chain_matmul, gen_matrices([3, 5, 2, 6]))
          gradcheck(torch.chain_matmul, gen_matrices([6, 2, 4, 8, 10]))
          gradgradcheck(torch.chain_matmul, gen_matrices([5, 10, 15, 5]))
          gradgradcheck(torch.chain_matmul, gen_matrices([3, 5, 2, 6]))
          gradgradcheck(torch.chain_matmul, gen_matrices([6, 2, 4, 8, 10]))
  
      @unittest.skipIf(IS_WINDOWS, """File open permission error on Windows,
              https://github.com/pytorch/pytorch/issues/34086""")
      def test_profiler_tracing(self):
          t1, t2 = torch.ones(1), torch.ones(1)
          with torch.autograd.profiler.profile() as prof:
              torch.add(t1, t2)
  
          with tempfile.NamedTemporaryFile(mode="w+") as f:
              prof.export_chrome_trace(f.name)
              # read the trace and expect valid json
              # if the JSON generated by export_chrome_trace is not valid, this will throw and fail the test.
              json.load(f)
  
          # Same test but for cuda.
          if not torch.cuda.is_available():
              return
  
          device = torch.device("cuda:0")
          t1, t2 = torch.ones(1, device=device), torch.ones(1, device=device)
          with torch.autograd.profiler.profile(use_cuda=True) as prof:
              torch.add(t1, t2)
  
          with tempfile.NamedTemporaryFile(mode="w+") as f:
              prof.export_chrome_trace(f.name)
              # Now validate the json
              json.load(f)
  
      def test_profiler(self):
          x = torch.randn(10, 10)
  
          with profile() as p:
              self.assertTrue(torch.autograd._profiler_enabled())
              y = x * 2 + 4
  
          self.assertFalse(torch.autograd._profiler_enabled())
  
          last_end = 0
          names = ['mul', 'add']
          self.assertEqual(len(p.function_events), len(names))
          for info, expected_name in zip(p.function_events, names):
              self.assertGreater(info.cpu_interval.start, last_end)
              self.assertEqual(info.name, expected_name)
              last_end = info.cpu_interval.end
  
      def test_record_function_callbacks(self):
          x = torch.randn(10, 10)
          with profile() as p:
              rf = torch.autograd._RecordFunction()
              torch.autograd._run_before_callbacks(rf, "foo")
              y = x * 2 + 4
              # ensure that we run destructor for RecordFunction, which invokes
              # end callbacks
              del rf
          function_events = p.function_events
          foo_event = [event for event in function_events if "foo" in event.name][0]
          self.assertEqual(foo_event.count, 1)
  
      def test_profiler_aggregation_fake(self):
          events = EventList()
          id = [0]
  
          def get_id():
              id[0] = id[0] + 1
              return id[0]
  
          # [[thread_id, [(start, end, id), ....]], ...]
          # Using list instead of a dict so order is guaranteed for any Python
          # version
          threads = [
              [1, [(0, 1, get_id()), (1, 2, get_id())]],
              [0, [(0, 2, get_id()), (1, 2, get_id()), (1, 3, get_id())]],
          ]
          for thread, ranges in threads:
              for range in ranges:
                  assert(len(range) == 3)
                  events.append(
                      FunctionEvent(
                          id=range[2],
                          name="",
                          thread=thread,
                          cpu_start=range[0],
                          cpu_end=range[1],
                      )
                  )
  
          events.populate_cpu_children()
  
          # Note that [1, 3] pushes out [0, 2] first. Then we record [1, 2]
          # as a child of [1, 3]
          res = [[], [], [], [], [4]]
  
          def get_children_ids(event):
              return [child.id for child in event.cpu_children]
  
          assert([get_children_ids(event) for event in events] == res)
  
      def test_profiler_function_event_avg(self):
          avg = FunctionEventAvg()
          avg.add(FunctionEvent(id=0, name="foo", thread=0, cpu_start=10, cpu_end=15))
          avg.add(FunctionEvent(id=1, name="foo", thread=0, cpu_start=20, cpu_end=30))
          avg.add(avg)
          self.assertEqual(avg.key, "foo")
  
          # aggregate stats
          self.assertEqual(avg.count, 4)
          self.assertEqual(avg.cpu_time_total, 30)
          self.assertEqual(avg.self_cpu_time_total, 30)
          self.assertEqual(avg.cuda_time_total, 0)
  
          # average stats
          self.assertEqual(avg.cpu_time, 7.5)
          self.assertEqual(avg.cuda_time_total, 0)
  
      def test_profiler_shapes(self):
          print("")
          layer1 = torch.nn.Linear(20, 30)
          layer2 = torch.nn.Linear(30, 40)
          input = torch.randn(128, 20)
          with profile(record_shapes=True) as prof:
              layer2(layer1(input))
  
          # type conversion
          assert(prof.function_events[0].input_shapes == [[30, 20]])
          # fc (addmm)
          assert(
              prof.function_events[1].input_shapes ==
              [[30], [128, 20], [20, 30], [], []]
          )
          assert(prof.function_events[2].input_shapes == [[40, 30]])
          assert(
              prof.function_events[3].input_shapes ==
              [[40], [128, 30], [30, 40], [], []]
          )
          print(prof.table())
          print(prof.key_averages(group_by_input_shape=True).table())
  
      def test_profiler_no_cuda(self):
          print("")
          layer = torch.nn.Linear(20, 30)
          x = torch.randn(128, 20)
          with profile(use_cuda=False) as prof:
              layer(x)
  
          prof_str = str(prof)
          print(prof_str)
          self.assertTrue('cpu' in prof_str.lower())
          self.assertTrue('cuda' not in prof_str.lower())
  
      def test_profiler_aggregation_lstm(self):
          print("")
          rnn = torch.nn.LSTM(10, 20, 2)
          total_time_s = 0
          with profile(record_shapes=True) as prof:
              for i in range(20):
                  input = torch.randn(5, 3, 10)
                  h = torch.randn(2, 3, 20)
                  c = torch.randn(2, 3, 20)
                  start = time.time()
                  rnn(input, (h, c))
                  end = time.time()
                  total_time_s += end - start
  
          print(prof.table(
              sort_by="self_cpu_time_total", row_limit=10, header="TEST"))
          print(prof.key_averages(group_by_input_shape=True).table(
              sort_by="self_cpu_time_total", row_limit=10))
  
          total_time_us = total_time_s * 1000.0 * 1000.0  # make it us which is profiler default
          print(
              "Total time based on python measurements: ",
              format_time(total_time_us)
          )
          print(
              "CPU time measurement python side overhead: {:.2f}%".format(
                  (total_time_us / prof.self_cpu_time_total - 1.0) * 100.0
              )
          )
  
          if sys.platform != "win32":
              with tempfile.NamedTemporaryFile() as trace_file:
                  prof.export_chrome_trace(trace_file.name)
  
      def test_record_function(self):
          x = torch.randn(10, 10)
  
          def forward(x):
              with record_function("outer"):
                  y = x * 2 + 4
                  with record_function("inner"):
                      y = y - 1
              y = y / 1
  
          forward(x)
  
          with profile() as p:
              forward(x)
  
          events = p.function_events
          start_order = [
              'profiler::_record_function_enter',
              'outer',
              'mul',
              'add',
              'profiler::_record_function_enter',
              'inner',
              'sub',
              'profiler::_record_function_exit',
              'profiler::_record_function_exit',
              'div',
          ]
          self.assertEqual(len(events), len(start_order))
          for info, expected_name in zip(events, start_order):
              self.assertEqual(info.name, expected_name)
  
          def count_events_before(before, target):
              matches = [e for e in events if e.name == before]
              self.assertEqual(len(matches), 1)
              match = matches[0]
  
              count = 0
              for e in events:
                  if e.name == target and e.cpu_interval.end <= match.cpu_interval.end:
                      count += 1
              return count
  
          self.assertEqual(
              count_events_before("inner", "profiler::_record_function_exit"),
              1,
          )
          self.assertEqual(
              count_events_before("outer", "profiler::_record_function_exit"),
              2,
          )
  
          # We can also use record_function to decorate arbitrary function
          @record_function('my_func')
          def f(x, y):
              return x + y
  
          with profile() as p:
              f(1, 2)
  
          self.assertTrue('my_func' in str(p))
  
      def test_record_function_multithreaded(self):
          rf = record_function("outer")
          rf.__enter__()
          with profile():
              # test that exiting the record function after starting a profile
              # doesn't throw.
              rf.__exit__()
  
          with profile():
              rf.__enter__()
          # test that exiting the record function after the profile has ended
          # doesn't throw.
          rf.__exit__()
  
  
      def test_dir(self):
          x = torch.randn(10, 10)
          keys = dir(x)
          self.assertIn('shape', keys)
  
          for key in keys:
              self.assertTrue(hasattr(x, key))
  
      def test_as_strided(self):
  
          def test(x, prepro_fn, size, strides, offset=None):
              x = x.to(torch.double).detach().requires_grad_()
  
              # Check that forward will **not** resize storage because it may
              # cause NaN in output and fail numerical Jacobian check consequently
              with torch.no_grad():
                  y = prepro_fn(x) if prepro_fn is not None else x
                  max_offset = sum((si - 1) * st for si, st in zip(size, strides))
                  max_offset += offset if offset is not None else y.storage_offset()
                  assert max_offset < len(y.storage()), "test case resizes storage"
  
              def closure(x):
                  if prepro_fn is not None:
                      x = prepro_fn(x)
                  return x.as_strided(size, strides, offset)
  
              gradcheck(closure, [x])
              gradgradcheck(closure, [x])
  
          # test
          test(torch.arange(0, 25), lambda x: x.view(5, 5), [3, 3], [6, 2], 2)
  
          # test crazy stride at dim with size 1 case
          test(torch.randn(12), None, [1, 2, 1, 5], [0, 5, 100, 1], 2)
  
          # test expand case
          test(torch.randn(5), None, [3, 3, 3], [0, 1, 0], 2)
          test(torch.randn(5), None, [3, 3, 3], [0, 0, 0], 4)
          test(torch.randn(5), lambda x: x.expand(5, 5), [5, 5], [0, 1], 0)
  
          # test non-expand overlapping case
          test(torch.randn(35), None, [6, 6], [5, 1], 2)
          test(torch.randn(15), None, [3, 2], [3, 6], 2)
  
          # test transpose case
          test(torch.randn(3, 4), None, [4, 3], [1, 4])
  
          # test "getting things outside the input" case
          x = torch.randn(6, 2)
          test(x[3:], None, [3, 2], [2, 1], 0)  # should be all zeros
          self.assertEqual(x[3:].as_strided([3, 2], [2, 1], 0), x[:3])
  
          # test select on expanded input case
          test(torch.randn(2, 3), lambda x: x.expand(10, 2, 3), [2, 3], [3, 1], 0)
  
      def _test_lerp_tensor_weights(self, cast):
          def construct_inputs(*shapes):
              start = cast(torch.randn(shapes[0])).requires_grad_()
              end = cast(torch.randn(shapes[1])).requires_grad_()
              weight = cast(torch.randn(shapes[2])).requires_grad_()
              return [start, end, weight]
  
          all_test_shapes = [((3, 3, 3), (3, 3, 3), (3, 3, 3)),  # no broadcasting
                             ((3,), (3, 3, 3), (3, 3, 3)),  # start broadcasting - 1
                             ((3, 3, 3), (3,), (3, 3, 3)),  # end broadcasting - 1
                             ((3, 3, 3), (3, 3, 3), (3,)),  # weight broadcasting - 1
                             ((), (3, 3, 3), (3, 3, 3)),  # start broadcasting - 2
                             ((3, 3, 3), (), (3, 3, 3)),  # end broadcasting - 2
                             ((3, 3, 3), (3, 3, 3), ()),  # weight broadcasting - 2
                             ((3, 3), (3, 3, 3), (3,))]  # all broadcasting
  
          for shapes in all_test_shapes:
              cur_inputs = construct_inputs(*shapes)
              gradcheck(torch.lerp, cur_inputs)
              gradgradcheck(torch.lerp, cur_inputs)
  
      def test_lerp_tensor_weights(self):
          self._test_lerp_tensor_weights(lambda t: t)
  
      def test_reduce_dtype(self):
          def test_reduction(op, has_no_dim):
              x = torch.randn(3, 3, dtype=torch.float, requires_grad=True)
  
              if has_no_dim:
                  grad1, = torch.autograd.grad([op(x)], [x])
                  grad2, = torch.autograd.grad([op(x, dtype=torch.double)], [x])
                  self.assertEqual(grad1, grad2)
                  self.assertEqual(grad2.dtype, torch.float)
  
              gi = torch.randn(op(x, dim=0).shape, dtype=torch.float)
              grad1, = torch.autograd.grad([op(x, dim=0)], [x], gi)
              grad2, = torch.autograd.grad([op(x, dim=0, dtype=torch.double)], [x], gi.double())
              self.assertEqual(grad1, grad2)
              self.assertEqual(grad2.dtype, torch.float)
  
          test_reduction(torch.sum, True)
          test_reduction(torch.prod, True)
          test_reduction(torch.cumsum, False)
          test_reduction(torch.cumprod, False)
  
      def test_inplace_view_backprop_base(self):
          # modify view and back-prop through base
          root = torch.randn(2, 2, requires_grad=True)
          x = root.clone()
          v1 = x.narrow(0, 0, 1)
          v1.mul_(2)
          x.sum().backward()
          self.assertEqual(root.grad.tolist(), [[2, 2], [1, 1]])
  
      def test_inplace_view_backprop_view_of_view(self):
          # modify view and backprop through view-of-view
          root = torch.randn(2, 2, requires_grad=True)
          x = root.clone()
          v1 = x.narrow(0, 0, 1)
          v2 = x.narrow(0, 0, 1)
          v1.mul_(2)
          v2.sum().backward()
          self.assertEqual(root.grad.tolist(), [[2, 2], [0, 0]])
  
      def test_inplace_view_of_view(self):
          # modify view-of-view and backprop through base
          root = torch.randn(2, 2, requires_grad=True)
          x = root.clone()
          v1 = x.narrow(0, 0, 1)
          v2 = v1.narrow(1, 1, 1)
          v2.mul_(2)
          x.sum().backward()
          self.assertEqual(root.grad.tolist(), [[1, 2], [1, 1]])
  
      def test_inplace_view_gradcheck(self):
          # gradcheck modifications to views
          a = torch.randn(4, 4, requires_grad=True)
          b = torch.randn(2, 2, requires_grad=True)
  
          def func(root, b):
              x = root.clone()
              x.narrow(1, 2, 2).narrow(0, 1, 2).mul_(b)
              x.narrow(1, 0, 2).narrow(0, 1, 2).mul_(b)
              return x
  
          gradcheck(func, [a, b], raise_exception=True)
          go = torch.randn(a.size(), requires_grad=True)
          gradgradcheck(func, (a, b), (go,))
  
      def test_inplace_view_makes_base_require_grad(self):
          # in-place modification to view makes base require grad
          a = torch.randn(4, 4, requires_grad=False)
          b = torch.randn(4, 2, requires_grad=True)
  
          def func(root, b):
              x = root.clone()
              self.assertFalse(x.requires_grad)
              x.narrow(1, 2, 2).mul_(b)
              self.assertTrue(x.requires_grad)
              return x
  
          gradcheck(func, [a, b], raise_exception=True)
          go = torch.randn(a.size(), requires_grad=True)
          gradgradcheck(func, (a, b), (go,))
  
      def test_inplace_view_backprop_view(self):
          # modify view and backprop through view
          a = Variable(torch.Tensor([2, 5]), requires_grad=False)
          b = Variable(torch.Tensor([3]), requires_grad=True)
          res = a.narrow(0, 1, 1).mul_(b)
          res.sum().backward()
          self.assertEqual(b.grad.tolist(), [5])
          self.assertIsNone(a.grad)
  
      def test_inplace_view_modify_base(self):
          # Test that an in-place operation on a base that forced it to require
          # grad also forces any previous views to require grad and backprop
          # correctly
          r = torch.ones(1, requires_grad=True)
  
          def fn(r):
              x = torch.ones(5)
              v = x.select(0, 1)
              self.assertFalse(v.requires_grad)
              self.assertIsNone(v.grad_fn)
              x.add_(r)  # v is now dependent on r due to the in-place op on x
              self.assertTrue(v.requires_grad)
              return v
  
          gradcheck(fn, [r])
          gradgradcheck(fn, [r])
  
      def test_inplace_view_python(self):
          # in-place modifications of Python-autograd created view
          a = torch.randn(4, 4, requires_grad=True)
          b = torch.randn(2, 2, requires_grad=True)
  
          class PyAdd(torch.autograd.Function):
              @staticmethod
              def forward(ctx, x, y):
                  ctx.mark_dirty(x)
                  x.add_(y)
                  return x
  
