code: from functools import reduce, wraps, partial
  from itertools import product
  from operator import mul
  import collections
  import operator
  import random
  
  import torch
  import numpy as np
  from torch._six import inf
  from torch.autograd import Variable
  import collections.abc
  
  from typing import List, Sequence, Tuple, Dict, Any, Union
  
  from torch.testing import \
      (make_non_contiguous, floating_types, floating_types_and, complex_types,
       floating_and_complex_types, floating_and_complex_types_and,
       all_types_and_complex_and, all_types_and, all_types_and_complex,
       integral_types_and, all_types)
  from .._core import _dispatch_dtypes
  from torch.testing._internal.common_device_type import \
      (skipIf, skipCUDAIfNoMagma, skipCUDAIfNoMagmaAndNoCusolver, skipCUDAIfNoCusolver,
       skipCPUIfNoLapack, skipCPUIfNoMkl, skipCUDAIfRocm, precisionOverride,)
  from torch.testing._internal.common_cuda import CUDA11OrLater, SM53OrLater
  from torch.testing._internal.common_utils import \
      (is_iterable_of_tensors,
       random_symmetric_matrix, random_symmetric_psd_matrix,
       make_fullrank_matrices_with_distinct_singular_values,
       random_symmetric_pd_matrix, make_symmetric_matrices,
       make_symmetric_pd_matrices,
       random_fullrank_matrix_distinct_singular_value, set_rng_seed, SEED,
       TEST_WITH_ROCM, IS_WINDOWS, IS_MACOS, make_tensor, TEST_SCIPY,
       torch_to_numpy_dtype_dict, slowTest, TEST_WITH_ASAN, _wrap_warn_once,
       GRADCHECK_NONDET_TOL,)
  
  from setuptools import distutils
  
  if TEST_SCIPY:
      import scipy.special
  
  
  class DecorateInfo(object):
      """Describes which test, or type of tests, should be wrapped in the given
         decorators when testing an operator. Any test that matches all provided
         arguments will be decorated. The decorators will only be applied if the
         active_if argument is True."""
  
      __slots__ = ['decorators', 'cls_name', 'test_name', 'device_type', 'dtypes', 'active_if']
  
      def __init__(self, decorators, cls_name=None, test_name=None, *,
                   device_type=None, dtypes=None, active_if=True):
          self.decorators = list(decorators) if isinstance(decorators, collections.abc.Sequence) else [decorators]
          self.cls_name = cls_name
          self.test_name = test_name
          self.device_type = device_type
          self.dtypes = dtypes
          self.active_if = active_if
  
      def is_active(self, cls_name, test_name, device_type, dtype):
          return (
              self.active_if and
              (self.cls_name is None or self.cls_name == cls_name) and
              (self.test_name is None or self.test_name == test_name) and
              (self.device_type is None or self.device_type == device_type) and
              (self.dtypes is None or dtype in self.dtypes)
          )
  
  
  class SkipInfo(DecorateInfo):
      """Describes which test, or type of tests, should be skipped when testing
         an operator. Any test that matches all provided arguments will be skipped.
         The skip will only be checked if the active_if argument is True."""
  
      def __init__(self, cls_name=None, test_name=None, *,
                   device_type=None, dtypes=None, active_if=True):
          super().__init__(decorators=skipIf(True, "Skipped!"), cls_name=cls_name,
                           test_name=test_name, device_type=device_type, dtypes=dtypes,
                           active_if=active_if)
  
  class SampleInput(object):
      """Represents sample inputs to a function."""
  
      __slots__ = ['input', 'args', 'kwargs', 'output_process_fn_grad', 'broadcasts_input']
  
      def __init__(self, input, *, args=tuple(), kwargs=None, output_process_fn_grad=None, broadcasts_input=False):
          # input is the first input to the op and must be either a Tensor or TensorList (Sequence[Tensor]).
          # This follows the typical pattern where for Tensor inputs op(t, ...) = t.op(...).
          # op with TensorList inputs do not support method or inplace variants.
          assert isinstance(input, torch.Tensor) or is_iterable_of_tensors(input)
          self.input: Union[torch.Tensor, Sequence[torch.Tensor]] = input
          self.args = args
          self.kwargs = kwargs if kwargs is not None else {}
          self.output_process_fn_grad = output_process_fn_grad
  
          # Specifies if `self.input` is broadcasted or not,
          # given that the operator supports broadcasting.
          # This field is used to verify the behavior for inplace variant.
          #
          # If a SampleInput is marked with `broadcasts_input=True`,
          # it is verified that we get a `RuntimerError` with this sample,
          # and inplace variant. Also inplace grad{grad} tests are skipped,
          # for such inputs (as they will error out otherwise).
          self.broadcasts_input = broadcasts_input
  
      def __repr__(self):
          arguments = [
              'input=Tensor' if isinstance(self.input, torch.Tensor) else f'input=TensorList[{len(self.input)}]',
              f'args={self.args}' if len(self.args) > 0 else None,
              f'kwargs={self.kwargs}' if len(self.kwargs) > 0 else None,
              (f'output_process_fn_grad={self.output_process_fn_grad}'
               if self.output_process_fn_grad is not None else None),
              f'broadcasts_input={self.broadcasts_input}']
  
          return f'SampleInput({", ".join(a for a in arguments if a is not None)})'
  
  class AliasInfo(object):
      """Class holds alias information. For example, torch.abs ->
      torch.absolute, torch.Tensor.absolute, torch.Tensor.absolute_
      """
  
      def __init__(self, alias_name):
          self.name = alias_name
          self.op = _getattr_qual(torch, alias_name)
          self.method_variant = getattr(torch.Tensor, alias_name, None)
          self.inplace_variant = getattr(torch.Tensor, alias_name + "_", None)
  
      def __call__(self, *args, **kwargs):
          return self.op(*args, **kwargs)
  
  
  _NOTHING = object()  # Unique value to distinguish default from anything else
  
  
  # Extension of getattr to support qualified names
  # e.g. _getattr_qual(torch, 'linalg.norm') -> torch.linalg.norm
  def _getattr_qual(obj, name, default=_NOTHING):
      try:
          for path in name.split('.'):
              obj = getattr(obj, path)
          return obj
      except AttributeError:
          if default is not _NOTHING:
              return default
          else:
              raise
  
  
  # Classes and methods for the operator database
  class OpInfo(object):
      """Operator information and helper functions for acquiring it."""
  
      def __init__(self,
                   name,  # the string name of the function
                   *,
                   op=None,  # the function variant of the operation, populated as torch.<name> if None
                   dtypes=floating_types(),  # dtypes this function is expected to work with
                   dtypesIfCPU=None,  # dtypes this function is expected to work with on CPU
                   dtypesIfCUDA=None,  # dtypes this function is expected to work with on CUDA
                   dtypesIfROCM=None,  # dtypes this function is expected to work with on ROCM
                   backward_dtypes=None,  # backward dtypes this function is expected to work with
                   backward_dtypesIfCPU=None,  # backward dtypes this function is expected to work with on CPU
                   backward_dtypesIfCUDA=None,  # backward dtypes this function is expected to work with on CUDA
                   backward_dtypesIfROCM=None,  # backward dtypes this function is expected to work with on ROCM
                   default_test_dtypes=None,  # dtypes to test with by default. Gets intersected
                                              # with the dtypes support on the tested device
                   assert_autodiffed=False,  # if a op's aten::node is expected to be symbolically autodiffed
                   autodiff_nonfusible_nodes=None,  # a list of strings with node names that are expected to be in a
                                                    # DifferentiableGraph when autodiffed. Ex: ['aten::add', 'aten::mm'],
                                                    # default is populated to be ['aten::(name of Python operator)']
                   autodiff_fusible_nodes=None,  # a list of strings with node names that are expected to be in FusionGroups
                                                 # inside of DifferentiableGraphs when this operation is autodiffed.
                                                 # Ex: ['aten::add', 'aten::mm'], defaults to an empty list
                                                 # Note: currently no ops use fusible nodes
                   supports_out=True,  # whether the op supports the out kwarg
                   skips=tuple(),  # information about which tests to skip
                   decorators=None,  # decorators to apply to generated tests
                   safe_casts_outputs=False,  # whether op allows safe casting when writing to out arguments
                   sample_inputs_func=None,  # function to generate sample inputs
                   aten_name=None,  # name of the corresponding aten:: operator
                   aliases=None,  # iterable of aliases, e.g. ("absolute",) for torch.abs
                   variant_test_name='',  # additional string to include in the test name
                   supports_autograd=True,  # support for autograd
                   supports_gradgrad=True,  # support second order gradients (this value is ignored if supports_autograd=False)
                   supports_inplace_autograd=None,  # whether the operation supports inplace autograd
                                                    # defaults to supports_autograd's value
                   supports_sparse=False,  # whether the op supports sparse inputs
                   gradcheck_wrapper=lambda op, *args, **kwargs: op(*args, **kwargs),  # wrapper function for gradcheck
                   check_batched_grad=True,  # check batched grad when doing gradcheck
                   check_batched_gradgrad=True,  # check batched grad grad when doing gradgradcheck
                   gradcheck_nondet_tol=0.0,  # tolerance for nondeterminism while performing gradcheck
                   gradcheck_fast_mode=None,  # Whether to use the fast implmentation for gradcheck/gradgradcheck.
                                              # When set to None, defers to the default value provided by the wrapper
                                              # function around gradcheck (testing._internal.common_utils.gradcheck)
                   ):
  
          # Validates the dtypes are generated from the dispatch-related functions
          for dtype_list in (dtypes, dtypesIfCPU, dtypesIfCUDA, dtypesIfROCM):
              assert isinstance(dtype_list, (_dispatch_dtypes, type(None)))
  
          self.name = name
          self.aten_name = aten_name if aten_name is not None else name
          self.variant_test_name = variant_test_name
  
          self.dtypes = set(dtypes)
          self.dtypesIfCPU = set(dtypesIfCPU) if dtypesIfCPU is not None else self.dtypes
          self.dtypesIfCUDA = set(dtypesIfCUDA) if dtypesIfCUDA is not None else self.dtypes
          self.dtypesIfROCM = set(dtypesIfROCM) if dtypesIfROCM is not None else self.dtypesIfCUDA
  
          self.backward_dtypes = set(backward_dtypes) if backward_dtypes is not None else self.dtypes
          self.backward_dtypesIfCPU = set(backward_dtypesIfCPU) if backward_dtypesIfCPU is not None else (
              self.dtypesIfCPU if dtypesIfCPU is not None else self.backward_dtypes)
          self.backward_dtypesIfCUDA = set(backward_dtypesIfCUDA) if backward_dtypesIfCUDA is not None else (
              self.dtypesIfCUDA if dtypesIfCUDA is not None else self.backward_dtypes)
          self.backward_dtypesIfROCM = set(backward_dtypesIfROCM) if backward_dtypesIfROCM is not None else (
              self.dtypesIfROCM if dtypesIfROCM is not None else self.backward_dtypesIfCUDA)
  
          self._default_test_dtypes = set(default_test_dtypes) if default_test_dtypes is not None else None
  
          # NOTE: if the op is unspecified it is assumed to be under the torch namespace
          self.op = op if op else _getattr_qual(torch, self.name)
          method_variant = getattr(torch.Tensor, name, None)
          # attributes like real, imag are not callable
          self.method_variant = method_variant if callable(method_variant) else None
          inplace_name = name + "_"
          self.inplace_variant = getattr(torch.Tensor, inplace_name, None)
          self.operator_variant = getattr(operator, name, None)
  
          self.supports_out = supports_out
          self.safe_casts_outputs = safe_casts_outputs
  
          self.skips = skips
          self.decorators = decorators
          self.sample_inputs_func = sample_inputs_func
  
          self.assert_autodiffed = assert_autodiffed
          self.autodiff_fusible_nodes = autodiff_fusible_nodes if autodiff_fusible_nodes else []
          if autodiff_nonfusible_nodes is None:
              self.autodiff_nonfusible_nodes = ['aten::' + self.name]
          else:
              self.autodiff_nonfusible_nodes = autodiff_nonfusible_nodes
  
          # autograd support
          self.supports_autograd = supports_autograd
          self.supports_inplace_autograd = supports_inplace_autograd
          if self.supports_inplace_autograd is None:
              self.supports_inplace_autograd = supports_autograd
  
          self.gradcheck_wrapper = gradcheck_wrapper
          self.supports_gradgrad = supports_gradgrad
          self.check_batched_grad = check_batched_grad
          self.check_batched_gradgrad = check_batched_gradgrad
          self.gradcheck_nondet_tol = gradcheck_nondet_tol
          self.gradcheck_fast_mode = gradcheck_fast_mode
  
          self.supports_sparse = supports_sparse
  
          self.aliases = ()
          if aliases is not None:
              self.aliases = tuple(AliasInfo(a) for a in aliases)  # type: ignore[assignment]
  
      def __call__(self, *args, **kwargs):
          """Calls the function variant of the operator."""
          return self.op(*args, **kwargs)
  
      def get_op(self):
          """Returns the function variant of the operator, torch.<op_name>."""
          return self.op
  
      def get_method(self):
          """Returns the method variant of the operator, torch.Tensor.<op_name>.
          Returns None if the operator has no method variant.
          """
          return self.method_variant
  
      def get_inplace(self):
          """Returns the inplace variant of the operator, torch.Tensor.<op_name>_.
          Returns None if the operator has no inplace variant.
          """
          return self.inplace_variant
  
      def get_operator_variant(self):
          """Returns operator variant of the operator, e.g. operator.neg
          Returns None if the operator has no operator variant.
          """
          return self.operator_variant
  
      def sample_inputs(self, device, dtype, requires_grad=False, **kwargs):
          """Returns an iterable of SampleInputs.
  
          These samples should be sufficient to test the function works correctly
          with autograd, TorchScript, etc.
          """
  
          # TODO: Remove the try/except once all operators have sample_inputs_func with
          #       **kwargs in their signature.
          try:
              samples = self.sample_inputs_func(self, device, dtype, requires_grad, **kwargs)
          except TypeError:
              samples = self.sample_inputs_func(self, device, dtype, requires_grad)
          return samples
  
      # Returns True if the test should be skipped and False otherwise
      def should_skip(self, cls_name, test_name, device_type, dtype):
          return any(si.is_active(cls_name, test_name, device_type, dtype)
                     for si in self.skips)
  
      def supported_dtypes(self, device_type):
          if device_type == 'cpu':
              return self.dtypesIfCPU
          if device_type == 'cuda':
              return self.dtypesIfROCM if TEST_WITH_ROCM else self.dtypesIfCUDA
          else:
              return self.dtypes
  
      def supported_backward_dtypes(self, device_type):
          if device_type == 'cpu':
              return self.backward_dtypesIfCPU
          if device_type == 'cuda':
              return self.backward_dtypesIfROCM if TEST_WITH_ROCM else self.backward_dtypesIfCUDA
          else:
              return self.backward_dtypes
  
      def supports_complex_autograd(self, device_type):
          if device_type == 'cpu':
              return any(dtype.is_complex for dtype in self.backward_dtypesIfCPU)
          if device_type == 'cuda':
              if TEST_WITH_ROCM:
                  return any(dtype.is_complex for dtype in self.backward_dtypesIfROCM)
              else:
                  return any(dtype.is_complex for dtype in self.backward_dtypesIfCUDA)
          else:
              return any(dtype.is_complex for dtype in self.backward_dtypes)
  
      def supports_dtype(self, dtype, device_type):
          return dtype in self.supported_dtypes(device_type)
  
      def default_test_dtypes(self, device_type):
          """Returns the default dtypes used to test this operator on the device.
  
          Equal to the operator's default_test_dtypes filtered to remove dtypes
          not supported by the device.
          """
          supported = self.supported_dtypes(device_type)
          return (supported if self._default_test_dtypes is None
                  else supported.intersection(self._default_test_dtypes))
  
  
  L = 20
  M = 10
  S = 5
  
  
  def sample_inputs_unary(op_info, device, dtype, requires_grad, **kwargs):
      low, high = op_info.domain
      low = low if low is None else low + op_info._domain_eps
      high = high if high is None else high - op_info._domain_eps
  
      return (SampleInput(make_tensor((L,), device=device, dtype=dtype,
                                      low=low, high=high,
                                      requires_grad=requires_grad)),
              SampleInput(make_tensor((), device=device, dtype=dtype,
                                      low=low, high=high,
                                      requires_grad=requires_grad)))
  
  # Metadata class for unary "universal functions (ufuncs)" that accept a single
  # tensor and have common properties like:
  class UnaryUfuncInfo(OpInfo):
      """Operator information for 'universal unary functions (unary ufuncs).'
      These are functions of a single tensor with common properties like:
        - they are elementwise functions
        - the input shape is the output shape
        - they typically have method and inplace variants
        - they typically support the out kwarg
        - they typically have NumPy or SciPy references
      See NumPy's universal function documentation
      (https://numpy.org/doc/1.18/reference/ufuncs.html) for more details
      about the concept of ufuncs.
      """
  
      def __init__(self,
                   name,  # the string name of the function
                   *,
                   ref,  # a reference function
                   dtypes=floating_types(),
                   dtypesIfCPU=None,
                   dtypesIfCUDA=None,
                   dtypesIfROCM=None,
                   default_test_dtypes=(
                       torch.uint8, torch.long, torch.half, torch.bfloat16,
                       torch.float32, torch.cfloat),  # dtypes which tests check by default
                   domain=(None, None),  # the [low, high) domain of the function
                   handles_large_floats=True,  # whether the op correctly handles large float values (like 1e20)
                   handles_extremals=True,  # whether the op correctly handles extremal values (like inf)
                   handles_complex_extremals=True,  # whether the op correct handles complex extremals (like inf -infj)
                   supports_complex_to_float=False,  # op supports casting from complex input to real output safely eg. angle
                   sample_inputs_func=sample_inputs_unary,
                   sample_kwargs=lambda device, dtype, input: ({}, {}),
                   supports_sparse=False,
                   **kwargs):
          super(UnaryUfuncInfo, self).__init__(name,
                                               dtypes=dtypes,
                                               dtypesIfCPU=dtypesIfCPU,
                                               dtypesIfCUDA=dtypesIfCUDA,
                                               dtypesIfROCM=dtypesIfROCM,
                                               default_test_dtypes=default_test_dtypes,
                                               sample_inputs_func=sample_inputs_func,
                                               supports_sparse=supports_sparse,
                                               **kwargs)
          self.ref = ref
          self.domain = domain
          self.handles_large_floats = handles_large_floats
          self.handles_extremals = handles_extremals
          self.handles_complex_extremals = handles_complex_extremals
          self.supports_complex_to_float = supports_complex_to_float
  
          # test_unary_ufuncs.py generates its own inputs to test the consistency
          # of the operator on sliced tensors, non-contig tensors, etc.
          # `sample_kwargs` is a utility function to provide kwargs
          # along with those inputs if required (eg. clamp).
          # It should return two dictionaries, first holding kwarg for
          # torch operator and second one for reference NumPy operator.
          self.sample_kwargs = sample_kwargs
  
          # Epsilon to ensure grad and gradgrad checks don't test values
          #   outside a function's domain.
          self._domain_eps = 1e-5
  
  def sample_inputs_tensor_split(op_info, device, dtype, requires_grad, **kwargs):
      return (SampleInput(make_tensor((S, S, S), device, dtype,
                                      low=None, high=None,
                                      requires_grad=requires_grad),
                          args=(torch.tensor([1, 2, 3]),),),
              SampleInput(make_tensor((S, S, S), device, dtype,
                                      low=None, high=None,
                                      requires_grad=requires_grad),
                          args=(torch.tensor(1),),),
              SampleInput(make_tensor((S, S, S), device, dtype,
                                      low=None, high=None,
                                      requires_grad=requires_grad),
                          args=(torch.tensor([1, 2, 3]),),
                          kwargs=dict(dim=1)),)
  
  def sample_inputs_linalg_det(op_info, device, dtype, requires_grad):
      kw = dict(device=device, dtype=dtype)
      inputs = [
          make_tensor((S, S), **kw),
          make_tensor((1, 1), **kw),  # 1x1
          random_symmetric_matrix(S, **kw),  # symmetric
          random_symmetric_psd_matrix(S, **kw),  # symmetric_psd
          random_symmetric_pd_matrix(S, **kw),  # symmetric_pd
  
          # dim2_null, rank1 and rank2 are disabled because of
          # https://github.com/pytorch/pytorch/issues/53364
          # we should re-enable them once the issue is solved
          # random_square_matrix_of_rank(S, S - 2, **kw),  # dim2_null
          # random_square_matrix_of_rank(S, 1, **kw),  # rank1
          # random_square_matrix_of_rank(S, 2, **kw),  # rank2
  
          random_fullrank_matrix_distinct_singular_value(S, **kw),  # distinct_singular_value
          make_tensor((3, 3, S, S), **kw),  # batched
          make_tensor((3, 3, 1, 1), **kw),  # batched_1x1
          random_symmetric_matrix(S, 3, **kw),  # batched_symmetric
          random_symmetric_psd_matrix(S, 3, **kw),  # batched_symmetric_psd
          random_symmetric_pd_matrix(S, 3, **kw),  # batched_symmetric_pd
          random_fullrank_matrix_distinct_singular_value(S, 3, 3, **kw),  # batched_distinct_singular_values
          make_tensor((0, 0), **kw),
          make_tensor((0, S, S), **kw),
      ]
      for t in inputs:
          t.requires_grad = requires_grad
      return [SampleInput(t) for t in inputs]
  
  def sample_inputs_linalg_matrix_power(op_info, device, dtype, requires_grad):
      # (<matrix_size>, (<batch_sizes, ...>))
      test_sizes = [
          (1, ()),
          (2, (0,)),
          (2, (2,)),
      ]
  
      inputs = []
      for matrix_size, batch_sizes in test_sizes:
          size = batch_sizes + (matrix_size, matrix_size)
          for n in (0, 3, 5):
              t = make_tensor(size, device, dtype, requires_grad=requires_grad)
              inputs.append(SampleInput(t, args=(n,)))
          for n in [-4, -2, -1]:
              t = random_fullrank_matrix_distinct_singular_value(matrix_size, *batch_sizes, device=device, dtype=dtype)
              t.requires_grad = requires_grad
              inputs.append(SampleInput(t, args=(n,)))
  
      return inputs
  
  def sample_inputs_hsplit(op_info, device, dtype, requires_grad):
      return (SampleInput(make_tensor((6,), device, dtype,
                                      low=None, high=None,
                                      requires_grad=requires_grad),
                          args=(2,),),
              SampleInput(make_tensor((S, S, S), device, dtype,
                                      low=None, high=None,
                                      requires_grad=requires_grad),
                          args=([1, 2, 3],),),)
  
  def sample_inputs_vsplit(op_info, device, dtype, requires_grad):
      return (SampleInput(make_tensor((6, S), device, dtype,
                                      low=None, high=None,
                                      requires_grad=requires_grad),
                          args=(2,),),
              SampleInput(make_tensor((S, S, S), device, dtype,
                                      low=None, high=None,
                                      requires_grad=requires_grad),
                          args=([1, 2, 3],),),)
  
  def sample_inputs_dsplit(op_info, device, dtype, requires_grad):
      return (SampleInput(make_tensor((S, S, S), device, dtype,
                                      low=None, high=None,
                                      requires_grad=requires_grad),
                          args=([1, 2, 3],),),
              SampleInput(make_tensor((S, S, 6), device, dtype,
                                      low=None, high=None,
                                      requires_grad=requires_grad),
                          args=(2,),),)
  
  def sample_inputs_linalg_multi_dot(op_info, device, dtype, requires_grad):
      # Each test case consists of the sizes in the chain of multiplications
      # e.g. [2, 3, 4, 5] generates matrices (2, 3) @ (3, 4) @ (4, 5)
      test_cases = [
          [1, 2, 1],
          [2, 0, 2],
          [0, 2, 2],
          [2, 2, 2, 2],
          [2, 3, 4, 5],
          [5, 4, 0, 2],
          [2, 4, 3, 5, 3, 2]
      ]
  
      result = []
      for sizes in test_cases:
          tensors = []
          for size in zip(sizes[:-1], sizes[1:]):
              t = make_tensor(size, device, dtype, requires_grad=requires_grad)
              tensors.append(t)
          result.append(SampleInput(tensors))
  
      return result
  
  def sample_inputs_linalg_matrix_norm(op_info, device, dtype, requires_grad, **kwargs):
      sizes = ((2, 2), (2, 3, 2))
      ords = ('fro', 'nuc', inf, -inf, 1, -1, 2, -2)
      dims = ((-2, -1), (-1, 0))
  
      inputs: List[SampleInput] = []
      for size, ord, dim, keepdim in product(sizes, ords, dims, [True, False]):
          t = make_tensor(size, device, dtype, requires_grad=requires_grad)
          inputs.append(SampleInput(t, args=(ord, dim, keepdim)))
  
      return inputs
  
  def sample_inputs_linalg_norm(op_info, device, dtype, requires_grad):
      test_sizes = [
          (S,),
          (0,),
          (S, S),
          (0, 0),
          (S, 0),
          (0, S),
          (S, S, S),
          (0, S, S),
          (S, 0, S),
          (0, 0, 0),
      ]
  
      vector_ords = (None, 0, 0.5, 1, 2, 3.5, inf, -0.5, -1, -2, -3.5, -inf)
      matrix_ords = (None, 'fro', 'nuc', 1, 2, inf, -1, -2, -inf)
  
      inputs = []
  
      for test_size in test_sizes:
          is_vector_norm = len(test_size) == 1
          is_matrix_norm = len(test_size) == 2
  
          for keepdim in [False, True]:
              inputs.append(SampleInput(
                  make_tensor(
                      test_size, device, dtype, low=None, high=None,
                      requires_grad=requires_grad),
                  kwargs=dict(
                      keepdim=keepdim)))
  
              if not (is_vector_norm or is_matrix_norm):
                  continue
  
              ords = vector_ords if is_vector_norm else matrix_ords
  
              for ord in ords:
  
                  inputs.append(SampleInput(
                      make_tensor(
                          test_size, device, dtype,
                          low=None, high=None,
                          requires_grad=requires_grad),
                      args=(ord,),
                      kwargs=dict(
                          keepdim=keepdim)))
  
                  if ord in ['nuc', 'fro']:
                      inputs.append(SampleInput(
                          make_tensor(
                              test_size, device, dtype,
                              low=None, high=None,
                              requires_grad=requires_grad),
                          kwargs=dict(
                              ord=ord,
                              keepdim=keepdim,
                              dim=(0, 1))))
          return inputs
  
  def sample_inputs_linalg_vector_norm(op_info, device, dtype, requires_grad, **kwargs):
      size_1D = (S,)
      size_2D = (2, 2)
  
      test_cases = [
          # input size, ord, dim args
          (size_1D, 2, None),
          (size_1D, 2, (0,)),
          (size_1D, 0, None),
          (size_1D, 0, (0,)),
          (size_1D, 0.9, None),
          (size_1D, 0.9, (0,)),
          (size_1D, 1, None),
          (size_1D, 1, (0,)),
          (size_1D, -2.1, None),
          (size_1D, -2.1, (0,)),
          (size_1D, inf, None),
          (size_1D, inf, (0,)),
          (size_1D, -inf, None),
          (size_1D, -inf, (0,)),
  