              @staticmethod
              def backward(ctx, grad):
                  return grad, grad
  
          def func(root, b):
              x = root.clone()
              PyAdd.apply(x.narrow(1, 2, 2).narrow(0, 1, 2), b)
              PyAdd.apply(x.narrow(1, 0, 2).narrow(0, 1, 2), b)
              return x
  
          gradcheck(func, [a, b], raise_exception=True)
          go = torch.randn(a.size(), requires_grad=True)
          gradgradcheck(func, (a, b), (go,))
  
      def test_inplace_view_non_contig(self):
          root = torch.ones(2, 3, 2).select(2, 1).t().requires_grad_(True)
          x = root.clone()
          v1 = x.narrow(0, 0, 1)
          v2 = v1.narrow(1, 1, 1)
          v2.mul_(2)
          x.sum().backward()
          self.assertEqual(root.grad.tolist(), [[1, 2], [1, 1], [1, 1]])
  
      def test_inplace_view_saved_output(self):
          # Test an in-place operation on a view in which the in-place op saves
          # its output. Previously, this created a reference cycle.
          dealloc = [0]
  
          class IncrementOnDelete(object):
              def __del__(self):
                  dealloc[0] += 1
  
          def test():
              root = torch.randn(3, 3, requires_grad=True)
              copy = root.clone()
              copy.grad_fn.register_hook(IncrementOnDelete())
              view = copy.view(9)
              torch.nn.functional.relu(view, inplace=True)
  
          test()
          self.assertEqual(dealloc[0], 1)
  
      def test_inplace_view_backward(self):
          # Issue #10532: Make sure that this does not raise RuntimeError.
          net = nn.Sequential(
              nn.InstanceNorm2d(2),
              nn.ReLU(True)
          )
  
          x = torch.tensor([[[[1.0, 1.0]]]], requires_grad=True)
          g, = torch.autograd.grad(net(x).pow(2), [x], grad_outputs=x.new_ones(x.shape) , create_graph=True)
          torch.autograd.grad(g.sum(), [x])
          self.assertEqual(x, torch.tensor([[[[1.0, 1.0]]]]))
  
          # https://discuss.pytorch.org/t/freeing-buffer-strange-behavior/31955/8
          inputs = torch.ones((1, 3, 256, 256), requires_grad=True)
  
          tmp1 = (inputs + 1).view_as(inputs)
          tmp2 = torch.nn.functional.threshold(tmp1, 0., 0., True)
          prob_interpolated = torch.sigmoid(tmp2)
  
          gradients = torch.autograd.grad(outputs=prob_interpolated, inputs=inputs,
                                          grad_outputs=torch.ones(prob_interpolated.size()),
                                          create_graph=True, retain_graph=True)[0]
  
          gradient_penalty = gradients.sum()
          gradient_penalty.backward()
  
          fn = gradient_penalty.grad_fn.next_functions[0][0].next_functions[1][0]
          self.assertEqual(fn.name(), "ThresholdBackwardBackward")
  
      def test_inplace_view_weak_grad_fn(self):
          # Issue 23502: Test that b's grad_fn is preserved.
          a = torch.arange(10.0, requires_grad=True)
  
          b = a.narrow(0, 0, 2).clone().view(-1)
          b.relu_()
  
          c = b.clone()
          del b
          gc.collect()
  
          s = c.sum()
          s.backward()
          self.assertEqual(s, torch.tensor(1.0))
  
          # Issue 23502: Ensure RuntimeError for modification of SavedVariable.
          a = torch.rand(10, requires_grad=True).narrow(0, 0, 10)
          b = a.relu_()
          c = b.add_(100)
          del b
          with self.assertRaises(RuntimeError):
              c.sum().backward(torch.ones(1, requires_grad=True))
  
      def test_mul_out(self):
          a = torch.randn(2, 2, requires_grad=True)
          b = torch.randn(2, 2, requires_grad=True)
          x = torch.zeros_like(a)
  
          # out=... functions don't support automatic differentiation currently
          self.assertRaisesRegex(RuntimeError, 'out=', lambda: torch.mul(a, b, out=x))
  
          # the inputs can require grad if we're in no_grad() mode
          with torch.no_grad():
              torch.mul(a, b, out=x)
              self.assertEqual(x, a * b)
  
      def test_mul_out_result_requires_grad(self):
          a = torch.randn(2, 2)
          b = torch.randn(2, 2)
          x = torch.zeros(2, 2, requires_grad=True)
          # we should throw an exception if the output requires grad
          self.assertRaisesRegex(RuntimeError, 'out=', lambda: torch.mul(a, b, out=x))
  
      def test_diagonal_derivative_requires_grad(self):
          # test that the backward requires grad
          # we do this is because diagonal_backward uses inplace
          # operations and gradgradcheck does not catch whether
          # they works as expected (it will succeed even if
          # the gradient has requires_grad == False
          a = torch.randn(5, 6, requires_grad=True)
          b = torch.diagonal(a)**2
          c = b.sum()
          d, = torch.autograd.grad(c, a, retain_graph=True, create_graph=True)
          self.assertTrue(d.requires_grad)
  
      def test_anomaly_detect_nan(self):
          size = 10
  
          class MyFunc(Function):
              @staticmethod
              def forward(ctx, inp1, inp2, fail_0th):
                  ctx.fail_0th = fail_0th
                  return inp1.sum(0, keepdim=True)
  
              @staticmethod
              def backward(ctx, gO):
                  gI = gO.clone().expand(size)
                  gI[0] = 0
                  gI[0] /= 0  # Generate a nan
                  if ctx.fail_0th:
                      return gI, None, None
                  else:
                      return None, gI, None
  
          inp = torch.rand(size, requires_grad=True)
          out = MyFunc.apply(inp, inp, True)
          out.backward()  # Should not fail
  
          inp = torch.rand(size, requires_grad=True)
          out = MyFunc.apply(inp, inp, True)
          with self.assertRaisesRegex(RuntimeError, "Function 'MyFuncBackward' returned nan values in its 0th output."):
              with warnings.catch_warnings(record=True) as w:
                  with detect_anomaly():
                      out.backward()
              self.assertIn('No forward pass information', str(w[0].message))
  
          inp = torch.rand(size, requires_grad=True)
          with self.assertRaisesRegex(RuntimeError, "Function 'MyFuncBackward' returned nan values in its 1th output."):
              with warnings.catch_warnings(record=True) as w:
                  with detect_anomaly():
                      out = MyFunc.apply(inp, inp, False)
                      out.backward()
              self.assertIn('MyFunc.apply', str(w[0].message))
  
      @skipIfNoLapack
      def test_eig_no_eigenvectors(self):
          A = torch.tensor([[1., 2.], [2., 4.]], dtype=torch.float32, requires_grad=True)
          w, v = torch.eig(A, eigenvectors=False)
          with self.assertRaisesRegex(RuntimeError, 'cannot compute backward'):
              torch.autograd.backward([w, v], [torch.ones_like(w), torch.ones_like(v)])
  
      @skipIfNoLapack
      def test_eig_complex_eigenvalues(self):
          A = torch.tensor([[0., -1.], [1., 0.]], dtype=torch.float32, requires_grad=True)
          w, v = torch.eig(A, eigenvectors=True)
          with self.assertRaisesRegex(RuntimeError, 'does not support complex eigenvalues'):
              torch.autograd.backward([w, v], [torch.ones_like(w), torch.ones_like(v)])
  
      @skipIfNoLapack
      def test_symeig_no_eigenvectors(self):
          A = torch.tensor([[1., 2.], [2., 4.]], dtype=torch.float32, requires_grad=True)
          w, v = torch.symeig(A, eigenvectors=False)
          with self.assertRaisesRegex(RuntimeError, 'cannot compute backward'):
              torch.autograd.backward([w, v], [torch.ones_like(w), torch.ones_like(v)])
  
      @skipIfNoLapack
      def test_svd_no_singularvectors(self):
          A = torch.randn(2, 2, dtype=torch.float32, requires_grad=True)
          u, s, v = torch.svd(A, compute_uv=False)
          with self.assertRaisesRegex(RuntimeError, 'cannot compute backward'):
              torch.autograd.backward([u, s, v], [torch.ones_like(u), torch.ones_like(s), torch.ones_like(v)])
  
      def test_no_grad_copy(self):
          # create autograd function that saves grad pointer as class static
          class MyFunc(Function):
              static_grad_ptr = None
  
              @staticmethod
              def forward(ctx, inp1, inp2):
                  return inp1 + inp2
  
              @staticmethod
              def backward(ctx, grad):
                  MyFunc.static_grad_ptr = grad.data_ptr()
                  return grad, grad
  
          class NonContGradFunc(Function):
              @staticmethod
              def forward(ctx, inp1):
                  ctx.size = inp1.size()
                  return torch.tensor([1.])
  
              @staticmethod
              def backward(ctx, grad):
                  return torch.ones(1).expand(ctx.size)
  
          a = torch.randn(5, 6, requires_grad=True)
          b = torch.randn(5, 6, requires_grad=True)
          # non-contiguous grad should be copied
          NonContGradFunc.apply(MyFunc.apply(a, b)).backward()
          self.assertFalse(a.grad.data_ptr() == MyFunc.static_grad_ptr)
          self.assertFalse(b.grad.data_ptr() == MyFunc.static_grad_ptr)
          # test case that should trigger no copy for one of a,b
          a.grad = b.grad = None
          MyFunc.apply(a, b)[1][0].backward()
          p_g = MyFunc.static_grad_ptr
          p_a = a.grad.data_ptr()
          p_b = b.grad.data_ptr()
          # check a,b uses different grad buffer
          self.assertFalse(p_a == p_b)
          # check one of them is using the computed buffer
          self.assertTrue(p_a == p_g or p_b == p_g)
  
      def test_no_grad_copy_sparse(self):
          # create autograd function that saves grad pointer as class static
          class MyFunc(Function):
              static_grad_ptr = None
  
              @staticmethod
              def forward(ctx, inp1, inp2):
                  return inp1 + inp2
  
              @staticmethod
              def backward(ctx, grad):
                  MyFunc.static_grad_ptr = grad._values().data_ptr()
                  return grad, grad
  
          class NonContGradFunc(Function):
              static_grad_ptr = None
  
              @staticmethod
              def forward(ctx, inp1, inp2):
                  return inp1 + inp2
  
              @staticmethod
              def backward(ctx, grad):
                  # Create a sparse tensor with non-contigous indices and values
                  # and return as grad.
                  v = torch.rand(1, 3)
                  i = torch.ones(1, 1, dtype=torch.long)
                  nv = v.expand(8, 3)
                  ni = i.expand(1, 8)
                  ngrad = torch.sparse.FloatTensor(ni, nv, torch.Size([10, 3]))
                  NonContGradFunc.static_grad_ptr = ngrad._values().data_ptr()
                  return ngrad, ngrad
  
          a = torch.randn(10, 3, requires_grad=True)
          b = torch.randn(10, 3, requires_grad=True)
          input = torch.tensor([1, 2, 4, 5, 4, 3, 2, 9])
          offsets = torch.tensor([0, 4])
          import torch.nn.functional as F
  
          # test case that should trigger no copy for one of a,b
          emb_matrix = MyFunc.apply(a, b)
          loss = F.embedding_bag(emb_matrix, input, offsets, sparse=True).sum()
          loss.backward(retain_graph=True)
          p_g = MyFunc.static_grad_ptr
          p_a = a.grad._values().data_ptr()
          p_b = b.grad._values().data_ptr()
          # check a,b uses different grad buffer
          self.assertFalse(p_a == p_b)
          # check one of them is using the computed buffer
          self.assertTrue(p_a == p_g or p_b == p_g)
  
          # Run backwards multiple times to ensure accumulation works.
          for i in range(10):
              loss.backward(retain_graph=True)
  
          # non-contiguous indices and value, we should trigger a copy.
          a.grad = b.grad = None
          emb_matrix = NonContGradFunc.apply(a, b)
          loss = F.embedding_bag(emb_matrix, input, offsets, sparse=True).sum()
          loss.backward(retain_graph=True)
          p_g = NonContGradFunc.static_grad_ptr
          p_a = a.grad._values().data_ptr()
          p_b = b.grad._values().data_ptr()
          # check a,b uses different grad buffer
          self.assertFalse(p_a == p_b)
          # Verify we cloned both grads.
          self.assertFalse(p_a == p_g)
          self.assertFalse(p_b == p_g)
  
          # Run backwards multiple times to ensure accumulation works.
          for i in range(10):
              loss.backward(retain_graph=True)
  
      def test_gradcheck_single_input(self):
          def f(inp):
              return inp.mul(5)
  
          gradcheck(f, torch.rand(10, dtype=torch.float64, requires_grad=True))
          gradgradcheck(f, torch.rand(10, dtype=torch.float64, requires_grad=True))
  
      def test_gradcheck_sparse_input(self):
          def fn(sparse):
              return torch.sparse.sum(sparse)
  
          gradcheck(fn, torch.rand(10).to_sparse().requires_grad_(True), check_sparse_nnz=True)
          with self.assertRaisesRegex(RuntimeError, 'gradcheck expects all tensor inputs are dense'):
              gradcheck(fn, torch.rand(10).to_sparse().requires_grad_(True), check_sparse_nnz=False)
  
      def test_gradcheck_nondeterministic(self):
          class NonDetFunc(Function):
              @staticmethod
              def forward(ctx, x, jitter=0.0):
                  ctx._jitter = jitter
                  return x
  
              @staticmethod
              def backward(ctx, grad_out):
                  return NonDetFunc.apply(grad_out, ctx._jitter) * (1 + torch.rand_like(grad_out) * ctx._jitter), None
  
          inp = torch.randn(5, 5, requires_grad=True)
          gradcheck(lambda x: NonDetFunc.apply(x, 0.0), inp)
          with self.assertRaisesRegex(RuntimeError, 'Backward is not reentrant'):
              gradcheck(lambda x: NonDetFunc.apply(x, 1e-6), inp)
          with self.assertRaisesRegex(RuntimeError, 'Backward is not reentrant'):
              gradgradcheck(lambda x: NonDetFunc.apply(x, 1e-12), inp)
          gradcheck(lambda x: NonDetFunc.apply(x, 0.0), inp, nondet_tol=1e-5)
          gradcheck(lambda x: NonDetFunc.apply(x, 1e-6), inp, nondet_tol=1e-5)
          gradgradcheck(lambda x: NonDetFunc.apply(x, 1e-12), inp, nondet_tol=1e-5)
  
      def test_version_counter(self):
          x = torch.randn(1, 2)
  
          # In-place op bumps version
          x_saved_version = x._version
          x.add_(1).add_(1)
          self.assertTrue(x._version > x_saved_version)
  
          # Differentiable view shares version counter
          xz = x[:]
          self.assertTrue(x._version == xz._version)
          xz.add_(1)
          self.assertTrue(x._version == xz._version)
  
          # `x.data = y` preserves version counter of `x`
          x_saved_version = x._version
          x.data = torch.randn(2, 3)
          self.assertTrue(x._version == x_saved_version)
          x.add_(1)
          self.assertTrue(x._version > x_saved_version)
          # Make sure `x` is still using the same version counter it shares with `xz`
          self.assertTrue(x._version == xz._version)
  
          # In-place op on `xz` also updates version of `x`,
          # because they share the version counter
          xz.add_(1)
          self.assertTrue(x._version == xz._version)
  
      def test_set_data_tensorimpl_type(self):
          # Dense tensor has impl of type `TensorImpl`, while sparse tensor has impl
          # of type `SparseTensorImpl`.
          x = torch.randn(1, 2)
          x_s = torch.sparse_coo_tensor(torch.zeros([1, 1]), torch.ones([1]))
          with self.assertRaisesRegex(RuntimeError, 'incompatible tensor type'):
              x.data = x_s
  
      def test_set_data_preserve_pyobj(self):
          a = torch.randn(1, 2)
          b = torch.randn(1, 2)
          b_id_saved = id(b)
          b.data = a
          self.assertTrue(b_id_saved == id(b))
  
      @unittest.skipIf(IS_WINDOWS, "Skipping because doesn't work for windows")
      def test_thread_shutdown(self):
          code = """import torch
  from torch.autograd import Function
  class MyFunction(Function):
      @staticmethod
      def forward(ctx, x):
          return x
  
      @staticmethod
      def backward(ctx, grad):
          return grad
  
  for shape in [(1,), ()]:
      v = torch.ones(shape, requires_grad=True)
      MyFunction.apply(v).backward()
  """
          s = TestCase.runWithPytorchAPIUsageStderr(code)
          self.assertRegex(s, "PYTORCH_API_USAGE torch.autograd.thread_shutdown")
  
      @unittest.skipIf(IS_MACOS, "Fails with SIGBUS on macOS; https://github.com/pytorch/pytorch/issues/25941")
      def test_deep_reentrant(self):
  
          class DeepReentrant(Function):
              @staticmethod
              def forward(ctx, x):
                  with torch.enable_grad():
                      ctx.x = Variable(x.detach(), requires_grad=True)
                      ctx.x = ctx.x - 1
                  return ctx.x.detach()
  
              @staticmethod
              def backward(ctx, x):
                  if ctx.x < 0:
                      return x
                  with torch.enable_grad():
                      DeepReentrant.apply(ctx.x).sum().backward()
                  return x
  
          # Test stack overflow escape mechanism
          v = torch.tensor(2000.0, requires_grad=True)
          # This will cause stack overflow if reentrant calls are handled
          # in the same thread recursively
          DeepReentrant.apply(v).sum().backward()
  
          # Test stack overflow escape mechanism multiple times
          # to ensure reusing workers in the pool works fine
          v2 = torch.tensor(200.0, requires_grad=True)
          DeepReentrant.apply(v2).sum().backward()
  
      def test_reentrant_priority(self):
          order = []
  
          class MyFunction(Function):
              @staticmethod
              def forward(ctx, x):
                  return x
  
              @staticmethod
              def backward(ctx, x):
                  order.append("MyFunction")
                  return x
  
          class Reentrant(Function):
              @staticmethod
              def forward(ctx, x):
                  with torch.enable_grad():
                      ctx.x = Variable(x.detach(), requires_grad=True)
                      ctx.x = ctx.x - 1
                  return ctx.x.detach()
  
              @staticmethod
              def backward(ctx, x):
                  order.append("Reentrant")
                  if ctx.x < 0:
                      return x
                  with torch.enable_grad():
                      Reentrant.apply(ctx.x).backward()
                  return x
  
          a = MyFunction.apply(torch.tensor(6.0, requires_grad=True))
          b = Reentrant.apply(torch.tensor(9.0, requires_grad=True))
          v = a * b
          v.backward()
          # The tasks for the Reentrant and MyFunction backward() will be added
          # to the queue in the autograd engine at the same time. The backward
          # for Reentrant will be executed first, which will then add other
          # backward tasks to the queue. We want to ensure all the reentrant tasks
          # are prioritized over the MyFunction backward task regardless of their
          # sequence numbers
          self.assertEqual(len(order), 11)
          self.assertEqual(order.count("Reentrant"), 10)
          self.assertEqual(order[-1], "MyFunction")
  
  
      @slowTest
      def test_checkpointing(self):
          num_inp = 2000
          nz_inp = 10
          nz_out = 10
          nz_bottleneck = 1000
  
          # small proxy network for some complex reasoning we want to do per input
          module = nn.Sequential(
              nn.Linear(nz_inp, nz_bottleneck),
              nn.ReLU(),
              nn.Linear(nz_bottleneck, nz_inp)
          )
  
          feat_combined = []
          for r in range(num_inp):
              data_r = torch.Tensor(1, nz_inp)
              data_r.uniform_()
              data_r.requires_grad = True
              feat_r = checkpoint(module, data_r)
              feat_combined.append(feat_r)
  
          # compute mean as a proxy for some joint reasoning
          mean_combined = torch.stack(feat_combined).mean()
          mean_combined.backward()
  
      def _test_reentrant_with_callbacks(self, install_callbacks_in_depths):
          counter = {}
          counter["inner"] = 0
          counter["outer"] = 0
  
          def inc_inner_counter():
              counter["inner"] += 1
  
          def inc_outer_counter():
              counter["outer"] += 1
  
          class MyFunc(Function):
              @staticmethod
              def forward(ctx, input):
                  return input
  
              @staticmethod
              @once_differentiable
              def backward(ctx, input):
                  if 1 in install_callbacks_in_depths:
                      # Add a callback to execute.
                      Variable._execution_engine.queue_callback(inc_inner_counter)
  
                  return input
  
          class MyReentrantFunc(Function):
              @staticmethod
              def forward(ctx, input):
                  return input
  
              @staticmethod
              @once_differentiable
              def backward(ctx, input):
                  if 0 in install_callbacks_in_depths:
                      # Add a callback to execute.
                      Variable._execution_engine.queue_callback(inc_outer_counter)
                  # Reentrant backward call.
                  tmp_inp = input.detach().requires_grad_()
                  with torch.enable_grad():
                      tmp_out = (MyFunc.apply(tmp_inp)).sum()
                  tmp_out.backward()
                  return input
  
          t1 = torch.rand((3, 3), requires_grad=True)
          t2 = MyReentrantFunc.apply(t1)
          t3 = t2.sum()
          torch.autograd.backward([t3])
  
          return counter
  
      def test_reentrant_with_callbacks_depth_0(self):
          # Verify callback is called only once.
          ret = self._test_reentrant_with_callbacks([0])
          self.assertEqual(1, ret["outer"])
          self.assertEqual(0, ret["inner"])
  
      def test_reentrant_with_callbacks_depth_1(self):
          # Verify callback is called only once.
          ret = self._test_reentrant_with_callbacks([1])
          self.assertEqual(0, ret["outer"])
          self.assertEqual(1, ret["inner"])
  
      def test_reentrant_with_callbacks_both_depths(self):
          # Verify callback is called twice.
          ret = self._test_reentrant_with_callbacks([0, 1])
          self.assertEqual(1, ret["outer"])
          self.assertEqual(1, ret["inner"])
  
      def test_reentrant_with_leaf_variable_hook(self):
          handle = None
          param = torch.rand(10, requires_grad=True)
  
          def add_gradient_penalty_to_grad(grad):
              handle.remove()
              old_param_grad = grad
              param.grad = None
              # Add some sort of gradient penalty by directly updating the gradients
              with torch.enable_grad():
                  g = grad.detach().requires_grad_()
                  new_param = param.detach().requires_grad_()
                  out = ((g * 2) + new_param).sum()
                  out.backward()
              res = g.grad + grad
              param.grad = old_param_grad
              return res
  
          handle = param.register_hook(add_gradient_penalty_to_grad)
          # Forward pass
          tmp = (param * param)
          loss = tmp.sum()
          # Compute the gradients
          loss.backward()
  
      def test_reentrant_with_non_leaf_variable_hook(self):
          handle = None
          param = torch.rand(10, requires_grad=True)
  
          def manual_increase_gradient(grad):
              handle.remove()
              # Add some sort of gradient penalty by directly updating the gradients
              with torch.enable_grad():
                  g = grad.detach().requires_grad_()
                  out = ((g * 2) + 5).sum()
                  out.backward()
              res = g.grad + grad
              return res
  
          # Forward pass
          tmp = (param * param)
          handle = tmp.register_hook(manual_increase_gradient)
          loss = tmp.sum()
          # Compute the gradients
          loss.backward()
          self.assertEqual(param.grad, 6 * param)
  
      def test_autograd_views_codegen(self):
          # This is not necessarily the absolute correct behavior, but this is the current
          # one. This test is here to make sure that any change to this behavior is detected
          # and not silent. The TODOs below mark the places with unexpected behavior.
          # Note that any change in these test will be BC-breaking and should be done carefully.
  
          # This test checks the behavior of two codegen functions (view_as and unbind)
          # with respect to view tracking and inplace operation on the output.
  
          def run_test(grad_mode, requires_grad, is_view, should_raise_tuple):
              def maybe_check_raise(fn, should_raise):
                  self.assertTrue(should_raise is None or isinstance(should_raise, str))
                  if should_raise is not None:
                      with self.assertRaisesRegex(RuntimeError, should_raise):
                          fn()
                  else:
                      fn()
  
              inp = torch.rand(2, requires_grad=requires_grad).clone()
              with torch.set_grad_enabled(grad_mode):
                  out = inp.view_as(inp)
              # Are they differentiable views?
              self.assertTrue(out._is_view() == is_view)
              # Are inplace allowed?
              maybe_check_raise(lambda: out.add_(1), should_raise_tuple[0])
  
              inp = torch.rand(2, requires_grad=requires_grad).clone()
              with torch.set_grad_enabled(grad_mode):
                  out = inp.unbind()
              # Are they differentiable views?
              self.assertTrue(out[0]._is_view() == is_view)
              self.assertTrue(out[1]._is_view() == is_view)
              # Are inplace allowed?
              maybe_check_raise(lambda: out[0].add_(1), should_raise_tuple[1])
              maybe_check_raise(lambda: out[1].add_(1), should_raise_tuple[2])
  
          # should_raise contains None if it should not raise
          # should_raise contains a string of the error if it should raise
          # The 3 elements are for view_as, first output of unbind and second output of unbind
          run_test(grad_mode=True, requires_grad=False, is_view=True,
                   should_raise_tuple=(None, None, None))
          inp_change_err = "Output {} of UnbindBackward is a view and is being modified inplace."
          run_test(grad_mode=True, requires_grad=True, is_view=True,
                   should_raise_tuple=(None, inp_change_err.format("0"), inp_change_err.format("1")))
          leaf_grad_err = "A view was created in no_grad mode and is being modified inplace"
          run_test(grad_mode=False, requires_grad=True, is_view=True,
                   should_raise_tuple=(leaf_grad_err, leaf_grad_err, leaf_grad_err))
          run_test(grad_mode=False, requires_grad=False, is_view=True,
                   should_raise_tuple=(None, None, None))
  
      def test_autograd_simple_views_python(self):
          # This is not necessarily the absolute correct behavior, but this is the current
          # one. This test is here to make sure that any change to this behavior is detected
          # and not silent. The TODOs below mark the places with unexpected behavior.
          # Note that any change in these test will be BC-breaking and should be done carefully.
  
          # This checks the autograd.Function behavior when we return one or multiple outputs
          # while one of these is an input, a view of an input or of a temporary tensor.
  
          # This indicator is used to track how many times the backward function was called
          bw_called = [0]
          # This indicator is used to check if the argument `ga` contains non-zero values
          ga_nz = [False]
  
          class IdOneOutput(Function):
              @staticmethod
              def forward(ctx, a, b, make_view):
                  if make_view:
                      a = a.narrow(0, 0, 2)
                  else:
                      a = a.clone()
                  return a
  
              @staticmethod
              def backward(ctx, ga):
                  bw_called[0] += 1
                  return ga, None, None
  
          class IdTwoOutput(Function):
              @staticmethod
              def forward(ctx, a, b, make_view):
                  if make_view:
                      a = a.narrow(0, 0, 2)
                  else:
                      a = a.clone()
                  return a, a + b
  
              @staticmethod
              def backward(ctx, ga, gab):
                  bw_called[0] += 1
                  if ga.eq(0).all():
                      ga_nz[0] = False
                  else:
                      ga_nz[0] = True
                  return ga + gab, gab, None
  
          err_msg_two_outputs = "Output 0 of IdTwoOutputBackward is a view and is being modified inplace."
          err_msg_two_outputs += " This view is the output of a function that returns multiple views."
  
          class ViewOfTemp(Function):
              @staticmethod
              def forward(ctx, a, make_view):
                  ctx.save_for_backward(a)
                  if make_view:
                      a = a.narrow(0, 0, 2)
                  else:
                      a = a.clone()
                  b = a.clone()
                  return b.select(0, 0)
  
              @staticmethod
              def backward(ctx, grad):
                  bw_called[0] += 1
                  a, = ctx.saved_tensors
                  res = torch.zeros_like(a)
                  res.select(0, 0).copy_(grad)
                  return res, None
  
          for fn_id in ["one_output", "two_output", "view_of_temp"]:
              for inplace in [True, False]:
                  for make_view in [True, False]:
                      # Used for special casing the tests below
                      output_is_a_view = (make_view or fn_id == "view_of_temp")
  
                      def fn(a, b):
                          # never modify a, b inplace for gracheck
                          a = a.clone()
                          b = b.clone()
                          if fn_id == "two_output":
                              tmp1, tmp2 = IdTwoOutput.apply(a, b, make_view)
                              if inplace:
                                  tmp1 += 3
                                  tmp2 += 3
                              else:
                                  tmp1 = tmp1 + 3
                                  tmp2 = tmp2 + 3
                              tmp = tmp1 * tmp2
                          else:
                              if fn_id == "one_output":
                                  tmp = IdOneOutput.apply(a, b, make_view)
                              else:
                                  tmp = ViewOfTemp.apply(a + b, make_view)
                              if inplace:
                                  tmp += 3
                              else:
                                  tmp = tmp + 3
  
                          return tmp.sum()
  
                      a = torch.ones(2, requires_grad=True)
                      b = torch.ones(2, requires_grad=True)
  
  
                      if fn_id == "two_output" and inplace and output_is_a_view:
                          with self.assertRaisesRegex(RuntimeError, err_msg_two_outputs):
                              fn(a, b)
                      else:
                          # Are the computed gradients correct ?
                          if inplace and output_is_a_view:
                              with warnings.catch_warnings(record=True) as w:
                                  if fn_id == "view_of_temp":
                                      # This will be fixed after the deprecation cycle and the warning becomes
                                      # an error.
                                      with self.assertRaisesRegex(RuntimeError, "Jacobian mismatch for output 0"):
                                          gradcheck(fn, (a, b))
                                  else:
                                      # This works but the custom backward is not called (or called with partial)
                                      # gradients as tested below
                                      gradcheck(fn, (a, b))
                              self.assertTrue(len(w) > 0)
                          else:
                              gradcheck(fn, (a, b))
  
                          # Was the custom backward called properly
                          bw_called[0] = 0
                          ga_nz[0] = True  # For the case where the backward is called
                          with warnings.catch_warnings(record=True) as w:
                              fn(a, b).backward()
  
                          expected_called = 1
                          expected_ga_nz = True
                          expected_warning = False
  
                          if output_is_a_view and inplace:
                              expected_called = 0
                              expected_warning = True
  
                          self.assertTrue(bw_called[0] == expected_called)
                          self.assertTrue(ga_nz[0] == expected_ga_nz)
                          self.assertTrue((len(w) == 1) == expected_warning)
  
      def test_autograd_complex_views_python(self):
          # This is not necessarily the absolute correct behavior, but this is the current
          # one. This test is here to make sure that any change to this behavior is detected
          # and not silent. The TODOs below mark the places with unexpected behavior.
          # Note that any change in these test will be BC-breaking and should be done carefully.
  
          # This checks that multiples views in the forward are properly traced and how they
          # behave with respect to inplace operations.
  
          # This indicator is used to track how many times the backward function was called
          bw_called = [0]
  
          class ComplexView(Function):
              @staticmethod
              def forward(ctx, a, idx):
                  res = a.narrow(0, idx, 1)
                  res = a.select(0, idx)
                  ctx.save_for_backward(a)
                  ctx.idx = idx
                  return res
  
              @staticmethod
              def backward(ctx, grad):
                  bw_called[0] += 1
                  a, = ctx.saved_tensors
                  res = torch.zeros_like(a)
                  res.select(0, ctx.idx).copy_(grad)
                  return res, None
  
          a = torch.ones(2, requires_grad=True)
          idx = 1
  
          bw_called[0] = 0
          out = ComplexView.apply(a.clone(), idx)
          out.sum().backward()
          self.assertTrue(bw_called[0] == 1)
  
          out = ComplexView.apply(a.clone(), idx)
          with warnings.catch_warnings(record=True) as w:
              out += 1
          self.assertEqual(len(w), 1)
  
      def test_autograd_inplace_views_python(self):
          # This is not necessarily the absolute correct behavior, but this is the current
          # one. This test is here to make sure that any change to this behavior is detected
          # and not silent. The TODOs below mark the places with unexpected behavior.
          # Note that any change in these test will be BC-breaking and should be done carefully.
  
          # This test checks custom autograd.Function that perform inplace operations
  
          bw_called = [0]
  
          # I) Single output
          class MyAdder(Function):
              @staticmethod
              def forward(ctx, a, b):
                  a.add_(b)
                  ctx.mark_dirty(a)
                  return a
  
              @staticmethod
              def backward(ctx, grad):
                  bw_called[0] += 1
                  return grad, grad
  
  
          a = torch.ones(2, requires_grad=True)
          b = torch.ones(2, requires_grad=True)
  
          # No extra inplace
          c = MyAdder.apply(a.clone(), b)
          c.sum().backward()
          self.assertTrue(bw_called[0] == 1)
  
          # With extra inplace on the output
          bw_called[0] = 0
          c = MyAdder.apply(a.clone(), b)
          c += 2
          c.sum().backward()
          self.assertTrue(bw_called[0] == 1)
  
          # The input is a view
          bw_called[0] = 0
          c = MyAdder.apply(a.clone().view_as(a), b)
          c.sum().backward()
          self.assertTrue(bw_called[0] == 1)
  
          # Should not give non-inputs to mark_dirty
          class MyAdderBad(Function):
              @staticmethod
              def forward(ctx, a, b):
                  c = 3 * a
                  c.add_(b)
                  ctx.mark_dirty(c)
                  return c
  
              @staticmethod
              def backward(ctx, grad):
                  bw_called[0] += 1
                  grad = 3 * grad
                  return grad, grad
  
          a = torch.ones(2, requires_grad=True)
          b = torch.ones(2, requires_grad=True)
  
          with warnings.catch_warnings(record=True) as w:
              MyAdderBad.apply(a.clone(), b)
          self.assertEqual(len(w), 1)
  
          # II) Multiple outputs
          class MyBadAdder(Function):
              @staticmethod
              def forward(ctx, a, b):
                  a.add_(b)
                  ctx.mark_dirty(a)
                  return a, a + b
  
              @staticmethod
              def backward(ctx, ga, gab):
                  bw_called[0] += 1
                  return ga + gab, ga + gab
  
          # No extra inplace
          bw_called[0] = 0
          c, d = MyBadAdder.apply(a.clone(), b)
          (c * d).sum().backward()
          self.assertTrue(bw_called[0] == 1)
  
          # With extra inplace on the output
          bw_called[0] = 0
          c, d = MyBadAdder.apply(a.clone(), b)
          c += 2
          (c * d).sum().backward()
          self.assertTrue(bw_called[0] == 1)
  
          # The input is a view
          inplace_on_view_err = "your Function modifies inplace an input that is a view of another Tensor"
          with self.assertRaisesRegex(RuntimeError, inplace_on_view_err):
              c, d = MyBadAdder.apply(a.clone().view_as(a), b)
  
          # III) Inplace + other op
          class MyOutPlaceAdder(Function):
              @staticmethod
              def forward(ctx, a, b):
                  a.add_(b)
                  ctx.mark_dirty(a)
                  return a.clone(), a + b
  
              @staticmethod
              def backward(ctx, ga, gab):
                  bw_called[0] += 1
                  return ga + gab, ga + 2 * gab
  
          # We don't reuse the input
          def fn(a, b):
              orig_a = a.clone().view_as(a)
              c, d = MyOutPlaceAdder.apply(orig_a, b)
              return (c * d).sum()
  
          bad_mark_dirty_err = "Some elements marked as dirty during the forward method were not returned as output."
          with self.assertRaisesRegex(RuntimeError, bad_mark_dirty_err):
              fn(a, b)
  
      def test_custom_function_return_view_in_nograd(self):
          class Alias(Function):
              @staticmethod
              def forward(ctx, x):
                  return x[:]
  
              @staticmethod
              def backward(ctx, gx):
                  return gx
  
          inp = torch.rand(2, requires_grad=True)
  
          with torch.no_grad():
              output = Alias.apply(inp)
  
          with torch.no_grad():
              expected_output = inp[:]
  