          (size_2D, 2, None),
          (size_2D, 2, (0,)),
          (size_2D, 2, (-1, 0)),
          (size_2D, 0, None),
          (size_2D, 0, (0,)),
          (size_2D, 0, (-1, 0)),
          (size_2D, 0.9, None),
          (size_2D, 0.9, (0,)),
          (size_2D, 0.9, (-1, 0)),
          (size_2D, 1, None),
          (size_2D, 1, (0,)),
          (size_2D, 1, (-1, 0)),
          (size_2D, -2.1, None),
          (size_2D, -2.1, (0,)),
          (size_2D, -2.1, (-1, 0)),
          (size_2D, inf, None),
          (size_2D, inf, (0,)),
          (size_2D, inf, (-1, 0)),
          (size_2D, -inf, None),
          (size_2D, -inf, (0,)),
          (size_2D, -inf, (-1, 0)),
      ]
      inputs = []
  
      for test_size, ord, dim in test_cases:
          for keepdim in [False, True]:
              inputs.append(SampleInput(
                  make_tensor(
                      test_size, device, dtype,
                      low=None, high=None,
                      requires_grad=requires_grad),
                  args=(ord,),
                  kwargs=dict(
                      keepdim=keepdim,
                      dim=dim)))
  
      return inputs
  
  # In order to use the kwarg alpha, partials should be used in an OpInfo's sample_inputs_func
  # eg. sample_inputs_func=partial(sample_inputs_binary_pwise, alpha=2)
  # Then one sample input would also be generated corresponding to the value of alpha provided.
  # In the future, kwargs 'alpha_floating', 'alpha_integral' & 'alpha_complex' can be used to
  # specify scalars of floating, integral & complex types as values for "alpha".
  def sample_inputs_binary_pwise(op_info, device, dtype, requires_grad, **kwargs):
      scalar = 3.14 + 3.14j if dtype.is_complex else (3.14 if dtype.is_floating_point else 3)
      scalar = 1 if dtype is torch.bool else scalar
      tests_list = [
          ((S, S, S), (S, S, S), False),
          ((S, S, S), (S, S), False),
          ((), (), False),
          ((S, S, S), (), False),
          ((S, S, S), scalar, False),
          ((), scalar, False)
      ]
      tests_with_lhs_broadcasting = [
          ((S, S), (S, S, S), True),
          ((), (S, S, S), True),
          ((S, 1, S), (M, S), True),
      ]
      test_cases = tests_list + tests_with_lhs_broadcasting  # type: ignore[operator]
      samples = []
      for first_shape, shape_or_scalar, broadcasts_input in test_cases:
          arg = shape_or_scalar
          if isinstance(shape_or_scalar, tuple):
              arg = make_tensor(shape_or_scalar, device=device, dtype=dtype,
                                requires_grad=requires_grad)
          samples.append(SampleInput(make_tensor(first_shape, device=device, dtype=dtype,
                                                 requires_grad=requires_grad),
                                     args=(arg,),
                                     broadcasts_input=broadcasts_input))
      # Adds an extra sample using "alpha" if it's passed in kwargs
      if 'alpha' in kwargs:
          a = make_tensor((S, S, S), device=device, dtype=dtype, requires_grad=requires_grad)
          b = make_tensor((S, S, S), device=device, dtype=dtype, requires_grad=requires_grad)
          sample = SampleInput(a, args=(b,), kwargs={'alpha': kwargs['alpha']})
          samples.append(sample)
      return tuple(samples)
  
  def sample_inputs_mm(op_info, device, dtype, requires_grad, **kwargs):
      args_list = (
          ((S, M), (M, S)),
      )
      inputs = tuple(SampleInput(make_tensor(first_shape, device, dtype,
                                             requires_grad=requires_grad),
                                 args=(make_tensor(second_shape, device, dtype,
                                       requires_grad=requires_grad),))
                     for first_shape, second_shape in args_list)
      return inputs
  
  def sample_inputs_addmm(op_info, device, dtype, requires_grad, **kwargs):
      alpha_val = kwargs.get('alpha', 2 + 3j if dtype.is_complex else 0.6)
      beta_val = kwargs.get('beta', 1 + 2j if dtype.is_complex else 0.2)
      tests_list = [
          ((2, 3), (2, 2), (2, 3), False)
      ]
      tests_with_lhs_broadcasting = [
          ((1,), (2, 2), (2, 3), True),
          ((), (2, 2), (2, 3), True)
      ]
      test_cases = tests_list + tests_with_lhs_broadcasting  # type: ignore[operator]
      inputs = tuple(SampleInput(make_tensor(shape_a, device, dtype, requires_grad=requires_grad),
                                 args=(make_tensor(shape_b, device, dtype,
                                                   requires_grad=requires_grad),
                                       make_tensor(shape_c, device, dtype,
                                                   requires_grad=requires_grad)),
                                 kwargs={'alpha': alpha_val, 'beta': beta_val},
                                 broadcasts_input=broadcasts_input)
                     for shape_a, shape_b, shape_c, broadcasts_input in test_cases)
      return inputs
  
  def sample_inputs_mv(self, device, dtype, requires_grad, **kwargs):
      return (
          SampleInput(
              make_tensor((S, M, ), device, dtype, low=None, high=None, requires_grad=requires_grad),
              args=(
                  make_tensor((M, ), device, dtype, low=None, high=None, requires_grad=requires_grad),
              )
          ),
      )
  
  def sample_inputs_bmm(self, device, dtype, requires_grad, **kwargs):
      return (
          SampleInput(
              make_tensor((M, S, M, ), device, dtype, low=None, high=None, requires_grad=requires_grad),
              args=(
                  make_tensor((M, M, S, ), device, dtype, low=None, high=None, requires_grad=requires_grad),
              )
          ),
      )
  
  def sample_inputs_dot_vdot(self, device, dtype, requires_grad, **kwargs):
      return (
          SampleInput(
              make_tensor((S, ), device, dtype, low=None, high=None, requires_grad=requires_grad),
              args=(
                  make_tensor((S, ), device, dtype, low=None, high=None, requires_grad=requires_grad),
              )
          ),
      )
  
  def sample_inputs_addmv(op_info, device, dtype, requires_grad, **kwargs):
      test_cases = (((S,), (S, M), (M,), 1, 1, False),
                    ((S,), (S, M), (M,), 0.2, 0.6, False),
                    )
  
      test_cases_with_broadcast = (((1,), (S, M), (M,), 1, 1, True),
                                   ((1,), (S, M), (M,), 0.2, 0.6, True),
                                   ((), (S, M), (M,), 1, 1, True),
                                   ((), (S, M), (M,), 0.2, 0.6, True),
                                   )
  
      cases = test_cases + test_cases_with_broadcast
      sample_inputs = []
      for input_args in cases:
          args = (make_tensor(input_args[0], device, dtype,
                              low=None, high=None,
                              requires_grad=requires_grad),
                  make_tensor(input_args[1], device, dtype,
                              low=None, high=None,
                              requires_grad=requires_grad),
                  make_tensor(input_args[2], device, dtype,
                              low=None, high=None,
                              requires_grad=requires_grad))
          alpha, beta = input_args[3], input_args[4]
          broadcasts_input = input_args[5]
          sample_inputs.append(SampleInput(args[0], args=(args[1], args[2]), kwargs=dict(beta=beta, alpha=alpha),
                                           broadcasts_input=broadcasts_input))
      return tuple(sample_inputs)
  
  def sample_inputs_addbmm(op_info, device, dtype, requires_grad, **kwargs):
      test_cases = [((S, M), (S, S, S), (S, S, M), 1, 1),
                    ((1,), (S, S, S), (S, S, M), 1, 1),
                    ((S, M), (S, S, S), (S, S, M), 0.6, 0.2),
                    ((1,), (S, S, S), (S, S, M), 0.6, 0.2),
                    ((), (S, S, S), (S, S, M), 1, 1),
                    ((), (S, S, S), (S, S, M), 0.6, 0.2),
                    ]
      sample_inputs = []
      for input_args in test_cases:
          args = (make_tensor(input_args[0], device, dtype,
                              low=None, high=None,
                              requires_grad=requires_grad),
                  make_tensor(input_args[1], device, dtype,
                              low=None, high=None,
                              requires_grad=requires_grad),
                  make_tensor(input_args[2], device, dtype,
                              low=None, high=None,
                              requires_grad=requires_grad))
          alpha, beta = input_args[3], input_args[4]
          sample_inputs.append(SampleInput(args[0], args=(args[1], args[2]), kwargs=dict(beta=beta, alpha=alpha)))
          if dtype.is_complex:
              sample_inputs.append(SampleInput(args[0], args=(args[1], args[2]),
                                               kwargs=dict(beta=beta * (1 + 2j), alpha=alpha * (2 + 3j))))
  
      return tuple(sample_inputs)
  
  def sample_inputs_addcmul_addcdiv(op_info, device, dtype, requires_grad, **kwargs):
      test_cases = [((S, S), (S, S), (S, S)),
                    ((S, S), (S, 1), (1, S)),
                    ((1,), (S, S, 1), (1, S)),
                    ((), (), ()),
                    ((S, S), (), ()),
                    ((), (S, S, 1), (1, S)),
                    ]
  
      sample_inputs = []
      for input_args in test_cases:
          args = tuple(make_tensor(arg, device, dtype, requires_grad=requires_grad) if isinstance(arg, tuple) else arg
                       for arg in input_args)
          sample_inputs.append(SampleInput(args[0], args=args[1:]))
  
          sample_inputs.append(SampleInput(args[0], args=args[1:], kwargs=dict(value=3.14)))
  
      return tuple(sample_inputs)
  
  def sample_inputs_baddbmm(op_info, device, dtype, requires_grad, **kwargs):
      test_cases = [((S, S, M), (S, S, S), (S, S, M), 1, 1, False),
                    ((1,), (S, S, S), (S, S, M), 1, 1, True),
                    ((S, S, M), (S, S, S), (S, S, M), 0.6, 0.2, False),
                    ((1,), (S, S, S), (S, S, M), 0.6, 0.2, True),
                    ((), (S, S, S), (S, S, M), 1, 1, True),
                    ((), (S, S, S), (S, S, M), 0.6, 0.2, True),
                    ]
      sample_inputs = []
      for (input_shape, batch1_shape, batch2_shape, alpha, beta, broadcasts_input) in test_cases:
          args = (make_tensor(input_shape, device, dtype,
                              low=None, high=None,
                              requires_grad=requires_grad),
                  make_tensor(batch1_shape, device, dtype,
                              low=None, high=None,
                              requires_grad=requires_grad),
                  make_tensor(batch2_shape, device, dtype,
                              low=None, high=None,
                              requires_grad=requires_grad))
          sample_inputs.append(SampleInput(args[0], args=(args[1], args[2]),
                               kwargs=dict(beta=beta, alpha=alpha), broadcasts_input=broadcasts_input))
          if dtype.is_complex:
              sample_inputs.append(SampleInput(args[0], args=(args[1], args[2]),
                                               kwargs=dict(beta=beta * (1 + 2j), alpha=alpha * (2 + 3j)),
                                               broadcasts_input=broadcasts_input))
      return tuple(sample_inputs)
  
  def sample_inputs_addr(op_info, device, dtype, requires_grad, **kwargs):
      input1 = SampleInput(
          make_tensor((S, M), device, dtype, low=None, high=None, requires_grad=requires_grad),
          args=(
              make_tensor((S, ), device, dtype, low=None, high=None, requires_grad=requires_grad),
              make_tensor((M, ), device, dtype, low=None, high=None, requires_grad=requires_grad)))
  
      input2 = SampleInput(
          make_tensor((), device, dtype, low=None, high=None, requires_grad=requires_grad),
          args=(
              make_tensor((S, ), device, dtype, low=None, high=None, requires_grad=requires_grad),
              make_tensor((M, ), device, dtype, low=None, high=None, requires_grad=requires_grad)))
  
      if dtype.is_complex:
          alpha, beta = 0.1 + 0.3j, 0.4 + 0.6j
      elif dtype.is_floating_point:
          alpha, beta = 0.2, 0.6
      else:
          alpha, beta = 2, 3
  
      input3 = SampleInput(
          make_tensor((S, M), device, dtype, low=None, high=None, requires_grad=requires_grad),
          args=(
              make_tensor((S, ), device, dtype, low=None, high=None, requires_grad=requires_grad),
              make_tensor((M, ), device, dtype, low=None, high=None, requires_grad=requires_grad)),
          kwargs=dict(beta=beta, alpha=alpha))
  
      input4 = SampleInput(
          make_tensor((), device, dtype, low=None, high=None, requires_grad=requires_grad),
          args=(
              make_tensor((S, ), device, dtype, low=None, high=None, requires_grad=requires_grad),
              make_tensor((M, ), device, dtype, low=None, high=None, requires_grad=requires_grad)),
          kwargs=dict(beta=beta, alpha=alpha))
  
      return (input1, input2, input3, input4)
  
  def sample_inputs_xlogy(self, device, dtype, requires_grad, **kwargs):
      return (
          SampleInput(
              make_tensor((S, S), device, dtype, low=None, high=None, requires_grad=requires_grad),
              args=(
                  make_tensor((S, S), device, dtype, low=0, high=None, requires_grad=requires_grad),
              )
          ),
      )
  
  
  def sample_inputs_xlog1py(self, device, dtype, requires_grad):
      make_arg = partial(make_tensor, device=device, dtype=dtype, requires_grad=requires_grad)
  
      def generator():
          # same shape
          yield SampleInput(make_arg((S, S)), args=(make_arg((S, S), low=-1),))
          # rhs broadcast
          yield SampleInput(make_arg((S, S)), args=(make_arg((S,), low=-1),))
          # all zero `x`
          with torch.no_grad():
              x = make_arg((S, S))
              x.fill_(0)
          yield SampleInput(x, args=(make_arg((S, S), low=-1),))
  
          # randomly zero-masked `x`
          x = make_arg((S, S))
          y = make_arg((S, S), low=-1)
          with torch.no_grad():
              x[torch.rand(x.shape) > 0.5] = 0
          yield SampleInput(x, args=(y,))
  
          # Scalar x
          # `input` has to be a tensor
          # yield SampleInput(0, args=(make_arg((S, S), low=-1),))
          # yield SampleInput(2.1, args=(make_arg((S, S), low=-1),))
  
          # Scalar y
          yield SampleInput(make_arg((S, S)), args=(-0.5,))
          yield SampleInput(make_arg((S, S)), args=(1.2,))
  
      return list(generator())
  
  
  def sample_inputs_logsumexp(self, device, dtype, requires_grad):
      inputs = (
          ((), (0,), True),
          ((S, S), (1,), True),
          ((S, S), (1,), False)
      )
      samples = []
  
      for shape, dim, keepdim in inputs:
          t = make_tensor(shape, device, dtype,
                          low=None, high=None,
                          requires_grad=requires_grad)
          samples.append(SampleInput(t, args=(dim, keepdim)))
  
      return tuple(samples)
  
  def sample_inputs_logcumsumexp(self, device, dtype, requires_grad):
      inputs = (
          ((S, S, S), 0),
          ((S, S, S), 1),
          ((), 0),
      )
      samples = []
  
      for shape, dim in inputs:
          t = make_tensor(shape, device, dtype,
                          low=None, high=None,
                          requires_grad=requires_grad)
          samples.append(SampleInput(t, args=(dim,)))
  
      return tuple(samples)
  
  def sample_inputs_trace(self, device, dtype, requires_grad, **kwargs):
      return (SampleInput((make_tensor((S, S), device, dtype,
                                       low=None, high=None,
                                       requires_grad=requires_grad))),)
  
  
  def sample_inputs_transpose_swapdims(self, device, dtype, requires_grad, **kwargs):
      make_arg = partial(make_tensor, dtype=dtype, device=device, requires_grad=requires_grad)
  
      cases = (((1, 2, 3), (-1, -2)),
               ((1, 2, 3), (-1, 2)),
               ((1, 2, 3), (1, -2)),
               ((1, 2, 3), (1, 2)),
               ((), (0, 0)),
               ((1, ), (0, 0)),
               ((M, M), (0, 1)),
               ((S, S, S), (2, 0)), )
  
      def generator():
          for shape, args in cases:
              yield SampleInput(make_arg(shape), args=args)
  
      return list(generator())
  
  
  def sample_inputs_linalg_invertible(op_info, device, dtype, requires_grad=False, **kwargs):
      """
      This function generates always invertible input for linear algebra ops using
      random_fullrank_matrix_distinct_singular_value.
      The input is generated as the itertools.product of 'batches' and 'ns'.
      In total this function generates 8 SampleInputs
      'batches' cases include:
          () - single input,
          (0,) - zero batched dimension,
          (2,) - batch of two matrices,
          (1, 1) - 1x1 batch of matrices
      'ns' gives 0x0 and 5x5 matrices.
      Zeros in dimensions are edge cases in the implementation and important to test for in order to avoid unexpected crashes.
      """
      from torch.testing._internal.common_utils import random_fullrank_matrix_distinct_singular_value
  
      batches = [(), (0, ), (2, ), (1, 1)]
      ns = [5, 0]
      out = []
      for batch, n in product(batches, ns):
          a = random_fullrank_matrix_distinct_singular_value(n, *batch, dtype=dtype, device=device)
          a.requires_grad = requires_grad
          out.append(SampleInput(a))
      return out
  
  def np_sinc_with_fp16_as_fp32(x):
      # Wraps numpy's sinc function so that fp16 values are promoted to fp32
      # before sinc is invoked. Context: numpy's sinc returns NaN when evaluated
      # at 0 for fp16.
      if x.dtype == np.float16:
          return np.sinc(x.astype(np.float32))
      else:
          return np.sinc(x)
  
  def sample_inputs_broadcast_to(op_info, device, dtype, requires_grad, **kwargs):
      test_cases = (
          ((S, 1, 1), (S, S, S)),
          ((S, 1, S), (S, S, S)),
          ((S, 1), (S, S, S)),
          ((1,), (S, S, S)),
          ((1, S), (1, 1, S)),
          ((), ()),
          ((), (1, 3, 2)),
      )
  
      return tuple(
          SampleInput(
              make_tensor(size, device, dtype, low=None, high=None, requires_grad=requires_grad),
              args=(shape,)) for size, shape in test_cases)
  
  def sample_inputs_cdist(op_info, device, dtype, requires_grad, **kwargs):
      small_S = 2
      test_cases = (
          ((S, S, 2), (S, S + 1, 2)),
          ((S, S), (S, S)),
          ((S, S, S), (S, S, S)),
          ((3, 5), (3, 5)),
          ((2, 3, 5), (2, 3, 5)),
          ((1, 2, 3), (1, 2, 3)),
          ((1, 1), (S, 1)),
          ((0, 5), (4, 5)),
          ((4, 5), (0, 5)),
          ((0, 4, 5), (3, 5)),
          ((4, 5), (0, 3, 5)),
          ((0, 4, 5), (1, 3, 5)),
          ((1, 4, 5), (0, 3, 5)),
          # Using S here would make this one test take 9s
          ((small_S, small_S, small_S + 1, 2), (small_S, small_S, small_S + 2, 2)),
          ((small_S, 1, 1, small_S), (1, small_S, small_S)),
          ((1, 1, small_S), (small_S, 1, small_S, small_S)),
      )
  
      samples = []
      for cm in ['use_mm_for_euclid_dist', 'donot_use_mm_for_euclid_dist']:
          for p in [0, 1, 2, 3, 0.5, 1.5, 2.5, float("inf")]:
              for t1_size, t2_size in test_cases:
                  # The args should never be non-contiguous as this is not supported in the backward
                  samples.append(SampleInput(
                      make_tensor(t1_size, device, dtype, requires_grad=requires_grad, noncontiguous=False),
                      args=(make_tensor(t2_size, device, dtype, requires_grad=requires_grad, noncontiguous=False), p, cm)))
  
      return samples
  
  def sample_inputs_comparison_ops(self, device, dtype, requires_grad, **kwargs):
      test_cases = (
          ((S, S, S), (S, S, S), False),
          ((S, S, S), (), False),
          ((S, S, S), (1,), False),
          ((S,), (1,), False),
          ((), (), False),
      )
      test_cases_lhs_broadcasting = (
          ((S, 1, S), (S, S, S), True),
          ((1,), (S, S, S), True),
          ((1, S), (1, 1, S), True),
          ((), (0,), True),
          ((), (S, S, S), True),
      )
      cases = test_cases + test_cases_lhs_broadcasting
      sample_inputs = list(SampleInput(make_tensor(first_shape, device, dtype,
                                                   requires_grad=requires_grad),
                                       args=(make_tensor(second_shape, device, dtype,
                                                         requires_grad=requires_grad),),
                                       broadcasts_input=broadcasts_input)
                           for first_shape, second_shape, broadcasts_input in cases)
      equal_tensors_non_bool = (
          ([[[-8, 6], [9, 0]], [[0, 5], [5, 7]]]),
          ([[[6, 5]], [[1, -5]]]),
          ([[2], [-1]]),
          ([0, -6]),
          ([3],),
      )
      equal_tensors_bool = (
          ([[[1, 0], [0, 0]], [[0, 1], [1, 0]]]),
          ([[[1, 1]], [[1, 0]]]),
          ([[1], [0]]),
          ([0, 1]),
          ([1],),
      )
      more_cases = equal_tensors_bool if dtype is torch.bool else equal_tensors_non_bool
      more_inputs = list(SampleInput(torch.tensor(elements, device=device, dtype=dtype,
                                                  requires_grad=requires_grad),
                                     args=(torch.tensor(elements, device=device, dtype=dtype,
                                                        requires_grad=requires_grad),))
                         for elements in more_cases)
      sample_inputs = [*sample_inputs, *more_inputs]
      return tuple(sample_inputs)
  
  def sample_inputs_div(self, device, dtype, requires_grad, rounding_mode=None, **kwargs):
      a = make_tensor((S, S, S), device, dtype, low=None, high=None, requires_grad=requires_grad)
      is_integral = not dtype.is_floating_point and not dtype.is_complex
      b = make_tensor((S, S, S), device, dtype, low=1 if is_integral else 0.1, high=None,
                      requires_grad=requires_grad)
  
      kwargs = None  # type: ignore[assignment]
      if rounding_mode is not None:
          kwargs = dict(rounding_mode=rounding_mode)
  
      return (
          SampleInput(a, args=(b,), kwargs=kwargs),
          SampleInput(a, args=(2,)),
      )
  
  def sample_inputs_stack(op_info, device, dtype, requires_grad, **kwargs):
      tensors = [
          make_tensor((S, S), device, dtype, requires_grad=requires_grad),
          make_tensor((S, S), device, dtype, requires_grad=requires_grad),
          make_tensor((S, S), device, dtype, requires_grad=requires_grad),
      ]
  
      return (SampleInput(tensors, args=(0,)),)
  
  def sample_inputs_hstack_dstack_vstack(op_info, device, dtype, requires_grad, **kwargs):
      tensors = [
          make_tensor((S, S), device, dtype, requires_grad=requires_grad),
          make_tensor((S, S), device, dtype, requires_grad=requires_grad),
          make_tensor((S, S), device, dtype, requires_grad=requires_grad),
      ]
  
      return (SampleInput(tensors),)
  
  def sample_inputs_hypot(op_info, device, dtype, requires_grad):
      input = make_tensor((S, S), device, dtype, requires_grad=requires_grad)
      args = make_tensor((S, S), device, dtype, requires_grad=requires_grad)
  
      return (
          SampleInput(input, args=(args,)),
      )
  
  def sample_inputs_gather(op_info, device, dtype, requires_grad, **kwargs):
      return (
          SampleInput(
              make_tensor((M, S), device, dtype, low=None, high=None, requires_grad=requires_grad),
              args=(0, gather_variable((S, S), 1, M, True, device=device))),
          SampleInput(
              make_tensor((M, S), device, dtype, low=None, high=None, requires_grad=requires_grad),
              args=(1, gather_variable((M, S // 2), 0, S, True, device=device))),
          SampleInput(
              make_tensor((), device, dtype, low=None, high=None, requires_grad=requires_grad),
              args=(0, torch.tensor([0], dtype=torch.int64, device=device))),
          SampleInput(
              make_tensor((S,), device, dtype, low=None, high=None, requires_grad=requires_grad),
              args=(0, torch.tensor(0, dtype=torch.int64, device=device))),
          SampleInput(
              make_tensor((), device, dtype, low=None, high=None, requires_grad=requires_grad),
              args=(0, torch.tensor(0, dtype=torch.int64, device=device))),
      )
  
  
  def sample_inputs_take_along_dim(op_info, device, dtype, requires_grad, **kwargs):
      return (SampleInput(make_tensor((S, S), device, dtype,
                                      low=None, high=None,
                                      requires_grad=requires_grad),
                          args=(gather_variable((S, S), 1, S, True, device=device), 0)),
  
              # `indices` broadcast
              SampleInput(make_tensor((S, S), device, dtype,
                                      low=None, high=None,
                                      requires_grad=requires_grad),
                          args=(gather_variable((1, S // 2), 0, S, True, device=device), 1)),
  
              # `self` broadcast
              SampleInput(make_tensor((1, S), device, dtype,
                                      low=None, high=None,
                                      requires_grad=requires_grad),
                          args=(gather_variable((S, S // 2), 0, S, True, device=device), 1)),
  
              # without `dim` arg
              SampleInput(make_tensor((S, S), device, dtype,
                                      low=None, high=None,
                                      requires_grad=requires_grad),
                          args=(gather_variable((S, S // 2), 0, S, True, device=device), )),
              SampleInput(make_tensor((S, S), device, dtype,
                                      low=None, high=None,
                                      requires_grad=requires_grad),
                          args=(gather_variable((S, S // 2), 0, S, True, device=device),)),
              )
  
  def sample_inputs_amax_amin(op_info, device, dtype, requires_grad, **kwargs):
      test_cases = (
          ((S, S, S), ()),
          ((S, S, S), (1,)),
          ((S, S, S), ((1, 2,),)),
          ((S, S, S), (1, True,)),
          ((), (0,)),
          ((), ()),
          ((), (0, True,)),
      )
      return tuple(SampleInput((make_tensor(size, device, dtype,
                                            low=None, high=None,
                                            requires_grad=requires_grad)),
                               args=args)
                   for size, args in test_cases)
  
  def sample_inputs_argmax_argmin(op_info, device, dtype, requires_grad, **kwargs):
      test_cases = (
          ((2, 2, 2), ()),
          ((2, 2, 2), (0,)),
          ((2, 2, 2), (1,)),
          ((2, 2, 2), (2,)),
          ((2, 2, 2), (2, True,)),
          ((2, 2, 2), (None,)),
          ((), (0,)),
          ((), ()),
          ((), (None, True,)),
          ((1,), ()),
          ((1,), (0,)),
          ((1,), (0, True)),
          ((2,), ()),
          ((2,), (0,)),
          ((2,), (0, True)),
          ((2, 2, 3), ()),
          ((2, 2, 3), (0,)),
          ((2, 2, 3), (1,)),
          ((2, 2, 3), (None, True)),
      )
      return tuple(SampleInput((make_tensor(size, device, dtype,
                                            requires_grad=requires_grad)),
                               args=args)
                   for size, args in test_cases)
  
  def sample_inputs_diff(op_info, device, dtype, requires_grad, **kwargs):
      test_cases = (
          ((1,), 0, None, None),
          ((S,), 0, None, None),
          ((S, 1), 0, None, None),
          ((S, 1), 1, None, None),
          ((S, S), 0, None, None),
          ((S, S), 1, None, None),
          ((S, S), 0, (1, S), (2, S)),
          ((S, S), 0, None, (2, S)),
          ((S, S, S), 1, None, None),
          ((S, S, S), 1, (S, 1, S), (S, 1, S)),)
  
      sample_inputs = []
      for size, dim, size_prepend, size_append in test_cases:
          args = (make_tensor(size, device, dtype,
                              low=None, high=None,
                              requires_grad=requires_grad), 1, dim,
                  make_tensor(size_prepend, device, dtype,
                              low=None, high=None,
                              requires_grad=requires_grad) if size_prepend else None,
                  make_tensor(size_append, device, dtype,
                              low=None, high=None,
                              requires_grad=requires_grad) if size_append else None)
          sample_inputs.append(SampleInput(args[0], args=(args[1], args[2])))
  
      return tuple(sample_inputs)
  
  def sample_inputs_gradient(op_info, device, dtype, requires_grad):
      sample_inputs = []
      test_cases_float = (
          ((S,), None, None),
          ((S,), 2., None),
          ((S, S), None, None),
          ((S, S), [2.0, 2.1], None),
          ((S, S), [2.0, 2.1], (0, 1)),
          ((4, 4, 4), [2., 1.], (0, 1)),
      )
      for size, spacing, dim in test_cases_float:
          t = make_tensor(size, device, dtype, low=None, high=None, requires_grad=requires_grad)
          sample_inputs.append(SampleInput(t, kwargs=dict(dim=dim, spacing=spacing)))
  
      test_cases_tensor = (
          ((3, 3, 3), ((1.1, 2.0, 3.5), (4.0, 2, 6.0)), (0, -1)),
          ((3, 3, 3), ((1.0, 3.0, 2.0), (8.0, 6.0, 1.0)), (0, 1)),
      )
      for size, coordinates, dim in test_cases_tensor:
          t = make_tensor(size, device, dtype, low=None, high=None, requires_grad=requires_grad)
          coordinates_tensor_list = []
          for coords in coordinates:
              a = torch.tensor(coords, dtype=dtype, device=device)
              coordinates_tensor_list.append(a)
          sample_inputs.append(SampleInput(t, kwargs=dict(dim=dim, spacing=coordinates_tensor_list)))
  
      return tuple(sample_inputs)
  
  def sample_inputs_index_select(op_info, device, dtype, requires_grad):
      return (
          SampleInput(
              make_tensor((S, S, S), device, dtype, low=None, high=None, requires_grad=requires_grad),
              args=(0, index_variable(2, S, device=device))),
          SampleInput(
              make_tensor((), device, dtype, low=None, high=None, requires_grad=requires_grad),
              args=(0, torch.tensor([0], dtype=torch.int64, device=device))),
          SampleInput(
              make_tensor((), device, dtype, low=None, high=None, requires_grad=requires_grad),
              args=(0, torch.tensor(0, dtype=torch.int64, device=device))),
      )
  
  def sample_inputs_getitem(op_info, device, dtype, requires_grad, **kwargs):
      test_args = [
          (dont_convert([1, 2]),),
          (slice(0, 3),),
          (dont_convert([slice(0, 3), 1]),),
          (dont_convert([[0, 2, 3], [1, 3, 3], [0, 0, 2]]),),
          (dont_convert([[0, 0, 3], [1, 1, 3], [0, 0, 2]]),),
          (dont_convert([slice(None), slice(None), [0, 3]]),),
          (dont_convert([slice(None), [0, 3], slice(None)]),),
          (dont_convert([[0, 3], slice(None), slice(None)]),),
          (dont_convert([[0, 3], [1, 2], slice(None)]),),
          (dont_convert([[0, 3], ]),),
          (dont_convert([[0, 3], slice(None)]),),
          (dont_convert([[0, 3], Ellipsis]),),
          (dont_convert([[0, 2, 3], [1, 3, 3], torch.LongTensor([0, 0, 2])]),),
          (index_variable(2, S, device=device),),
          (mask_not_all_zeros((S,)),),
      ]
  
      return tuple(SampleInput(
          make_tensor((S, S, S), device, dtype, low=None, high=None, requires_grad=requires_grad),
          args=args)
          for args in test_args)
  
  def sample_inputs_index_put(op_info, device, dtype, requires_grad, **kwargs):
      inputs = []
      for accumulate in [False, True]:
          # Test with indices arg
          inputs.append(SampleInput(
              make_tensor((S, S,), device, dtype, low=None, high=None, requires_grad=requires_grad),
              args=(
                  (index_variable(2, S, device=device), ),
                  make_tensor((2, S), device, dtype, low=None, high=None)),
              kwargs=dict(accumulate=accumulate)))
  
          # Test with mask arg
          mask = torch.zeros(S, dtype=torch.bool) if accumulate else mask_not_all_zeros((S,))
          inputs.append(SampleInput(
              make_tensor((S, S), device, dtype, low=None, high=None, requires_grad=requires_grad),
              args=(
                  (mask, ),
                  make_tensor((S,), device, dtype, low=None, high=None),),
              kwargs=dict(accumulate=accumulate)))
  
      return inputs
  
  # Missing to test the nondeterminism of the operation
  # https://github.com/pytorch/pytorch/issues/53352
  def sample_inputs_index_add(op_info, device, dtype, requires_grad, **kwargs):
      # These testa are pretty much the same as those from index_copy.
      # Perhaps merge?
      make_arg = partial(make_tensor, dtype=dtype, device=device, requires_grad=requires_grad)
  
      t = make_arg((S, S))
      s = make_arg((S, S))
      # non-contiguous target
      t_nonctg = t.transpose(0, 1)
      # non-contiguous source
      s_nonctg = s.transpose(0, 1)
  
      idx = make_arg((S,), dtype=torch.int64, low=0, high=S)
      idx_nonctg = make_arg((S,), dtype=torch.int64, low=0, high=S, noncontiguous=True)
      samples = [SampleInput(tensor, args=(1, idx, source))
                 for tensor, idx, source in product([t, t_nonctg], [idx, idx_nonctg], [s, s_nonctg])]
      samples.extend(SampleInput(tensor, args=(1, idx, source), kwargs=dict(alpha=a))
                     for tensor, idx, source, a in product([t, t_nonctg], [idx, idx_nonctg], [s, s_nonctg], [-1, 0, 2]))
  
      # Add scalar cases
      scalar_sizes = [(), (1,)]
      ts = (make_arg(size) for size in scalar_sizes)
      idxs = (make_arg(size, dtype=torch.int64, low=0, high=1) for size in scalar_sizes)
      ss = (make_arg(size) for size in scalar_sizes)
  
      samples.extend(SampleInput(t, args=(0, idx, s)) for t, idx, s in product(ts, idxs, ss))
      samples.extend(SampleInput(t, args=(0, idx, s), kwargs=dict(alpha=a)) for t, idx, s, a in product(ts, idxs, ss, [-1, 0, 2]))
      return samples
  
  def sample_inputs_sort(op_info, device, dtype, requires_grad, **kwargs):
      def apply_grad(t):
          if dtype in floating_types_and(torch.float16, torch.bfloat16):
              t.requires_grad_(requires_grad)
  
      def small_3d_unique(dtype, device):
          res = torch.randperm(S * S * S, dtype=torch.int64, device=device).view(S, S, S)
          res = res.to(dtype)
          apply_grad(res)
          return res
  
      def large_1d_unique(dtype, device):
          res = torch.randperm(L * L * L, dtype=torch.int64, device=device)
          res = res.to(dtype)
          apply_grad(res)
          return res
  
      samples = []
      # Test case for large tensor.
      largesample = SampleInput(large_1d_unique(dtype, device))
      samples.append(largesample)
  
      # Test cases for small 3d tensors.
      # Imitates legacy tests from test/test_torch.py
      t = small_3d_unique(dtype, device)
      dims = range(-3, 3)
      flag = [True, False]
      for dim, descending, stable in product(dims, flag, flag):
          # default schema without stable sort
          samples.append(SampleInput(t, args=(dim, descending)))
          # schema with stable sort, no CUDA support yet
          if torch.device(device).type == 'cpu':
              samples.append(
                  SampleInput(t, kwargs=dict(dim=dim, descending=descending, stable=stable))
              )
  
      # Test cases for scalar tensor
      scalar = torch.tensor(1, dtype=dtype, device=device)
      apply_grad(scalar)
      samples.append(SampleInput(scalar))
      samples.append(SampleInput(scalar, args=(0,)))
      samples.append(SampleInput(scalar, args=(0, True)))
      # no CUDA support for stable sort yet
      if not device.startswith('cuda'):
          samples.append(SampleInput(scalar, kwargs=dict(stable=True)))
          samples.append(SampleInput(scalar, kwargs=dict(dim=0, stable=True)))
          samples.append(SampleInput(scalar, kwargs=dict(dim=0, descending=True, stable=True)))
      return samples
  
  def sample_inputs_index_fill(op_info, device, dtype, requires_grad, **kwargs):
      samples = []
      t = make_tensor((S, S, S), device, dtype,
                      low=None, high=None,
                      requires_grad=requires_grad)
      fill_val = torch.tensor(-1 + 1j if t.is_complex() else -1)
      # non-contiguous input
      t01 = t.transpose(0, 1)
      t02 = t.transpose(0, 2)
      t12 = t.transpose(1, 2)
      idx = index_variable(1, S, device=device)
      # non-contiguous index
      idx_nonctg = torch.empty_strided((S,), (2,), device=device, dtype=torch.int64)
      idx_nonctg.copy_(idx)
      for d in range(t.dim()):
          for tensor in [t, t01, t02, t12]:
              samples.append(SampleInput(tensor, args=(d, idx, fill_val)))
              samples.append(SampleInput(tensor, args=(d, -idx - 1, fill_val)))
              samples.append(SampleInput(tensor, args=(d, idx_nonctg, fill_val)))
  
      make_arg = partial(make_tensor, device=device, dtype=dtype, requires_grad=requires_grad)
      index_tensor = partial(torch.tensor, device=device, dtype=torch.long)
  
      def unique_idx(numel, max_idx):
          # Generate unique random indices vector of `numel`
          # elements in range [0, max_idx).
          indices = random.sample(range(max_idx), numel)
          return index_tensor(indices)
  
      samples.append(SampleInput(make_arg((S, S)), args=(0, unique_idx(2, S), 2)))
      samples.append(SampleInput(make_arg((S, S)), args=(0, unique_idx(2, S), make_arg(()))))
      samples.append(SampleInput(make_arg((S, S)), args=(0, index_tensor(0), 2)))
      samples.append(SampleInput(make_arg(()), args=(0, index_tensor([0]), 2)))
      samples.append(SampleInput(make_arg(()), args=(0, index_tensor(0), 2)))
  
      # Duplicate indices
      samples.append(SampleInput(make_arg((S, S)), args=(0, index_tensor([0, 0]), 2)))
      samples.append(SampleInput(make_arg((S, S)), args=(0, index_tensor([0, 0, 2]), make_arg(()))))
  
      return samples
  
  def sample_inputs_max_min_binary(op_info, device, dtype, requires_grad, **kwargs):
      inputs = []
      args_for_binary_op = (
          ((S, S, S), (S, S, S),),
          ((S, S, S), (S,),),
          ((S,), (S, S, S),),
          ((S, 1, S), (S, S),),
          ((S, S), (S, S),),
          ((), (),),
          ((S, S, S), (),),
          ((), (S, S, S),),
      )
      inputs = list((SampleInput(make_tensor(input_tensor, device, dtype,
                                             low=None, high=None,
                                             requires_grad=requires_grad),
                                 args=(make_tensor(other_tensor, device, dtype,
                                                   low=None, high=None,
                                                   requires_grad=requires_grad),),))
                    for input_tensor, other_tensor in args_for_binary_op)
      return inputs
  
  def sample_inputs_hardswish(self, device, dtype, requires_grad):
      N = 5
      # make sure we are testing -3 -> 3 range. default is -10 -> 10 so maybe unnecessary ?
      tensors = [SampleInput(make_tensor((N * 2, N * 2), device=device, dtype=dtype,
                 requires_grad=requires_grad, low=-5, high=5)) for _ in range(1, N)]
      return tensors
  
  def sample_inputs_max_min_reduction_with_dim(op_info, device, dtype, requires_grad, **kwargs):
      inputs = []
      args_for_reduction_with_dim = (
          ((S, S, S), (1,),),
          ((S, S, S), (1, True, ),),
          ((), (0,),),
          ((), (0, True,),),
      )
      inputs = list((SampleInput(make_tensor(input_tensor, device, dtype,
                                             low=None, high=None,
                                             requires_grad=requires_grad),
                                 args=args,))
                    for input_tensor, args in args_for_reduction_with_dim)
      return inputs
  
  def sample_inputs_max_min_reduction_no_dim(op_info, device, dtype, requires_grad, **kwargs):
      inputs = []
      inputs.append(SampleInput(make_tensor((S, S, S), device, dtype,
                                            low=None, high=None,
                                            requires_grad=requires_grad),))
      inputs.append(SampleInput(make_tensor((), device, dtype,
                                            low=None, high=None,
                                            requires_grad=requires_grad),))
      return inputs
  
  # Generates input tensors for testing reduction ops
  def _generate_reduction_inputs(device, dtype, requires_grad):
      yield make_tensor((), device, dtype, requires_grad=requires_grad)
      yield make_tensor((2,), device, dtype, requires_grad=requires_grad)
      yield make_tensor((2, 3), device, dtype, requires_grad=requires_grad, noncontiguous=True)
      yield make_tensor((3, 2, 1, 2, 2), device, dtype, requires_grad=requires_grad)
  
  # Generates a subset of possible dim and keepdim kwargs for a tensor
  # with ndim dims appropriate for testing. If supports_multiple_dims
  # is True (default) then dim kwarg can be a list of dims.
  def _generate_reduction_kwargs(ndim, supports_multiple_dims=True):
      for keepdim in [True, False]:
          # Always test reducing inner and outer most dimensions
          yield {'dim': 0, 'keepdim': keepdim}
          yield {'dim': -1, 'keepdim': keepdim}
  
          # Also reduce middle dimension
          if ndim > 2:
              yield {'dim': ndim // 2, 'keepdim': keepdim}
  
          if supports_multiple_dims:
              # Always test reducing all dims
              yield {'dim': tuple(range(ndim)), 'keepdim': keepdim}
  
              # Test reducing both first and last dimensions
              if ndim > 1:
                  yield {'dim': (0, ndim - 1), 'keepdim': keepdim}
  
              # Test reducing every other dimension starting with the second
              if ndim > 3:
                  yield {'dim': tuple(range(1, ndim, 2)), 'keepdim': keepdim}
  
  # Wraps sample_inputs_reduction function to provide the additional supports_multiple_dims args
  def sample_inputs_reduction_wrapper(supports_multiple_dims):
      # Generates sample inputs for reduction ops that contain the input tensor
      # and dim and keepdim kwargs. If a reduction op needs to test additional
      # args/kwargs then create a separate sample_inputs function
      def fn(op_info, device, dtype, requires_grad):
          inputs = []
  
          for t in _generate_reduction_inputs(device, dtype, requires_grad):
              # Add case without dim and keepdim kwargs
              inputs.append(SampleInput(t))
              for kwargs in _generate_reduction_kwargs(t.ndim, supports_multiple_dims):
                  inputs.append(SampleInput(t, kwargs=kwargs))
  
          return inputs
  
      return fn
  
  def sample_inputs_reduction_quantile(op_info, device, dtype, requires_grad):
      test_quantiles = (0.5, make_tensor((2,), device, dtype, low=0, high=1))
      test_interpolations = ['linear', 'midpoint']
  
      inputs = []
      for quantiles in test_quantiles:
          for t in _generate_reduction_inputs(device, dtype, requires_grad):
              # Add case without dim and keepdim kwargs
              inputs.append(SampleInput(t, args=(quantiles,)))
              for kwargs in _generate_reduction_kwargs(t.ndim, supports_multiple_dims=False):
                  # Interpolation kwarg for now is only supported when providing both dim and keepdim
                  for interpolation in test_interpolations:
                      kwargs['interpolation'] = interpolation
                      inputs.append(SampleInput(t, args=(quantiles,), kwargs=kwargs))
  
      return inputs
  
  def sample_inputs_topk(op_info, device, dtype, requires_grad, **kwargs):
      def get_tensor_input(size):
          return make_tensor(size, device, dtype, requires_grad=requires_grad)
  
      inputs = []
      inputs.append(SampleInput(get_tensor_input((S, M, S)), args=(3,)))
      inputs.append(SampleInput(get_tensor_input((S, M, S)), args=(3, 1)))
      inputs.append(SampleInput(get_tensor_input((S, M, S)), args=(3, -2)))
      inputs.append(SampleInput(get_tensor_input((S, M, S)), args=(3, 1, True)))
      inputs.append(SampleInput(get_tensor_input((S, M, S)), args=(3, -2, True)))
      inputs.append(SampleInput(get_tensor_input((S, M, S)), args=(3, 1, True, True)))
      inputs.append(SampleInput(get_tensor_input((S, M, S)), args=(3, -2, True, True)))
  
      inputs.append(SampleInput(get_tensor_input(()), args=(1,)))
      inputs.append(SampleInput(get_tensor_input(()), args=(1, 0)))
      inputs.append(SampleInput(get_tensor_input(()), args=(1, -1)))
      inputs.append(SampleInput(get_tensor_input(()), args=(1, 0, True)))
      inputs.append(SampleInput(get_tensor_input(()), args=(1, -1, True)))
      inputs.append(SampleInput(get_tensor_input(()), args=(1, 0, True, True)))
      inputs.append(SampleInput(get_tensor_input(()), args=(1, -1, True, True)))
  
      return inputs
  
  def sample_inputs_outer(op_info, device, dtype, requires_grad, **kwargs):
      inputs = []
      arg_a = make_tensor((S,), device, dtype, requires_grad=requires_grad)
      arg_b = make_tensor((M,), device, dtype, requires_grad=requires_grad)
      inputs.append(SampleInput(arg_a, args=(arg_b,)))
      return inputs
  
  def sample_inputs_dist(op_info, device, dtype, requires_grad):
      make_arg = partial(make_tensor, device=device, dtype=dtype, requires_grad=requires_grad)
      sizes = ((S, S, S), (S,), (S, 1, S), (), (S, S))
      ps = (2, 4)
  
      def generate_samples():
          for size_x, size_y, p in product(sizes, sizes, ps):
              yield SampleInput(make_arg(size_x), args=(make_arg(size_y), p))
  
      return list(generate_samples())
  
  # Missing to test the nondeterminism of the operation
  # https://github.com/pytorch/pytorch/issues/53352
  def sample_inputs_index_copy(op_info, device, dtype, requires_grad, **kwargs):
      def make_arg(shape, low=None, high=None, dtype=dtype):
          return make_tensor(shape, device=device, dtype=dtype,
                             low=low, high=high,
                             requires_grad=requires_grad)
  
      t = make_arg((S, S))
      s = make_arg((S, S))
      # non-contiguous input
      t01 = t.transpose(0, 1)
      # non-contiguous input
      s01 = s.transpose(0, 1)
  
      # idx is a permutation of 0...S-1 for this function to be deterministic
      idx = torch.randperm(S, device=device, dtype=torch.int64)
      # non-contiguous index
      idx_nonctg = torch.repeat_interleave(idx, 2, dim=-1)[::2]
      # index_copy_ does not support negative indices
      # idx_neg = -idx - 1
      samples = [SampleInput(tensor, args=(1, idx, source))
                 for tensor, idx, source in product([t, t01], [idx, idx_nonctg], [s, s01])]
  
      # Add scalar cases
      scalar_sizes = [(), (1,)]
      ts = (make_arg(size) for size in scalar_sizes)
      idxs = (make_arg(size, dtype=torch.int64, low=0, high=1) for size in scalar_sizes)
      ss = (make_arg(size) for size in scalar_sizes)
  
      samples.extend(SampleInput(t, args=(0, idx, s)) for t, idx, s in product(ts, idxs, ss))
      return samples
  
  def sample_inputs_mode(op_info, device, dtype, requires_grad):
      inputs = []
      args = (
          ((S, S, S), (),),
          ((S, S, S), (1, ),),
          ((S, S, S), (1, True, ),),
          ((), (),),
          ((), (0,),),
          ((), (0, True,),),
      )
      inputs = list((SampleInput(make_tensor(input_tensor, device, dtype,
                                             low=None, high=None,
                                             requires_grad=requires_grad),
                                 args=args,))
                    for input_tensor, args in args)
      return inputs
  
  # Missing to test the nondeterminism of the operation
  # https://github.com/pytorch/pytorch/issues/53352
  def sample_inputs_put(op_info, device, dtype, requires_grad):
      make_arg = partial(make_tensor, dtype=dtype, device=device, requires_grad=requires_grad)
      make_idx = partial(make_tensor, low=0, dtype=torch.int64, device=device, requires_grad=False)
  
      S = 3
  
      def gen_inputs():
          # Generic inputs
          tgt_gen = (make_arg((S, S), noncontiguous=not ctg) for ctg in (True, False))
          src_gen = (make_arg((S,), noncontiguous=not ctg) for ctg in (True, False))
          idx = torch.randperm(S * S, device=device, dtype=torch.int64)[:S]
          idx_nonctg = torch.repeat_interleave(idx, 2, dim=-1)[::2]
          idx_neg = -idx - 1
          idx_list = [idx, idx_nonctg, idx_neg]
          for tgt, idx, src, acc in product(tgt_gen, idx_list, src_gen, (True, False)):
              yield SampleInput(input=tgt, args=(idx, src, acc))
  
          # Scalar cases
          scalar_sizes = [(), (1,)]
          tgt_gen = (make_arg(size) for size in scalar_sizes)
          idx_gen = (make_idx(size, high=1) for size in scalar_sizes)
          src_gen = (make_arg(size) for size in scalar_sizes)
          for tgt, idx, src, acc in product(tgt_gen, idx_gen, src_gen, (True, False)):
              yield SampleInput(input=tgt, args=(idx, src, acc))
  
          # Empty cases
          tgt_sizes = [(0,), (), (1,), (3, 2)]
          tgt_gen = (make_arg(size) for size in tgt_sizes)
          idx = make_idx((0,), high=1)
          src = make_arg((0,))
          for tgt, acc in product(tgt, (True, False)):
              yield SampleInput(input=tgt, args=(idx, src, acc))
  
      return list(gen_inputs())
  
  def sample_inputs_take(op_info, device, dtype, requires_grad):
      make_arg = partial(make_tensor, dtype=dtype, device=device, requires_grad=requires_grad)
      make_idx = partial(make_tensor, low=0, dtype=torch.int64, device=device, requires_grad=False)
  
      S = 3
  
      def gen_inputs():
          # Generic inputs: take S elements out of S * S
          src_gen = (make_arg((S, S), noncontiguous=not ctg) for ctg in (True, False))
          idx = make_idx((S,), high=S * S)
          idx_nonctg = make_idx((S,), high=S * S, noncontiguous=True)
          idx_neg = -idx - 1
          idx_list = [idx, idx_nonctg, idx_neg]
          for src, idx in product(src_gen, idx_list):
              yield SampleInput(input=src, args=(idx,))
  
          # Scalar cases
          scalar_sizes = [(), (1,)]
          src_gen = (make_arg(size) for size in scalar_sizes)
          idx_gen = (make_idx(size, high=1) for size in scalar_sizes)
          for src, idx in product(src_gen, idx_gen):
              yield SampleInput(input=src, args=(idx,))
  
          # Empty cases
          src_sizes = [(0,), (), (1,), (3, 2)]
          src_gen = (make_arg(size) for size in src_sizes)
          idx = make_idx((0,), high=1)
          for src in src_gen:
              yield SampleInput(input=src, args=(idx,))
  
      return list(gen_inputs())
  
  def sample_movedim_moveaxis(op_info, device, dtype, requires_grad):
      return (
          SampleInput(
              make_tensor((4, 3, 2, 1), device, dtype, low=None, high=None, requires_grad=requires_grad),
              args=((0, 1, 2, 3), (3, 2, 1, 0))),
          SampleInput(
              make_tensor((4, 3, 2, 1), device, dtype, low=None, high=None, requires_grad=requires_grad),
              args=((0, -1, -2, -3), (-3, -2, -1, -0)))
      )
  
  
  def sample_repeat_tile(op_info, device, dtype, requires_grad, **kwargs):
      rep_dims = ((), (0, ), (1, ), (0, 2), (1, 1), (2, 3), (2, 3, 2), (0, 2, 3), (2, 1, 1, 1),)
      shapes = ((), (0,), (2,), (3, 0), (3, 2), (3, 0, 1))
  
      if requires_grad:
          # Tests for variant_consistency_jit, grad, gradgrad
          # are slower. Use smaller bags of `rep_dims` and `shapes`
          # in this case.
          rep_dims = ((), (0, ), (0, 2), (1, 1), (2, 3), (1, 3, 2), (3, 1, 1))  # type: ignore[assignment]
          shapes = ((), (0,), (2,), (3, 2))  # type: ignore[assignment]
  
      tensors = [make_tensor(shape, device, dtype,
                             low=None, high=None,
                             requires_grad=requires_grad) for shape in shapes]
  
      samples = []
      for rep_dim, tensor in product(rep_dims, tensors):
          for t in (tensor, tensor.T):
              if op_info.name == 'repeat' and len(rep_dim) >= t.dim():
                  # `torch.repeat` errors for `len(rep_dims) < t.dim()`,
                  # so we filter such combinations.
                  samples.append(SampleInput(t, args=(rep_dim,),))
              elif op_info.name == 'tile':
                  samples.append(SampleInput(t, args=(rep_dim,),))
  
      return samples
  
  
  def sample_inputs_narrow(op_info, device, dtype, requires_grad, **kwargs):
      shapes_and_args = (
          ((S, S, S), (1, 2, 2)),
          ((S, S, S), (-1, 2, 2)),
          ((S, S, S), (1, 0, 0)),
          ((S, S, S), (-1, 0, 0)),
      )
  
      def generator():
          for shape, args in shapes_and_args:
              tensor = make_tensor(shape, device, dtype, low=None, high=None,
                                   requires_grad=requires_grad)
              yield SampleInput(tensor, args=args)
  
      return list(generator())
  
  
  def sample_unsqueeze(op_info, device, dtype, requires_grad, **kwargs):
      shapes_and_axes = [
          ((3, 4, 5), 0),
          ((3, 4, 5), 1),
          ((3, 4, 5), 3),
          ((3, 4, 5), -1),
          ((3, 4, 5), -3),
          ((), 0)
      ]
  
      samples = []
      for shape, axis in shapes_and_axes:
          tensor = make_tensor(shape, device, dtype, low=None, high=None,
                               requires_grad=requires_grad)
          samples.append(SampleInput(tensor, args=(axis,),))
  
      return samples
  
  
  def sample_inputs_squeeze(op_info, device, dtype, requires_grad, **kwargs):
      shapes_and_args = (
          ((S, 1, S, 1), ()),
          ((1, 1, 1, 1), ()),
          ((S, 1, S, 1), (1,)),
          ((S, 1, S, 1), (-1,)),
          ((S, 1, S, 1), (2,)),
          ((S, 1, S, 1), (-2,)),
          ((), (0, )),
      )
  
      def generator():
          for shape, args in shapes_and_args:
              tensor = make_tensor(shape, device, dtype, low=None, high=None,
                                   requires_grad=requires_grad)
  
              yield SampleInput(tensor, args=args)
  
      return list(generator())
  
  
  # TODO: reconcile with torch.linalg.det and torch.linalg.slogdet
  # Creates matrices with a positive nonzero determinant
  def sample_inputs_logdet(op_info, device, dtype, requires_grad, **kwargs):
      def make_nonzero_det(A, *, sign=1, min_singular_value=0.1, **kwargs):
          u, s, vh = torch.linalg.svd(A, full_matrices=False)
          s.clamp_(min=min_singular_value)
          A = (u * s.unsqueeze(-2)) @ vh
          det = A.det()
          if sign is not None:
              if A.dim() == 2:
                  if (det < 0) ^ (sign < 0):
                      A[0, :].neg_()
              else:
                  cond = ((det < 0) ^ (sign < 0)).nonzero()
                  if cond.size(0) > 0:
                      for i in range(cond.size(0)):
                          A[list(cond[i])][0, :].neg_()
          return A
  
      samples = []
  
      # cases constructed using make_tensor()
      tensor_shapes = (
          (S, S),
          (1, 1),
          (3, 3, S, S),
          (3, 3, 1, 1)
      )
  
      for shape in tensor_shapes:
          t = make_tensor(shape, device=device, dtype=dtype)
          d = make_nonzero_det(t).requires_grad_(requires_grad)
          samples.append(SampleInput(d))
  
      # cases constructed using:
      #  1) make_symmetric_matrices
      #  2) make_symmetric_pd_matrices
      #  3) make_fullrank_matrices_with_distinct_singular_values
      symmetric_shapes = (
          (S, S),
          (3, S, S),
      )
  
  
      def _helper(constructor, *shape, **kwargs):
          t = constructor(*shape, device=device, dtype=dtype)
          d = make_nonzero_det(t, **kwargs).requires_grad_(requires_grad)
          samples.append(SampleInput(d))
  
      for shape in symmetric_shapes:
          _helper(make_symmetric_matrices, *shape)
          _helper(make_symmetric_pd_matrices, *shape)
          _helper(make_fullrank_matrices_with_distinct_singular_values, *shape, min_singular_value=0)
  
      return tuple(samples)
  
  def np_unary_ufunc_integer_promotion_wrapper(fn):
      # Wrapper that passes PyTorch's default scalar
      #   type as an argument to the wrapped NumPy
      #   unary ufunc when given an integer input.
      #   This mimicks PyTorch's integer->floating point
      #   type promotion.
      #
      # This is necessary when NumPy promotes
      #   integer types to double, since PyTorch promotes
      #   integer types to the default scalar type.
  