          # Calling the custom function should operate as if we called an equivalent op
          self.assertEqual(output.requires_grad, expected_output.requires_grad)
  
          # Check that in-place modification on view throws
          leaf_grad_err = "A view was created in no_grad mode and is being modified inplace"
          with self.assertRaisesRegex(RuntimeError, leaf_grad_err):
              output.zero_()
  
      def test_grad_mode_restored_reentrant(self):
          class MyFunction(Function):
              @staticmethod
              def forward(ctx, inp):
                  return inp.clone()
  
              @staticmethod
              def backward(ctx, go):
                  original = torch._C.is_grad_enabled()
                  with torch.enable_grad():
                      self.assertTrue(torch._C.is_grad_enabled())
                      foo = torch.rand(go.size(), requires_grad=True)
                      grad, = torch.autograd.grad(
                          foo ** 3, foo, grad_outputs=go
                      )
                      self.assertTrue(torch._C.is_grad_enabled())
                  self.assertTrue(torch._C.is_grad_enabled() == original)
                  return grad
  
          inp = torch.rand(3, requires_grad=True)
  
          # Case where original==False
          MyFunction.apply(inp).sum().backward()
          # Case where original==True
          MyFunction.apply(inp).sum().backward(create_graph=True)
  
      def test_power_function(self):
          a = torch.tensor([0., 0., 0.])
          b = torch.tensor([-1., 0., 1.], requires_grad=True)
          c = torch.sum(a**b)
          c.backward()
          self.assertEqual(b.grad, torch.tensor([-inf, 0., 0.]), allow_inf=True)
  
          s = 0
          b = torch.tensor([-1., 0., 1.], requires_grad=True)
          c = torch.sum(s**b)
          c.backward()
          self.assertEqual(b.grad, torch.tensor([-inf, 0., 0.]), allow_inf=True)
  
      def test_custom_function_error(self):
          class BadFw(Function):
              @staticmethod
              def backward(ctx, foo):
                  return foo
  
          class BadBw(Function):
              @staticmethod
              def forward(ctx, foo):
                  return foo.clone()
  
          inp = torch.rand(1, requires_grad=True)
          with self.assertRaisesRegex(NotImplementedError, "must implement the forward"):
              BadFw.apply(inp)
  
          with self.assertRaisesRegex(RuntimeError, "must implement the backward"):
              BadBw.apply(inp).sum().backward()
  
      def test_leaky_relu_inplace_with_neg_slope(self):
          for device in torch.testing.get_all_device_types():
              a = torch.tensor([-1., 1.], device=device, requires_grad=True)
              b = torch.nn.functional.leaky_relu_(a.clone(), -2)
              with self.assertRaisesRegex(RuntimeError, "call out-of-place version"):
                  b.backward(torch.ones(2, device=device))
  
              a = torch.tensor([-1., 1.], device=device, requires_grad=True)
              b = torch.nn.functional.rrelu_(a.clone(), -5.0, 1.0)
              with self.assertRaisesRegex(RuntimeError, "call out-of-place version"):
                  b.backward(torch.ones(2, device=device))
  
      def test_custom_function_local_inplace(self):
          class MyFn(torch.autograd.Function):
              @staticmethod
              def forward(ctx, inp, inplace):
                  view = inp.clone()[:3]
                  if inplace:
                      view += 2
                  return view
  
              @staticmethod
              def backward(ctx, grad):
                  return grad, None
  
          base = torch.rand(10, requires_grad=True)
  
          foo = MyFn.apply(base, False)
          self.assertEqual(foo.grad_fn.__class__.__name__, "MyFnBackward")
  
          foo = MyFn.apply(base, True)
          self.assertEqual(foo.grad_fn.__class__.__name__, "MyFnBackward")
  
  
  def index_variable(shape, max_indices):
      if not isinstance(shape, tuple):
          shape = (shape,)
      index = torch.rand(*shape).mul_(max_indices).floor_().long()
      return index
  
  
  def index_perm_variable(shape, max_indices):
      if not isinstance(shape, tuple):
          shape = (shape,)
  
      index = torch.randperm(max_indices).narrow(0, 0, reduce(mul, shape)).view(shape)
      return index
  
  
  def gather_variable(shape, index_dim, max_indices, duplicate=False):
      assert len(shape) == 2
      assert index_dim < 2
      batch_dim = 1 - index_dim
      index = torch.LongTensor(*shape)
      for i in range(shape[index_dim]):
          index.select(index_dim, i).copy_(
              torch.randperm(max_indices)[:shape[batch_dim]])
      if duplicate:
          index.select(batch_dim, 0).copy_(index.select(batch_dim, 1))
      return index
  
  
  def bernoulli_scalar():
      return torch.tensor(0, dtype=torch.uint8).bernoulli_()
  
  
  def gradgradcheck_method_precision_override(test_name):
      # these are just empirical observations, we should improve
      gradgradcheck_precision_override = {
          'test_norm': {'atol': 2e-2, 'rtol': 1e-2},
          'test_norm_1_5': {'atol': 1.5e-2, 'rtol': 1e-2},
          'test_norm_3': {'atol': 5e-2, 'rtol': 1e-2},
          'test_dist': {'atol': 5e-2, 'rtol': 1e-2},
          'test_dist_4': {'atol': 8e-2, 'rtol': 1e-2},
      }
      non_broadcasted_test_name = test_name.split("_broadcast")[0]
      override = gradgradcheck_precision_override.get(non_broadcasted_test_name)
      if override:
          if 'broadcast_lhs' in test_name or 'broadcast_rhs' in test_name:
              # errors accumulated across 1 dimension
              override = {'atol': override['atol'] * S, 'rtol': override['atol'] * S}
          elif 'broadcast_all' in test_name:
              # errors accumulated across multiple dimensions
              override = {'atol': override['atol'] * S * S, 'rtol': override['atol'] * S * S}
      return override
  
  def run_grad_and_gradgrad_checks(test_case, name, test_name, apply_method, output_variable,
                                   input_variables, run_gradgradcheck=True):
      test_case.assertTrue(gradcheck(apply_method, input_variables, eps=1e-6, atol=PRECISION))
      if name in EXCLUDE_GRADGRADCHECK or test_name in EXCLUDE_GRADGRADCHECK_BY_TEST_NAME:
          return
      gradgradcheck_precision_override = gradgradcheck_method_precision_override(test_name)
      if gradgradcheck_precision_override is not None:
          atol = gradgradcheck_precision_override['atol']
          rtol = gradgradcheck_precision_override['rtol']
          test_case.assertTrue(gradgradcheck(apply_method, input_variables, None, atol=atol, rtol=rtol,
                                             gen_non_contig_grad_outputs=True))
      else:
          test_case.assertTrue(gradgradcheck(apply_method, input_variables, gen_non_contig_grad_outputs=True))
  
  
  def run_functional_checks(test_case, test_name, name, apply_fn, run_grad_checks,
                            f_args_variable, f_args_tensor):
      output_variable = apply_fn(*f_args_variable)
  
      if run_grad_checks:
          run_grad_and_gradgrad_checks(test_case, name, test_name, apply_fn,
                                       output_variable, f_args_variable)
  
      self_variable = f_args_variable[0]
      if isinstance(output_variable, torch.Tensor) and output_variable.requires_grad and self_variable is not None:
          output_variable.backward(randn_like(output_variable))
          test_case.assertEqual(self_variable.type(), self_variable.grad.type())
          test_case.assertEqual(self_variable.size(), self_variable.grad.size())
  
  
  def add_test(
          name,
          self_size,
          args,
          variant_name='',
          check_ad=(),  # only used in test_jit
          dim_args_idx=(),
          skipTestIf=(),
          output_process_fn=lambda x: x,
          kwargs=None):
      kwargs = kwargs if kwargs else {}
      basic_test_name = 'test_' + name
      if variant_name != '':
          basic_test_name += '_' + variant_name
  
      for dim_perm in product([-1, 1], repeat=len(dim_args_idx)):
          test_name = basic_test_name
          new_args = [arg * dim_perm[dim_args_idx.index(i)] if i in dim_args_idx else arg for i, arg in enumerate(args)]
          test_name = basic_test_name + ''.join('_neg' + str(i) for i, idx in enumerate(dim_perm) if idx < 0)
          new_args = tuple(new_args)
  
          # for-loop bodies don't define scopes, so we have to save the variables
          # we want to close over in some way
          def do_test(self, device, name=name, self_size=self_size, args=new_args, test_name=test_name,
                      output_process_fn=output_process_fn):
              def check(name):
                  is_magic_method = name[:2] == '__' and name[-2:] == '__'
                  is_inplace = name[-1] == "_" and not is_magic_method
                  self_variable = create_input((self_size,), device=device)[0][0]
                  # FixMe: run grad checks on inplace self
                  if is_inplace:
                      self_variable.requires_grad = False
                  # need to record this because methods can change the size (e.g. unsqueeze)
                  args_variable, kwargs_variable = create_input(args, requires_grad=not is_inplace, call_kwargs=kwargs, device=device)
                  self_tensor = deepcopy(self_variable)
                  args_tensor = deepcopy(unpack_variables(args_variable))
                  if not exclude_tensor_method(name, test_name):
                      output_variable = getattr(self_variable, name)(*args_variable, **kwargs_variable)
                      output_tensor = getattr(self_tensor, name)(*args_tensor, **kwargs_variable)
                      if not isinstance(output_tensor, torch.Tensor) and not istuple(output_tensor):
                          # TODO: I'm not sure why we insert an outer dimension
                          # here, seems a bit strange
                          output_tensor = torch.tensor((output_tensor, ), dtype=torch.float, device=device)
                      self.assertEqual(unpack_variables(output_variable), output_tensor)
                      # TODO: check that both have changed after adding all inplace ops
  
                      def fn(*inputs):
                          output = getattr(inputs[0], name)(*inputs[1:], **kwargs)
                          return output_process_fn(output)
  
                      if not is_inplace and name not in EXCLUDE_GRADCHECK:
                          run_grad_and_gradgrad_checks(self, name, test_name, fn,
                                                       output_variable, (self_variable,) + args_variable)
  
                  # functional interface tests
                  if hasattr(torch, name) and name not in EXCLUDE_FUNCTIONAL:
                      def fn(*inputs):
                          output = getattr(torch, name)(*inputs, **kwargs)
                          return output_process_fn(output)
  
                      f_args_variable = (self_variable,) + args_variable
                      f_args_tensor = (self_tensor,) + args_tensor
                      # could run the gradchecks again, but skip since we did it for the methods above.
                      run_gradcheck = exclude_tensor_method(name, test_name) and not is_inplace and name not in EXCLUDE_GRADCHECK
                      run_functional_checks(self, test_name, name, fn,
                                            run_gradcheck, f_args_variable, f_args_tensor)
  
                  # check for correct type of input and input.grad
                  if not is_inplace:
                      self_variable = create_input((self_size,), requires_grad=True)[0][0]
                      args_variable, kwargs_variable = create_input(args, requires_grad=False, call_kwargs=kwargs)
                      if hasattr(self_variable, name):
                          output_variable = getattr(self_variable, name)(*args_variable, **kwargs_variable)
                      else:
                          self_and_args_variable = (self_variable,) + args_variable
                          output_variable = getattr(torch, name)(*self_and_args_variable, **kwargs_variable)
                      if isinstance(output_variable, torch.autograd.Variable):
                          if output_variable.is_sparse:
                              rand = randn_like(output_variable.to_dense()).to_sparse()
                          else:
                              rand = randn_like(output_variable)
                          output_variable.backward(rand)
                          self.assertTrue(type(self_variable) == type(self_variable.grad))
                          self.assertTrue(self_variable.size() == self_variable.grad.size())
  
                      # compare grads to inplace grads
                      inplace_name = name + '_'
                      # can't broadcast inplace to left hand side
                      skip_inplace = ('broadcast_lhs' in test_name or
                                      'broadcast_all' in test_name)
                      if hasattr(torch.ones(1), inplace_name) and not skip_inplace:
                          output_variable = getattr(self_variable, name)(*args_variable, **kwargs_variable)
                          if not isinstance(output_variable, tuple):
                              output_variable = (output_variable,)
                          inplace_self_variable = deepcopy(self_variable)
                          inplace_self_variable_copy = tuple(i.clone() if isinstance(i, torch.Tensor) else i
                                                             for i in (inplace_self_variable,))
                          inplace_args_variable = deepcopy(args_variable)
                          inplace_args_variable_copy = tuple(i.clone() if isinstance(i, torch.Tensor) else i
                                                             for i in inplace_args_variable)
  
                          inplace_output_variable = (
                              getattr(inplace_self_variable_copy[0], inplace_name)(*inplace_args_variable_copy,
                                                                                   **kwargs_variable))
                          if not isinstance(inplace_output_variable, tuple):
                              inplace_output_variable = (inplace_output_variable,)
                          self.assertEqual(inplace_output_variable, output_variable)
                          # Check that gradient is the same
                          for inp_i, i in zip((inplace_self_variable,) + inplace_args_variable,
                                              (self_variable,) + args_variable):
                              if not isinstance(inp_i, torch.Tensor):
                                  assert not isinstance(i, torch.Tensor)
                                  continue
                              if inp_i.grad is not None:
                                  with torch.no_grad():
                                      inp_i.grad.zero_()
                              if i.grad is not None:
                                  with torch.no_grad():
                                      i.grad.zero_()
                          for io, o in zip(inplace_output_variable, output_variable):
                              grad = randn_like(io).double()
                              io.backward(grad)
                              o.backward(grad)
                          for inp_i, i in zip((inplace_self_variable,) + inplace_args_variable,
                                              (self_variable,) + args_variable):
                              if not isinstance(inp_i, torch.Tensor):
                                  continue
                              self.assertEqual(inp_i.grad, i.grad)
  
              check(name)
              inplace_name = name + '_'
              # can't broadcast inplace to left hand side
              broadcast_skip_inplace = 'broadcast_lhs' in test_name or 'broadcast_all' in test_name
              if hasattr(torch.ones(1), inplace_name) and not broadcast_skip_inplace:
                  check(inplace_name)
  
          assert not hasattr(TestAutograd, test_name), 'Two tests have the same name: ' + test_name
  
          for skip in skipTestIf:
              do_test = skip(do_test)
  
          setattr(TestAutogradDeviceType, test_name, do_test)
  
  
  class TestAutogradFunctional(TestCase):
      def _assert_same_struct(self, res, base):
          # base and res should be Tensors or tuple of Tensors with the same size
          if torch.is_tensor(base):
              self.assertTrue(torch.is_tensor(res))
              self.assertEqual(base.size(), res.size())
          elif isinstance(base, tuple):
              self.assertTrue(isinstance(res, tuple))
              self.assertEqual(len(base), len(res))
              for el_base, el_res in zip(base, res):
                  self.assertTrue(torch.is_tensor(el_base))
                  self.assertTrue(torch.is_tensor(el_res))
                  self.assertEqual(el_base.size(), el_res.size())
          else:
              # Wrong base
              raise RuntimeError("The base given to `_assert_same_struct` doesn't have"
                                 " the right structure.")
  
      def _assert_interleaved_struct(self, res, base1, base2):
          # base1 and base2 can be Tensors or tuples of Tensors.
          # If they are tuples, res should be a tuple as well.
          # The indexing works as follow for base1, base2 being
          # - tuple, tuple: res[i][j][k][l] = (base1[i][k], base2[j][l])
          # - tuple, Tensor: res[i][k][l] = (base1[i][k], base2[l])
          # - Tensor, tuple: res[i][j][l] = (base1[i], base2[j][l])
          # - Tensor, Tensor: res[k][l] = (base1[k], base2[l])
          if torch.is_tensor(base1) and torch.is_tensor(base2):
              self.assertTrue(torch.is_tensor(res))
              self.assertEqual(res.size(), base1.size() + base2.size())
          elif isinstance(base1, tuple) and torch.is_tensor(base2):
              self.assertTrue(isinstance(res, tuple))
              self.assertEqual(len(res), len(base1))
              for el_res, el_base1 in zip(res, base1):
                  self.assertTrue(torch.is_tensor(el_res))
                  self.assertTrue(torch.is_tensor(el_base1))
                  self.assertEqual(el_res.size(), el_base1.size() + base2.size())
          elif torch.is_tensor(base1) and isinstance(base2, tuple):
              self.assertTrue(isinstance(res, tuple))
              self.assertEqual(len(res), len(base2))
              for el_res, el_base2 in zip(res, base2):
                  self.assertTrue(torch.is_tensor(el_res))
                  self.assertTrue(torch.is_tensor(el_base2))
                  self.assertEqual(el_res.size(), base1.size() + el_base2.size())
          elif isinstance(base1, tuple) and isinstance(base2, tuple):
              self.assertTrue(isinstance(res, tuple))
              self.assertEqual(len(res), len(base1))
              for el_res, el_base1 in zip(res, base1):
                  self.assertTrue(isinstance(el_res, tuple))
                  self.assertEqual(len(res), len(base2))
                  for el_el_res, el_base2 in zip(el_res, base2):
                      self.assertTrue(torch.is_tensor(el_el_res))
                      self.assertTrue(torch.is_tensor(el_base2))
                      self.assertEqual(el_el_res.size(), el_base1.size() + el_base2.size())
          else:
              # Wrong bases
              raise RuntimeError("The bases given to `_assert_interleaved_struct` don't have"
                                 " the right structure.")
  
      def test_vjp_err_check(self):
          def foo(a):
              return 3 * a.narrow(0, 0, 3)
  
          def bar(a):
              return 3 * a.narrow(0, 0, 3), "bar"
  
          inp = torch.rand(4)
          v = torch.ones(3)
          with self.assertRaisesRegex(TypeError, "The inputs given to vjp must be either a Tensor"):
              res = autogradF.vjp(foo, (inp, 2), v)
  
          with self.assertRaisesRegex(TypeError, "The outputs of the user-provided function given to vjp must"):
              res = autogradF.vjp(bar, inp, v)
  
          with self.assertRaisesRegex(RuntimeError, "The vector v can only be None if the user-provided function returns"):
              res = autogradF.vjp(foo, inp)
  
          with self.assertRaisesRegex(RuntimeError, "The given v should contain a single Tensor."):
              res = autogradF.vjp(foo, inp, (torch.ones_like(inp), torch.ones_like(inp)))
  
          with self.assertRaisesRegex(RuntimeError, "v has invalid size: should be torch.Size"):
              res = autogradF.vjp(foo, inp, v[:2])
  
          res = autogradF.vjp(foo, inp, v)[1]
          self._assert_same_struct(res, inp)
  
      def test_vjp_err_check_strict(self):
          def foo(a):
              return a.detach()
  
          def bar(a):
              # Make a non-leaf Tensor that requires_grad but that is not connected to the input
              return a.long().float().requires_grad_().clone()
  
          inp = torch.rand(4)
          v = torch.rand(4)
          with self.assertRaisesRegex(RuntimeError, "Output 0 of the user-provided function does not require gradients."):
              res = autogradF.vjp(foo, inp, v, strict=True)
          res = autogradF.vjp(foo, inp, v, strict=False)
          self._assert_same_struct(res[1], inp)
          self.assertEqual(res[1].abs().sum(), 0.)
  
          with self.assertRaisesRegex(RuntimeError, "The output of the user-provided function is independent of input 0"):
              res = autogradF.vjp(bar, inp, v, strict=True)
          res = autogradF.vjp(bar, inp, v, strict=False)
          self._assert_same_struct(res[1], inp)
          self.assertEqual(res[1].abs().sum(), 0.)
  