      # Helper to determine if promotion is needed
      def is_integral(dtype):
          return dtype in [np.bool_, bool, np.uint8, np.int8, np.int16, np.int32, np.int64]
  
      # NOTE: Promotion in PyTorch is from integer types to the default dtype
      np_dtype = torch_to_numpy_dtype_dict[torch.get_default_dtype()]
  
      @wraps(fn)
      def wrapped_fn(x):
          if is_integral(x.dtype):
              return fn(x, dtype=np_dtype)
          return fn(x)
  
      return wrapped_fn
  
  
  # Metadata class for Fast Fourier Transforms in torch.fft.
  class SpectralFuncInfo(OpInfo):
      """Operator information for torch.fft transforms. """
  
      def __init__(self,
                   name,  # the string name of the function
                   *,
                   ref=None,  # Reference implementation (probably in np.fft namespace)
                   dtypes=floating_and_complex_types(),
                   ndimensional: bool,  # Whether dim argument can be a tuple
                   decorators=None,
                   **kwargs):
          decorators = list(decorators) if decorators is not None else []
          decorators += [
              skipCPUIfNoMkl,
              skipCUDAIfRocm,
              # gradgrad is quite slow
              DecorateInfo(slowTest, 'TestGradients', 'test_fn_gradgrad'),
          ]
  
          super().__init__(name=name,
                           dtypes=dtypes,
                           decorators=decorators,
                           **kwargs)
          self.ref = ref if ref is not None else _getattr_qual(np, name)
          self.ndimensional = ndimensional
  
  
      def sample_inputs(self, device, dtype, requires_grad=False, **kwargs):
          nd_tensor = make_tensor((S, S + 1, S + 2), device, dtype, low=None, high=None,
                                  requires_grad=requires_grad)
          tensor = make_tensor((31,), device, dtype, low=None, high=None,
                               requires_grad=requires_grad)
  
          if self.ndimensional:
              return [
                  SampleInput(nd_tensor, kwargs=dict(s=(3, 10), dim=(1, 2), norm='ortho')),
                  SampleInput(nd_tensor, kwargs=dict(norm='ortho')),
                  SampleInput(nd_tensor, kwargs=dict(s=(8,))),
                  SampleInput(tensor),
  
                  *(SampleInput(nd_tensor, kwargs=dict(dim=dim))
                    for dim in [-1, -2, -3, (0, -1)]),
              ]
          else:
              return [
                  SampleInput(nd_tensor, kwargs=dict(n=10, dim=1, norm='ortho')),
                  SampleInput(nd_tensor, kwargs=dict(norm='ortho')),
                  SampleInput(nd_tensor, kwargs=dict(n=7)),
                  SampleInput(tensor),
  
                  *(SampleInput(nd_tensor, kwargs=dict(dim=dim))
                    for dim in [-1, -2, -3]),
              ]
  
  
  class ShapeFuncInfo(OpInfo):
      """Early version of a specialized OpInfo for Shape manipulating operations like tile and roll"""
      def __init__(self,
                   name,  # the string name of the function
                   *,
                   ref,  # a reference function
                   dtypes=floating_types(),
                   dtypesIfCPU=None,
                   dtypesIfCUDA=None,
                   dtypesIfROCM=None,
                   sample_inputs_func=None,
                   **kwargs):
          super(ShapeFuncInfo, self).__init__(name,
                                              dtypes=dtypes,
                                              dtypesIfCPU=dtypesIfCPU,
                                              dtypesIfCUDA=dtypesIfCUDA,
                                              dtypesIfROCM=dtypesIfROCM,
                                              sample_inputs_func=sample_inputs_func,
                                              **kwargs)
          self.ref = ref
  
  def sample_inputs_foreach(self, device, dtype, N):
      tensors = [make_tensor((N, N), device, dtype) for _ in range(N)]
      return tensors
  
  
  def get_foreach_method_names(name):
      # get torch inplace reference function
      method_name = "_foreach_" + name
      method_name_inplace = "_foreach_" + name + "_"
  
      method = getattr(torch, method_name, None)
      method_inplace = getattr(torch, method_name_inplace, None)
  
      ref = getattr(torch.Tensor, name, None)
  
      return method, method_inplace, ref
  
  class ForeachUnaryFuncInfo(OpInfo):
      """Early version of a specialized OpInfo for foreach unary functions"""
      def __init__(self,
                   name,
                   dtypes=floating_and_complex_types(),
                   dtypesIfCPU=all_types_and_complex(),
                   dtypesIfCUDA=floating_and_complex_types_and(torch.half),
                   dtypesIfROCM=None,
                   safe_casts_outputs=True,
                   sample_inputs_func=sample_inputs_foreach,
                   **kwargs):
          super(ForeachUnaryFuncInfo, self).__init__("_foreach_" + name,
                                                     dtypes=dtypes,
                                                     dtypesIfCPU=dtypesIfCPU,
                                                     dtypesIfCUDA=dtypesIfCUDA,
                                                     dtypesIfROCM=dtypesIfROCM,
                                                     safe_casts_outputs=safe_casts_outputs,
                                                     sample_inputs_func=sample_inputs_func,
                                                     **kwargs)
  
          foreach_method, foreach_method_inplace, torch_ref_method = get_foreach_method_names(name)
          self.method_variant = foreach_method
          self.inplace_variant = foreach_method_inplace
          self.ref = torch_ref_method
  
  
  def sample_inputs_linalg_cholesky_inverse(op_info, device, dtype, requires_grad=False):
      # Generate Cholesky factors of positive-definite (non-singular) Hermitian (symmetric) matrices
      from torch.testing._internal.common_utils import random_hermitian_pd_matrix
      inputs = (
          torch.zeros(0, 0, dtype=dtype, device=device),  # 0x0 matrix
          torch.zeros(0, 2, 2, dtype=dtype, device=device),  # zero batch of matrices
          random_hermitian_pd_matrix(S, dtype=dtype, device=device),  # single matrix
          random_hermitian_pd_matrix(S, 2, dtype=dtype, device=device),  # batch of matrices
      )
      test_cases = (torch.linalg.cholesky(a) for a in inputs)
      out = []
      for a in test_cases:
          a.requires_grad = requires_grad
          out.append(SampleInput(a))
          out.append(SampleInput(a, kwargs=dict(upper=True)))
      return out
  
  def sample_inputs_linalg_lstsq(op_info, device, dtype, requires_grad=False, **kwargs):
      from torch.testing._internal.common_utils import random_well_conditioned_matrix
      out = []
      for batch in ((), (3,), (3, 3)):
          shape = batch + (3, 3)
          # NOTE: inputs are not marked with `requires_grad` since
          # linalg_lstsq is not differentiable
          a = random_well_conditioned_matrix(*shape, dtype=dtype, device=device)
          b = make_tensor(shape, device, dtype, low=None, high=None)
          out.append(SampleInput(a, args=(b,)))
      return out
  
  def sample_inputs_householder_product(op_info, device, dtype, requires_grad, **kwargs):
      """
      This function generates input for torch.linalg.householder_product (torch.orgqr).
      The first argument should be a square matrix or batch of square matrices, the second argument is a vector or batch of vectors.
      Empty, square, rectangular, batched square and batched rectangular input is generated.
      """
      # Each column of the matrix is getting multiplied many times leading to very large values for
      # the Jacobian matrix entries and making the finite-difference result of grad check less accurate.
      # That's why gradcheck with the default range [-9, 9] fails and [-2, 2] is used here.
      samples = (
          SampleInput(make_tensor((S, S), device, dtype, low=-2, high=2, requires_grad=requires_grad),
                      args=(make_tensor((S,), device, dtype, low=-2, high=2, requires_grad=requires_grad),)),
  
          SampleInput(make_tensor((S + 1, S), device, dtype, low=-2, high=2, requires_grad=requires_grad),
                      args=(make_tensor((S,), device, dtype, low=-2, high=2, requires_grad=requires_grad),)),
  
          SampleInput(make_tensor((2, 1, S, S), device, dtype, low=-2, high=2, requires_grad=requires_grad),
                      args=(make_tensor((2, 1, S,), device, dtype, low=-2, high=2, requires_grad=requires_grad),)),
  
          SampleInput(make_tensor((2, 1, S + 1, S), device, dtype, low=-2, high=2, requires_grad=requires_grad),
                      args=(make_tensor((2, 1, S,), device, dtype, low=-2, high=2, requires_grad=requires_grad),)),
  
          SampleInput(make_tensor((0, 0), device, dtype, low=None, high=None, requires_grad=requires_grad),
                      args=(make_tensor((0,), device, dtype, low=None, high=None, requires_grad=requires_grad),)),
  
          SampleInput(make_tensor((S, S), device, dtype, low=-2, high=2, requires_grad=requires_grad),
                      args=(make_tensor((0,), device, dtype, low=None, high=None, requires_grad=requires_grad),)),
      )
  
      return samples
  
  def sample_inputs_ormqr(op_info, device, dtype, requires_grad):
      # create a helper function wrapping `make_tensor`
      make_input = partial(make_tensor, dtype=dtype, device=device, requires_grad=requires_grad)
  
      def gen_inputs():
          batches = [(), (0, ), (2, ), (2, 1)]
          ns = [5, 2, 0]
          tf = [True, False]
          for batch, (m, n), left, transpose in product(batches, product(ns, ns), tf, tf):
              reflectors = make_input((*batch, m, n))
              tau = make_input((*batch, min(m, n)))
              other_matrix_shape = (m, n) if left else (n, m)
              other = make_input((*batch, *other_matrix_shape))
              kwargs = {"left": left, "transpose": transpose}
              yield SampleInput(reflectors, args=(tau, other,), kwargs=kwargs)
  
      return tuple(gen_inputs())
  
  def sample_inputs_linalg_cholesky(op_info, device, dtype, requires_grad=False, **kwargs):
      """
      This function generates always positive-definite input for torch.linalg.cholesky using
      random_hermitian_pd_matrix.
      The input is generated as the itertools.product of 'batches' and 'ns'.
      In total this function generates 8 SampleInputs
      'batches' cases include:
          () - single input,
          (0,) - zero batched dimension,
          (2,) - batch of two matrices,
          (1, 1) - 1x1 batch of matrices
      'ns' gives 0x0 and 5x5 matrices.
      Zeros in dimensions are edge cases in the implementation and important to test for in order to avoid unexpected crashes.
      """
      from torch.testing._internal.common_utils import random_hermitian_pd_matrix
  
      batches = [(), (0, ), (2, ), (1, 1)]
      ns = [5, 0]
      out = []
      for batch, n in product(batches, ns):
          a = random_hermitian_pd_matrix(n, *batch, dtype=dtype, device=device)
          a.requires_grad = requires_grad
          out.append(SampleInput(a))
      return out
  
  def sample_inputs_symeig(op_info, device, dtype, requires_grad=False):
      out = sample_inputs_linalg_invertible(op_info, device, dtype, requires_grad)
  
      for o in out:
          o.kwargs = {"upper": bool(np.random.choice([True, False])),
                      "eigenvectors": True}
          # A gauge-invariant function
          o.output_process_fn_grad = lambda output: (output[0], abs(output[1]))
      return out
  
  
  def sample_inputs_linalg_eigh(op_info, device, dtype, requires_grad=False, **kwargs):
      """
      This function generates input for torch.linalg.eigh/eigvalsh with UPLO="U" or "L" keyword argument.
      """
      def out_fn(output):
          if isinstance(output, tuple):
              # eigh function
              return output[0], abs(output[1])
          else:
              # eigvalsh function
              return output
  
      samples = sample_inputs_linalg_invertible(op_info, device, dtype, requires_grad)
      for sample in samples:
          sample.kwargs = {"UPLO": np.random.choice(["L", "U"])}
          sample.output_process_fn_grad = out_fn
  
      return samples
  
  
  def sample_inputs_linalg_slogdet(op_info, device, dtype, requires_grad=False):
      def out_fn(output):
          return output[1]
  
      samples = sample_inputs_linalg_invertible(op_info, device, dtype, requires_grad)
      for sample in samples:
          sample.output_process_fn_grad = out_fn
  
      return samples
  
  
  def sample_inputs_linalg_pinv_hermitian(op_info, device, dtype, requires_grad=False, **kwargs):
      """
      This function generates input for torch.linalg.pinv with hermitian=True keyword argument.
      """
      out = sample_inputs_linalg_invertible(op_info, device, dtype, requires_grad, **kwargs)
      for o in out:
          o.kwargs = {"hermitian": True}
      return out
  
  def sample_inputs_linalg_solve(op_info, device, dtype, requires_grad=False, vector_rhs_allowed=True, **kwargs):
      """
      This function generates always solvable input for torch.linalg.solve
      Using random_fullrank_matrix_distinct_singular_value gives a non-singular (=invertible, =solvable) matrices 'a'.
      The first input to torch.linalg.solve is generated as the itertools.product of 'batches' and 'ns'.
      The second input is generated as the product of 'batches', 'ns' and 'nrhs'.
      In total this function generates 18 SampleInputs
      'batches' cases include:
          () - single input,
          (0,) - zero batched dimension,
          (2,) - batch of two matrices.
      'ns' gives 0x0 and 5x5 matrices.
      and 'nrhs' controls the number of vectors to solve for:
          () - using 1 as the number of vectors implicitly
          (1,) - same as () but explicit
          (3,) - solve for 3 vectors.
      Zeros in dimensions are edge cases in the implementation and important to test for in order to avoid unexpected crashes.
      'vector_rhs_allowed' controls whether to include nrhs = () to the list of SampleInputs.
      torch.solve / triangular_solve / cholesky_solve (opposed to torch.linalg.solve) do not allow
      1D tensors (vectors) as the right-hand-side.
      Once torch.solve / triangular_solve / cholesky_solve and its testing are removed,
      'vector_rhs_allowed' may be removed here as well.
      """
      from torch.testing._internal.common_utils import random_fullrank_matrix_distinct_singular_value
  
      batches = [(), (0, ), (2, )]
      ns = [5, 0]
      if vector_rhs_allowed:
          nrhs = [(), (1,), (3,)]
      else:
          nrhs = [(1,), (3,)]
      out = []
      for n, batch, rhs in product(ns, batches, nrhs):
          a = random_fullrank_matrix_distinct_singular_value(n, *batch, dtype=dtype, device=device)
          a.requires_grad = requires_grad
          b = torch.randn(*batch, n, *rhs, dtype=dtype, device=device)
          b.requires_grad = requires_grad
          out.append(SampleInput(a, args=(b,)))
      return out
  
  
  def sample_inputs_legacy_solve(op_info, device, dtype, requires_grad=False, **kwargs):
      """
      This function generates always solvable input for legacy solve functions
      (the ones that are not in torch.linalg module).
      The difference from sample_inputs_linalg_solve is that here the right-hand-side of A x = b equation
      should have b.ndim >= 2, vectors are not allowed.
      Also the arguments order is swapped.
      """
      out = sample_inputs_linalg_solve(
          op_info, device, dtype, requires_grad=requires_grad, vector_rhs_allowed=False
      )
  
      # Reverses tensor order
      for sample in out:
          sample.input, sample.args = sample.args[0], (sample.input,)
  
      return out
  
  
  def sample_inputs_lu(op_info, device, dtype, requires_grad=False, **kwargs):
      # not needed once OpInfo tests support Iterables
      def generate_samples():
          batch_shapes = ((), (3,), (3, 3))
          for batch_shape, get_infos in product(batch_shapes, (True, False)):
              shape = batch_shape + (S, S)
              input = make_tensor(shape, device, dtype, requires_grad=requires_grad, low=None, high=None)
              yield SampleInput(input, args=(True, get_infos))
  
      return list(generate_samples())
  
  
  def sample_inputs_lu_unpack(op_info, device, dtype, requires_grad=False, **kwargs):
      # not needed once OpInfo tests support Iterables
      def generate_samples():
          for lu_sample in sample_inputs_lu(op_info, device, dtype, requires_grad, **kwargs):
              lu_data, pivots = lu_sample.input.lu()
              yield SampleInput(lu_data, args=(pivots,))
  
              # generate rectangular inputs
              lu_data_shape = lu_data.shape
              batch_shape = lu_data_shape[:-2]
              n = lu_data_shape[-2]
  
              for shape_inc in ((1, 0), (0, 1)):
                  lu_data, pivots = make_tensor(
                      batch_shape + (n + shape_inc[0], n + shape_inc[1]),
                      device, dtype,
                      requires_grad=False,
                      low=None, high=None
                  ).lu()
                  lu_data.requires_grad_(requires_grad)
                  yield SampleInput(lu_data, args=(pivots,))
  
      return list(generate_samples())
  
  
  def sample_inputs_roll(op_info, device, dtype, requires_grad=False, **kwargs):
      make_arg = partial(make_tensor, device=device, dtype=dtype, requires_grad=requires_grad)
  
      args = ((0, 0), (1, 2), (0, 2), (2, 0), (-1, 0), (10000, 1), (2,), ((1, 2, -1), (0, 1, 2)))
  
      def generator():
          for arg in args:
              yield SampleInput(make_arg((S, S, S)), args=arg)
  
      return list(generator())
  
  
  def sample_inputs_rot90(op_info, device, dtype, requires_grad=False, **kwargs):
      make_arg = partial(make_tensor, device=device, dtype=dtype, requires_grad=requires_grad)
  
      args = ((1, (0, 1),),
              (1, (1, 2),),
              (1, (1, -1),),
              ())
  
      def generator():
          for arg in args:
              yield SampleInput(make_arg((S, S, S)), args=arg)
  
      return list(generator())
  
  
  def sample_inputs_std_var(op_info, device, dtype, requires_grad, **kwargs):
      tensor_nd = make_tensor((S, S, S), device=device, dtype=dtype,
                              low=None, high=None, requires_grad=requires_grad)
      tensor_1d = make_tensor((S,), device=device, dtype=dtype,
                              low=None, high=None, requires_grad=requires_grad)
  
      return [
          SampleInput(tensor_nd),
          SampleInput(tensor_nd, kwargs=dict(dim=1)),
          SampleInput(tensor_nd, kwargs=dict(dim=1, unbiased=True, keepdim=True)),
          SampleInput(tensor_1d, kwargs=dict(dim=0, unbiased=True, keepdim=True)),
          SampleInput(tensor_1d, kwargs=dict(dim=0, unbiased=False, keepdim=False)),
  
          SampleInput(tensor_nd, kwargs=dict(dim=(1,), correction=S // 2)),
          SampleInput(tensor_nd, kwargs=dict(dim=None, correction=0, keepdim=True)),
      ]
  
  
  def _sample_inputs_svd(op_info, device, dtype, requires_grad=False, is_linalg_svd=False):
      """
      This function generates input for torch.svd with distinct singular values so that autograd is always stable.
      Matrices of different size:
          square matrix - S x S size
          tall marix - S x (S-2)
          wide matrix - (S-2) x S
      and batched variants of above are generated.
      Each SampleInput has a function 'output_process_fn_grad' attached to it that is applied on the output of torch.svd
      It is needed for autograd checks, because backward of svd doesn't work for an arbitrary loss function.
      """
      from torch.testing._internal.common_utils import random_fullrank_matrix_distinct_singular_value
  
      # svd and linalg.svd returns V and V.conj().T, respectively. So we need to slice
      # along different dimensions when needed (this is used by
      # test_cases2:wide_all and wide_all_batched below)
      if is_linalg_svd:
          def slice_V(v):
              return v[..., :(S - 2), :]
  
          def uv_loss(usv):
              u00 = usv[0][0, 0]
              v00_conj = usv[2][0, 0]
              return u00 * v00_conj
      else:
          def slice_V(v):
              return v[..., :, :(S - 2)]
  
          def uv_loss(usv):
              u00 = usv[0][0, 0]
              v00_conj = usv[2][0, 0].conj()
              return u00 * v00_conj
  
      test_cases1 = (  # some=True (default)
          # loss functions for complex-valued svd have to be "gauge invariant",
          # i.e. loss functions shouldn't change when sigh of the singular vectors change.
          # the simplest choice to satisfy this requirement is to apply 'abs'.
          (random_fullrank_matrix_distinct_singular_value(S, dtype=dtype).to(device),
              lambda usv: usv[1]),  # 'check_grad_s'
          (random_fullrank_matrix_distinct_singular_value(S, dtype=dtype).to(device),
              lambda usv: abs(usv[0])),  # 'check_grad_u'
          (random_fullrank_matrix_distinct_singular_value(S, dtype=dtype).to(device),
              lambda usv: abs(usv[2])),  # 'check_grad_v'
          # this test is important as it checks the additional term that is non-zero only for complex-valued inputs
          # and when the loss function depends both on 'u' and 'v'
          (random_fullrank_matrix_distinct_singular_value(S, dtype=dtype).to(device),
              uv_loss),  # 'check_grad_uv'
          (random_fullrank_matrix_distinct_singular_value(S, dtype=dtype).to(device)[:(S - 2)],
              lambda usv: (abs(usv[0]), usv[1], abs(usv[2][..., :, :(S - 2)]))),  # 'wide'
          (random_fullrank_matrix_distinct_singular_value(S, dtype=dtype).to(device)[:, :(S - 2)],
              lambda usv: (abs(usv[0]), usv[1], abs(usv[2]))),  # 'tall'
          (random_fullrank_matrix_distinct_singular_value(S, 2, dtype=dtype).to(device),
              lambda usv: (abs(usv[0]), usv[1], abs(usv[2]))),  # 'batched'
          (random_fullrank_matrix_distinct_singular_value(S, 2, dtype=dtype).to(device)[..., :(S - 2), :],
              lambda usv: (abs(usv[0]), usv[1], abs(usv[2]))),  # 'wide_batched'
          (random_fullrank_matrix_distinct_singular_value(S, 2, dtype=dtype).to(device)[..., :, :(S - 2)],
              lambda usv: (abs(usv[0]), usv[1], abs(usv[2]))),  # 'tall_batched'
      )
      test_cases2 = (  # some=False
          (random_fullrank_matrix_distinct_singular_value(S, dtype=dtype).to(device)[:(S - 2)],
              lambda usv: (abs(usv[0]), usv[1], abs(slice_V(usv[2])))),  # 'wide_all'
          (random_fullrank_matrix_distinct_singular_value(S, dtype=dtype).to(device)[:, :(S - 2)],
              lambda usv: (abs(usv[0][:, :(S - 2)]), usv[1], abs(usv[2]))),  # 'tall_all'
          (random_fullrank_matrix_distinct_singular_value(S, 2, dtype=dtype).to(device)[..., :(S - 2), :],
              lambda usv: (abs(usv[0]), usv[1], abs(slice_V(usv[2])))),  # 'wide_all_batched'
          (random_fullrank_matrix_distinct_singular_value(S, 2, dtype=dtype).to(device)[..., :, :(S - 2)],
              lambda usv: (abs(usv[0][..., :, :(S - 2)]), usv[1], abs(usv[2]))),  # 'tall_all_batched'
      )
  
      out = []
      for a, out_fn in test_cases1:
          a.requires_grad = requires_grad
          if is_linalg_svd:
              kwargs = {'full_matrices': False}
          else:
              kwargs = {'some': True}
          out.append(SampleInput(a, kwargs=kwargs, output_process_fn_grad=out_fn))
  
      for a, out_fn in test_cases2:
          a.requires_grad = requires_grad
          if is_linalg_svd:
              kwargs = {'full_matrices': True}
          else:
              kwargs = {'some': False}
          out.append(SampleInput(a, kwargs=kwargs, output_process_fn_grad=out_fn))
  
      return out
  
  
  def sample_inputs_permute(op_info, device, dtype, requires_grad, **kwargs):
      make_arg = partial(make_tensor, device=device, dtype=dtype, requires_grad=requires_grad)
  
      cases = [((1, 2, 3, 4), (0, 2, 3, 1)),
               ((1, 2, 3, 4), (0, -2, -1, 1)),
               ((), ()),
               ((1, 2, 3, 4), (2, 1, 3, 0))]
  
      def generator():
          for shape, args in cases:
              yield SampleInput(make_arg(shape), args=(args,))
  
      return list(generator())
  
  
  # Based on erstwhile method_tests tests & some tensor_op_tests for pow
  def sample_inputs_pow(op_info, device, dtype, requires_grad, **kwargs):
      samples = []
  
      if dtype in [torch.float16, torch.bfloat16, torch.float32, torch.float64]:
          test_cases = (
              ((2, 2), 0, 5, 1e-3, requires_grad, (2, 2), 0, 1, 0.1, requires_grad, False),
              ((2, 2), 0, 5, 1e-3, requires_grad, (1,), 0, 1, 0.1, requires_grad, False),
              ((), 1e-3, 1e-3 + 1, 0, True, (), 0.1, 1.1, 0, False, False),
              ((2, 2), 0, 5, 1e-3, requires_grad, (), 0.1, 1.1, 1, False, False),
          )
          tests_require_resizing = (
              ((1,), 0, 5, 1e-3, requires_grad, (2, 2), 0, 1, 0.1, requires_grad, True),
              ((2, 1, 2), 0, 5, 1e-3, requires_grad, (1, 2, 1), 0, 1, 0.1, requires_grad, True),
              ((), 1e-3, 1e-3 + 1, 0, True, (1, S, 1), 0, 1, 0.1, requires_grad, True),
          )
          cases = test_cases + tests_require_resizing
          samples = list(SampleInput(make_tensor(shape_b, low=low_b, high=high_b,
                                                 requires_grad=b_grad, device=device,
                                                 dtype=dtype) + additive_b,
                                     args=(make_tensor(shape_e, low=low_e, high=high_e,
                                                       requires_grad=e_grad, device=device,
                                                       dtype=dtype) + additive_e,),
                                     broadcasts_input=broadcasts_input)
                         for shape_b, low_b, high_b, additive_b, b_grad, shape_e, low_e,
                         high_e, additive_e, e_grad, broadcasts_input in cases)
          tensor_scalar_inputs = (
              ((2, 2), 0, 5, 1e-3, requires_grad, (3.14,)),
              ((), 1e-3, 1e-3 + 1, 0, True, (3.14,))
          )
          more_samples = list(SampleInput(make_tensor(shape, dtype=dtype, device=device,
                                                      high=high, low=low,
                                                      requires_grad=b_grad) + additive,
                                          args=exp)
                              for shape, low, high, additive, b_grad, exp in tensor_scalar_inputs)
          samples = [*samples, *more_samples]
      elif dtype in [torch.complex64, torch.complex128]:
          args_tuple = (
              ((2, 2), 0, 5, requires_grad, (3.14,)),
              ((), 0, 1, True, (3.14,)),
              ((), 0, 1, True, (3.14j,))
          )
          samples = list(SampleInput(make_tensor(shape, dtype=dtype, device=device,
                                                 high=high, low=low,
                                                 requires_grad=b_grad) + 1e-3 * (1 + 1j),
                                     args=arg)
                         for shape, low, high, b_grad, arg in args_tuple)
      elif dtype == torch.bool:
          arg_tuple = (0, 1, 1., 2.3)
          samples = list(SampleInput(make_tensor((2, 2), device=device, dtype=dtype,
                                                 requires_grad=requires_grad),
                                     args=(arg,))
                         for arg in arg_tuple)
          dtypes_list = [torch.float64, torch.float32, torch.int64, torch.int32]
          more_samples = list(SampleInput(make_tensor((2, 2), device, dtype=torch.bool,
                                                      requires_grad=requires_grad),
                                          args=(make_tensor((2, 2), device, dtype=dtype,
                                                            requires_grad=requires_grad),))
                              for dtype in dtypes_list)
          samples = [*samples, *more_samples]
          samples.append(SampleInput(make_tensor((2, 2, 2), device, dtype=torch.bool,
                                                 requires_grad=requires_grad),
                                     args=(make_tensor((2, 1), device, dtype=torch.float64,
                                                       requires_grad=requires_grad),)))
      else:
          exp_tuple = (1, 2, 3)
          samples = list(SampleInput(make_tensor((2, 2), device, dtype,
                                                 requires_grad=requires_grad),
                                     args=(arg,))
                         for arg in exp_tuple)
          samples.append(SampleInput(make_tensor((2, 2), device, dtype,
                                                 requires_grad=requires_grad),
                                     args=(make_tensor((2, 2), device, dtype,
                                                       requires_grad=requires_grad),)))
      return tuple(samples)
  
  def sample_inputs_svd(op_info, device, dtype, requires_grad=False, **kwargs):
      return _sample_inputs_svd(op_info, device, dtype, requires_grad, is_linalg_svd=False)
  
  def sample_inputs_linalg_svd(op_info, device, dtype, requires_grad=False, **kwargs):
      return _sample_inputs_svd(op_info, device, dtype, requires_grad, is_linalg_svd=True)
  
  def sample_inputs_linalg_svdvals(op_info, device, dtype, requires_grad=False, **kwargs):
      batches = [(), (0, ), (2, ), (1, 1)]
      ns = [5, 2, 0]
      samples = []
      for batch, (m, n) in product(batches, product(ns, ns)):
          a = make_tensor((*batch, m, n), device, dtype, low=None, high=None, requires_grad=requires_grad)
          samples.append(SampleInput(a))
      return samples
  
  def sample_inputs_eig(op_info, device, dtype, requires_grad=False, **kwargs):
      eigvecs = make_tensor((S, S), device=device, dtype=dtype,
                            low=None, high=None)
      eigvals = make_tensor((S,), device=device, dtype=dtype,
                            low=None, high=None)
      # we produce only diagonazible inputs which do not have
      # complex eigenvalues for real inputs, as there is no
      # backward implementation for real inputs with complex
      # eigenvalues yet.
      input = (eigvecs * eigvals.unsqueeze(-2)) @ eigvecs.inverse()
      input.requires_grad_(requires_grad)
  
      def process_output(eigpair):
          eigvals, eigvecs = eigpair
          if dtype.is_complex:
              # eig produces eigenvectors which are normalized to 1 norm.
              # Note that if v is an eigenvector, so is v * e^{i \phi},
              # and |v| = |v * e^{i \phi}| = 1.
              # This, however, makes the eigenvector backward computation process
              # rather unstable unless the objective function is gauge-invariant,
              # that is if f(z) == f(|z|), for example.
              # Hence for complex inputs we ignore the phases and return only
              # the absolute values.
              return eigvals, eigvecs.abs()
          else:
              return eigvals, eigvecs
  
      return [
          SampleInput(
              input,
              kwargs=dict(eigenvectors=True),
              output_process_fn_grad=process_output
          ),
      ]
  
  
  def sample_inputs_einsum(op_info, device, dtype, requires_grad=False, **kwargs):
      x = make_tensor((3,), device, dtype, requires_grad=requires_grad)
      y = make_tensor((4,), device, dtype, requires_grad=requires_grad)
      A = make_tensor((2, 3,), device, dtype, requires_grad=requires_grad, noncontiguous=True)
      B = make_tensor((1, 3,), device, dtype, requires_grad=requires_grad)
      C = make_tensor((1, 2, 3,), device, dtype, requires_grad=requires_grad)
      D = make_tensor((1, 3, 4,), device, dtype, requires_grad=requires_grad, noncontiguous=True)
      E = make_tensor((4, 4,), device, dtype, requires_grad=requires_grad)
      H = make_tensor((3, 3,), device, dtype, requires_grad=requires_grad, noncontiguous=True)
      I = make_tensor((1, 3, 1,), device, dtype, requires_grad=requires_grad)
  
      inputs = []
  
      # Vector operations
      inputs.append(SampleInput([x], args=('i->',)))                      # sum
      inputs.append(SampleInput([x, y], args=('i,j->ij',)))               # outer
  
      # Matrix operations
      inputs.append(SampleInput([A], args=("ij->i",)))                    # col sum
      inputs.append(SampleInput([A, B], args=("ij,kj->ik",)))             # matmul
      inputs.append(SampleInput([A, E], args=("ij,Ab->ijAb",)))           # matrix outer product
  
      # Tensor operations
      inputs.append(SampleInput([C, D], args=("aij,ajk->aik",)))          # batch matmul
      inputs.append(SampleInput([D, E], args=("aij,jk->aik",)))           # tensor matrix contraction
      inputs.append(SampleInput([C, B], args=("ijk,ik->j",)))             # non contiguous
  
      # Test diagonals
      inputs.append(SampleInput([I], args=('iji->j',)))                   # non-contiguous trace
  
      # Test ellipsis
      inputs.append(SampleInput([H], args=("i...->...",)))
      inputs.append(SampleInput([C, x], args=('...ik, ...j -> ij',)))
  
      return inputs
  
  
  def sample_inputs_linalg_qr(op_info, device, dtype, requires_grad=False, **kwargs):
      """
      This function generates input for torch.linalg.qr
      The input is generated as the itertools.product of 'batches' and 'ns'.
      """
      batches = [(), (0,), (2, ), (1, 1)]
      ns = [5, 2, 0]
      out = []
      for batch, (m, n) in product(batches, product(ns, ns)):
          a = torch.randn(*batch, m, n, dtype=dtype, device=device, requires_grad=requires_grad)
          out.append(SampleInput(a))
      return out
  
  def sample_inputs_geqrf(op_info, device, dtype, requires_grad=False):
      batches = [(), (0, ), (2, ), (1, 1)]
      ns = [5, 2, 0]
      samples = []
      for batch, (m, n) in product(batches, product(ns, ns)):
          # TODO: CUDA path doesn't work with batched or empty inputs
          if torch.device(device).type == 'cuda' and (batch != () or m == 0 or n == 0):
              continue
          a = make_tensor((*batch, m, n), device, dtype, low=None, high=None, requires_grad=requires_grad)
          samples.append(SampleInput(a))
      return samples
  
  def sample_inputs_flip(op_info, device, dtype, requires_grad, **kwargs):
      tensors = (
          make_tensor((S, M, S), device, dtype, low=None, high=None, requires_grad=requires_grad),
          make_tensor((S, 0, M), device, dtype, low=None, high=None, requires_grad=requires_grad)
      )
  
      dims = ((0, 1, 2), (0,), (0, 2), (-1,), ())
  
      samples = [SampleInput(tensor, kwargs={'dims': dim}) for tensor, dim in product(tensors, dims)]
  
      return samples
  
  def sample_inputs_fliplr_flipud(op_info, device, dtype, requires_grad, **kwargs):
      tensors = (
          make_tensor((S, M, S), device, dtype, low=None, high=None, requires_grad=requires_grad),
          make_tensor((S, 0, M), device, dtype, low=None, high=None, requires_grad=requires_grad)
      )
      return [SampleInput(tensor) for tensor in tensors]
  
  # TODO: clamp shares tensors among its sample inputs --- we should prohibit this!
  def sample_inputs_clamp(op_info, device, dtype, requires_grad, **kwargs):
      x = make_tensor((S, M, S), device, dtype, low=None, high=None, requires_grad=requires_grad)
      lb = make_tensor((S, M, S), device, dtype, low=None, high=None, requires_grad=requires_grad)
      ub = make_tensor((S, M, S), device, dtype, low=None, high=None, requires_grad=requires_grad)
  
      def detach(tensor):
          return tensor.clone().detach_().requires_grad_(requires_grad)
  
      return [
          SampleInput(detach(x), args=(lb, ub)),
          SampleInput(detach(x), args=(detach(lb[0]), detach(ub[0]))),
          SampleInput(detach(x), args=(detach(lb[:, :1]),)),
      ]
  
  def sample_inputs_clamp_scalar(op_info, device, dtype, requires_grad):
      tensors = (
          make_tensor((2, 3, 2), device, dtype, low=None, high=None, requires_grad=requires_grad),
          make_tensor((2, 0, 3), device, dtype, low=None, high=None, requires_grad=requires_grad),
      )
      if dtype is torch.uint8:
          min_max_vals = ((2, 5), (3, 7))
      else:
          min_max_vals = ((0, 1), (-1, 1))
      output = [SampleInput(tensor, args=vals) for tensor, vals in product(tensors, min_max_vals)]
      output += [SampleInput(tensors[0], args=(0.5, None)), SampleInput(tensors[0], args=(None, 0.5))]
      empty_tensor = make_tensor((), device=device, dtype=dtype, low=None, high=None, requires_grad=requires_grad)
      output += [SampleInput(empty_tensor, args=(0.0, 1.0)), ]
      return output
  
  def sample_kwargs_clamp_scalar(device, dtype, input):
      if dtype is torch.uint8:
          min_val, max_val = (random.randint(1, 3), random.randint(4, 8))
      elif dtype.is_floating_point:
          min_val, max_val = (random.uniform(-8, 0), random.uniform(1, 8))  # type: ignore[assignment]
      else:
          min_val, max_val = (random.randint(-8, 0), random.randint(1, 8))
      return {'min': min_val, 'max': max_val}, {'a_min': min_val, 'a_max': max_val}
  
  def sample_inputs_cumprod(op_info, device, dtype, requires_grad, **kwargs):
      def make_arg(shape):
          # shrink values to be in the interval [-1, +1] for better precision in gradgradcheck
          return make_tensor(shape, device, dtype, low=-1, high=+1, requires_grad=requires_grad)
  
      def prod_zeros(dim_select):
          assert len(dim_select) == 2
          result = make_arg(3 * (S,))
          with torch.no_grad():
              result.narrow(dim_select[0], 0, 1).narrow(dim_select[1], 1, 1).zero_()
              result.narrow(dim_select[0], 2, 1).narrow(dim_select[1], 3, 1).zero_()
              result.narrow(dim_select[0], 4, 1).narrow(dim_select[1], 3, 1).zero_()
          return result
  
      # will not be needed once OpInfo tests suport Iterables
      def sample_generator():
          for dim in range(3):
              yield SampleInput(make_arg((S, S, S)), args=(dim,))
          # Scalar tensors and empty tensor
          for size in [(), (1,), (0,)]:
              yield SampleInput(make_arg(size), args=(0,))
  
          yield SampleInput(prod_zeros([0, 1]), args=(1,))
          yield SampleInput(prod_zeros([0, 2]), args=(1,))
          yield SampleInput(prod_zeros([1, 2]), args=(1,))
  
          # test dtype kwarg
          yield SampleInput(prod_zeros([1, 2]), args=(1,), kwargs={'dtype': dtype})
  
      return list(sample_generator())
  
  def sample_inputs_view_as_complex(op_info, device, dtype, requires_grad, **kwargs):
      return [SampleInput(make_tensor((S, 2), device, dtype, requires_grad=requires_grad),)]
  
  def sample_inputs_view_as_real(op_info, device, dtype, requires_grad, **kwargs):
      tensors = (
          make_tensor((S, S), device, dtype, requires_grad=requires_grad),
          make_tensor((), device, dtype, requires_grad=requires_grad)
      )
      return [SampleInput(tensor) for tensor in tensors]
  
  def sample_inputs_copysign(op_info, device, dtype, requires_grad, **kwargs):
      def _make_tensor(*shape, low=None, high=None):
          return make_tensor(shape, device, dtype, low=low, high=high, requires_grad=requires_grad)
  
      cases = [
          # no broadcast
          ((S, S, S), (S, S, S), False),
          # broadcast rhs
          ((S, S, S), (S, S), False),
  
          # scalar
          ((S, S), 3.14, False),
          # scalar positive zero
          ((S, S), 0.0, False),
          # scalar negative zero
          ((S, S), -0.0, False),
      ]
  
      # broadcast lhs
      cases.append(((S, S), (S, S, S), True))
      # broadcast all
      cases.append(((S, 1, S), (M, S), True))
  
      def generator():
          for input_shape, arg_val, broadcasts_input in cases:
              if isinstance(arg_val, tuple):
                  arg = _make_tensor(*arg_val)
              else:
                  # arg_val is scalar
                  arg = arg_val
  
              yield SampleInput(_make_tensor(*input_shape), args=(arg, ), broadcasts_input=broadcasts_input)
  
      return list(generator())
  
  def sample_inputs_prod(op_info, device, dtype, requires_grad):
      def make_arg(shape):
          # shrink values to be in the interval [-1, +1] for better precision in gradgradcheck
          return make_tensor(shape, device, dtype, low=-1, high=+1, requires_grad=requires_grad)
  
      def prod_single_zero():
          result = make_arg(2 * (S,))
          with torch.no_grad():
              result[0, 1] = 0
          return result
  
      # will not be needed once OpInfo tests support Iterables
      def sample_generator():
          for sample in sample_inputs_cumprod(op_info, device, dtype, requires_grad):
              yield SampleInput(sample.input)  # only Tensor, ignore other inputs
              yield sample
              sample.kwargs['keepdim'] = True
              yield sample
          yield SampleInput(prod_single_zero())
          yield SampleInput(make_arg((3, 3, 3)), args=(1,))
          yield SampleInput(make_arg((3, 3, 3)), args=(1,), kwargs={'keepdim': True})
  
          # test zero scalar tensor
          zero = make_arg(())
          with torch.no_grad():
              zero.zero_()
          yield SampleInput(zero)
          yield SampleInput(zero, args=(0,))
          yield SampleInput(zero, args=(0,), kwargs={'keepdim': True})
  
      return list(sample_generator())
  
  def sample_inputs_diag(op_info, device, dtype, requires_grad, **kwargs):
      vec_sample = SampleInput(make_tensor((M, ), device, dtype, low=None, high=None, requires_grad=requires_grad))
  
      tensors = (
          make_tensor((M, M), device, dtype, low=None, high=None, requires_grad=requires_grad),
          make_tensor((3, 5), device, dtype, low=None, high=None, requires_grad=requires_grad),
          make_tensor((5, 3), device, dtype, low=None, high=None, requires_grad=requires_grad),
      )
  
      args = ((), (2,), (-2,), (1,), (2,))
  
      samples = []
      for tensor, arg in product(tensors, args):
          samples.append(SampleInput(tensor, args=arg))
  
      return samples + [vec_sample]
  
  def sample_inputs_logit(op_info, device, dtype, requires_grad, **kwargs):
      low, high = op_info.domain
  
      # Note: Operator is very sensitive at points near the
      # start and end of domain and leads to NaN for float16
      # if domain_eps is 1e-5.
      domain_eps = op_info._domain_eps if dtype != torch.float16 else 3e-2
  
      low = low + domain_eps
      high = high - domain_eps
  
      samples = (
          SampleInput(make_tensor((S, S, S), device, dtype, low=low, high=high, requires_grad=requires_grad)),
          SampleInput(make_tensor((S, S, S), device, dtype, low=low,
                                  high=high, requires_grad=requires_grad), args=(0.2,)),
          SampleInput(make_tensor((), device, dtype, low=low, high=high, requires_grad=requires_grad)),
          SampleInput(make_tensor((), device, dtype, low=low,
                                  high=high, requires_grad=requires_grad), args=(0.2,)),
      )
  
      return samples
  
  def sample_inputs_floor_divide(op_info, device, dtype, requires_grad, **kwargs):
      lhs = make_tensor((S, S, S), device, dtype, low=None, high=None, requires_grad=requires_grad)
      rhs = make_tensor((S, S, S), device, dtype, low=None, high=None, requires_grad=requires_grad)
      # Avoid integer divide by 0
      if not (dtype.is_floating_point or dtype.is_complex):
          rhs[rhs == 0] = 1
  
      return [
          SampleInput(lhs, args=(rhs,)),
          SampleInput(lhs, args=(rhs[0],)),
          SampleInput(lhs, args=(3.14,)),
      ]
  
  
  def sample_inputs_masked_scatter(op_info, device, dtype, requires_grad, **kwargs):
      make_arg = partial(make_tensor, device=device, dtype=dtype, requires_grad=requires_grad)
  
      def samples_generator():
          yield SampleInput(make_arg((S, S)), args=(torch.randn(S, S, device=device) > 0, make_arg((S, S))))
          yield SampleInput(make_arg((S, S)), args=(torch.randn((S,), device=device) > 0, make_arg((S, S))))
          yield SampleInput(make_arg((S, S)), args=(bernoulli_scalar().to(device), make_arg((S, S))))
          yield SampleInput(make_arg((S,)),
                            args=(torch.randn(S, S, device=device) > 0, make_arg((S, S))),
                            broadcasts_input=True)
  
      samples = tuple(samples_generator())
      return samples
  
  
  def sample_inputs_masked_fill(op_info, device, dtype, requires_grad, **kwargs):
      make_arg = partial(make_tensor, device=device, dtype=dtype, requires_grad=requires_grad)
  
      def sample_generator():
          yield SampleInput(make_arg((S, S)), args=(torch.randn(S, S, device=device) > 0, 10))
          yield SampleInput(make_arg((S, S)), args=(torch.randn(S, S, device=device) > 0, make_arg(())))
          yield SampleInput(make_arg((S, S)), args=(torch.randn(S, device=device) > 0, 10))
          yield SampleInput(make_arg(()), args=(torch.randn((), device=device) > 0, 10))
          yield SampleInput(make_arg(()), args=(torch.randn((), device=device) > 0, make_arg(())))
          yield SampleInput(make_arg((S, S)), args=(torch.randn((), device=device) > 0, 10))
  
          yield SampleInput(make_arg((S,)),
                            args=(torch.randn(S, S, device=device) > 0, make_arg(())),
                            broadcasts_input=True)
          yield SampleInput(make_arg((S,)),
                            args=(torch.randn(S, S, device=device) > 0, 10),
                            broadcasts_input=True)
  
      samples = tuple(sample_generator())
      return samples
  
  def sample_inputs_masked_select(op_info, device, dtype, requires_grad, **kwargs):
      samples = (
          SampleInput(make_tensor((M, M), device, dtype, low=None, high=None, requires_grad=requires_grad),
                      args=(torch.randn(M, M, device=device) > 0,)),
  
          SampleInput(make_tensor((M, M), device, dtype, low=None, high=None, requires_grad=requires_grad),
                      args=(torch.randn((M,), device=device) > 0,)),
  
          SampleInput(make_tensor((M,), device, dtype, low=None, high=None, requires_grad=requires_grad),
                      args=(torch.randn((M, M), device=device) > 0,)),
  
          SampleInput(make_tensor((M, 1, M), device, dtype, low=None, high=None, requires_grad=requires_grad),
                      args=(torch.randn((M, M), device=device) > 0,)),
  
          SampleInput(make_tensor((), device, dtype, low=None, high=None, requires_grad=requires_grad),
                      args=(torch.tensor(1, device=device, dtype=torch.bool),)),
  
          SampleInput(make_tensor((M, M), device, dtype, low=None, high=None, requires_grad=requires_grad),
                      args=(torch.tensor(1, device=device, dtype=torch.bool),)),
  
          SampleInput(make_tensor((), device, dtype, low=None, high=None, requires_grad=requires_grad),
                      args=(torch.randn((M, M), device=device) > 0,)),
      )
  
      return samples
  
  def sample_inputs_matrix_exp(op_info, device, dtype, requires_grad, **kwargs):
      samples = (
          SampleInput(make_tensor((S, S), device, dtype, requires_grad=requires_grad)),
          SampleInput(make_tensor((S, S, S), device, dtype, requires_grad=requires_grad)),
      )
  
      return samples
  
  def sample_inputs_matmul(op_info, device, dtype, requires_grad):
      test_cases = (((L,), (L,)),
                    ((S, M), (M,)),
                    ((M,), (M, S)),
                    ((S, M), (M, S)),
                    ((S, S, M), (M,)),
                    ((S, S, M), (M, S)),
                    ((M,), (S, M, S)),
                    ((S, M), (S, M, S)),
                    ((S, S, M, M), (S, S, M, S)),
                    ((S, S, M, M), (M,)),
                    ((M,), (S, S, M, S)))
      sample_inputs = []
      for lhs_shape, rhs_shape in test_cases:
          lhs = make_tensor(lhs_shape, device, dtype, low=None, high=None, requires_grad=requires_grad)
          rhs = make_tensor(rhs_shape, device, dtype, low=None, high=None, requires_grad=requires_grad)
          sample_inputs.append(SampleInput(lhs, args=(rhs,)))
      return tuple(sample_inputs)
  
  
  def sample_inputs_polar(op_info, device, dtype, requires_grad, **kwargs):
      def _make_tensor_helper(shape, low=None, high=None):
          return make_tensor(shape, device, dtype, low=low, high=high, requires_grad=requires_grad)
  
      samples = (
          SampleInput(_make_tensor_helper((S, S), low=0), args=(_make_tensor_helper((S, S)),)),
          SampleInput(_make_tensor_helper((), low=0), args=(_make_tensor_helper(()),)),
      )
  
      return samples
  
  def sample_inputs_complex(op_info, device, dtype, requires_grad, **kwargs):
      def _make_tensor_helper(shape):
          return make_tensor(shape, device, dtype, requires_grad=requires_grad)
  
      samples = (
          SampleInput(_make_tensor_helper((S, S)), args=(_make_tensor_helper((S, S)),)),
          SampleInput(_make_tensor_helper(()), args=(_make_tensor_helper(()),)),
      )
  
      return samples
  
  
  def sample_inputs_polygamma(op_info, device, dtype, requires_grad, **kwargs):
      make_arg = partial(make_tensor, device=device, dtype=dtype, requires_grad=requires_grad)
      tensor_shapes = ((S, S), ())
      ns = (1, 2, 3, 4, 5)
  
      def generator():
          for shape, n in product(tensor_shapes, ns):
              yield SampleInput(make_arg(shape), args=(n,))
  
      return list(generator())
  
  
  def sample_inputs_mvlgamma(op_info, device, dtype, requires_grad, **kwargs):
      make_arg = partial(make_tensor, device=device, dtype=dtype, requires_grad=requires_grad)
      tensor_shapes = ((S, S), ())
      ns = (1, 2, 3, 4, 5)
  
      # Since the accepted lower bound for input
      # to mvlgamma depends on `p` argument,
      # the following function computes the lower bound
      # which we pass to `make_tensor`.
      def compute_min_val(p):
          return (p - 1.) / 2
  
      def generator():
          for shape, n in product(tensor_shapes, ns):
              min_val = compute_min_val(n)
              yield SampleInput(make_arg(shape, low=min_val), args=(n,))
  
      return list(generator())
  
  
  # Since `mvlgamma` has multiple entries,
  # there are multiple common skips for the additional
  # entries. Following function is a helper to that end.
  def skips_mvlgamma(skip_redundant=False):
      skips = (
          # outside domain values are hard error for mvlgamma op.
          SkipInfo('TestUnaryUfuncs', 'test_float_domains'),
      )
      if not skip_redundant:
          # Redundant tests
          skips = skips + (  # type: ignore[assignment]
              SkipInfo('TestGradients'),
              SkipInfo('TestOpInfo'),
              SkipInfo('TestCommon'),
          )
      return skips
  
  
  # To test reference numerics against multiple values of argument `p`,
  # we make multiple OpInfo entries with each entry corresponding to different value of p.
  # We run the op tests from test_ops.py only for `p=1` to avoid redundancy in testing.
  # Class `MvlGammaInfo` already contains the basic information related to the operator,
  # it only takes arguments like `domain`, `skips` and `sample_kwargs`, which
  # differ between the entries.
  class MvlGammaInfo(UnaryUfuncInfo):
      def __init__(self, variant_test_name, domain, skips, sample_kwargs):
          super(MvlGammaInfo, self).__init__(
              'mvlgamma',
              ref=reference_mvlgamma if TEST_SCIPY else _NOTHING,
              variant_test_name=variant_test_name,
              domain=domain,
              decorators=(precisionOverride({torch.float16: 5e-2}),),
              dtypes=floating_types(),
              dtypesIfCUDA=floating_types_and(torch.half),
              sample_inputs_func=sample_inputs_mvlgamma,
              supports_out=False,
              skips=skips,
              sample_kwargs=sample_kwargs)
  
  
  def sample_inputs_entr(op_info, device, dtype, requires_grad, **kwargs):
      low, _ = op_info.domain
  
      if requires_grad:
          low = 0 + op_info._domain_eps
  
      return (SampleInput(make_tensor((L,), device, dtype,
                                      low=low,
                                      requires_grad=requires_grad)),
              SampleInput(make_tensor((), device, dtype,
                                      low=low,
                                      requires_grad=requires_grad)))
  
  def sample_inputs_rsub(op_info, device, dtype, requires_grad, variant='tensor', **kwargs):
      def _make_tensor_helper(shape, low=None, high=None):
          return make_tensor(shape, device, dtype, low=low, high=high, requires_grad=requires_grad)
  
      def _samples_with_alpha_helper(args, alphas, filter_fn=lambda arg_alpha: True):
          filtered_product = filter(filter_fn, product(args, alphas))  # type: ignore[var-annotated]
          return (SampleInput(input, args=(arg,), kwargs=dict(alpha=alpha))
                  for (input, arg), alpha in filtered_product)
  
      int_alpha, float_alpha, complex_alpha = 2, 0.1, 1 + 0.6j
  
      if variant == 'tensor':
          samples = (
              SampleInput(_make_tensor_helper((S, S)), args=(_make_tensor_helper((S, S)),)),
              SampleInput(_make_tensor_helper((S, S)), args=(_make_tensor_helper((S,)),)),
              SampleInput(_make_tensor_helper((S,)), args=(_make_tensor_helper((S, S)),)),
              SampleInput(_make_tensor_helper(()), args=(_make_tensor_helper(()),)),
              SampleInput(_make_tensor_helper(()), args=(_make_tensor_helper((S,)),)),
              SampleInput(_make_tensor_helper((S,)), args=(_make_tensor_helper(()),)),
          )
  
          if dtype.is_complex:
              alphas = [int_alpha, float_alpha, complex_alpha]
          elif dtype.is_floating_point:
              alphas = [int_alpha, float_alpha]
          else:
              alphas = [int_alpha]
  
          args = ((_make_tensor_helper((S, S)), _make_tensor_helper((S, S))),
                  (_make_tensor_helper((S, S)), _make_tensor_helper((S,))),
                  (_make_tensor_helper(()), _make_tensor_helper(())))
          samples += tuple(_samples_with_alpha_helper(args, alphas))  # type: ignore[assignment]
      elif variant == 'scalar':
          # Scalar Other
          samples = (SampleInput(_make_tensor_helper((S, S)), args=(0.5,)),
                     SampleInput(_make_tensor_helper(()), args=(0.5,)),
                     SampleInput(_make_tensor_helper((S, S)), args=(1.5j,)),
                     SampleInput(_make_tensor_helper(()), args=(1.5j,)),
                     SampleInput(_make_tensor_helper((S, S)), args=(0.4 + 1.2j,)),
                     SampleInput(_make_tensor_helper(()), args=(1.2 + 1.76j,)))
  
          scalar_args = [(_make_tensor_helper((S, S)), 0.5), (_make_tensor_helper(()), 0.5),
                         (_make_tensor_helper((S, S)), 2.7j), (_make_tensor_helper(()), 2.7j),
                         (_make_tensor_helper((S, S)), 1 - 2.7j), (_make_tensor_helper(()), 1 + 2.7j)]
  
          alphas = [int_alpha, float_alpha, complex_alpha]
  
          def filter_fn(arg_alpha):
              arg, alpha = arg_alpha
              if isinstance(alpha, complex):
                  if dtype.is_complex or isinstance(arg[1], complex):
                      return True
                  else:
                      # complex alpha is valid only if either `self` or `other` is complex
                      return False
  
              # Non-Complex Alpha
              return True
  
          # Samples with alpha (scalar version) covers the following cases
          # self    | other   | alpha
          # -----------------------------------------
          # real    | real    | real (int and float)
          # real    | complex | real and complex
          # complex | real    | real and complex
          # complex | complex | real and complex
          #
          # It does not cover
          # real    | real    | complex
          # x = torch.randn(2, requires_grad=True, dtype=torch.float64)
          # torch.rsub(x, 1, alpha=1. + 1.6j)
          # RuntimeError: value cannot be converted to type double without overflow: (-1,-1.6)
  
          samples += tuple(_samples_with_alpha_helper(scalar_args, alphas, filter_fn=filter_fn))  # type: ignore[assignment]
      else:
          raise Exception("Invalid variant!")
  
      return samples
  
  def sample_inputs_cumulative_ops(op_info, device, dtype, requires_grad, supports_dtype_kwargs=True, **kwargs):
      def _make_tensor_helper(shape, low=None, high=None):
          return make_tensor(shape, device, dtype, low=low, high=high, requires_grad=requires_grad)
  
      samples = [
          SampleInput(_make_tensor_helper((S, S, S)), args=(0,)),
          SampleInput(_make_tensor_helper((S, S, S)), args=(1,)),
          SampleInput(_make_tensor_helper(()), args=(0,)),
      ]
  
      if supports_dtype_kwargs:
          # NOTE: if `dtype` is not same as input, then inplace variants fail with
          # `provided dtype must match the dtype of self tensor in cumsum`
          samples.append(SampleInput(_make_tensor_helper((S, S, S)), args=(1,), kwargs={'dtype': dtype}))
  
      return samples
  
  
  def sample_inputs_unfold(op_info, device, dtype, requires_grad, **kwargs):
      test_cases = (
          ((), (0, 1, 1)),
          ((S, S, S, S), (0, 3, 1)),
          ((S, S, S, S), (1, 3, 1)),
          ((S, S, S, S), (2, 3, 1)),
          ((S, S, S, S), (3, 3, 1)),
          ((S, S, S, S), (0, 3, 2)),
          ((S, S, S, S), (1, 3, 2)),
          ((S, S, S, S), (2, 3, 2)),
          ((S, S, S, S), (3, 3, 2)),
          ((S, S, S, S), (0, 4, 1)),
          ((S, S, S, S), (1, 4, 1)),
          ((S, S, S, S), (2, 4, 1)),
          ((S, S, S, S), (3, 4, 1)),
          ((M,), (0, 3, 1)),
          ((M,), (0, 3, 2)),
          ((M,), (0, 3, 3)),
          ((1000,), (0, 3, 11)),
          ((1000,), (0, 2, 27)),
          ((10, 10), (0, 1, 2)),
          ((10, 10), (1, 2, 3)),
          ((10, 10), (1, 2, 2)),
          ((S, S, S), (2, 3, 2)),
      )
  
      sample_inputs = []
      for shape, arguments in test_cases:
          sample_inputs += [SampleInput(make_tensor(shape, device, dtype,
                                        low=None, high=None,
                                        requires_grad=requires_grad),
                                        args=arguments)]
      return sample_inputs
  
  
  def sample_inputs_atan2(op_info, device, dtype, requires_grad, **kwargs):
      make_arg = partial(make_tensor, device=device, dtype=dtype, requires_grad=requires_grad)
      cases = (
          ((S, S, S), (S, S, S), False),
          ((), (), False),
          ((S, S, S), (S,), False),
          ((S,), (S, S, S), True),
          ((S, 1, S), (S, S), True),
      )
  
      def generator():
          for x_shape, y_shape, broadcasts_input in cases:
              yield SampleInput(make_arg(x_shape), args=(make_arg(y_shape),),
                                broadcasts_input=broadcasts_input)
  
      return list(generator())
  
  def sample_inputs_msort(op_info, device, dtype, requires_grad):
      def apply_grad(t):
          if dtype in floating_types_and(torch.float16, torch.bfloat16):
              t.requires_grad_(requires_grad)
  
      def large_1d_unique(dtype, device):
          res = torch.randperm(L * L * L, dtype=torch.int64, device=device)
          res = res.to(dtype)
          apply_grad(res)
          return res
  
      samples = []
      # Test case for large tensor.
      largesample = SampleInput(large_1d_unique(dtype, device))
  
      sample = SampleInput(make_tensor((S, M, S), device, dtype,
                                       low=None, high=None,
                                       requires_grad=requires_grad))
  
      return [largesample, sample]
  
  def sample_inputs_lerp(op_info, device, dtype, requires_grad, **kwargs):
      make_arg = partial(make_tensor, dtype=dtype, device=device, requires_grad=requires_grad)
  
      samples = (
          # no broadcast
          SampleInput(make_arg((S, S)), args=(make_arg((S, S)), 0.4)),
          # broadcast rhs
          SampleInput(make_arg((S, S)), args=(make_arg((S,)), 0.4)),
          # scalar tensor
          SampleInput(make_arg(()), args=(make_arg(()), 0.4)),
          # broadcast rhs scalar-tensor
          SampleInput(make_arg((S, S)), args=(make_arg(()), 0.4)),
          # broadcast rhs with weight tensor
          SampleInput(make_arg((S, S)), args=(make_arg((S,)), make_arg((S, S)))),
          # broadcast rhs and weight tensor
          SampleInput(make_arg((S, S)), args=(make_arg((S, 1)), make_arg((S,)))),
          # broadcast_lhs
          SampleInput(make_arg((S,)), args=(make_arg((S, S)), 0.4), broadcasts_input=True),
          # scalar broadcast_lhs
          SampleInput(make_arg(()), args=(make_arg((S, S)), 0.4), broadcasts_input=True),
          # broadcast all
          SampleInput(make_arg((S, 1)), args=(make_arg((S, S)), 0.4), broadcasts_input=True),
          # tensor broadcast all
          SampleInput(make_arg((S, 1)), args=(make_arg((S, S)), make_arg((S, 1))),
                      broadcasts_input=True),
      )
  
      if dtype.is_complex:
          samples = samples + (  # type: ignore[assignment]
              # no broadcast
              SampleInput(make_arg((S, S)), args=(make_arg((S, S)), 0.4j)),
              SampleInput(make_arg((S, S)), args=(make_arg((S, S)), 1.2 + 0.1j)),
              # broadcast rhs
              SampleInput(make_arg((S, S)), args=(make_arg((S,)), 0.4j)),
              SampleInput(make_arg((S, S)), args=(make_arg((S, S)), 5.4 + 9j)),
              # scalar tensor
              SampleInput(make_arg(()), args=(make_arg(()), 0.4j)),
              SampleInput(make_arg(()), args=(make_arg(()), 6.1 + 0.004j)),
              # broadcast rhs scalar-tensor
              SampleInput(make_arg((S, S)), args=(make_arg(()), 0.4j)),
              SampleInput(make_arg((S, S)), args=(make_arg(()), 1 + 2j)),
          )
  
      return samples
  
  def sample_inputs_tensordot(self, device, dtype, requires_grad, **kwargs):
      cases = (
          ((2, 2, 2), (2, 2, 2), (2)),
          ((2, 2, 1), (2, 1, 2), ([0, 1], [2, 0])),
      )
      samples = []
      for first_shape, second_shape, dims in cases:
          samples.append(SampleInput(make_tensor(first_shape, device, dtype,
                                     requires_grad=requires_grad),
                         args=(make_tensor(second_shape, device, dtype,
                               requires_grad=requires_grad),),
                         kwargs=dict(dims=dims,)))
      return tuple(samples)
  
  def sample_inputs_kron(op_info, device, dtype, requires_grad):
      test_cases = (
          ((S, S), (M, L)),
      )
  
      sample_inputs = []
      for input_shape, other_shape in test_cases:
          input = make_tensor(input_shape, device, dtype, low=None, high=None, requires_grad=requires_grad)
          other = make_tensor(other_shape, device, dtype, low=None, high=None, requires_grad=requires_grad)
          sample = SampleInput(input, args=(other,))
          sample_inputs.append(sample)
      return tuple(sample_inputs)
  
  def sample_inputs_inner(self, device, dtype, requires_grad, **kwargs):
      return (
          SampleInput(
              make_tensor((S, ), device, dtype, requires_grad=requires_grad),
              args=(
                  make_tensor((S, ), device, dtype, requires_grad=requires_grad),
              )
          ),
          SampleInput(
              make_tensor((), device, dtype, requires_grad=requires_grad),
              args=(
                  make_tensor((S, S), device, dtype, requires_grad=requires_grad),
              )
          ),
      )
  