          # The Jacobian does not depend on the input
          def foo(a):
              return a.clone()
  
          inp.requires_grad_()
          with self.assertRaisesRegex(RuntimeError, "jacobian of the user-provided function is independent of input 0."):
              res = autogradF.vjp(foo, inp, v, create_graph=True, strict=True)
          res = autogradF.vjp(foo, inp, v, create_graph=True, strict=False)
          self._assert_same_struct(res[1], inp)
          self.assertEqual(res[1], v)
  
      def test_vjp_output(self):
          def reducer(x):
              return x.sum(dim=1)
          inputs = torch.rand(4, 4)
          v = torch.ones(4)
          res = autogradF.vjp(reducer, inputs, v)
          self._assert_same_struct(res[1], inputs)
          self.assertIsNone(res[0].grad_fn)
          self.assertIsNone(res[1].grad_fn)
  
          def adder(x, y):
              return 2 * x + 3 * y
  
          inputs = (torch.rand(2), torch.rand(2))
          v = torch.ones(2)
          out, vjp_val = autogradF.vjp(adder, inputs, v)
          self._assert_same_struct(vjp_val, inputs)
          self.assertIsNone(out.grad_fn)
          self.assertIsNone(vjp_val[0].grad_fn)
          self.assertIsNone(vjp_val[1].grad_fn)
  
          def adder(x, y):
              return 2 * x + 3 * y, x + y
  
          inputs = (torch.rand(2), torch.rand(2))
          v = (torch.tensor([1., 0.]), torch.tensor([1., 0.]))
          out, vjp_val = autogradF.vjp(adder, inputs, v)
          self._assert_same_struct(vjp_val, inputs)
          self.assertIsNone(out[0].grad_fn)
          self.assertIsNone(out[1].grad_fn)
          self.assertIsNone(vjp_val[0].grad_fn)
          self.assertIsNone(vjp_val[1].grad_fn)
  
      def test_vjp_scalar(self):
          def reducer(x):
              return x.sum()
          inputs = torch.rand(4, 4)
          v = torch.ones([])
          res = autogradF.vjp(reducer, inputs, v)
          self._assert_same_struct(res[0], v)
          self._assert_same_struct(res[1], inputs)
  
          res = autogradF.vjp(reducer, inputs)
          self._assert_same_struct(res[0], v)
          self._assert_same_struct(res[1], inputs)
  
          def expander(x):
              return x.unsqueeze(0).repeat(4)
          inputs = torch.rand([])
          v = torch.ones(4)
          res = autogradF.vjp(expander, inputs, v)
          self._assert_same_struct(res[0], v)
          self._assert_same_struct(res[1], inputs)
  
      def test_vjp_create_graph(self):
          def reducer(x):
              return x.sum(dim=1)
          inputs = torch.rand(2, 2)
          v = torch.ones(2)
  
          inputs.requires_grad_()
          v.requires_grad_()
          res = autogradF.vjp(reducer, inputs, v, create_graph=True)
          self._assert_same_struct(res[1], inputs)
          self.assertIsNotNone(res[0].grad_fn)
          self.assertIsNotNone(res[1].grad_fn)
  
          gradcheck(lambda inp, v: autogradF.vjp(reducer, inputs, v, create_graph=True), (inputs, v))
          gradgradcheck(lambda inp, v: autogradF.vjp(reducer, inputs, v, create_graph=True), (inputs, v))
  
          def adder(x, y):
              return 2 * x + 3 * y, x * y
  
          inputs = (torch.rand(2, requires_grad=True), torch.rand(2, requires_grad=True))
          v = (torch.tensor([1., 0.], requires_grad=True), torch.tensor([1., 0.], requires_grad=True))
  
          gradcheck(lambda *args: autogradF.vjp(adder, args[:2], args[2:], create_graph=True)[1], inputs + v)
          gradgradcheck(lambda *args: autogradF.vjp(adder, args[:2], args[2:], create_graph=True)[1], inputs + v)
  
          def foo(*args):
              x, y = args[:2]
              v = args[2:]
  
              x = x.cos()
              val, grad = autogradF.vjp(adder, (x, y), v, create_graph=True)
  
              return val[0].exp() + val[1].exp() + grad[0].exp() + grad[1].exp() + x.exp() + y.exp()
  
          gradcheck(foo, inputs + v)
          gradgradcheck(foo, inputs + v)
  
      def test_jvp_err_check(self):
          def foo(a):
              return 3 * a.narrow(0, 0, 3)
  
          def bar(a):
              return 3 * a.narrow(0, 0, 3), "bar"
  
          inp = torch.rand(4)
          v = torch.rand(4)
          with self.assertRaisesRegex(TypeError, "The inputs given to jvp must be either a Tensor"):
              res = autogradF.jvp(foo, (inp, 2), v)
  
          with self.assertRaisesRegex(TypeError, "The outputs of the user-provided function given to jvp must"):
              res = autogradF.jvp(bar, inp, v)
  
          with self.assertRaisesRegex(RuntimeError, "The vector v can only be None if the input to the user-provided function"):
              res = autogradF.jvp(foo, inp)
  
          with self.assertRaisesRegex(RuntimeError, "The given v should contain a single Tensor."):
              res = autogradF.jvp(foo, inp, (v, v))
  
          with self.assertRaisesRegex(RuntimeError, "v has invalid size: should be torch.Size"):
              res = autogradF.jvp(foo, inp, v[:2])
  
          res = autogradF.jvp(foo, inp, v)[1]
          self._assert_same_struct(res, foo(inp))
  
      def test_jvp_err_check_strict(self):
          def foo(a):
              return a.detach()
  
          def bar(a):
              # Make a non-leaf Tensor that requires_grad but that is not connected to the input
              return a.long().float().requires_grad_().clone()
  
          inp = torch.rand(4)
          v = torch.rand(4)
          with self.assertRaisesRegex(RuntimeError, "Output 0 of the user-provided function does not require gradients."):
              res = autogradF.jvp(foo, inp, v, strict=True)
          res = autogradF.jvp(foo, inp, v, strict=False)
          self._assert_same_struct(res[1], res[0])
          self.assertEqual(res[1].abs().sum(), 0.)
  
          with self.assertRaisesRegex(RuntimeError, "The output of the user-provided function is independent of input 0"):
              res = autogradF.jvp(bar, inp, v, strict=True)
          res = autogradF.jvp(bar, inp, v, strict=False)
          self._assert_same_struct(res[1], res[0])
          self.assertEqual(res[1].abs().sum(), 0.)
  
          # The Jacobian does not depend on the input
          def foo(a):
              return a.clone()
  
          inp.requires_grad_()
          with self.assertRaisesRegex(RuntimeError, "jacobian of the user-provided function is independent of input 0."):
              res = autogradF.jvp(foo, inp, v, create_graph=True, strict=True)
          res = autogradF.jvp(foo, inp, v, create_graph=True, strict=False)
          self._assert_same_struct(res[1], inp)
          self.assertEqual(res[1], v)
  
      def test_jvp_output(self):
          def reducer(x):
              return x.sum(dim=1)
          inputs = torch.rand(4, 4)
          v = torch.ones(4, 4)
          res = autogradF.jvp(reducer, inputs, v)
          self._assert_same_struct(res[1], res[0])
          self.assertIsNone(res[0].grad_fn)
          self.assertIsNone(res[1].grad_fn)
  
          def adder(x, y):
              return 2 * x + 3 * y
  
          inputs = (torch.rand(2), torch.rand(2))
          v = (torch.ones(2), torch.ones(2))
          out, jvp_val = autogradF.jvp(adder, inputs, v)
          self._assert_same_struct(jvp_val, out)
          self.assertIsNone(out.grad_fn)
          self.assertIsNone(jvp_val[0].grad_fn)
          self.assertIsNone(jvp_val[1].grad_fn)
  
          def adder(x, y):
              return 2 * x + 3 * y, x + y
  
          inputs = (torch.rand(2), torch.rand(2))
          v = (torch.tensor([1., 0.]), torch.tensor([1., 0.]))
          out, jvp_val = autogradF.jvp(adder, inputs, v)
          self._assert_same_struct(jvp_val, out)
          self.assertIsNone(out[0].grad_fn)
          self.assertIsNone(out[1].grad_fn)
          self.assertIsNone(jvp_val[0].grad_fn)
          self.assertIsNone(jvp_val[1].grad_fn)
  
      def test_jvp_scalar(self):
          def reducer(x):
              return x.sum()
          inputs = torch.rand(4, 4)
          v = torch.ones(4, 4)
          res = autogradF.jvp(reducer, inputs, v)
          self._assert_same_struct(res[0], torch.zeros([]))
          self._assert_same_struct(res[1], res[0])
  
          def expander(x):
              return x.unsqueeze(0).repeat(4)
          inputs = torch.rand([])
          v = torch.ones([])
          res = autogradF.jvp(expander, inputs, v)
          self._assert_same_struct(res[0], torch.zeros(4))
          self._assert_same_struct(res[1], res[0])
  
          res = autogradF.jvp(expander, inputs)
          self._assert_same_struct(res[0], torch.zeros(4))
          self._assert_same_struct(res[1], res[0])
  
      def test_jvp_create_graph(self):
          def reducer(x):
              return x.sum(dim=1)
          inputs = torch.rand(2, 2)
          v = torch.ones(2, 2)
  
          inputs.requires_grad_()
          v.requires_grad_()
          res = autogradF.jvp(reducer, inputs, v, create_graph=True)
          self._assert_same_struct(res[1], res[0])
          self.assertIsNotNone(res[0].grad_fn)
          self.assertIsNotNone(res[1].grad_fn)
  
          gradcheck(lambda inp, v: autogradF.jvp(reducer, inp, v, create_graph=True), (inputs, v))
          gradgradcheck(lambda inp, v: autogradF.jvp(reducer, inp, v, create_graph=True), (inputs, v))
  
          def adder(x, y):
              return 2 * x + 3 * y, x * y
  
          inputs = (torch.rand(2, requires_grad=True), torch.rand(2, requires_grad=True))
          v = (torch.tensor([1., 0.], requires_grad=True), torch.tensor([1., 0.], requires_grad=True))
  
          gradcheck(lambda *args: autogradF.jvp(adder, args[:2], args[2:], create_graph=True)[1], inputs + v)
          gradgradcheck(lambda *args: autogradF.jvp(adder, args[:2], args[2:], create_graph=True)[1], inputs + v)
  
          def foo(*args):
              x, y = args[:2]
              v = args[2:]
  
              x = x.cos()
              val, grad = autogradF.jvp(adder, (x, y), v, create_graph=True)
  
              return val[0].exp() + val[1].exp() + grad[0].exp() + grad[1].exp() + x.exp() + y.exp()
  
          gradcheck(foo, inputs + v)
          gradgradcheck(foo, inputs + v)
  
      def test_jacobian_err_check(self):
          def foo(a):
              return 3 * a.narrow(0, 0, 3)
  
          def bar(a):
              return 3 * a.narrow(0, 0, 3), "bar"
  
          inp = torch.rand(4)
          with self.assertRaisesRegex(TypeError, "The inputs given to jacobian must be either a Tensor"):
              res = autogradF.jacobian(foo, (inp, 2))
  
          with self.assertRaisesRegex(TypeError, "The outputs of the user-provided function given to jacobian must"):
              res = autogradF.jacobian(bar, inp)
  
          res = autogradF.jacobian(foo, inp)
          self._assert_interleaved_struct(res, foo(inp), inp)
  
          def foo(a, b):
              return b, 3 * a.narrow(0, 0, 3)
  
          inp = (torch.rand(4), torch.rand(5))
  
          res = autogradF.jacobian(foo, inp)
          self._assert_interleaved_struct(res, foo(*inp), inp)
  
      def test_jacobian_err_check_strict(self):
          def foo(a):
              return a.detach()
  
          def bar(a):
              # Make a non-leaf Tensor that requires_grad but that is not connected to the input
              return a.long().float().requires_grad_().clone()
  
          inp = torch.rand(4)
          with self.assertRaisesRegex(RuntimeError, "Output 0 of the user-provided function does not require gradients."):
              res = autogradF.jacobian(foo, inp, strict=True)
          res = autogradF.jacobian(foo, inp, strict=False)
          self._assert_interleaved_struct(res, foo(inp), inp)
          self.assertEqual(res.abs().sum(), 0.)
  
          with self.assertRaisesRegex(RuntimeError, "Output 0 of the user-provided function is independent of input 0."):
              res = autogradF.jacobian(bar, inp, strict=True)
          res = autogradF.jacobian(bar, inp, strict=False)
          self._assert_interleaved_struct(res, foo(inp), inp)
          self.assertEqual(res.abs().sum(), 0.)
  
          # The Jacobian does not depend on the input
          def foo(a):
              return a.clone()
  
          inp.requires_grad_()
          with self.assertRaisesRegex(RuntimeError, "jacobian of the user-provided function is independent of input 0."):
              res = autogradF.jacobian(foo, inp, create_graph=True, strict=True)
          res = autogradF.jacobian(foo, inp, create_graph=True, strict=False)
          self._assert_interleaved_struct(res, inp, inp)
          self.assertEqual(res, torch.eye(4))
  
      def test_jacobian_output(self):
          def exp_reducer(x):
              return x.exp().sum(dim=1)
  
          inputs = torch.rand(4, 4)
          res = autogradF.jacobian(exp_reducer, inputs)
          self._assert_interleaved_struct(res, exp_reducer(inputs), inputs)
          self.assertIsNone(res.grad_fn)
  
          def identity(x):
              return x.clone()
  
          inputs = torch.rand(4)
          res = autogradF.jacobian(identity, inputs)
          self._assert_interleaved_struct(res, identity(inputs), inputs)
          self.assertIsNone(res.grad_fn)
          self.assertEqual(res, torch.eye(4))
  
          def add_exp_reducer(x, y):
              return (x + y.exp()).sum(dim=1)
  
          inputs = (torch.rand(4, 4), torch.rand(4, 4))
          res = autogradF.jacobian(add_exp_reducer, inputs)
          self._assert_interleaved_struct(res, add_exp_reducer(*inputs), inputs)
          self.assertIsNone(res[0].grad_fn)
          self.assertIsNone(res[1].grad_fn)
  
      def test_jacobian_scalar(self):
          def reducer(x):
              return x.sum()
          inputs = torch.rand(4, 4)
          res = autogradF.jacobian(reducer, inputs)
          self._assert_same_struct(res, inputs)
  
          def expander(x):
              return x.unsqueeze(0).repeat(4)
          inputs = torch.rand([])
          res = autogradF.jacobian(expander, inputs)
          self._assert_same_struct(res, torch.zeros(4))
  
      def test_jacobian_create_graph(self):
          def exp_reducer(x):
              return x.exp().sum(dim=1)
  
          inputs = torch.rand(4, 4, requires_grad=True)
          res = autogradF.jacobian(exp_reducer, inputs, create_graph=True)
          self._assert_interleaved_struct(res, exp_reducer(inputs), inputs)
          self.assertIsNotNone(res.grad_fn)
  
          gradcheck(lambda inp: autogradF.jacobian(exp_reducer, inp, create_graph=True), inputs)
          gradgradcheck(lambda inp: autogradF.jacobian(exp_reducer, inp, create_graph=True), inputs)
  
          def add_exp_reducer(x, y):
              return (x + y).exp().sum(dim=1)
  
          inputs = (torch.rand(4, 4, requires_grad=True), torch.rand(4, 4, requires_grad=True))
          res = autogradF.jacobian(add_exp_reducer, inputs, create_graph=True)
          self._assert_interleaved_struct(res, add_exp_reducer(*inputs), inputs)
          self.assertIsNotNone(res[0].grad_fn)
          self.assertIsNotNone(res[1].grad_fn)
  