  # Tests for scatter when passing the reduce argument are missing
  # Reference: https://github.com/pytorch/pytorch/issues/56464
  def sample_inputs_scatter(op_info, device, dtype, requires_grad):
      def _tensor(shape, dtype=dtype, low=None, high=None):
          return make_tensor(shape, device, dtype, low=low, high=high, requires_grad=requires_grad)
  
      def _gather(shape, index_dim, max_indices):
          return gather_variable(shape, index_dim, max_indices, device=device)
  
      zero = torch.tensor(0, dtype=torch.long, device=device)
      test_cases = (
          (_tensor((M, S)), (0, _gather((S, S), 1, M), _tensor((S, S)))),
          (_tensor((M, S)), (1, _gather((S, S), 0, S), _tensor((S, S)))),
          (_tensor((M, S)), (-1, _gather((S, S), 0, S), _tensor((S, S)))),
          (_tensor((M, S)), (0, _gather((M, S // 2), 1, M), _tensor((M, S // 2)))),
          (_tensor((M, S)), (1, _gather((M, S // 2), 0, S), _tensor((M, S // 2)))),
          (_tensor((M, S)), (-1, _gather((M, S // 2), 0, S), _tensor((M, S // 2)))),
          (_tensor(()), (0, zero.clone().detach(), _tensor(()))),
          (_tensor(()), (0, zero.clone().detach(), 2.5)),
      )
  
      return [SampleInput(tensor, args=args) for tensor, args in test_cases]
  
  def sample_inputs_scatter_add(op_info, device, dtype, requires_grad):
      def _tensor(shape, dtype=dtype, low=None, high=None):
          return make_tensor(shape, device, dtype, low=low, high=high, requires_grad=requires_grad)
  
      def _gather(shape, index_dim, max_indices):
          return gather_variable(shape, index_dim, max_indices, device=device)
  
      zero = torch.tensor(0, dtype=torch.long, device=device)
      test_cases = (
          (_tensor((M, S)), (0, _gather((S, S), 1, M), _tensor((S, S)))),
          (_tensor((M, S)), (1, _gather((S, S), 0, S), _tensor((S, S)))),
          (_tensor((M, S)), (-1, _gather((S, S), 0, S), _tensor((S, S)))),
          (_tensor((M, S)), (0, _gather((M, S // 2), 1, M), _tensor((M, S // 2)))),
          (_tensor((M, S)), (1, _gather((M, S // 2), 0, S), _tensor((M, S // 2)))),
          (_tensor((M, S)), (-1, _gather((M, S // 2), 0, S), _tensor((M, S // 2)))),
          (_tensor(()), (0, zero.clone().detach(), _tensor(()))),
      )
  
      return [SampleInput(tensor, args=args) for tensor, args in test_cases]
  
  
  def sample_inputs_ravel(op_info, device, dtype, requires_grad, **kwargs):
      samples = (SampleInput(make_tensor((S, S, S), device, dtype,
                                         low=None, high=None,
                                         requires_grad=requires_grad)),
                 SampleInput(make_tensor((), device, dtype,
                                         low=None, high=None,
                                         requires_grad=requires_grad)),)
  
      return samples
  
  
  def sample_inputs_view_reshape(op_info, device, dtype, requires_grad, **kwargs):
      make_arg = partial(make_tensor, dtype=dtype, device=device, requires_grad=requires_grad)
  
      cases = (((S, S, S), (S * S, S)),
               ((S * S, S), (S, S, S)),
               ((S,), (S,)),
               ((), ()),
               ((), (1,)))
  
      def generator():
          for case in cases:
              shape, args = case
              yield(SampleInput(make_arg(shape), args=(args, )))
  
      return list(generator())
  
  
  def sample_inputs_view_as_reshape_as(op_info, device, dtype, requires_grad, **kwargs):
      make_arg = partial(make_tensor, dtype=dtype, device=device)
  
      cases = (((S, S, S), (S * S, S)),
               ((), ()),
               ((), (1, 1)),
               )
  
      def generator():
          for case in cases:
              shape, shape_other = case
              yield(SampleInput(make_arg(shape, requires_grad=requires_grad),
                                args=(make_arg(shape_other, requires_grad=False), )))
  
      return list(generator())
  
  
  def sample_inputs_select(op_info, device, dtype, requires_grad, **kwargs):
      make_arg = partial(make_tensor, dtype=dtype, device=device, requires_grad=requires_grad)
  
      cases = (((S, S, S), (1, 2)),
               ((S, S, S), (-1, 2)),
               ((S, S, S), (-1, -1)),
               ((S, S, S), (1, -1)),
               ((S,), (0, 2))
               )
  
      def generator():
          for shape, args in cases:
              yield SampleInput(make_arg(shape), args=args)
  
      return list(generator())
  
  
  def sample_inputs_rbinops(op_info, device, dtype, requires_grad, supports_dtype_kwargs=True, **kwargs):
      def _make_tensor_helper(shape, low=None, high=None):
          return make_tensor(shape, device, dtype, low=low, high=high, requires_grad=requires_grad)
  
      scalar: Union[int, float, complex] = 3
  
      if dtype.is_floating_point:
          scalar = 3.14
      elif dtype.is_complex:
          scalar = 3.14j
  
      samples = [
          SampleInput(_make_tensor_helper((S, S, S)), args=(scalar,)),
          SampleInput(_make_tensor_helper(()), args=(scalar,)),
      ]
  
      return samples
  
  
  def sample_inputs_expand(op_info, device, dtype, requires_grad, **kwargs):
      make_arg = partial(make_tensor, dtype=dtype, device=device, requires_grad=requires_grad)
  
      cases = (((S, 1, 1), (S, S, S)),
               ((S, 1, S), (S, S, S)),
               ((S, 1), (S, S, S)),
               ((1,), (S, S, S)),
               ((1, S), (1, 1, S)),
               ((), ()),
               ((), (1, 3, 2)),
               )
  
      def generator():
          for case in cases:
              shape, args = case
              yield(SampleInput(make_arg(shape), args=(args, )))
  
      return list(generator())
  
  
  def sample_inputs_expand_as(op_info, device, dtype, requires_grad, **kwargs):
      make_arg = partial(make_tensor, dtype=dtype, device=device)
  
      cases = (((S, 1, 1), (S, S, S)),
               ((), ()),
               ((), (1, 1)),
               )
  
      def generator():
          for case in cases:
              shape, shape_other = case
              yield(SampleInput(make_arg(shape, requires_grad=requires_grad),
                                args=(make_arg(shape_other, requires_grad=False), )))
  
      return list(generator())
  
  
  def sample_inputs_chunk(op_info, device, dtype, requires_grad, **kwargs):
      make_arg = partial(make_tensor, dtype=dtype, device=device)
  
      cases = (((S, S, S), (2,)),
               ((S, S, S), (S, 1)),
               ((S, S, S), (S, -1)))
  
      def generator():
          for case in cases:
              shape, args = case
              yield(SampleInput(make_arg(shape, requires_grad=requires_grad), args=args))
  
      return list(generator())
  
  
  foreach_unary_op_db: List[OpInfo] = [
      ForeachUnaryFuncInfo('exp'),
      ForeachUnaryFuncInfo('acos'),
      ForeachUnaryFuncInfo('asin'),
      ForeachUnaryFuncInfo('atan'),
      ForeachUnaryFuncInfo('cos'),
      ForeachUnaryFuncInfo('cosh'),
      ForeachUnaryFuncInfo('log'),
      ForeachUnaryFuncInfo('log10'),
      ForeachUnaryFuncInfo('log2'),
      ForeachUnaryFuncInfo('tan'),
      ForeachUnaryFuncInfo('tanh'),
      ForeachUnaryFuncInfo('sin'),
      ForeachUnaryFuncInfo('sinh'),
  
      ForeachUnaryFuncInfo('neg',
                           dtypes=all_types_and_complex(),
                           dtypesIfCPU=all_types_and_complex(),
                           dtypesIfCUDA=all_types_and_complex(),
                           sample_inputs_func=sample_inputs_foreach,
                           safe_casts_outputs=False),
  
      ForeachUnaryFuncInfo('sqrt',
                           dtypes=floating_types(),
                           dtypesIfCPU=floating_and_complex_types_and(torch.bfloat16),
                           dtypesIfCUDA=floating_and_complex_types_and(torch.half)),
  
      ForeachUnaryFuncInfo('ceil',
                           dtypes=floating_types(),
                           dtypesIfCPU=floating_types_and(torch.bfloat16),
                           dtypesIfCUDA=floating_types_and(torch.half, torch.bfloat16)),
  
      ForeachUnaryFuncInfo('erf',
                           dtypes=floating_types(),
                           dtypesIfCPU=floating_types_and(torch.bfloat16),
                           dtypesIfCUDA=floating_types_and(torch.half)),
  
      ForeachUnaryFuncInfo('erfc',
                           dtypes=floating_types(),
                           dtypesIfCPU=floating_types_and(torch.bfloat16),
                           dtypesIfCUDA=floating_types_and(torch.half, torch.bfloat16)),
  
      ForeachUnaryFuncInfo('expm1',
                           dtypes=floating_types(),
                           dtypesIfCPU=floating_types_and(torch.bfloat16),
                           dtypesIfCUDA=floating_types_and(torch.half, torch.bfloat16)),
  
      ForeachUnaryFuncInfo('floor',
                           dtypes=floating_types(),
                           dtypesIfCPU=floating_types_and(torch.bfloat16),
                           dtypesIfCUDA=floating_types_and(torch.half, torch.bfloat16)),
  
      ForeachUnaryFuncInfo('log1p',
                           dtypes=floating_types(),
                           dtypesIfCPU=floating_types_and(torch.bfloat16),
                           dtypesIfCUDA=floating_types_and(torch.half)),
  
      ForeachUnaryFuncInfo('round',
                           dtypes=floating_types(),
                           dtypesIfCPU=floating_types_and(torch.bfloat16),
                           dtypesIfCUDA=floating_types_and(torch.half, torch.bfloat16)),
  
      ForeachUnaryFuncInfo('frac',
                           dtypes=floating_types(),
                           dtypesIfCPU=floating_types_and(torch.bfloat16),
                           dtypesIfCUDA=floating_types_and(torch.half, torch.bfloat16)),
  
      ForeachUnaryFuncInfo('reciprocal',
                           dtypes=floating_types(),
                           dtypesIfCPU=floating_types_and(torch.bfloat16),
                           dtypesIfCUDA=floating_types_and(torch.half)),
  
      ForeachUnaryFuncInfo('sigmoid',
                           dtypes=floating_types(),
                           dtypesIfCPU=floating_types_and(torch.bfloat16),
                           dtypesIfCUDA=floating_types_and(torch.half)),
  
      ForeachUnaryFuncInfo('trunc',
                           dtypes=floating_types(),
                           dtypesIfCPU=floating_types_and(torch.bfloat16),
                           dtypesIfCUDA=floating_types_and(torch.half, torch.bfloat16)),
  
      ForeachUnaryFuncInfo('abs',
                           dtypes=all_types_and_complex_and(torch.bfloat16, torch.half, torch.bool),
                           dtypesIfCPU=all_types_and_complex_and(torch.bfloat16, torch.half),
                           dtypesIfCUDA=all_types_and_complex_and(torch.bfloat16, torch.half, torch.bool),
                           safe_casts_outputs=False)
  ]
  
  def reference_sign(x):
      if x.dtype == np.bool_:
          # `np.sign` doesn't support `bool`.
          # >>> np.sign(True)
          # ufunc 'sign' did not contain a loop
          # with signature matching types dtype('bool') -> dtype('bool')
          return np.sign(x, dtype=np.uint8).astype(np.bool_)
      return np.sign(x)
  
  
  def reference_sgn(x):
      # NumPy doesn't have an equivalent to `torch.sgn` when the dtype is complex.
      # For complex inputs, `np.sign` returns sign(x.real) + 0j if x.real != 0 else sign(x.imag) + 0j.
      # while `torch.sgn` returns, 0 if abs(input) == 0 else input/abs(input)
      if x.dtype not in [np.complex64, np.complex128]:
          return reference_sign(x)
  
      out = (x / np.abs(x))
      if out.ndim == 0:
          # Handle x == 0 case
          if (x == 0):
              # Can't assign to np.complex object
              # So make a new one.
              return np.array(complex(0, 0), dtype=x.dtype)
          return out
  
      # Handle x == 0 case
      mask = (x == 0)
      out[mask] = complex(0, 0)
      return out
  
  
  def reference_sigmoid(x):
      # 'scipy.special.expit' not supported for the input types
      if x.dtype in [np.complex64, np.complex128]:
          return (1 / (1 + np.exp(-x)))
      return scipy.special.expit(x)
  
  
  def reference_lgamma(x):
      # scipy.special.gammaln returns `-inf` when input is `-inf`.
      # While Pytorch, C and C++, all return `inf` when input is `-inf`.
      # Reference:
      # https://en.cppreference.com/w/cpp/numeric/math/lgamma
      # https://en.cppreference.com/w/c/numeric/math/lgamma
  
      # To handle the above discrepancy,
      # we replace -inf with inf so values
      # that were originally -inf map to inf as expected
      if x.dtype.kind == 'f':
          x = np.where(x == float('-inf'), np.array(float('inf'), dtype=x.dtype), x)
  
      out = scipy.special.gammaln(x)
  
      if x.dtype == np.float16:
          # `scipy.special.gammaln` returns output of float32 when input is float16,
          # while `torch.lgamma` preserves `float16`. But due to smaller range of float16,
          # Pytorch version outputs `inf` while SciPy returns finite values.
          out = out.astype(np.float16)
  
      return out
  
  def reference_polygamma(x, n):
      # WEIRD `scipy.special.polygamma` behavior
      # >>> scipy.special.polygamma(0, np.array(501, dtype=np.float32)).dtype
      # dtype('float64')
      # >>> scipy.special.polygamma(0, np.array([501], dtype=np.float32)).dtype
      # dtype('float32')
      #
      # Thus we cast output to the default torch dtype.
      np_dtype = torch_to_numpy_dtype_dict[torch.get_default_dtype()]
      return scipy.special.polygamma(n, x).astype(np_dtype)
  
  
  def reference_mvlgamma(x, d):
      if x.dtype == np.float16:
          return scipy.special.multigammaln(x, d).astype(np.float16)
  
      return scipy.special.multigammaln(x, d)
  
  
  def gradcheck_wrapper_hermitian_input(op, input, *args, **kwargs):
      """Gradcheck wrapper for functions that take Hermitian matrices as input.
  
      They require a modified function because the finite-difference algorithm
      for calculating derivatives does not preserve the Hermitian property of the input.
      """
      return op(input + input.conj().transpose(-2, -1), *args, **kwargs)
  
  
  def gradcheck_wrapper_triangular_input(op, input, *args, upper=False, **kwargs):
      """Gradcheck wrpper for functions that take lower or upper triangular matrices as input.
  
      They require a modified function because the finite-difference algorithm
      for calculating derivatives does not preserve the triangular property of the input.
      """
      return op(input.triu() if upper else input.tril(), upper)
  
  
  # Operator database (sorted alphabetically)
  op_db: List[OpInfo] = [
      UnaryUfuncInfo('abs',
                     aliases=('absolute', ),
                     ref=np.abs,
                     dtypes=all_types_and_complex_and(torch.half, torch.bfloat16),
                     dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                     skips=(
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  device_type='cpu', dtypes=[torch.cfloat]),
                         # Reference: https://github.com/pytorch/pytorch/issues/49224
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                  dtypes=[torch.int8], active_if=TEST_WITH_ASAN),
                         # TODO: Fix test_out_arg_all_dtypes as torch.empty_like(expected_output) where expected_output=op(input)
                         # We can break the logic of the loop over all possible types but it is OK.
                         # https://github.com/pytorch/pytorch/blob/master/test/test_unary_ufuncs.py#L440-L449
                         SkipInfo('TestUnaryUfuncs', 'test_out_arg_all_dtypes',
                                  dtypes=[torch.cfloat, torch.cdouble]),
                     ),
                     supports_inplace_autograd=False,
                     assert_autodiffed=True),
      # NOTE: CPU complex acos produces incorrect outputs (https://github.com/pytorch/pytorch/issues/42952)
      UnaryUfuncInfo('acos',
                     aliases=('arccos', ),
                     ref=np.arccos,
                     domain=(-1, 1),
                     handles_complex_extremals=False,
                     dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                     dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                     # "rsqrt_cpu" not implemented for 'BFloat16'
                     backward_dtypesIfCPU=all_types_and_complex_and(torch.bool),
                     assert_autodiffed=True,
                     decorators=(precisionOverride({torch.float16: 1e-2,
                                                    torch.bfloat16: 1e-1,
                                                    torch.complex64: 1e-2}),),
                     safe_casts_outputs=True,
                     skips=(
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                         SkipInfo('TestGradients', 'test_fn_grad',
                                  dtypes=[torch.cdouble], active_if=IS_WINDOWS),
                         SkipInfo('TestGradients', 'test_method_grad',
                                  dtypes=[torch.cdouble], active_if=IS_WINDOWS),
                         SkipInfo('TestGradients', 'test_inplace_grad',
                                  dtypes=[torch.cdouble], active_if=IS_WINDOWS),
                     )),
      # NOTE: the derivative for inplace acosh is not implemented
      UnaryUfuncInfo('acosh',
                     aliases=('arccosh', ),
                     ref=np.arccosh,
                     domain=(1, float('inf')),
                     dtypes=all_types_and_complex_and(torch.bool),
                     dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                     # "rsqrt_cuda" not implemented for 'BFloat16'
                     backward_dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half),
                     safe_casts_outputs=True,
                     decorators=(precisionOverride({torch.bfloat16: 5e-2}),),
                     supports_inplace_autograd=False,
                     skips=(
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  device_type='cuda', dtypes=[torch.cdouble],
                                  active_if=IS_WINDOWS),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  device_type='cuda', dtypes=[torch.cdouble],
                                  active_if=IS_WINDOWS),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                  device_type='cuda', dtypes=[torch.cdouble],
                                  active_if=IS_WINDOWS),
                         # Reference: https://github.com/pytorch/pytorch/issues/50692
                         SkipInfo('TestGradients', 'test_fn_grad',
                                  device_type='cuda', dtypes=[torch.cdouble], active_if=IS_WINDOWS),
                         SkipInfo('TestGradients', 'test_method_grad',
                                  device_type='cuda', dtypes=[torch.cdouble], active_if=IS_WINDOWS),
                     )),
      OpInfo('add',
             dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.float16),
             assert_autodiffed=True,
             sample_inputs_func=partial(sample_inputs_binary_pwise, alpha=2),
             supports_inplace_autograd=False),
      OpInfo('mul',
             aliases=('multiply',),
             dtypes=all_types_and_complex_and(torch.float16, torch.bfloat16, torch.bool),
             assert_autodiffed=True,
             sample_inputs_func=sample_inputs_binary_pwise),
      OpInfo('sub',
             aliases=('subtract',),
             dtypes=all_types_and_complex_and(torch.bfloat16, torch.float16),
             assert_autodiffed=True,
             sample_inputs_func=partial(sample_inputs_binary_pwise, alpha=2),
             supports_inplace_autograd=False),
      OpInfo('addmm',
             # This addmm OpInfo is for when alpha and beta are not both equal to 1.
             # alpha=beta=1 is tested in the following opinfo, because that special case will
             # trigger addmm being decomposed by a jit pass.
             dtypes=floating_and_complex_types_and(torch.float16),
             dtypesIfCPU=all_types_and_complex_and(torch.float16, torch.bfloat16),
             dtypesIfROCM=floating_and_complex_types_and(torch.float16, torch.bfloat16),
             dtypesIfCUDA=floating_and_complex_types_and(torch.float16, *[torch.bfloat16] if CUDA11OrLater else []),
             assert_autodiffed=True,
             supports_inplace_autograd=False,
             gradcheck_nondet_tol=GRADCHECK_NONDET_TOL,
             sample_inputs_func=sample_inputs_addmm),
      OpInfo('addmm',
             # When alpha=beta=1 as compile-time constants, JIT will decompose addmm into mm and add.
             variant_test_name='decomposed',
             dtypes=floating_and_complex_types_and(torch.float16),
             dtypesIfCPU=all_types_and_complex_and(torch.float16, torch.bfloat16),
             dtypesIfROCM=floating_and_complex_types_and(torch.float16, torch.bfloat16),
             dtypesIfCUDA=floating_and_complex_types_and(torch.float16, *[torch.bfloat16] if CUDA11OrLater else []),
             assert_autodiffed=True,
             supports_inplace_autograd=False,
             gradcheck_nondet_tol=GRADCHECK_NONDET_TOL,
             autodiff_nonfusible_nodes=['aten::add', 'aten::mm'],
             sample_inputs_func=partial(sample_inputs_addmm, alpha=1, beta=1)),
      OpInfo('addmv',
             dtypes=floating_types(),
             dtypesIfCPU=all_types_and_complex_and(torch.bfloat16),
             dtypesIfCUDA=floating_types_and(torch.float16, torch.complex64, torch.complex128,
                                             *[torch.bfloat16] if CUDA11OrLater else []),
             dtypesIfROCM=floating_types_and(torch.half),
             supports_inplace_autograd=False,
             skips=(
                 # issue may fix: https://github.com/pytorch/pytorch/issues/55589
                 # AssertionError: UserWarning not triggered : Resized a non-empty tensor but did not warn about it.
                 SkipInfo('TestCommon', 'test_out', dtypes=(torch.float32,)),
                 # Reference: https://github.com/pytorch/pytorch/issues/55589
                 SkipInfo('TestCommon', 'test_variant_consistency_eager'),
             ),
             sample_inputs_func=sample_inputs_addmv),
      OpInfo('addbmm',
             dtypes=floating_types(),
             dtypesIfCPU=all_types_and_complex_and(torch.float16, torch.bfloat16),
             dtypesIfCUDA=floating_and_complex_types_and(torch.float16, *[torch.bfloat16] if CUDA11OrLater else []),
             dtypesIfROCM=floating_types_and(torch.half),
             skips=(
                 # addbmm does not correctly warn when resizing out= inputs
                 SkipInfo('TestCommon', 'test_out'),
                 # cuda gradchecks are slow
                 # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
                 SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),
                 # https://github.com/pytorch/pytorch/issues/55907
                 SkipInfo('TestCommon', 'test_variant_consistency_eager'),
                 SkipInfo('TestOpInfo', 'test_supported_backward', dtypes=(torch.bfloat16, ),
                          device_type='cuda', active_if=not SM53OrLater)),
             sample_inputs_func=sample_inputs_addbmm),
      OpInfo('baddbmm',
             dtypes=floating_types_and(torch.half),
             dtypesIfCPU=all_types_and_complex_and(torch.float16, torch.bfloat16),
             dtypesIfCUDA=floating_types_and(torch.float16, torch.complex64, torch.complex128,
                                             *[torch.bfloat16] if CUDA11OrLater else []),
             skips=(
                 # baddbmm does not correctly warn when resizing out= inputs
                 SkipInfo('TestCommon', 'test_out'),
                 # cuda gradchecks are slow
                 # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
                 SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),
                 SkipInfo('TestOpInfo', 'test_supported_backward', dtypes=(torch.bfloat16, ),
                          device_type='cuda', active_if=not SM53OrLater)),
             sample_inputs_func=sample_inputs_baddbmm),
      OpInfo('dot',
             dtypes=all_types_and_complex_and(torch.float16),
             dtypesIfCUDA=floating_and_complex_types_and(torch.float16, *[torch.bfloat16] if CUDA11OrLater else []),
             assert_autodiffed=True,
             sample_inputs_func=sample_inputs_dot_vdot),
      OpInfo('vdot',
             dtypes=all_types_and_complex_and(torch.float16),
             dtypesIfCUDA=floating_and_complex_types_and(torch.float16, *[torch.bfloat16] if CUDA11OrLater else []),
             sample_inputs_func=sample_inputs_dot_vdot),
      OpInfo('bmm',
             dtypes=all_types_and_complex_and(torch.bfloat16, torch.float16),
             dtypesIfCUDA=floating_and_complex_types_and(torch.float16, *[torch.bfloat16] if CUDA11OrLater else []),
             assert_autodiffed=True,
             skips=(
                 # bmm does not correctly warn when resizing out= inputs
                 SkipInfo('TestCommon', 'test_out'),
                 # cuda gradchecks are slow
                 # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
                 SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),
                 SkipInfo('TestOpInfo', 'test_supported_backward', dtypes=(torch.bfloat16, ),
                          device_type='cuda', active_if=not SM53OrLater)),
             sample_inputs_func=sample_inputs_bmm),
      OpInfo('mv',
             dtypes=all_types_and_complex_and(torch.float16, torch.bfloat16),
             dtypesIfCUDA=floating_and_complex_types_and(torch.float16, *[torch.bfloat16] if CUDA11OrLater else []),
             skips=(
                 # bmm does not correctly warn when resizing out= inputs
                 SkipInfo('TestCommon', 'test_out'),
                 SkipInfo('TestOpInfo', 'test_supported_backward', dtypes=(torch.float16,)),
                 # mv calls into addmv which doesn't fully support float16
                 # RuntimeError: "addmv_impl_cpu" not implemented for 'Half'
                 SkipInfo('TestOpInfo', 'test_supported_dtypes', dtypes=(torch.float16,)),),
             assert_autodiffed=True,
             sample_inputs_func=sample_inputs_mv),
      OpInfo('addr',
             dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.float16),
             backward_dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
             backward_dtypesIfCUDA=all_types_and_complex_and(torch.bool),
             # Reference: https://github.com/pytorch/pytorch/issues/50747
             supports_inplace_autograd=False,
             skips=(
                 # Reference: https://github.com/pytorch/pytorch/issues/50747
                 SkipInfo('TestCommon', 'test_variant_consistency_eager',
                          dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.float16)),),
             sample_inputs_func=sample_inputs_addr,
             gradcheck_nondet_tol=GRADCHECK_NONDET_TOL),
      OpInfo('addcmul',
             dtypes=all_types_and_complex(),
             dtypesIfCUDA=all_types_and_complex_and(torch.float16, torch.bfloat16),
             assert_autodiffed=True,
             supports_inplace_autograd=False,
             skips=(
                 # TODO: update sample inputs with for_inplace_variant kwarg to support this test
                 SkipInfo('TestCommon', 'test_variant_consistency_eager'),),
             sample_inputs_func=sample_inputs_addcmul_addcdiv),
      OpInfo('addcdiv',
             dtypes=floating_and_complex_types(),
             dtypesIfCUDA=floating_and_complex_types_and(torch.float16, torch.bfloat16),
             supports_inplace_autograd=False,
             skips=(
                 # TODO: update sample inputs with for_inplace_variant kwarg to support this test
                 SkipInfo('TestCommon', 'test_variant_consistency_eager'),),
             sample_inputs_func=sample_inputs_addcmul_addcdiv),
      OpInfo('amax',
             dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
             sample_inputs_func=sample_inputs_amax_amin,),
      OpInfo('amin',
             dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
             sample_inputs_func=sample_inputs_amax_amin),
      OpInfo('argmax',
             dtypes=all_types_and(torch.float16, torch.bfloat16),
             supports_autograd=False,
             sample_inputs_func=sample_inputs_argmax_argmin,),
      OpInfo('argmin',
             dtypes=all_types_and(torch.float16, torch.bfloat16),
             supports_autograd=False,
             sample_inputs_func=sample_inputs_argmax_argmin,),
      UnaryUfuncInfo('asin',
                     aliases=('arcsin', ),
                     ref=np.arcsin,
                     domain=(-1, 1),
                     supports_sparse=True,
                     decorators=(precisionOverride({torch.bfloat16: 1e-2}),),
                     safe_casts_outputs=True,
                     dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                     dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                     # "rsqrt_cpu" not implemented for 'BFloat16'
                     backward_dtypesIfCPU=all_types_and_complex_and(torch.bool),
                     assert_autodiffed=True,
                     skips=(
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  device_type='cuda', dtypes=[torch.cdouble],
                                  active_if=IS_WINDOWS),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  device_type='cuda', dtypes=[torch.cdouble],
                                  active_if=IS_WINDOWS)
                     )),
      # NOTE: derivative for inplace asinh is not implemented
      UnaryUfuncInfo('asinh',
                     aliases=('arcsinh', ),
                     ref=np.arcsinh,
                     dtypes=all_types_and_complex_and(torch.bool),
                     dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                     # "rsqrt_cuda" not implemented for 'BFloat16'
                     backward_dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half),
                     safe_casts_outputs=True,
                     decorators=(precisionOverride({torch.bfloat16: 5e-2}),),
                     supports_inplace_autograd=False,
                     skips=(
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  device_type='cuda', dtypes=[torch.cdouble],
                                  active_if=IS_WINDOWS),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  device_type='cuda', dtypes=[torch.cdouble],
                                  active_if=IS_WINDOWS),
                     )),
      UnaryUfuncInfo('atan',
                     aliases=('arctan', ),
                     ref=np.arctan,
                     dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                     dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                     assert_autodiffed=True,
                     decorators=(precisionOverride({torch.bfloat16: 1e-2}),),
                     safe_casts_outputs=True,
                     skips=(
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  device_type='cuda', dtypes=[torch.cfloat, torch.cdouble],
                                  active_if=IS_WINDOWS),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  device_type='cuda', dtypes=[torch.cfloat, torch.cdouble],
                                  active_if=IS_WINDOWS),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                  device_type='cuda', dtypes=[torch.cfloat, torch.cdouble],
                                  active_if=IS_WINDOWS),
                     )),
      OpInfo('atan2',
             dtypes=all_types_and(torch.bool),
             dtypesIfCPU=all_types_and(torch.bool),
             dtypesIfCUDA=all_types_and(torch.bool, torch.half, torch.bfloat16),
             sample_inputs_func=sample_inputs_atan2,
             ),
      UnaryUfuncInfo('atanh',
                     aliases=('arctanh', ),
                     ref=np.arctanh,
                     domain=(-1, 1),
                     dtypes=all_types_and_complex_and(torch.bool),
                     dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                     safe_casts_outputs=True,
                     decorators=(precisionOverride({torch.bfloat16: 1e-2}),),
                     supports_inplace_autograd=False,
                     skips=(
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  device_type='cuda', dtypes=[torch.cfloat, torch.cdouble],
                                  active_if=IS_WINDOWS),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  device_type='cuda', dtypes=[torch.cfloat],
                                  active_if=IS_WINDOWS),
                     )),
      OpInfo('broadcast_to',
             dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             supports_out=False,
             sample_inputs_func=sample_inputs_broadcast_to),
      UnaryUfuncInfo('bitwise_not',
                     ref=np.bitwise_not,
                     dtypes=integral_types_and(torch.bool),
                     supports_autograd=False),
      OpInfo('cdist',
             dtypes=floating_types(),
             supports_out=False,
             supports_gradgrad=False,
             sample_inputs_func=sample_inputs_cdist),
      UnaryUfuncInfo('ceil',
                     ref=np.ceil,
                     dtypes=floating_types_and(torch.bfloat16),
                     dtypesIfCUDA=floating_types_and(torch.half, torch.bfloat16),
                     assert_autodiffed=True),
      OpInfo('cholesky',
             dtypes=floating_and_complex_types(),
             check_batched_gradgrad=False,
             sample_inputs_func=sample_inputs_linalg_cholesky,
             gradcheck_wrapper=gradcheck_wrapper_hermitian_input,
             decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack],
             skips=(
                 # cuda gradchecks are slow
                 # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
                 SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)),
      OpInfo('cholesky_inverse',
             dtypes=floating_and_complex_types(),
             backward_dtypes=floating_types(),
             # TODO: RuntimeError: cholesky_inverse does not support automatic differentiation for outputs
             # with complex dtype.
             check_batched_gradgrad=False,
             sample_inputs_func=sample_inputs_linalg_cholesky_inverse,
             gradcheck_wrapper=gradcheck_wrapper_triangular_input,
             decorators=[skipCUDAIfNoMagma, skipCPUIfNoLapack],
             skips=(
                 # cholesky_inverse does not correctly warn when resizing out= inputs
                 SkipInfo('TestCommon', 'test_out'),)),
      OpInfo('chunk',
             dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.float16),
             sample_inputs_func=sample_inputs_chunk,
             supports_out=False),
      OpInfo('symeig',
             dtypes=floating_and_complex_types(),
             check_batched_gradgrad=False,
             sample_inputs_func=sample_inputs_symeig,
             gradcheck_wrapper=gradcheck_wrapper_hermitian_input,
             decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack],
             skips=(
                 # cuda gradchecks are slow
                 # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
                 SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)
             ),
      # NOTE: clamp has seperate opinfos for scalar min/max (unary op) vs. tensors
      OpInfo('clamp',
             aliases=('clip',),
             dtypes=all_types_and(torch.half, torch.bfloat16),
             dtypesIfCPU=all_types_and(torch.bfloat16),
             dtypesIfCUDA=all_types_and(torch.half, torch.bfloat16),
             assert_autodiffed=True,
             sample_inputs_func=sample_inputs_clamp),
      UnaryUfuncInfo('clamp',
                     variant_test_name='scalar',
                     aliases=('clip', ),
                     decorators=(precisionOverride({torch.bfloat16: 7e-2, torch.float16: 1e-2}),),
                     ref=np.clip,
                     dtypes=all_types_and(torch.bfloat16),
                     dtypesIfCUDA=all_types_and(torch.half, torch.bfloat16),
                     assert_autodiffed=True,
                     skips=(
                         # Reference: https://github.com/pytorch/pytorch/issues/54841
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  device_type='cpu', dtypes=[torch.bfloat16]),
                     ),
                     sample_kwargs=sample_kwargs_clamp_scalar,
                     sample_inputs_func=sample_inputs_clamp_scalar),
      UnaryUfuncInfo('positive',
                     ref=np.positive,
                     dtypes=all_types_and_complex_and(torch.half, torch.bfloat16),
                     supports_out=False,
                     ),
      UnaryUfuncInfo('conj',
                     ref=np.conj,
                     dtypes=all_types_and_complex_and(torch.bool,
                                                      torch.bfloat16, torch.half),
                     skips=(
                         # File "test_unary_ufuncs.py", line 289, in test_reference_numerics
                         #  if not torch.can_cast(numpy_to_torch_dtype_dict[expected.dtype.type], dtype):
                         # KeyError: <class 'numpy.intc'>
                         # Following error in Windows CI
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                  dtypes=[torch.int],
                                  active_if=IS_WINDOWS),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  dtypes=[torch.int],
                                  active_if=IS_WINDOWS),
                     )),
      OpInfo('view_as_real',
             dtypes=complex_types(),
             sample_inputs_func=sample_inputs_view_as_real,
             ),
      OpInfo('view_as_complex',
             dtypes=floating_types_and(torch.half),
             supports_out=False,
             skips=(
                 # "sum_cpu/sum_cuda" not implemented for 'ComplexHalf'
                 SkipInfo('TestOpInfo', 'test_supported_backward', dtypes=(torch.half,)),
             ),
             sample_inputs_func=sample_inputs_view_as_complex),
      OpInfo('complex',
             dtypes=floating_types(),
             sample_inputs_func=sample_inputs_complex,
             ),
      OpInfo('copysign',
             dtypes=all_types_and(torch.bool, torch.half, torch.bfloat16),
             sample_inputs_func=sample_inputs_copysign,
             supports_inplace_autograd=False,
             ),
      UnaryUfuncInfo('cos',
                     ref=np.cos,
                     dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                     dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                     backward_dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half),
                     assert_autodiffed=True,
                     handles_large_floats=False,
                     safe_casts_outputs=True,
                     decorators=(precisionOverride({torch.bfloat16: 1e-2}),),
                     skips=(
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  dtypes=[torch.cfloat, torch.cdouble], active_if=IS_WINDOWS),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal', device_type='cpu',
                                  dtypes=[torch.cfloat, torch.cdouble], active_if=IS_MACOS),
                     )),
      UnaryUfuncInfo('cosh',
                     ref=np_unary_ufunc_integer_promotion_wrapper(np.cosh),
                     dtypes=all_types_and_complex_and(torch.bool),
                     dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                     safe_casts_outputs=True,
                     assert_autodiffed=True,
                     skips=(
                         # Reference: https://github.com/pytorch/pytorch/issues/48641
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  device_type='cpu', dtypes=[torch.int8]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  dtypes=[torch.cfloat, torch.cdouble], active_if=IS_WINDOWS),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  dtypes=[torch.cfloat, torch.cdouble], active_if=IS_WINDOWS),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal', device_type='cpu',
                                  dtypes=[torch.cfloat, torch.cdouble], active_if=IS_MACOS),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard', device_type='cpu',
                                  dtypes=[torch.cfloat, torch.cdouble], active_if=IS_MACOS),
                     )),
      OpInfo('cumsum',
             dtypesIfCPU=all_types_and_complex_and(torch.bool),
             dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half),
             skips=(
                 # "cumsum_out_{cpu,cuda}" not implemented for 'Bool'
                 SkipInfo('TestOpInfo', 'test_supported_dtypes',
                          dtypes=(torch.bool,)),
                 # cumsum does not handle correctly out= dtypes
                 SkipInfo('TestCommon', 'test_out'),
             ),
             sample_inputs_func=sample_inputs_cumulative_ops),
      OpInfo('cumprod',
             dtypes=all_types_and_complex_and(torch.bool),
             dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.float16),
             skips=(
                 # "cumprod_out_{cpu, cuda}" not implemented for 'Bool'
                 SkipInfo('TestOpInfo', 'test_supported_dtypes',
                          dtypes=(torch.bool,)),
                 # cumprod does not handle correctly out= dtypes
                 SkipInfo('TestCommon', 'test_out',
                          dtypes=[torch.float32]),
             ),
             # gradgradcheck fails in fast_mode=True: #56275
             sample_inputs_func=sample_inputs_cumprod,
             gradcheck_fast_mode=False),
      OpInfo('cummax',
             dtypesIfCPU=all_types_and(torch.bool),
             dtypesIfCUDA=all_types_and(torch.bool, torch.half),
             sample_inputs_func=partial(sample_inputs_cumulative_ops, supports_dtype_kwargs=False),
             gradcheck_nondet_tol=GRADCHECK_NONDET_TOL),
      OpInfo('cummin',
             dtypesIfCPU=all_types_and(torch.bool),
             dtypesIfCUDA=all_types_and(torch.bool, torch.half),
             sample_inputs_func=partial(sample_inputs_cumulative_ops, supports_dtype_kwargs=False),
             gradcheck_nondet_tol=GRADCHECK_NONDET_TOL),
      UnaryUfuncInfo('deg2rad',
                     ref=np.radians,
                     decorators=(precisionOverride({torch.bfloat16: 7e-1,
                                                    torch.float16: 7e-1}),),
                     dtypes=all_types_and(torch.bool, torch.half, torch.bfloat16),
                     skips=(
                         # Reference: https://github.com/pytorch/pytorch/pull/51283#issuecomment-770614273
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  dtypes=[torch.bfloat16]),
                     ),
                     safe_casts_outputs=True),
      OpInfo('diff',
             op=torch.diff,
             dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             sample_inputs_func=sample_inputs_diff),
      OpInfo('div',
             variant_test_name='no_rounding_mode',
             dtypes=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
             sample_inputs_func=sample_inputs_div,
             skips=(SkipInfo('TestOpInfo', 'test_duplicate_method_tests'),),
             assert_autodiffed=True),
      OpInfo('div',
             variant_test_name='true_rounding',
             dtypes=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
             sample_inputs_func=partial(sample_inputs_div, rounding_mode=None),
             skips=(SkipInfo('TestOpInfo', 'test_duplicate_method_tests'),),
             assert_autodiffed=True),
      OpInfo('div',
             variant_test_name='trunc_rounding',
             dtypes=all_types_and(torch.half, torch.bfloat16),
             sample_inputs_func=partial(sample_inputs_div, rounding_mode='trunc'),
             skips=(SkipInfo('TestOpInfo', 'test_duplicate_method_tests'),),
             assert_autodiffed=True),
      OpInfo('div',
             variant_test_name='floor_rounding',
             dtypes=all_types_and(torch.half, torch.bfloat16),
             sample_inputs_func=partial(sample_inputs_div, rounding_mode='floor'),
             skips=(SkipInfo('TestOpInfo', 'test_duplicate_method_tests'),),
             assert_autodiffed=True),
      UnaryUfuncInfo('exp',
                     ref=np_unary_ufunc_integer_promotion_wrapper(np.exp),
                     dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                     dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                     skips=(
                         # Reference: https://github.com/pytorch/pytorch/pull/50093#pullrequestreview-561791547
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal', dtypes=[torch.bfloat16]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard', dtypes=[torch.bfloat16]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal', dtypes=[torch.bfloat16]),
                         # Reference: https://github.com/pytorch/pytorch/issues/48010
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                     ),
                     assert_autodiffed=True,
                     safe_casts_outputs=True),
      OpInfo('expand',
             op=lambda self, shape: self.expand(shape),
             dtypes=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
             sample_inputs_func=sample_inputs_expand,
             skips=(
                 # Because expand does not have a function variant.
                 SkipInfo('TestCommon', 'test_variant_consistency_jit'),),
             supports_out=False),
      OpInfo('expand_as',
             op=lambda self, other: self.expand_as(other),
             dtypes=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
             sample_inputs_func=sample_inputs_expand_as,
             skips=(
                 # Because expand_as does not have a function variant.
                 SkipInfo('TestCommon', 'test_variant_consistency_jit'),),
             supports_out=False),
      OpInfo('diag',
             dtypes=all_types_and_complex_and(torch.bool),
             dtypesIfCPU=all_types_and_complex_and(torch.bool),
             dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
             sample_inputs_func=sample_inputs_diag),
      OpInfo('eq',
             dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.float16),
             supports_autograd=False,
             sample_inputs_func=sample_inputs_comparison_ops),
      OpInfo('fmax',
             op=torch.fmax,
             dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
             sample_inputs_func=sample_inputs_max_min_binary,),
      OpInfo('fmin',
             op=torch.fmin,
             dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
             sample_inputs_func=sample_inputs_max_min_binary,),
      UnaryUfuncInfo('frac',
                     ref=lambda x: np.modf(x)[0],
                     dtypes=floating_types_and(torch.bfloat16, torch.float16),
                     dtypesIfCUDA=floating_types_and(torch.float16, torch.bfloat16),
                     assert_autodiffed=True,
                     # Reference for disabling extremals
                     # https://github.com/pytorch/pytorch/issues/51948
                     handles_extremals=False),
      SpectralFuncInfo('fft.fft',
                       aten_name='fft_fft',
                       ref=np.fft.fft,
                       ndimensional=False,
                       dtypes=all_types_and_complex_and(torch.bool),
                       default_test_dtypes=floating_and_complex_types()),
      SpectralFuncInfo('fft.fftn',
                       aten_name='fft_fftn',
                       ref=np.fft.fftn,
                       ndimensional=True,
                       dtypes=all_types_and_complex_and(torch.bool),
                       default_test_dtypes=floating_and_complex_types(),
                       decorators=[precisionOverride(
                           {torch.float: 1e-4, torch.cfloat: 1e-4})],),
      SpectralFuncInfo('fft.hfft',
                       aten_name='fft_hfft',
                       ref=np.fft.hfft,
                       ndimensional=False,
                       dtypes=all_types_and_complex_and(torch.bool),
                       default_test_dtypes=floating_and_complex_types(),
                       check_batched_gradgrad=False),
      SpectralFuncInfo('fft.rfft',
                       aten_name='fft_rfft',
                       ref=np.fft.rfft,
                       ndimensional=False,
                       dtypes=all_types_and(torch.bool),
                       default_test_dtypes=floating_and_complex_types(),
                       check_batched_grad=False,
                       check_batched_gradgrad=False),
      SpectralFuncInfo('fft.rfftn',
                       aten_name='fft_rfftn',
                       ref=np.fft.rfftn,
                       ndimensional=True,
                       dtypes=all_types_and(torch.bool),
                       default_test_dtypes=floating_and_complex_types(),
                       check_batched_grad=False,
                       check_batched_gradgrad=False,
                       decorators=[precisionOverride({torch.float: 1e-4})],),
      SpectralFuncInfo('fft.ifft',
                       aten_name='fft_ifft',
                       ref=np.fft.ifft,
                       ndimensional=False,
                       dtypes=all_types_and_complex_and(torch.bool),
                       default_test_dtypes=floating_and_complex_types()),
      SpectralFuncInfo('fft.ifftn',
                       aten_name='fft_ifftn',
                       ref=np.fft.ifftn,
                       ndimensional=True,
                       dtypes=all_types_and_complex_and(torch.bool),
                       default_test_dtypes=floating_and_complex_types(),
                       decorators=[
                           DecorateInfo(
                               precisionOverride({torch.float: 1e-4, torch.cfloat: 1e-4}),
                               'TestFFT', 'test_reference_nd')],
                       ),
      SpectralFuncInfo('fft.ihfft',
                       aten_name='fft_ihfft',
                       ref=np.fft.ihfft,
                       ndimensional=False,
                       dtypes=all_types_and(torch.bool),
                       default_test_dtypes=floating_types(),
                       check_batched_grad=False),
      SpectralFuncInfo('fft.irfft',
                       aten_name='fft_irfft',
                       ref=np.fft.irfft,
                       ndimensional=False,
                       dtypes=all_types_and_complex_and(torch.bool),
                       default_test_dtypes=floating_and_complex_types(),
                       check_batched_gradgrad=False),
      SpectralFuncInfo('fft.irfftn',
                       aten_name='fft_irfftn',
                       ref=np.fft.irfftn,
                       ndimensional=True,
                       dtypes=all_types_and_complex_and(torch.bool),
                       default_test_dtypes=floating_and_complex_types(),
                       check_batched_gradgrad=False,
                       decorators=[
                           DecorateInfo(
                               precisionOverride({torch.float: 1e-4, torch.cfloat: 1e-4}),
                               'TestFFT', 'test_reference_nd')],
                       ),
      UnaryUfuncInfo('floor',
                     ref=np.floor,
                     dtypes=floating_types_and(torch.bfloat16),
                     dtypesIfCUDA=floating_types_and(torch.half, torch.bfloat16),
                     assert_autodiffed=True),
      OpInfo('flip',
             op=torch.flip,
             dtypes=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
             sample_inputs_func=sample_inputs_flip,
             supports_out=False),
      OpInfo('fliplr',
             op=torch.fliplr,
             dtypes=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
             sample_inputs_func=sample_inputs_fliplr_flipud,
             supports_out=False),
      OpInfo('flipud',
             op=torch.flipud,
             dtypes=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
             sample_inputs_func=sample_inputs_fliplr_flipud,
             supports_out=False),
      UnaryUfuncInfo('i0',
                     ref=np.i0,
                     decorators=(precisionOverride({torch.bfloat16: 3e-1,
                                                    torch.float16: 5e-1}),),
                     dtypes=floating_types_and(torch.bfloat16),
                     dtypesIfCUDA=floating_types_and(torch.half, torch.bfloat16),
                     supports_autograd=False),
      UnaryUfuncInfo('special.i0e',
                     aten_name='special_i0e',
                     ref=scipy.special.i0e if TEST_SCIPY else _NOTHING,
                     decorators=(precisionOverride({torch.bfloat16: 3e-1,
                                                    torch.float16: 3e-1}),),
                     dtypes=all_types_and(torch.bool, torch.bfloat16),
                     dtypesIfCUDA=all_types_and(torch.bool, torch.half, torch.bfloat16),
                     supports_autograd=False,
                     safe_casts_outputs=True),
      OpInfo('floor_divide',
             dtypes=all_types_and(torch.half, torch.bfloat16),
             sample_inputs_func=sample_inputs_floor_divide,
             decorators=[_wrap_warn_once("floor_divide is deprecated, and will be removed")],
             skips=(
                 # `test_duplicate_method_tests` doesn't raise any warning, as it doesn't actually
                 # call the operator.
                 SkipInfo('TestOpInfo', 'test_duplicate_method_tests'),),
             supports_autograd=False,
             ),
      UnaryUfuncInfo('frexp',
                     op=torch.frexp,
                     ref=np.frexp,
                     dtypes=floating_types_and(torch.half),
                     # skip testing torch.frexp as it is not supported by ROCm platform yet
                     decorators=[skipCUDAIfRocm],
                     supports_out=False,
                     skips=(
                         # skips below tests as torch.frexp returns tuple-like (mantissa, exponent) as outputs,
                         # while theses tests currently requires output to a single tensor.
                         SkipInfo('TestUnaryUfuncs', 'test_batch_vs_slicing'),
                         SkipInfo('TestUnaryUfuncs', 'test_contig_vs_every_other'),
                         SkipInfo('TestUnaryUfuncs', 'test_contig_vs_transposed'),
                         SkipInfo('TestUnaryUfuncs', 'test_non_contig_expand'),
                         SkipInfo('TestUnaryUfuncs', 'test_variant_consistency'),
  