          gradcheck(lambda *inp: autogradF.jacobian(add_exp_reducer, inp, create_graph=True), inputs)
          gradgradcheck(lambda *inp: autogradF.jacobian(add_exp_reducer, inp, create_graph=True), inputs)
  
          def foo(x, y):
              x = x.cos()
              val, jac = autogradF.jacobian(add_exp_reducer, (x, y), create_graph=True)
  
              res = val[0].exp().sum() + val[1].exp().sum() + jac[0].exp().sum()
              res = res + jac[1].exp().sum() + x.exp().sum() + y.exp().sum()
              return res
  
          gradcheck(foo, inputs)
          gradgradcheck(foo, inputs)
  
      def test_hessian_err_check(self):
          def foo(a):
              return 3 * a.narrow(0, 0, 3).exp().sum()
  
          def bar(a):
              return 3 * a.narrow(0, 0, 3), "bar"
  
          def bar2(a):
              return 3 * a.narrow(0, 0, 3)
  
          def bar3(a):
              return 3 * a.narrow(0, 0, 3), 3 * a.narrow(0, 0, 3)
  
          inp = torch.rand(4)
          with self.assertRaisesRegex(TypeError, "The inputs given to hessian must be either a Tensor"):
              res = autogradF.hessian(foo, (inp, 2))
  
          with self.assertRaisesRegex(TypeError, "The outputs of the user-provided function given to hessian must"):
              res = autogradF.hessian(bar, inp)
  
          err_msg_out = "The Tensor returned by the function given to hessian should contain a single element"
          with self.assertRaisesRegex(RuntimeError, err_msg_out):
              res = autogradF.hessian(bar2, inp)
  
          with self.assertRaisesRegex(RuntimeError, "The function given to hessian should return a single Tensor"):
              res = autogradF.hessian(bar3, inp)
  
          res = autogradF.hessian(foo, inp)
          self._assert_interleaved_struct(res, inp, inp)
  
          def foo(a, b):
              return (3 * b.narrow(0, 0, 3) * a.narrow(0, 0, 3)).sum()
  
          inp = (torch.rand(4), torch.rand(5))
  
          res = autogradF.hessian(foo, inp)
          self._assert_interleaved_struct(res, inp, inp)
  
      def test_hessian_err_check_strict(self):
          def foo(a):
              return a.detach().sum()
  
          def bar(a):
              # Make a non-leaf Tensor that requires_grad but that is not connected to the input
              return a.long().float().requires_grad_().clone().sum()
  
          def bar2(a):
              # A Linear function for which the jacobian is independent of the input
              return (3 * a).sum()
  
          inp = torch.rand(4)
          with self.assertRaisesRegex(RuntimeError, "Output 0 of the user-provided function does not require gradients."):
              res = autogradF.hessian(foo, inp, strict=True)
          res = autogradF.hessian(foo, inp, strict=False)
          self._assert_interleaved_struct(res, inp, inp)
          self.assertEqual(res.abs().sum(), 0.)
  
          with self.assertRaisesRegex(RuntimeError, "jacobian of the user-provided function with respect to input 0"):
              res = autogradF.hessian(bar, inp, strict=True)
          res = autogradF.hessian(bar, inp, strict=False)
          self._assert_interleaved_struct(res, inp, inp)
          self.assertEqual(res.abs().sum(), 0.)
  
          with self.assertRaisesRegex(RuntimeError, "jacobian of the user-provided function with respect to input 0 is"):
              res = autogradF.hessian(bar2, inp, strict=True)
          res = autogradF.hessian(bar2, inp, strict=False)
          self._assert_interleaved_struct(res, inp, inp)
          self.assertEqual(res.abs().sum(), 0.)
  
      def test_hessian_output(self):
          def pow_reducer(x):
              return x.pow(3).sum()
  
          inputs = torch.rand(2, 2)
          res = autogradF.hessian(pow_reducer, inputs)
          self._assert_interleaved_struct(res, inputs, inputs)
          self.assertIsNone(res.grad_fn)
  
          def add_pow_reducer(x, y):
              return (x + y).pow(3).sum()
  
          inputs = (torch.rand(2, 2), torch.rand(2, 2))
          res = autogradF.hessian(add_pow_reducer, inputs)
          self._assert_interleaved_struct(res, inputs, inputs)
          self.assertIsNone(res[0][0].grad_fn)
          self.assertIsNone(res[0][1].grad_fn)
          self.assertIsNone(res[1][0].grad_fn)
          self.assertIsNone(res[1][1].grad_fn)
  
      def test_hessian_scalar(self):
          def reducer(x):
              return x.sum()
          inputs = torch.rand(4, 4)
          res = autogradF.hessian(reducer, inputs)
          self._assert_interleaved_struct(res, inputs, inputs)
  
          inputs = torch.rand([])
          res = autogradF.hessian(reducer, inputs)
          self._assert_same_struct(res, inputs)
  
          def bad_reducer(x):
              return x.sum().view(1, 1, 1)
          inputs = torch.rand(4, 4)
          res = autogradF.hessian(bad_reducer, inputs)
          self._assert_interleaved_struct(res, inputs, inputs)
  
      def test_hessian_create_graph(self):
          def pow_reducer(x):
              return x.pow(3).sum()
  
          inputs = torch.rand(2, 2, requires_grad=True)
          res = autogradF.hessian(pow_reducer, inputs, create_graph=True)
          self._assert_interleaved_struct(res, inputs, inputs)
          self.assertIsNotNone(res.grad_fn)
  
          gradcheck(lambda inp: autogradF.hessian(pow_reducer, inp, create_graph=True), inputs)
          gradgradcheck(lambda inp: autogradF.hessian(pow_reducer, inp, create_graph=True), inputs)
  
          def add_pow_reducer(x, y):
              return (x + y).pow(3).sum()
  
          inputs = (torch.rand(2, 2, requires_grad=True), torch.rand(2, 2, requires_grad=True))
          res = autogradF.hessian(add_pow_reducer, inputs, create_graph=True)
          self._assert_interleaved_struct(res, inputs, inputs)
          self.assertIsNotNone(res[0][0].grad_fn)
          self.assertIsNotNone(res[0][1].grad_fn)
          self.assertIsNotNone(res[1][0].grad_fn)
          self.assertIsNotNone(res[1][1].grad_fn)
  
          def flatten(inp):
              return tuple(el_lvl2 for el_lvl1 in inp for el_lvl2 in el_lvl1)
  
          gradcheck(lambda *inp: flatten(autogradF.hessian(add_pow_reducer, inp, create_graph=True)), inputs)
          gradgradcheck(lambda *inp: flatten(autogradF.hessian(add_pow_reducer, inp, create_graph=True)), inputs)
  
          def foo(x, y):
              x = x.cos()
              val, hess = autogradF.hessian(add_pow_reducer, (x, y), create_graph=True)
  
              res = val[0].cos().sum() + val[1].cos().sum() + hess[0].cos().sum()
              res = res + hess[1].cos().sum() + x.cos().sum() + y.cos().sum()
              return res
  
          gradcheck(foo, inputs)
          gradgradcheck(foo, inputs)
  
      def test_vhp_err_check(self):
          def foo(a):
              return 3 * a.narrow(0, 0, 3).exp().sum()
  
          def bar(a):
              return 3 * a.narrow(0, 0, 3), "bar"
  
          def bar2(a):
              return 3 * a.narrow(0, 0, 3)
  
          inp = torch.rand(4)
          v = torch.rand(4)
          with self.assertRaisesRegex(TypeError, "The inputs given to vhp must be either a Tensor"):
              res = autogradF.vhp(foo, (inp, 2), v)
  
          with self.assertRaisesRegex(TypeError, "The outputs of the user-provided function given to vhp must"):
              res = autogradF.vhp(bar, inp, v)
  
          err_msg_out = "The Tensor returned by the function given to vhp should contain a single element"
          with self.assertRaisesRegex(RuntimeError, err_msg_out):
              res = autogradF.vhp(bar2, inp, v)
  
          with self.assertRaisesRegex(RuntimeError, "v has invalid size:"):
              res = autogradF.vhp(foo, inp, torch.rand(5))
  
          with self.assertRaisesRegex(TypeError, "The v given to vhp must be either a Tensor or a tuple of Tensors"):
              res = autogradF.vhp(foo, inp, (v, 2))
  
          res = autogradF.vhp(foo, inp, v)
          self._assert_same_struct(res[1], inp)
  
          def foo(a, b):
              return (3 * b.narrow(0, 0, 3) * a.narrow(0, 0, 3)).sum()
  
          inp = (torch.rand(4), torch.rand(5))
          v = (torch.rand(4), torch.rand(5))
  
          res = autogradF.vhp(foo, inp, v)
          self._assert_same_struct(res[1], inp)
  
      def test_vhp_err_check_strict(self):
          def foo(a):
              return a.detach().sum()
  
          def bar(a):
              # Make a non-leaf Tensor that requires_grad but that is not connected to the input
              return a.long().float().requires_grad_().clone().sum()
  
          def bar2(a):
              # A Linear function for which the jacobian is independent of the input
              return (3 * a).sum()
  
          inp = torch.rand(4)
          v = torch.rand(4)
          with self.assertRaisesRegex(RuntimeError, "Output 0 of the user-provided function does not require gradients."):
              res = autogradF.vhp(foo, inp, v, strict=True)
          res = autogradF.vhp(foo, inp, v, strict=False)
          self._assert_same_struct(res[1], inp)
          self.assertEqual(res[1].abs().sum(), 0.)
  
          with self.assertRaisesRegex(RuntimeError, "The output of the user-provided function is independent of input 0"):
              res = autogradF.vhp(bar, inp, v, strict=True)
          res = autogradF.vhp(bar, inp, v, strict=False)
          self._assert_same_struct(res[1], inp)
          self.assertEqual(res[1].abs().sum(), 0.)
  
          with self.assertRaisesRegex(RuntimeError, "jacobian of the user-provided function with respect to input 0 is"):
              res = autogradF.vhp(bar2, inp, v, strict=True)
          res = autogradF.vhp(bar2, inp, v, strict=False)
          self._assert_same_struct(res[1], inp)
          self.assertEqual(res[1].abs().sum(), 0.)
  
      def test_vhp_output(self):
          def foo(a):
              return 3 * a.narrow(0, 0, 3).exp().sum()
  
          inputs = torch.rand(4, 4)
          v = torch.ones(4, 4)
          res = autogradF.vhp(foo, inputs, v)
          self._assert_same_struct(res[1], inputs)
          self.assertIsNone(res[0].grad_fn)
          self.assertIsNone(res[1].grad_fn)
  
          def bar(a, b):
              return (a + 3 * b.narrow(0, 0, 3)).exp().sum()
  
          inputs = (torch.rand(3), torch.rand(4))
          v = (torch.ones(3), torch.ones(4))
          out, vhp_val = autogradF.vhp(bar, inputs, v)
          self._assert_same_struct(vhp_val, inputs)
          self.assertIsNone(out.grad_fn)
          self.assertIsNone(vhp_val[0].grad_fn)
          self.assertIsNone(vhp_val[1].grad_fn)
  
      def test_vhp_scalar(self):
          def reducer(x):
              return x.sum()
          inputs = torch.rand(4, 4)
          v = torch.ones(4, 4)
          res = autogradF.vhp(reducer, inputs, v)
          self._assert_same_struct(res[1], inputs)
  
          inputs = torch.rand([])
          v = torch.rand([])
          res = autogradF.vhp(reducer, inputs, v)
          self._assert_same_struct(res[1], inputs)
  
          res = autogradF.vhp(reducer, inputs)
          self._assert_same_struct(res[1], inputs)
  
          def bad_reducer(x):
              return x.sum().view(1, 1, 1)
          inputs = torch.rand(4, 4)
          v = torch.rand(4, 4)
          res = autogradF.vhp(bad_reducer, inputs, v)
          self._assert_same_struct(res[1], inputs)
  
      def test_vhp_create_graph(self):
          def foo(a):
              return 3 * a.narrow(0, 0, 3).exp().sum()
  
          inputs = torch.rand(4, 4, requires_grad=True)
          v = torch.ones(4, 4, requires_grad=True)
          res = autogradF.vhp(foo, inputs, v, create_graph=True)
          self._assert_same_struct(res[1], inputs)
          self.assertIsNotNone(res[0].grad_fn)
          self.assertIsNotNone(res[1].grad_fn)
  
          gradcheck(lambda inp, v: autogradF.vhp(foo, inp, v, create_graph=True), (inputs, v))
          gradgradcheck(lambda inp, v: autogradF.vhp(foo, inp, v, create_graph=True), (inputs, v))
  
          def bar(a, b):
              return (a + 3 * b.narrow(0, 0, 3)).exp().sum()
  
          inputs = (torch.rand(3, requires_grad=True), torch.rand(4, requires_grad=True))
          v = (torch.ones(3, requires_grad=True), torch.ones(4, requires_grad=True))
          out, vhp_val = autogradF.vhp(bar, inputs, v, create_graph=True)
          self._assert_same_struct(vhp_val, inputs)
          self.assertIsNotNone(out.grad_fn)
          self.assertIsNotNone(vhp_val[0].grad_fn)
          self.assertIsNotNone(vhp_val[1].grad_fn)
  
          gradcheck(lambda *args: autogradF.vhp(bar, args[:2], args[2:], create_graph=True)[1], inputs + v)
          gradgradcheck(lambda *args: autogradF.vhp(bar, args[:2], args[2:], create_graph=True)[1], inputs + v)
  
          def foo(*args):
              x, y = args[:2]
              v = args[2:]
  
              x = x.cos()
              val, grad = autogradF.vhp(bar, (x, y), v, create_graph=True)
  
              return val.cos() + grad[0].cos().sum() + grad[1].cos() + x.cos().sum() + y.cos()
  
          gradcheck(foo, inputs + v)
          gradgradcheck(foo, inputs + v)
  
      def test_hvp_err_check(self):
          def foo(a):
              return 3 * a.narrow(0, 0, 3).exp().sum()
  
          def bar(a):
              return 3 * a.narrow(0, 0, 3), "bar"
  
          def bar2(a):
              return 3 * a.narrow(0, 0, 3)
  
          inp = torch.rand(4)
          v = torch.rand(4)
          res = autogradF.hvp(foo, inp, v)
          with self.assertRaisesRegex(TypeError, "The inputs given to hvp must be either a Tensor"):
              res = autogradF.hvp(foo, (inp, 2), v)
  
          with self.assertRaisesRegex(TypeError, "The outputs of the user-provided function given to hvp must"):
              res = autogradF.hvp(bar, inp, v)
  
          err_msg_out = "The Tensor returned by the function given to hvp should contain a single element"
          with self.assertRaisesRegex(RuntimeError, err_msg_out):
              res = autogradF.hvp(bar2, inp, v)
  
          with self.assertRaisesRegex(RuntimeError, "v has invalid size:"):
              res = autogradF.hvp(foo, inp, torch.rand(5))
  
          with self.assertRaisesRegex(TypeError, "The v given to hvp must be either a Tensor or a tuple of Tensors"):
              res = autogradF.hvp(foo, inp, (v, 2))
  
          res = autogradF.hvp(foo, inp, v)
          self._assert_same_struct(res[1], inp)
  
          def foo(a, b):
              return (3 * b.narrow(0, 0, 3) * a.narrow(0, 0, 3)).sum()
  
          inp = (torch.rand(4), torch.rand(5))
          v = (torch.rand(4), torch.rand(5))
  
          res = autogradF.hvp(foo, inp, v)
          self._assert_same_struct(res[1], inp)
  
      def test_hvp_err_check_strict(self):
          def foo(a):
              return a.detach().sum()
  
          def bar(a):
              # Make a non-leaf Tensor that requires_grad but that is not connected to the input
              return a.long().float().requires_grad_().clone().sum()
  
          def bar2(a):
              # A Linear function for which the jacobian is independent of the input
              return (3 * a).sum()
  
          inp = torch.rand(4)
          v = torch.rand(4)
          with self.assertRaisesRegex(RuntimeError, "Output 0 of the user-provided function does not require gradients."):
              res = autogradF.hvp(foo, inp, v, strict=True)
          res = autogradF.hvp(foo, inp, v, strict=False)
          self._assert_same_struct(res[1], inp)
          self.assertEqual(res[1].abs().sum(), 0.)
  
          with self.assertRaisesRegex(RuntimeError, "The output of the user-provided function is independent of input 0"):
              res = autogradF.hvp(bar, inp, v, strict=True)
          res = autogradF.hvp(bar, inp, v, strict=False)
          self._assert_same_struct(res[1], inp)
          self.assertEqual(res[1].abs().sum(), 0.)
  
          with self.assertRaisesRegex(RuntimeError, "jacobian of the user-provided function with respect to input 0 is"):
              res = autogradF.hvp(bar2, inp, v, strict=True)
          res = autogradF.hvp(bar2, inp, v, strict=False)
          self._assert_same_struct(res[1], inp)
          self.assertEqual(res[1].abs().sum(), 0.)
  
      def test_hvp_output(self):
          def foo(a):
              return 3 * a.narrow(0, 0, 3).exp().sum()
  
          inputs = torch.rand(4, 4)
          v = torch.ones(4, 4)
          res = autogradF.hvp(foo, inputs, v)
          self._assert_same_struct(res[1], inputs)
          self.assertIsNone(res[0].grad_fn)
          self.assertIsNone(res[1].grad_fn)
  
          def bar(a, b):
              return (a + 3 * b.narrow(0, 0, 3)).exp().sum()
  
          inputs = (torch.rand(3), torch.rand(4))
          v = (torch.ones(3), torch.ones(4))
          out, hvp_val = autogradF.hvp(bar, inputs, v)
          self._assert_same_struct(hvp_val, inputs)
          self.assertIsNone(out.grad_fn)
          self.assertIsNone(hvp_val[0].grad_fn)
          self.assertIsNone(hvp_val[1].grad_fn)
  
      def test_hvp_scalar(self):
          def reducer(x):
              return x.exp().sum()
          inputs = torch.rand(4, 4)
          v = torch.ones(4, 4)
          res = autogradF.hvp(reducer, inputs, v)
          self._assert_same_struct(res[1], inputs)
  
          inputs = torch.rand([])
          v = torch.rand([])
          res = autogradF.hvp(reducer, inputs, v)
          self._assert_same_struct(res[1], inputs)
  
          res = autogradF.hvp(reducer, inputs)
          self._assert_same_struct(res[1], inputs)
  
          def bad_reducer(x):
              return x.exp().sum().view(1, 1, 1)
          inputs = torch.rand(4, 4)
          v = torch.rand(4, 4)
          res = autogradF.hvp(bad_reducer, inputs, v)
          self._assert_same_struct(res[1], inputs)
  
      def test_hvp_create_graph(self):
          def foo(a):
              return 3 * a.narrow(0, 0, 3).exp().sum()
  
          inputs = torch.rand(4, 4, requires_grad=True)
          v = torch.ones(4, 4, requires_grad=True)
          res = autogradF.hvp(foo, inputs, v, create_graph=True)
          self._assert_same_struct(res[1], inputs)
          self.assertIsNotNone(res[0].grad_fn)
          self.assertIsNotNone(res[1].grad_fn)
  
          gradcheck(lambda inp, v: autogradF.hvp(foo, inp, v, create_graph=True), (inputs, v))
          gradgradcheck(lambda inp, v: autogradF.hvp(foo, inp, v, create_graph=True), (inputs, v))
  
          def bar(a, b):
              return (a + 3 * b.narrow(0, 0, 3)).exp().sum()
  
          inputs = (torch.rand(3, requires_grad=True), torch.rand(4, requires_grad=True))
          v = (torch.ones(3, requires_grad=True), torch.ones(4, requires_grad=True))
          out, hvp_val = autogradF.hvp(bar, inputs, v, create_graph=True)
          self._assert_same_struct(hvp_val, inputs)
          self.assertIsNotNone(out.grad_fn)
          self.assertIsNotNone(hvp_val[0].grad_fn)
          self.assertIsNotNone(hvp_val[1].grad_fn)
  
          gradcheck(lambda *args: autogradF.hvp(bar, args[:2], args[2:], create_graph=True)[1], inputs + v)
          gradgradcheck(lambda *args: autogradF.hvp(bar, args[:2], args[2:], create_graph=True)[1], inputs + v)
  
          def foo(*args):
              x, y = args[:2]
              v = args[2:]
  
              x = x.cos()
              val, grad = autogradF.hvp(bar, (x, y), v, create_graph=True)
  
              return val.cos() + grad[0].cos().sum() + grad[1].cos() + x.cos().sum() + y.cos()
  
          gradcheck(foo, inputs + v)
          gradgradcheck(foo, inputs + v)
  
      def test_jacobian_match_vjp_jvp(self):
          def foo(x):
              return x ** 3 + x.sum()
  
          inputs = torch.rand(4)
          v = torch.rand(4)
  
          jac = autogradF.jacobian(foo, inputs)
          jvp = autogradF.jvp(foo, inputs, v)[1]
          vjp = autogradF.vjp(foo, inputs, v)[1]
  
          self.assertEqual(jvp, torch.mm(jac, v.unsqueeze(1)).squeeze(1))
          self.assertEqual(vjp, torch.mm(v.unsqueeze(0), jac).squeeze(0))
  
      def test_hessian_match_vhp_hvp(self):
          def foo(a):
              return 3 * a.narrow(0, 0, 3).exp().sum()
  
          inputs = torch.rand(4)
          v = torch.rand(4)
  
          hes = autogradF.hessian(foo, inputs)
          hvp = autogradF.hvp(foo, inputs, v)[1]
          vhp = autogradF.vhp(foo, inputs, v)[1]
  
          self.assertEqual(hvp, torch.mm(hes, v.unsqueeze(1)).squeeze(1))
          self.assertEqual(vhp, torch.mm(v.unsqueeze(0), hes).squeeze(0))
  
  
  # Generic device type autograd tests.
  class TestAutogradDeviceType(TestCase):
  
      # skip this test if running on rocm, because in cdist
      # we use __shfl_down_sync on CUDA for fast reduction
      # and it gives incorrect results on rocm platform
      @skipCUDAIfRocm
      def test_cdist(self, device):
          def _test_cdist_for_size(sizex, sizey=None):
              if sizey is None:
                  sizey = sizex
              for p in [0, 1, 2, 3, 1.5, 2.5, float('inf')]:
                  x = torch.randn(sizex, device=device, dtype=torch.double)
                  y = torch.randn(sizey, device=device, dtype=torch.double)
                  eps = 1e-6
                  # to avoid extremum
                  x = x - (((x - y) < eps).double() * 2 * eps)
                  x.requires_grad = True
                  y.requires_grad = True
                  f_args_variable = (x, y)
  
                  def f(a, b):
                      return torch.cdist(a, b, p)
                  f_args_tensor = deepcopy(unpack_variables(f_args_variable))
                  run_functional_checks(self, "test_cdist", "cdist", f,
                                        True, f_args_variable, f_args_tensor)
  
          def _test_euclidean_large_cdist(sizex, sizey=None):
              if sizey is None:
                  sizey = sizex
              x = torch.randn(sizex, device=device, dtype=torch.float)
              y = torch.randn(sizey, device=device, dtype=torch.float)
              eps = 1e-6
              # to avoid extremum
              x = x - (((x - y) < eps).float() * 2 * eps)
              x.requires_grad = True
              y.requires_grad = True
              f_args_variable = (x, y)
              dist = torch.cdist(x, y, p=2)
              # Do a backward pass to check that it is valid for large
              # matrices
              loss = dist.sum()
              loss.backward()
  
          _test_cdist_for_size((S, S))
          _test_cdist_for_size((S, S, S))
          _test_cdist_for_size((3, 5))
          _test_cdist_for_size((2, 3, 5))
          _test_cdist_for_size((1, 2, 3))
          _test_cdist_for_size((1, 1), (S, 1))
          _test_euclidean_large_cdist((2000, 5))
  
  
      # NOTE: flaky on ROCm CI
      @skipCUDAIfRocm
      def test_sparse_ctor_getter_backward(self, device):
          # See NOTE [ Sparse: autograd and API ] on the expected behavior of this test
          def _test(size, sparse_dim, nnz, device):
              v_size = [nnz] + list(size[sparse_dim:])
              i = torch.rand(sparse_dim, nnz)
              i.mul_(torch.tensor(size[:sparse_dim]).unsqueeze(1).to(i))
              i = i.to(torch.long)
  
              inp = torch.randn(v_size, requires_grad=True)
              other = self.genSparseTensor(size, sparse_dim, nnz, is_uncoalesced=True)[0]
              other = other.to(device)
  
              def fn(v):
                  x = torch.sparse_coo_tensor(i, v, size, device=device)
                  y = (x + other).coalesce()
                  yv = y.values()
                  new_v = yv.tanh()
                  z = torch.sparse_coo_tensor(y.indices(), new_v, y.size())
                  return z.coalesce().values()
  
              gradcheck(fn, (inp,))
              # FIXME: make gradgradcheck work.
              # gradgradcheck(fn, (inp,))
  
              # assert that _values is non-differentiable
              with self.assertRaisesRegex(RuntimeError, "does not have a grad_fn"):
                  other.detach().requires_grad_()._values().backward(torch.ones_like(other._values()))
  
          for empty_i, empty_v, empty_nnz in product([True, False], repeat=3):
              sparse_size = [] if empty_i else [2, 1]
              dense_size = [1, 0, 2] if empty_v else [1, 2]
              nnz = 0 if empty_nnz else 5
              _test(sparse_size + dense_size, len(sparse_size), nnz, device)
  
      # autograd tests via common_method_invocations don't allow input tensors to
      # be sparse (RuntimeError: gradcheck expects all tensor inputs are dense when
      # check_sparse_nnz is set to False.)
      def test_sparse_mask_autograd(self, device):
          tensor = torch.randn(3, requires_grad=True, device=device)
          mask = torch.ones(3, device=device)
          mask[1] = 0
          mask = mask.to_sparse()
          converted = tensor.sparse_mask(mask).to_dense()
          converted.sum().backward()
          self.assertEqual(tensor.grad, mask.to_dense())
  
      def test_pyscalar_conversions(self, device):
          def _test_pyscalar_conversions(t, integral_conv):
              # integral -> integral
              l = t(torch.zeros(1, 1, 1, dtype=torch.long))
              pyscalar = -12345
              l[0] = pyscalar
              self.assertEqual(integral_conv(l), pyscalar)
  
              # floating point -> floating point
              f = Variable(t(torch.randn(1, 1)))
              pyscalar = -12345.1
              f[0] = pyscalar
              self.assertEqual(float(f), pyscalar)
              f[0] = nan
              self.assertTrue(math.isnan(float(f)))
              f[0] = inf
              self.assertEqual(float(f), inf, allow_inf=True)
              f[0] = -inf
              self.assertEqual(float(f), -inf, allow_inf=True)
  
              # integral -> floating point
              # check we can convert something that loses precision
              pyscalar = 1234567890123456789
              self.assertNotEqual(pyscalar, integral_conv(float(pyscalar)))
              l[0] = pyscalar
              self.assertEqual(float(l), float(pyscalar))
  
              # floating point -> integral
              f[0] = nan
              self.assertRaises(ValueError, lambda: integral_conv(f[0]))
              f[0] = inf
              self.assertRaises(OverflowError, lambda: integral_conv(f[0]))
              f[0] = -inf
              self.assertRaises(OverflowError, lambda: integral_conv(f[0]))
              f[0] = sys.float_info.max
              self.assertEqual(integral_conv(f), sys.float_info.max)
  
              # bool, nonzero
              def test_nonzero(tensor, value, expected):
                  tensor[0] = value
                  self.assertEqual(expected, bool(tensor))
                  self.assertEqual(expected, True if tensor else False)
  
              test_nonzero(l, 0, False)
              test_nonzero(l, -2, True)
              test_nonzero(f, 0.0, False)
              test_nonzero(f, sys.float_info.min, True)
              test_nonzero(f, nan, bool(nan))
              test_nonzero(f, inf, bool(inf))
              test_nonzero(f, -inf, bool(-inf))
  
  
          _test_pyscalar_conversions(lambda x: x.to(device), lambda x: int(x))
          if sys.version_info[0] == 2:
              _test_pyscalar_conversions(lambda x: x.to(device), lambda x: long(x))
  
      @dtypesIfCUDA(torch.half, torch.float, torch.double, torch.int8, torch.int16, torch.int32, torch.int64)
      @dtypes(torch.float, torch.double, torch.int8, torch.int16, torch.int32, torch.int64)
      def test_set_requires_grad_only_for_floats(self, device, dtype):
          def f1():
              a = torch.ones(1, dtype=dtype, device=device)
              a.requires_grad_()
  
          def f2():
              a = torch.ones(1, dtype=dtype, device=device)
              a.requires_grad = True
  
          def f3():
              torch.ones(1, dtype=dtype, device=device, requires_grad=True)
  
          a = torch.ones(1, dtype=dtype, device=device)
          a.requires_grad = False  # should always work
          a.requires_grad_(False)
  
          for f in [f1, f2, f3]:
              if dtype.is_floating_point:
                  f()
              else:
                  with self.assertRaisesRegex(RuntimeError, 'floating point', msg="dt: {} device: {}".format(a.dtype, a.device)):
                      f()
  
      @onlyCUDA
      def test_advanced_indexing_backwards_large(self, device):
          # See https://github.com/pytorch/pytorch/issues/22843
          n = (1 << 16)
          x = torch.rand(n, 1, device=device, requires_grad=True)
          a = x[:, [0]]
          a.sum().backward()
          self.assertEqual(x.grad, torch.ones(n, 1, device=device))
  
      def _test_reentrant_parent_error_on_cpu(self, device):
          t1 = torch.rand([3, 3], requires_grad=True)
          t2 = torch.rand([3, 3], device=device, requires_grad=True)
          t3 = torch.rand([3, 3], device=device, requires_grad=True)
  
          # Parent graph cpu graph.
          t4 = t1 * t1
          t5 = TestAutograd.SimulateBackwardError.apply(t4)
  
          # Child gpu graph (much longer than parent graph).
          prev = t2 * t2
          for i in range(10):
              prev = prev * t2
          reentrant_root = prev
  
          class ReentrantFunc(Function):
              @staticmethod
              def forward(ctx, inp):
                  return inp.clone()
  
              @staticmethod
              def backward(ctx, grad):
                  # Reentrant backward in child will take much longer.
                  reentrant_root.backward()
                  return grad
  
          # Parent gpu graph.
          t6 = ReentrantFunc.apply(t3)
          t7 = t6 * t6
  
          # Parent graph will error out first, while child graph will continue executing.
          with self.assertRaisesRegex(RuntimeError, "Simulate error"):
              torch.autograd.backward([t5.sum(), t7.sum()])
  
          # No grads should be accumulated since child graph will stop execution
          # after parent receives error.
          self.assertIsNone(t2.grad)
          self.assertIsNone(t1.grad)
          self.assertIsNone(t3.grad)
  
      @onlyCUDA
      def test_reentrant_parent_error_on_cpu(self, device):
          before = CudaMemoryLeakCheck.get_cuda_memory_usage()
  
          # Run as separate function so that gc can clean up everything when we
          # check for memory usage.
          self._test_reentrant_parent_error_on_cpu(device)
  
          # Wait for autograd thread to cleanup failed tasks.
          after = CudaMemoryLeakCheck.get_cuda_memory_usage()
          start = time.time()
          while before != after and time.time() - start < 30:
              time.sleep(0.1)
              after = CudaMemoryLeakCheck.get_cuda_memory_usage()
  
          self.assertEqual(before, after)
  
      # test for backward in https://github.com/pytorch/pytorch/issues/15511
      def test_pdist_large(self, device):
          def func(x):
              return torch.pdist(x, p=2)
  
          # shape[0] should be able to be (roughly) arbitrarily large, but the kernel
          # is currently limited to smaller sizes (see issue above); this is just testing
          # a floor.
          shape = (1000, 1)
          x = torch.randn(shape, device=device).requires_grad_()
          output = torch.pdist(x, p=2)
          # just run a single backward, as gradcheck/gradgradcheck is expensive here
          output.sum().backward()
  
      def test_where_functional(self, device):
          x = torch.randn(5, 5, device=device, requires_grad=True)
          y = torch.randn(5, 5, device=device, requires_grad=True)
          cond = mask_not_all_zeros((5, 5)).to(device=device)
  
          def where(cond, x, y):
              return torch.where(cond, x, y)
  
          gradcheck(where, [cond, x, y], raise_exception=True)
          gradgradcheck(where, [cond, x, y], [torch.randn(5, 5, device=device)])
  
          x = torch.randn(5, 1, 5, device=device, requires_grad=True)
          y = torch.randn(5, 5, 1, device=device, requires_grad=True)
          gradcheck(where, [cond, x, y], raise_exception=True)
          gradgradcheck(where, [cond, x, y], [torch.randn(5, 5, 5, device=device)])
  
      @skipCUDAIfRocm
      @unittest.skipIf(IS_WINDOWS, """Test is flaky on Windows:
              https://github.com/pytorch/pytorch/issues/34870""")
      def test_ctc_loss(self, device):
          batch_size = 64
          num_labels = 101
          target_length = 15
          gradcheck_input_size = 10
  
          ZERO_NONE = 0
          ZERO_SOME = 1
          ZERO_ALL = 2
  
          # input_length, vary_lengths, zero_lengths
          tests = [(150, False, ZERO_NONE),
                   (150, True, ZERO_NONE),
                   (50, True, ZERO_SOME),
                   (50, True, ZERO_ALL)]
  
          if 'cuda' in device:
              tests += [(50, False, ZERO_NONE),
                        (50, True, ZERO_NONE),
                        (150, True, ZERO_SOME),
                        (150, True, ZERO_ALL)]
  
          for input_length, vary_lengths, zero_mode in tests:
              targets = torch.randint(1, num_labels, (batch_size, target_length),
                                      device=device, dtype=torch.long)
              x = torch.randn(gradcheck_input_size, device=device, requires_grad=True)
              tile_factors = torch.randn(input_length * batch_size * num_labels // gradcheck_input_size + 1,
                                         device=device)
              input_lengths = [(torch.randint(input_length // 2, input_length + 1, ()).item()
                                if vary_lengths or i == 0 else input_length) for i in range(batch_size)]
              if zero_mode == ZERO_ALL:
                  target_lengths = [0 for _ in range(batch_size)]
              else:
                  target_lengths = [(torch.randint(target_length // 2, target_length + 1, ()).item()
                                     if vary_lengths else target_length) for _ in range(batch_size)]
                  if zero_mode == ZERO_SOME:
                      idxes = torch.randint(0, batch_size, (10,))
                      for i in idxes:
                          target_lengths[i] = 0
  
              def ctc_after_softmax(x):
                  x_full = ((x[:, None] * tile_factors[None, :]).view(-1)[:input_length * batch_size * num_labels]
                            .view(input_length, batch_size, num_labels))
                  log_probs = torch.log_softmax(x_full, 2)
                  return torch.nn.functional.ctc_loss(log_probs, targets, input_lengths, target_lengths)
  
              gradcheck(ctc_after_softmax, [x])
  
      @onlyCUDA
      @skipCUDAIfRocm
      @skipCUDAIfCudnnVersionLessThan(7600)
      def test_ctc_loss_cudnn(self, device):
          batch_size = 16
          input_length = 30
          num_labels = 101
          target_length = 15
          targets = torch.randint(1, num_labels, (batch_size * target_length,),
                                  device='cuda', dtype=torch.long)
          log_probs = torch.log_softmax(torch.randn(input_length, batch_size, num_labels, device='cuda', dtype=torch.float), 2)
          log_probs.requires_grad_()
  
          input_lengths = batch_size * [input_length]
          target_lengths = batch_size * [target_length]
          grad_out = torch.randn(batch_size, device='cuda', dtype=torch.float)
          with torch.backends.cudnn.flags(enabled=False):
              loss_native = torch.nn.functional.ctc_loss(log_probs, targets, input_lengths, target_lengths, reduction='none')
              grad_native, = torch.autograd.grad(loss_native, log_probs, grad_out)
          loss_cudnn = torch.nn.functional.ctc_loss(log_probs, targets.to('cpu', torch.int32),
                                                    input_lengths, target_lengths, reduction='none')
          self.assertTrue("Cudnn" in str(loss_cudnn.grad_fn))
          grad_cudnn, = torch.autograd.grad(loss_cudnn, log_probs, grad_out)
          self.assertEqual(grad_cudnn, grad_native, prec=1e-4)
  
      @onlyCUDA
      def test_free_unneeded_tensor(self, device):
          x = torch.randn(2, 3, 10, 10, device=device, requires_grad=True)
          m = torch.randn(1, 3, 1, 1, device=device)
  
          z = x.sum()
          base_mem = torch.cuda.memory_allocated()
          z = ((x + 2) * m).sum()
          end_mem = torch.cuda.memory_allocated()
  
          # In the end the memory usage should remain equal, because neither of
          # (x + 2) and ((x + 2) * m) should be kept alive for backward, while the
          # previous allocation of z had the same size as the current one.
          self.assertEqual(base_mem, end_mem)
  
      @onlyCUDA
      def test_pin_memory(self, device):
          x = torch.randn(2, 2, requires_grad=True)
          self.assertEqual(x, x.pin_memory())
          self.assertIsNot(x, x.pin_memory())
          self.assertTrue(x.pin_memory().requires_grad)
          gradcheck(lambda x: x.pin_memory(), [x])
          gradgradcheck(lambda x: x.pin_memory(), [x])
  
      @skipCUDAIfRocm
      @onlyCUDA
      def test_profiler_emit_nvtx(self, device):
          # This test is not intended to ensure correctness of nvtx ranges.
          # That would require something a great deal more complex (you'd have to create a
          # profile in a subprocess, open it, and parse the sql somehow).
          # This test is merely intended to catch if emit_nvtx breaks on construction.
          a = torch.tensor([1, 2, 3], dtype=torch.float32, device=device)
          with torch.cuda.profiler.profile():
              with emit_nvtx():
                  a.add(1.0)
  
      @onlyCUDA
      def test_rnn_backward_to_input_but_not_parameters(self, device):
          # this checks whether it is possible to not require
          # weight parameters, but require inputs, see #7722
          l = torch.nn.LSTM(2, 3).to(device)
          for p in l.parameters():
              p.requires_grad = False
          s = torch.randn(1, 1, 2, requires_grad=True, device=device)
          out, _ = l(s)
          out.sum().backward()
          self.assertFalse(s.grad is None or s.grad.abs().sum().item() == 0)
  
      @onlyCUDA
      def test_lstmcell_backward_only_one_output_grad(self, device):
          # checks that undefined gradients doen't hamper the backward
          # see #11872
          l = torch.nn.LSTMCell(2, 3).to(device).double()
          s = torch.randn(1, 2, device=device, dtype=torch.double, requires_grad=True)
          for i in range(2):
              out = l(s)[i]
              out.sum().backward()
              self.assertFalse(s.grad is None or s.grad.abs().sum().item() == 0)
  
      def _test_rnn_mod(self, mod, inp):
          from functools import partial
  
          def flatten_out(mod, inp):
              out = mod(inp)
              return tuple([t if isinstance(t, torch.Tensor) else tt for t in out for tt in t])
          gradcheckfunc = partial(flatten_out, mod)
          with torch.backends.cudnn.flags(enabled=False):
              torch.autograd.gradcheck(gradcheckfunc, inp)
              torch.autograd.gradgradcheck(gradcheckfunc, inp)
  
      def test_LSTM_grad_and_gradgrad(self, device):
          hsize = 4
          inp = torch.rand(1, 3, hsize, device=device, dtype=torch.float64, requires_grad=True)
          for bias in [True, False]:
              mod = torch.nn.LSTM(hsize, hsize, bias=bias).to(device).to(torch.float64)
              self._test_rnn_mod(mod, inp)
  
      def test_GRU_grad_and_gradgrad(self, device):
          hsize = 4
          inp = torch.rand(1, 3, hsize, device=device, dtype=torch.float64, requires_grad=True)
          for bias in [True, False]:
              mod = torch.nn.GRU(hsize, hsize, bias=bias).to(device).to(torch.float64)
              self._test_rnn_mod(mod, inp)
  
      @deviceCountAtLeast(1)
      def test_grad_assignment(self, devices):
          x = torch.randn(5, 5, device=devices[0])
  
          # Tests that the wrong shape raises
          with self.assertRaises(RuntimeError):
              x.grad = torch.randn(2, 2, device=devices[0])
  
          # Tests that the wrong dtype raises
          with self.assertRaises(RuntimeError):
              x.grad = torch.randn(5, 5, dtype=torch.long, device=devices[0])
  
          # Tests that self-assignment raises
          with self.assertRaises(RuntimeError):
              x.grad = x
  
          # Tests device -> cpu grad assignment raises
          if self.device_type != 'cpu':
              with self.assertRaises(RuntimeError):
                  t_cpu = torch.rand(5, 5)
                  t_cpu.grad = torch.randn(5, 5, device=devices[0])
  
          # Tests half type on CUDA
          if self.device_type == 'cuda':
              x = x.to(dtype=torch.half, device=devices[0])
              x.grad = torch.zeros_like(x)
  
          # Tests cross-device assignment raises
          if len(devices) > 1:
              x = torch.randn(5, 5, device=devices[0])
              with self.assertRaises(RuntimeError):
                  x.grad = torch.randn(5, 5, device=devices[1])
  
      @deviceCountAtLeast(1)
      @dtypes(torch.float, torch.double)
      def test_requires_grad_factory(self, devices, dtype):
          fns = [torch.ones_like, torch.testing.randn_like]
          x = torch.randn(2, 3, dtype=dtype, device=devices[0])
  
          for fn in fns:
              for requires_grad in [True, False]:
                  output = fn(x, dtype=dtype, device=devices[0], requires_grad=requires_grad)
                  self.assertEqual(requires_grad, output.requires_grad)
                  self.assertIs(dtype, output.dtype)
                  self.assertEqual(devices[0], str(x.device))
  
      @deviceCountAtLeast(2)
      def test_unused_output_device(self, devices):
          from torch.nn.parallel._functions import Broadcast
          x = torch.randn(5, 5, dtype=torch.float, device=devices[0], requires_grad=True)
          outputs = Broadcast.apply(list(range(len(devices))), x)
          y = outputs[-1] * 2
          y.sum().backward()
          self.assertEqual(x.grad, torch.ones(5, 5) * 2)
  
      @deviceCountAtLeast(2)
      def test_backward_device(self, devices):
          # check that current device matches the variable's device
          device = [None]
  
          class Identity(torch.autograd.Function):
              @staticmethod
              def forward(ctx, x):
                  return x.clone()
  
              @staticmethod
              def backward(ctx, grad_output):
                  device[0] = grad_output.device
                  return grad_output.clone()
  
          v = torch.randn(1, device=devices[1], requires_grad=True)
          Identity.apply(v).backward()
          self.assertEqual(str(device[0]), devices[1])
  
      @deviceCountAtLeast(2)
      def test_inputbuffer_add_multidevice(self, devices):
          input = torch.randn(1, device=devices[0], requires_grad=True)
          output = input.to(device=devices[1]) + input.to(device=devices[1])
          output.backward()
  
      @onlyCPU
      def test_copy_(self, device):
          # At the time of writing this test, copy_ is not generated from native_functions.yaml
          # there was a bug that bfloat16 was not recognized as floating.
          x = torch.randn(10, device=device, requires_grad=True)
          floating_dt = [dt for dt in torch.testing.get_all_dtypes() if dt.is_floating_point]
          for dt in floating_dt:
              y = torch.empty(10, device=device, dtype=dt)
              y.copy_(x)
              self.assertTrue(y.requires_grad)
              z = x.to(torch.bfloat16)
              self.assertTrue(z.requires_grad)
  
      @onlyCUDA
      def test_simple_reentrant_cross_device(self, device):
          class ReentrantFunc(Function):
              _cpu_mode = True
              @staticmethod
              def forward(ctx, x):
                  return x * (x + 2)
  
              @staticmethod
              def backward(ctx, grad_output):
                  with torch.enable_grad():
                      if ReentrantFunc._cpu_mode:
                          new_param = torch.randn(2, 2, requires_grad=True)
                          (new_param ** 2).sum().backward()
                      else:
                          new_param = torch.randn(2, 2, device=device, requires_grad=True)
                          (new_param ** 2).sum().backward()
                  return grad_output
  
          # Reentrant starts on GPU thread, finishs on GPU thread
          x = torch.randn(2, 2, device=device, requires_grad=True)
          out = ReentrantFunc.apply(x)
          out.sum().backward()
  
          # Reentrant starts on CPU thread, finishs on GPU thread
          x = torch.randn(2, 2, requires_grad=True)
          # set ReentrantFunc node to GPU to emit tasks to GPU queue
          ReentrantFunc._cpu_mode = False
          out = ReentrantFunc.apply(x)
          out.sum().backward()
  
          # Reentrant starts on GPU thread, finishs on CPU thread
          x = torch.randn(2, 2, device=device, requires_grad=True)
          # set ReentrantFunc node to CPU to emit tasks to CPU queue
          ReentrantFunc._cpu_mode = True
          out = ReentrantFunc.apply(x)
          out.sum().backward()
  
      @onlyCUDA
      def test_cross_device_reentrant_autograd(self, device):
          # Output on gpu so that this task will be associated with the gpu thread
          def fn_on_gpu(inp):
              # Artificially increase the priority of the next op to make sure it runs
              # as soon as we reach it before the ops of branch1.
              dummy = inp * 2 * 2 * 2 * 2
              return inp.to(device=device)
  
          def parent_on_cpu(inp):
              # Slow branch of ops on gpu so that the work queue for the gpu thread
              # won't empty too quickly. They also have smaller priorities than the
              # ones created by fn_on_gpu
              branch1 = inp.to(device=device)
              branch1 = branch1 / branch1
              branch1 = branch1 / branch1
              branch1 = branch1 / branch1
              # Perform checkpoint on cpu tensors. So the last op performed in the reentrant
              # autograd is an AccumulateGrad that runs on the cpu thread for the gpu thread.
              # So the cpu thread will notify the gpu thread with an empty NodeTask.
              branch2 = checkpoint(fn_on_gpu, inp)
              out = branch2 + branch1
              return out
  
          inp = torch.rand(2, requires_grad=True)
          out = parent_on_cpu(inp)
          # This will segfault if the empty NodeTask is not handled properly in the
          # gpu thread ReadyQueue
          out.sum().backward()
  
  class TestMultithreadAutograd(TestCase):
      def _run_py_multithread_fn(self, fn, args=(), num_threads=10, kwargs=None):
          threads = []
          for _ in range(num_threads):
              p = threading.Thread(target=fn, args=(args))
              p.start()
              threads.append(p)
  
          for p in threads:
              p.join()
  
      def test_simple_backward(self):
          # simple multithreaded backward that create threads in the beginning of training
          # and everything else is training separately, i.e. inputs, operations, etc.
          def train_fn():
              x = torch.ones(5, 5, requires_grad=True)
              y = (x + 3) * (x + 4) * 0.5
              y.sum().backward()
              self.assertEqual(x.grad, x + 3.5)
  
          self._run_py_multithread_fn(train_fn)
  
  
      def test_simple_backward_same_input(self):
          # simple multithreaded backward with only shared inputs (i.e. This is common
          # for things like Hogwild multithreaded training with multiple CPU threads)
          def train_fn_backward(x):
              y = (x + 3) * (x + 4) * 0.5
              y.sum().backward()
  
          x = torch.ones(5, 5, requires_grad=True)
          self._run_py_multithread_fn(train_fn_backward, (x,))
          # Since we are calling backward from multiple threads
          # and all threads share the same input, when we do backward
          # concurrently, different backwards will all accumulate to
          # the same .grad for each input, and the gradients should
          # be equal to num_threads * gradient
          self.assertEqual(x.grad, 10 * (x + 3.5))
  
          def train_fn_grad(x):
              y = (x + 3) * (x + 4) * 0.5
              grads = torch.autograd.grad(y.sum(), x)
              self.assertEqual(len(grads), 1)
              self.assertEqual(grads[0], x + 3.5)
  
          # since we use functional grad() api, gradients will not
          # be accumulate to the same place and should be the same
          self._run_py_multithread_fn(train_fn_grad, (x,))
  
  
      def test_python_thread_in_middle(self):
          # User might write a network that starts on one CPU thread, then runs its second half
          # concurrently with other threads (either via python threading or fork/join calls),
          # then calls backward()/grad() on BOTH threads, like a Y pattern from input at the
          # bottom to output at the top. This way part of the GraphTask is being shared across
          # different threads and we need to ensure user specify retain_graph=True, otherwise
          # error out with the correct error message
  
          # Case 1: multiple backward with python threads, retain_graph=False
          # should throw error in some threads with no retain_graph.
          success_vs_raises = [0, 0]
  
          def train_fn_no_retain_graph(x):
              y = x + x ** 2
              try:
                  y.sum().backward()
                  success_vs_raises[0] += 1
              except RuntimeError as error:
                  success_vs_raises[1] += 1
                  self.assertRegex(str(error), "Specify retain_graph=True")
  
          x_no_retain = torch.ones(5, 5, requires_grad=True)
          y_no_retain = x_no_retain + x_no_retain ** 2
          self._run_py_multithread_fn(train_fn_no_retain_graph, (y_no_retain,), num_threads=5)
          # at least one thread will be success in this case, all other threads should raise
          # with the error that throw to user to recommend them specify retain_graph=True
          self.assertTrue(success_vs_raises[0] >= 1)
  
          # multiple backward with python threads, no error with retain_graph=True
          def train_fn_retain_graph(x):
              y = x + x ** 2
              y.sum().backward(retain_graph=True)
  
          x_retain = torch.ones(5, 5, requires_grad=True)
          y_retain = x_retain + x_retain ** 2
          self._run_py_multithread_fn(train_fn_retain_graph, (y_retain,), num_threads=5)
          # result should equal to num_thread * gradients
          self.assertEqual(x_retain.grad, 5 * (4 * x_retain ** 3 + 6 * (x_retain ** 2) + 4 * x_retain + 1))
  
  
      def test_fork_join_in_middle(self):
          # multiple backward with jit threads (fork/join primitive)
          # similar to test_python_thread_in_middle, we test with retain_graph=False/True
  
          # Case 1: multiple grad() calls with jit threads, retain_graph=False
          # should throw error in some threads with no retain_graph.
          @torch.jit.script
          def train_fn_jit_no_retain(middle, orig_x):
              y = middle + middle ** 2
              return torch.autograd.grad([y.sum()], [orig_x])
  
          @torch.jit.script
          def train_fn_fork_join_calls_no_retain(x):
              y_no_retain = (x + 3) * (x + 4) * 0.5
  
              fut = torch.jit._fork(train_fn_jit_no_retain, y_no_retain, x)
              grad_hat = train_fn_jit_no_retain(y_no_retain, x)
              grad = torch.jit._wait(fut)
              return grad, grad_hat
  
          try:
              train_fn_fork_join_calls_no_retain(torch.randn(5, 5, requires_grad=True))
          except RuntimeError as error:
              self.assertRegex(str(error), "Specify retain_graph=True")
  
          # Case 2: no error with retain_graph=True
          @torch.jit.script
          def train_fn_jit_retain(middle, orig_x):
              y = middle + middle ** 2
              return torch.autograd.grad([y.sum()], [orig_x], retain_graph=True)
  
          @torch.jit.script
          def train_fn_fork_join_calls_retain(x):
              y_retain = (x + 3) * (x + 4) * 0.5
              fut1 = torch.jit._fork(train_fn_jit_retain, y_retain, x)
              fut2 = torch.jit._fork(train_fn_jit_retain, y_retain, x)
              grad = train_fn_jit_retain(y_retain, x)
              grad1 = torch.jit._wait(fut1)
              grad2 = torch.jit._wait(fut2)
              return grad, grad1, grad2
  
          grad, grad1, grad2 = train_fn_fork_join_calls_retain(torch.randn(5, 5, requires_grad=True))
          self.assertEqual(grad, grad1)
          self.assertEqual(grad, grad2)
  
  
  
  for test in method_tests():
      add_test(*test)
  
  
  # e.g., TestAutogradDeviceTypeCPU and TestAutogradDeviceTypeCUDA
  instantiate_device_type_tests(
      TestAutogradDeviceType,
      globals(),
      # Exclude ROCM for now, there are a lot of failures.  See
      # https://github.com/pytorch/pytorch/issues/30845
      except_for='cuda' if TEST_WITH_ROCM else None
  )
  
  if __name__ == '__main__':
      run_tests()
  