                         # skips test_reference_numerics due to error in Windows CI.
                         # The np.frexp returns exponent as np.intc dtype on Windows platform,
                         # and np.intc does not have the correspond torch dtype
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                  active_if=IS_WINDOWS),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  active_if=IS_WINDOWS),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  active_if=IS_WINDOWS),
                     )),
      OpInfo('ge',
             aliases=('greater_equal',),
             dtypes=all_types_and(torch.bool, torch.bfloat16, torch.float16),
             supports_autograd=False,
             sample_inputs_func=sample_inputs_comparison_ops),
      OpInfo('geqrf',
             dtypes=floating_and_complex_types(),
             dtypesIfCPU=floating_and_complex_types(),
             supports_autograd=False,
             sample_inputs_func=sample_inputs_geqrf,
             decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack],),
      OpInfo('gt',
             aliases=('greater',),
             dtypes=all_types_and(torch.bool, torch.bfloat16, torch.float16),
             supports_autograd=False,
             sample_inputs_func=sample_inputs_comparison_ops),
      UnaryUfuncInfo('imag',
                     ref=np.imag,
                     dtypes=complex_types(),
                     supports_out=False,
                     supports_autograd=False,
                     skips=(
                         # Skip since real and imag don't have out variants.
                         SkipInfo('TestUnaryUfuncs', 'test_out_arg_all_dtypes'),
                     )),
      OpInfo('gradient',
             dtypes=floating_and_complex_types_and(torch.int8, torch.int16,
                                                   torch.int32, torch.int64,
                                                   torch.bfloat16, torch.half),
             supports_out=False,
             skips=(
                 # following tests give a runtime error with undefined value tensor
                 # see discussion : https://github.com/pytorch/pytorch/issues/56660
                 SkipInfo('TestCommon', 'test_variant_consistency_jit', dtypes=(torch.float32, torch.complex64)),
             ),
             supports_inplace_autograd=False,
             sample_inputs_func=sample_inputs_gradient),
      OpInfo('inverse',
             op=torch.inverse,
             dtypes=floating_and_complex_types(),
             check_batched_gradgrad=False,
             gradcheck_nondet_tol=GRADCHECK_NONDET_TOL,
             sample_inputs_func=sample_inputs_linalg_invertible,
             decorators=[skipCUDAIfNoMagmaAndNoCusolver, skipCUDAIfRocm, skipCPUIfNoLapack],
             skips=(
                 # cuda gradchecks are slow
                 # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
                 SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)),
      OpInfo('le',
             aliases=('less_equal',),
             dtypes=all_types_and(torch.bool, torch.bfloat16, torch.float16),
             supports_autograd=False,
             sample_inputs_func=sample_inputs_comparison_ops),
      OpInfo('linalg.det',
             op=torch.linalg.det,
             aliases=('det', ),
             dtypes=floating_and_complex_types(),
             # det doesn't support complex autograd, https://github.com/pytorch/pytorch/issues/57358
             backward_dtypes=floating_types(),
             aten_name='linalg_det',
             sample_inputs_func=sample_inputs_linalg_det,
             decorators=[skipCUDAIfNoMagma, skipCPUIfNoLapack],
             supports_inplace_autograd=False,
             skips=(
                 # The following tests fail only on ROCm. This is probably
                 # related to the fact that the current linalg.det backward is
                 # unstable if the matrix has repeated singular values, see
                 # https://github.com/pytorch/pytorch/issues/53364
                 SkipInfo('TestGradients', 'test_fn_grad', device_type='cuda',
                          dtypes=(torch.float64,), active_if=TEST_WITH_ROCM),
                 SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda',
                          dtypes=(torch.float64,), active_if=TEST_WITH_ROCM),
                 SkipInfo('TestCommon', 'test_variant_consistency_jit', device_type='cuda',
                          dtypes=(torch.float64, torch.float32), active_if=TEST_WITH_ROCM),
             )),
      OpInfo('linalg.cholesky',
             aten_name='linalg_cholesky',
             dtypes=floating_and_complex_types(),
             # TODO: RuntimeError: While computing batched gradients,
             # got: vmap: Calling Tensor.as_strided is not supported
             # unless the batch dims being vmapped over are at the front of the tensor (in memory layout).
             check_batched_gradgrad=False,
             sample_inputs_func=sample_inputs_linalg_cholesky,
             gradcheck_wrapper=gradcheck_wrapper_hermitian_input,
             decorators=[skipCUDAIfNoMagmaAndNoCusolver, skipCUDAIfRocm, skipCPUIfNoLapack],
             skips=(
                 # cuda gradchecks are slow
                 # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
                 SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)
             ),
      OpInfo('linalg.cholesky_ex',
             aten_name='linalg_cholesky_ex',
             dtypes=floating_and_complex_types(),
             check_batched_gradgrad=False,
             sample_inputs_func=sample_inputs_linalg_cholesky,
             gradcheck_wrapper=gradcheck_wrapper_hermitian_input,
             decorators=[skipCUDAIfNoMagmaAndNoCusolver, skipCUDAIfRocm, skipCPUIfNoLapack],
             skips=(
                 # cuda gradchecks are slow
                 # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
                 SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)
             ),
      OpInfo('linalg.eig',
             aten_name='linalg_eig',
             op=torch.linalg.eig,
             dtypes=floating_and_complex_types(),
             supports_autograd=False,
             sample_inputs_func=sample_inputs_linalg_invertible,
             decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack]),
      OpInfo('linalg.eigvals',
             aten_name='linalg_eigvals',
             op=torch.linalg.eigvals,
             dtypes=floating_and_complex_types(),
             supports_autograd=False,
             sample_inputs_func=sample_inputs_linalg_invertible,
             decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack]),
      OpInfo('linalg.eigh',
             aten_name='linalg_eigh',
             dtypes=floating_and_complex_types(),
             check_batched_gradgrad=False,
             sample_inputs_func=sample_inputs_linalg_eigh,
             gradcheck_wrapper=gradcheck_wrapper_hermitian_input,
             decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack],
             skips=(
                 # cuda gradchecks are slow
                 # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
                 SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)
             ),
      OpInfo('linalg.eigvalsh',
             aten_name='linalg_eigvalsh',
             dtypes=floating_and_complex_types(),
             check_batched_gradgrad=False,
             sample_inputs_func=sample_inputs_linalg_eigh,
             gradcheck_wrapper=gradcheck_wrapper_hermitian_input,
             decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack],),
      OpInfo('linalg.householder_product',
             aten_name='linalg_householder_product',
             op=torch.linalg.householder_product,
             aliases=('orgqr', ),
             dtypes=floating_and_complex_types(),
             # TODO: backward uses in-place operations that vmap doesn't like
             check_batched_grad=False,
             check_batched_gradgrad=False,
             sample_inputs_func=sample_inputs_householder_product,
             decorators=[skipCUDAIfNoCusolver, skipCUDAIfRocm, skipCPUIfNoLapack,
                         # gradgrad checks are slow
                         DecorateInfo(slowTest, 'TestGradients', 'test_fn_gradgrad'), ]),
      OpInfo('linalg.lstsq',
             aten_name='linalg_lstsq',
             op=torch.linalg.lstsq,
             dtypes=floating_and_complex_types(),
             supports_out=True,
             sample_inputs_func=sample_inputs_linalg_lstsq,
             check_batched_grad=False,
             check_batched_gradgrad=False,
             decorators=[skipCUDAIfNoMagma, skipCPUIfNoLapack],
             skips=(
                 # skip because `linalg_lstsq` is not differentiable
                 SkipInfo('TestGradients', 'test_fn_grad'),
                 SkipInfo('TestCommon', 'test_variant_consistency_jit'),
             )),
      OpInfo('linalg.matrix_power',
             aliases=('matrix_power',),
             aten_name='linalg_matrix_power',
             dtypes=floating_and_complex_types(),
             supports_inplace_autograd=False,
             decorators=[skipCUDAIfNoMagmaAndNoCusolver, skipCPUIfNoLapack, skipCUDAIfRocm],
             sample_inputs_func=sample_inputs_linalg_matrix_power,
             gradcheck_nondet_tol=GRADCHECK_NONDET_TOL),
      OpInfo('linalg.multi_dot',
             # Need this lambda because gradcheck does not work with TensorList inputs
             aten_name='linalg_multi_dot',
             dtypes=floating_and_complex_types_and(torch.half),
             dtypesIfCPU=all_types_and_complex_and(torch.half, torch.bfloat16),
             dtypesIfCUDA=floating_and_complex_types_and(torch.half, *[torch.bfloat16] if CUDA11OrLater else []),
             supports_inplace_autograd=False,
             # Batched grad checks fail for empty input tensors (see https://github.com/pytorch/pytorch/issues/53407)
             check_batched_grad=False,
             check_batched_gradgrad=False,
             sample_inputs_func=sample_inputs_linalg_multi_dot,
             gradcheck_nondet_tol=GRADCHECK_NONDET_TOL),
      OpInfo('linalg.norm',
             op=torch.linalg.norm,
             dtypes=floating_and_complex_types_and(torch.float16, torch.bfloat16),
             decorators=[skipCUDAIfNoMagma, skipCPUIfNoLapack],
             sample_inputs_func=sample_inputs_linalg_norm,
             aten_name='linalg_norm',
             skips=(
                 # linalg.norm does not correctly warn when resizing out= inputs
                 SkipInfo('TestCommon', 'test_out'),
             )),
      OpInfo('linalg.matrix_norm',
             aten_name='linalg_matrix_norm',
             dtypes=floating_and_complex_types(),
             decorators=[skipCUDAIfNoMagma, skipCPUIfNoLapack],
             sample_inputs_func=sample_inputs_linalg_matrix_norm,
             skips=(
                 # linalg.matrix_norm does not correctly warn when resizing out= inputs
                 SkipInfo('TestCommon', 'test_out'),
             )),
      OpInfo('linalg.qr',
             aten_name='linalg_qr',
             op=torch.linalg.qr,
             dtypes=floating_and_complex_types(),
             # batched gradients do not work for empty inputs
             # https://github.com/pytorch/pytorch/issues/50743#issuecomment-767376085
             check_batched_gradgrad=False,
             sample_inputs_func=sample_inputs_linalg_qr,
             decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack],
             skips=(
                 # cuda gradchecks are slow
                 # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
                 SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)),
      OpInfo('linalg.slogdet',
             aten_name='linalg_slogdet',
             op=torch.linalg.slogdet,
             dtypes=floating_and_complex_types(),
             sample_inputs_func=sample_inputs_linalg_slogdet,
             decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack]),
      OpInfo('linalg.vector_norm',
             op=torch.linalg.vector_norm,
             dtypes=floating_and_complex_types_and(torch.float16, torch.bfloat16),
             decorators=[skipCUDAIfNoMagma, skipCPUIfNoLapack],
             sample_inputs_func=sample_inputs_linalg_vector_norm,
             aten_name='linalg_vector_norm',
             skips=(
                 # linalg.vector_norm does not correctly warn when resizing out= inputs
                 SkipInfo('TestCommon', 'test_out'),
             )),
      UnaryUfuncInfo('log',
                     ref=np.log,
                     domain=(0, float('inf')),
                     dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                     dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                     assert_autodiffed=True,
                     safe_casts_outputs=True,
                     decorators=(precisionOverride({torch.bfloat16: 5e-2}),),
                     skips=(
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                  active_if=IS_WINDOWS),
                     )),
      UnaryUfuncInfo('log10',
                     ref=np.log10,
                     domain=(0, float('inf')),
                     decorators=(precisionOverride({torch.bfloat16: 5e-2}),),
                     dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                     assert_autodiffed=True,
                     dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                     safe_casts_outputs=True,
                     skips=(
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                  active_if=IS_WINDOWS),
                     )),
      UnaryUfuncInfo('log1p',
                     ref=np.log1p,
                     domain=(-1, float('inf')),
                     dtypes=all_types_and(torch.bool, torch.bfloat16),
                     dtypesIfCUDA=all_types_and(torch.bool, torch.half, torch.bfloat16),
                     decorators=(precisionOverride({torch.bfloat16: 1e-1}),),
                     safe_casts_outputs=True,
                     assert_autodiffed=True),
      UnaryUfuncInfo('log2',
                     ref=np.log2,
                     domain=(0, float('inf')),
                     dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                     dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                     assert_autodiffed=True,
                     safe_casts_outputs=True,
                     decorators=(precisionOverride({torch.bfloat16: 1e-1}),),
                     skips=(
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  dtypes=[torch.cfloat, torch.cdouble]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                  dtypes=[torch.cfloat, torch.cdouble]),
                     )),
      OpInfo('logaddexp',
             dtypes=floating_types(),
             dtypesIfCUDA=floating_types_and(torch.bfloat16),
             dtypesIfROCM=floating_types_and(torch.bfloat16),
             sample_inputs_func=lambda op_info, device, dtype, requires_grad=False, **kwargs:
             (SampleInput(make_tensor((S, S), device, dtype, requires_grad=requires_grad),
                          args=(make_tensor((S, S), device, dtype, requires_grad=requires_grad),)),)),
      OpInfo('logaddexp2',
             dtypes=floating_types(),
             dtypesIfCUDA=floating_types_and(torch.bfloat16),
             dtypesIfROCM=floating_types_and(torch.bfloat16),
             sample_inputs_func=lambda op_info, device, dtype, requires_grad=False, **kwargs:
             (SampleInput(make_tensor((S, S), device, dtype, requires_grad=requires_grad),
                          args=(make_tensor((S, S), device, dtype, requires_grad=requires_grad),)),)),
      UnaryUfuncInfo('logical_not',
                     ref=np.logical_not,
                     decorators=(precisionOverride({torch.bfloat16: 7e-1,
                                                    torch.float16: 5e-1}),),
                     dtypes=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                     safe_casts_outputs=True,
                     supports_autograd=False,
                     skips=(
                         # The function variant always returns BoolTensor
                         # while the inplace variant preserves the input dtype.
                         # >>> t = torch.randn(3)
                         # >>> torch.logical_not(t)
                         # tensor([False, False, False])
                         # >>> torch.logical_not(t).dtype
                         # torch.bool
                         # >>> t.logical_not_().dtype
                         # torch.float32
                         SkipInfo('TestUnaryUfuncs', 'test_variant_consistency',
                                  dtypes=all_types_and_complex_and(torch.half, torch.bfloat16)),
                         SkipInfo('TestCommon', 'test_variant_consistency_eager',
                                  dtypes=all_types_and_complex_and(torch.half, torch.bfloat16)),
                     )),
      OpInfo('lt',
             aliases=('less',),
             dtypes=all_types_and(torch.bool, torch.bfloat16, torch.float16),
             supports_autograd=False,
             sample_inputs_func=sample_inputs_comparison_ops),
      OpInfo('lu',
             op=torch.lu,
             dtypes=floating_and_complex_types(),
             supports_inplace_autograd=False,
             check_batched_gradgrad=False,
             supports_out=False,
             sample_inputs_func=sample_inputs_lu,
             decorators=[skipCUDAIfNoMagmaAndNoCusolver, skipCUDAIfRocm, skipCPUIfNoLapack],
             skips=(
                 # cuda gradchecks are slow
                 # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
                 SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),
                 # we skip jit tests because lu_backward is impelemented as autograd.Function,
                 # which does not support autograd with scripting
                 SkipInfo('TestCommon', 'test_variant_consistency_jit'),
                 # Skip operator schema test because this is a functional and not an operator
                 SkipInfo('TestOperatorSignatures', 'test_get_torch_func_signature_exhaustive'),
             )),
      OpInfo('lu_unpack',
             op=torch.lu_unpack,
             dtypes=floating_and_complex_types(),
             supports_inplace_autograd=False,
             # we use in-place operations which cannot be avoided.
             # This cases vmap failures, hence we skip batched gradient checks
             check_batched_grad=False,
             supports_out=True,
             sample_inputs_func=sample_inputs_lu_unpack,
             decorators=[skipCUDAIfNoMagmaAndNoCusolver, skipCUDAIfRocm, skipCPUIfNoLapack],
             skips=(
                 # cuda gradchecks are slow
                 # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
                 SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),
             )),
      OpInfo('masked_fill',
             dtypes=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
             sample_inputs_func=sample_inputs_masked_fill,
             supports_out=False),
      OpInfo('masked_scatter',
             dtypes=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
             sample_inputs_func=sample_inputs_masked_scatter,
             supports_out=False),
      OpInfo('masked_select',
             dtypes=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
             sample_inputs_func=sample_inputs_masked_select),
      OpInfo('matrix_exp',
             dtypesIfCPU=floating_and_complex_types_and(torch.bfloat16),
             dtypesIfCUDA=floating_and_complex_types_and(torch.float16, torch.bfloat16),
             sample_inputs_func=sample_inputs_matrix_exp,
             supports_out=False),
      OpInfo('matmul',
             dtypes=floating_types(),
             dtypesIfCPU=all_types_and_complex(),
             dtypesIfCUDA=floating_and_complex_types_and(torch.float16, *[torch.bfloat16] if CUDA11OrLater else []),
             dtypesIfROCM=floating_types_and(torch.half, torch.bfloat16),
             assert_autodiffed=True,
             sample_inputs_func=sample_inputs_matmul,
             skips=(
                 # matmul does not correctly warn when resizing out= inputs
                 SkipInfo('TestCommon', 'test_out'),
                 # https://github.com/pytorch/pytorch/issues/55754
                 SkipInfo('TestGradients', 'test_fn_grad',
                          device_type='cpu', dtypes=(torch.complex128,)),
                 # https://github.com/pytorch/pytorch/issues/55755
                 SkipInfo('TestOpInfo', 'test_unsupported_dtypes',
                          device_type='cpu', dtypes=(torch.float16,)),
                 # Backward for BFloat16 isn't supported because of the error
                 # "RuntimeError: CUDA error: CUBLAS_STATUS_NOT_SUPPORTED when
                 # calling cublasGemmStridedBatchedExFix."
                 SkipInfo('TestOpInfo', 'test_supported_backward',
                          device_type='cuda', dtypes=(torch.bfloat16,)),)),
      OpInfo('max',
             op=torch.max,
             variant_test_name='binary',
             dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
             sample_inputs_func=sample_inputs_max_min_binary,
             assert_autodiffed=True,),
      OpInfo('max',
             op=torch.max,
             variant_test_name='reduction_with_dim',
             dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
             sample_inputs_func=sample_inputs_max_min_reduction_with_dim,
             skips=(
                 # max does not correctly warn when resizing out= inputs
                 SkipInfo('TestCommon', 'test_out'),)),
      OpInfo('max',
             op=torch.max,
             variant_test_name='reduction_no_dim',
             dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
             supports_out=False,
             sample_inputs_func=sample_inputs_max_min_reduction_no_dim,),
      OpInfo('min',
             op=torch.min,
             variant_test_name='binary',
             dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
             sample_inputs_func=sample_inputs_max_min_binary,
             assert_autodiffed=True,),
      OpInfo('min',
             op=torch.min,
             variant_test_name='reduction_with_dim',
             dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
             sample_inputs_func=sample_inputs_max_min_reduction_with_dim,
             skips=(
                 # min does not correctly warn when resizing out= inputs
                 SkipInfo('TestCommon', 'test_out'),
             )),
      OpInfo('min',
             op=torch.min,
             variant_test_name='reduction_no_dim',
             dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
             supports_out=False,
             sample_inputs_func=sample_inputs_max_min_reduction_no_dim,),
      OpInfo('sum',
             dtypes=all_types_and_complex_and(torch.float16, torch.bfloat16, torch.bool),
             supports_out=False,
             sample_inputs_func=sample_inputs_reduction_wrapper(supports_multiple_dims=True)),
      OpInfo('nansum',
             dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
             dtypesIfCPU=all_types_and(torch.float16, torch.bool),
             supports_out=False,
             sample_inputs_func=sample_inputs_reduction_wrapper(supports_multiple_dims=True)),
      # TODO(@heitorschueroff) Add test for dtype kwarg
      OpInfo('mean',
             dtypes=floating_and_complex_types_and(torch.float16, torch.bfloat16),
             assert_autodiffed=True,
             sample_inputs_func=sample_inputs_reduction_wrapper(supports_multiple_dims=True),
             # Need to skip out test because one of the overload for mean does not support it
             # TODO(@heitorschueroff) fix this when implementing ReductionInfo
             skips=(SkipInfo('TestCommon', 'test_out'),)),
      OpInfo('quantile',
             dtypes=floating_types(),
             sample_inputs_func=sample_inputs_reduction_quantile),
      OpInfo('nanquantile',
             dtypes=floating_types(),
             sample_inputs_func=sample_inputs_reduction_quantile),
      OpInfo('maximum',
             op=torch.maximum,
             dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
             sample_inputs_func=sample_inputs_max_min_binary,),
      OpInfo('minimum',
             op=torch.minimum,
             dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
             sample_inputs_func=sample_inputs_max_min_binary,),
      OpInfo('nn.functional.hardswish',
             supports_autograd=True,
             assert_autodiffed=True,
             sample_inputs_func=sample_inputs_hardswish,
             dtypesIfCUDA=floating_types_and(torch.half, torch.bfloat16),
             supports_gradgrad=False,
             supports_out=False,
             autodiff_fusible_nodes=["aten::hardswish"]),
      OpInfo('topk',
             dtypes=all_types(),
             dtypesIfCUDA=all_types_and(torch.bfloat16, torch.float16),
             sample_inputs_func=sample_inputs_topk,
             skips=(
                 # Topk is not raising a warning when the out is resized
                 SkipInfo('TestCommon', 'test_out'),
             )),
      OpInfo('mm',
             dtypes=floating_and_complex_types_and(torch.half),
             dtypesIfCPU=all_types_and_complex_and(torch.float16, torch.bfloat16),
             dtypesIfCUDA=floating_and_complex_types_and(torch.float16, *[torch.bfloat16] if CUDA11OrLater else []),
             assert_autodiffed=True,
             sample_inputs_func=sample_inputs_mm,
             skips=(
                 # mm does not correctly warn when resizing out= inputs
                 SkipInfo('TestCommon', 'test_out'),
             )),
      OpInfo('mode',
             op=torch.mode,
             dtypes=all_types_and(torch.float16, torch.bfloat16, torch.bool),
             sample_inputs_func=sample_inputs_mode,),
      MvlGammaInfo(variant_test_name='mvlgamma_p_1',
                   domain=(1e-4, float('inf')),
                   skips=skips_mvlgamma(),
                   sample_kwargs=lambda device, dtype, input: ({'p': 1}, {'d': 1})),
      MvlGammaInfo(variant_test_name='mvlgamma_p_3',
                   domain=(1.1, float('inf')),
                   skips=skips_mvlgamma(skip_redundant=True) + (
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard', dtypes=(torch.float16,)),
                   ),
                   sample_kwargs=lambda device, dtype, input: ({'p': 3}, {'d': 3})),
      MvlGammaInfo(variant_test_name='mvlgamma_p_5',
                   domain=(2.1, float('inf')),
                   skips=skips_mvlgamma(skip_redundant=True) + (
                       SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard', dtypes=(torch.float16,)),
                   ),
                   sample_kwargs=lambda device, dtype, input: ({'p': 5}, {'d': 5})),
      OpInfo('ne',
             aliases=('not_equal',),
             dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.float16),
             supports_autograd=False,
             sample_inputs_func=sample_inputs_comparison_ops),
      OpInfo('narrow',
             dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.float16),
             supports_out=False,
             sample_inputs_func=sample_inputs_narrow),
      UnaryUfuncInfo('neg',
                     aliases=('negative', ),
                     ref=np.negative,
                     dtypes=all_types_and_complex_and(torch.half, torch.bfloat16),
                     assert_autodiffed=True,),
      OpInfo('dist',
             op=torch.dist,
             dtypes=floating_and_complex_types_and(torch.half, torch.bfloat16),
             # "pow" not implemented for 'BFloat16' or 'half'
             backward_dtypes=floating_and_complex_types(),
             sample_inputs_func=sample_inputs_dist,
             skips=(
                 # dist does not correctly warn when resizing out= inputs
                 SkipInfo('TestCommon', 'test_out'),
             )),
      OpInfo('outer',
             op=torch.outer,
             aliases=('ger', ),
             dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             sample_inputs_func=sample_inputs_outer,),
      OpInfo('ormqr',
             op=torch.ormqr,
             dtypes=floating_and_complex_types(),
             supports_autograd=False,
             sample_inputs_func=sample_inputs_ormqr,
             decorators=[skipCUDAIfNoCusolver, skipCPUIfNoLapack]),
      OpInfo('permute',
             dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             supports_out=False,
             assert_autodiffed=True,
             sample_inputs_func=sample_inputs_permute),
      OpInfo('pow',
             dtypes=all_types_and_complex_and(torch.half, torch.bfloat16, torch.bool),
             # Due to AVX2 curently not being fully supported for Float16, log_vml_cpu can't be enabled
             # for Float16, causing this test to fail. pow's autograd for Float16 is thus currently
             # unsupported on CPU.
             backward_dtypes=all_types_and_complex_and(torch.bfloat16, torch.bool),
             sample_inputs_func=sample_inputs_pow,
             supports_inplace_autograd=False,
             assert_autodiffed=True),
      OpInfo('float_power',
             dtypes=all_types_and_complex_and(torch.half, torch.bfloat16, torch.bool),
             sample_inputs_func=sample_inputs_pow),
      OpInfo('prod',
             dtypes=all_types_and_complex_and(torch.bool),
             dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             # "cumprod_cuda" not implemented for 'BFloat16'
             backward_dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.float16),
             skips=(
                 # prod does not support the (Tensor, *, out) overload
                 SkipInfo('TestCommon', 'test_out',
                          dtypes=[torch.float32]),
             ),
             sample_inputs_func=sample_inputs_prod,
             gradcheck_nondet_tol=GRADCHECK_NONDET_TOL),
      OpInfo('qr',
             op=torch.qr,
             dtypes=floating_and_complex_types(),
             sample_inputs_func=sample_inputs_linalg_qr,
             # batched gradients do not work for empty inputs
             # https://github.com/pytorch/pytorch/issues/50743#issuecomment-767376085
             check_batched_gradgrad=False,
             decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack],
             skips=(
                 # cuda gradchecks are slow
                 # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
                 SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)),
      UnaryUfuncInfo('rad2deg',
                     ref=np.degrees,
                     decorators=(precisionOverride({torch.bfloat16: 7e-1,
                                                    torch.float16: 7e-1}),),
                     dtypes=all_types_and(torch.bool, torch.half, torch.bfloat16),
                     skips=(
                         # Reference: https://github.com/pytorch/pytorch/pull/51283#issuecomment-770614273
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                  dtypes=[torch.bfloat16]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  dtypes=[torch.bfloat16]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  dtypes=[torch.bfloat16]),
                     ),
                     safe_casts_outputs=True),
      UnaryUfuncInfo('real',
                     ref=np.real,
                     dtypes=complex_types(),
                     supports_out=False,
                     supports_autograd=False,
                     skips=(
                         # Skip since real and imag don't have out variants.
                         SkipInfo('TestUnaryUfuncs', 'test_out_arg_all_dtypes'),
                     )),
      OpInfo('roll',
             dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.half),
             supports_out=False,
             sample_inputs_func=sample_inputs_roll),
      OpInfo('rot90',
             dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.half),
             supports_out=False,
             sample_inputs_func=sample_inputs_rot90),
      UnaryUfuncInfo('round',
                     ref=np.round,
                     dtypes=floating_types_and(torch.bfloat16),
                     dtypesIfCUDA=floating_types_and(torch.half, torch.bfloat16),
                     assert_autodiffed=True,),
      UnaryUfuncInfo('sin',
                     ref=np.sin,
                     dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                     dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                     assert_autodiffed=True,
                     handles_large_floats=False,
                     handles_complex_extremals=False,
                     safe_casts_outputs=True,
                     decorators=(precisionOverride({torch.bfloat16: 1e-2}),)),
      UnaryUfuncInfo('sinc',
                     ref=np_sinc_with_fp16_as_fp32,
                     dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                     dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                     handles_large_floats=False,
                     handles_complex_extremals=False,
                     safe_casts_outputs=True,
                     decorators=(precisionOverride({torch.bfloat16: 1e-2,
                                                    torch.float16: 1e-2}),),
                     skips=(
                         # Reference: https://github.com/pytorch/pytorch/issues/49133
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                  dtypes=[torch.cfloat]),
                     )),
      UnaryUfuncInfo('sinh',
                     ref=np_unary_ufunc_integer_promotion_wrapper(np.sinh),
                     dtypes=all_types_and_complex_and(torch.bool),
                     dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                     safe_casts_outputs=True,
                     assert_autodiffed=True,
                     decorators=(precisionOverride({torch.float16: 1e-2}),),
                     skips=(
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                  active_if=(IS_MACOS or IS_WINDOWS)),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                  active_if=(IS_MACOS or IS_WINDOWS)),
                         # Reference: https://github.com/pytorch/pytorch/issues/48641
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  device_type='cpu', dtypes=[torch.int8]),
                     )),
      UnaryUfuncInfo('sign',
                     ref=reference_sign,
                     dtypes=all_types_and(torch.bool, torch.bfloat16, torch.half),
                     dtypesIfCUDA=all_types_and(torch.bool, torch.bfloat16, torch.half),
                     skips=(
                         # Reference: https://github.com/pytorch/pytorch/issues/41245
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  dtypes=[torch.bfloat16, torch.float16, torch.float32, torch.float64]),
                     )),
      UnaryUfuncInfo('sgn',
                     ref=reference_sgn,
                     dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.half),
                     skips=(
                         # Reference: https://github.com/pytorch/pytorch/issues/41245
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  dtypes=[torch.bfloat16, torch.float16, torch.float32, torch.float64]),
                         # Reference: https://github.com/pytorch/pytorch/issues/53958
                         # Test fails in comparison on Nan as the `equal_nan` is True for
                         # comparing the CPU tensors.
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  device_type='cpu', dtypes=[torch.complex64, torch.complex128]),
                         # Reference: https://github.com/pytorch/pytorch/issues/48486
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  device_type='cpu', dtypes=[torch.complex64])
                     )),
      OpInfo('__radd__',
             op=torch.Tensor.__radd__,
             dtypes=all_types_and_complex_and(torch.bfloat16, torch.half, torch.bool),
             sample_inputs_func=sample_inputs_rbinops,
             supports_out=False,
             skips=(SkipInfo('TestCommon', 'test_variant_consistency_jit',),),
             assert_autodiffed=True,
             autodiff_nonfusible_nodes=['aten::add'],),
      OpInfo('__rdiv__',
             op=torch.Tensor.__rdiv__,
             dtypes=all_types_and_complex_and(torch.bfloat16, torch.half, torch.bool),
             sample_inputs_func=sample_inputs_rbinops,
             supports_out=False,
             skips=(SkipInfo('TestCommon', 'test_variant_consistency_jit',),),
             assert_autodiffed=True,
             autodiff_nonfusible_nodes=['aten::mul', 'aten::reciprocal'],),
      OpInfo('__rmul__',
             op=torch.Tensor.__rmul__,
             dtypes=all_types_and_complex_and(torch.bfloat16, torch.half, torch.bool),
             sample_inputs_func=sample_inputs_rbinops,
             supports_out=False,
             skips=(SkipInfo('TestCommon', 'test_variant_consistency_jit',),),
             assert_autodiffed=True,
             autodiff_nonfusible_nodes=['aten::mul'],),
      OpInfo('__rpow__',
             op=torch.Tensor.__rpow__,
             dtypes=all_types_and_complex_and(torch.bfloat16, torch.half, torch.bool),
             sample_inputs_func=sample_inputs_rbinops,
             supports_out=False,
             skips=(
                 # Reference: https://github.com/pytorch/pytorch/issues/54774
                 # "log2" "_vml_cpu" not implemented for Half
                 SkipInfo('TestOpInfo', 'test_supported_backward', device_type='cpu',
                          dtypes=(torch.float16,)),
  
                 SkipInfo('TestCommon', 'test_variant_consistency_jit',),),
             assert_autodiffed=True,
             autodiff_nonfusible_nodes=['aten::pow'],),
      OpInfo('__rsub__',
             op=torch.Tensor.__rsub__,
             dtypes=all_types_and_complex_and(torch.bfloat16, torch.half),
             sample_inputs_func=sample_inputs_rbinops,
             supports_out=False,
             skips=(SkipInfo('TestCommon', 'test_variant_consistency_jit',),),
             assert_autodiffed=True,
             autodiff_nonfusible_nodes=['aten::rsub'],),
      OpInfo('rsub',
             dtypes=all_types_and_complex_and(torch.bfloat16, torch.half),
             variant_test_name='rsub_tensor',
             supports_out=False,
             supports_inplace_autograd=False,
             skips=(
                 # Reference: https://github.com/pytorch/pytorch/issues/53797
                 # JIT doesn't understand complex literals
                 SkipInfo('TestCommon', 'test_variant_consistency_jit',
                          dtypes=[torch.cfloat, torch.cdouble]),
             ),
             sample_inputs_func=partial(sample_inputs_rsub, variant='tensor'),),
      OpInfo('rsub',
             dtypes=all_types_and_complex_and(torch.bfloat16, torch.half),
             variant_test_name='rsub_scalar',
             supports_out=False,
             supports_inplace_autograd=False,
             sample_inputs_func=partial(sample_inputs_rsub, variant='scalar'),
             skips=(
                 # Reference: https://github.com/pytorch/pytorch/issues/53797
                 # JIT doesn't understand complex literals
                 SkipInfo('TestCommon', 'test_variant_consistency_jit',
                          dtypes=all_types_and_complex_and(torch.bfloat16, torch.half)),),
             assert_autodiffed=True,),
      OpInfo('select',
             dtypes=all_types_and_complex_and(torch.bfloat16, torch.half, torch.bool),
             sample_inputs_func=sample_inputs_select,
             supports_out=False),
      UnaryUfuncInfo('signbit',
                     ref=np.signbit,
                     dtypes=all_types_and(torch.bool, torch.bfloat16, torch.half),
                     supports_autograd=False,),
      OpInfo('solve',
             op=torch.solve,
             dtypes=floating_and_complex_types(),
             sample_inputs_func=sample_inputs_legacy_solve,
             check_batched_gradgrad=False,
             decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack],
             # cuda gradchecks are slow
             # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
             skips=(SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)),
      OpInfo('std',
             dtypes=floating_and_complex_types_and(torch.half),
             dtypesIfCUDA=floating_and_complex_types_and(torch.half, torch.bfloat16),
             # std doesn't support complex autograd, https://github.com/pytorch/pytorch/issues/57358
             backward_dtypesIfCPU=floating_types_and(torch.half),
             backward_dtypesIfCUDA=floating_types_and(torch.half, torch.bfloat16),
             sample_inputs_func=sample_inputs_std_var,
             # TODO: std does support out in some signatures
             supports_out=False,
             assert_autodiffed=True,
             ),
      UnaryUfuncInfo('tan',
                     ref=np.tan,
                     dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                     dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                     assert_autodiffed=True,
                     safe_casts_outputs=True,
                     skips=(
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  device_type='cpu', dtypes=[torch.bfloat16]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  device_type='cpu', dtypes=[torch.bfloat16]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                  device_type='cpu', dtypes=[torch.bfloat16]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                  active_if=(IS_MACOS or IS_WINDOWS)),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                  active_if=(IS_MACOS or IS_WINDOWS)),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                  active_if=(IS_MACOS or IS_WINDOWS)),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  device_type='cuda', dtypes=[torch.float64],
                                  active_if=TEST_WITH_ROCM),
                     )),
      UnaryUfuncInfo('tanh',
                     ref=np.tanh,
                     decorators=(precisionOverride({torch.bfloat16: 1e-2}),),
                     dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                     dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                     # "tanh_backward_cpu" not implemented for 'BFloat16'
                     backward_dtypesIfCPU=all_types_and_complex_and(torch.bool),
                     assert_autodiffed=True,
                     safe_casts_outputs=True,
                     skips=(
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                  active_if=(IS_MACOS or IS_WINDOWS)),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                  active_if=(IS_MACOS or IS_WINDOWS)),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                  active_if=(IS_MACOS or IS_WINDOWS)),
                     )),
      OpInfo('tensor_split',
             dtypes=all_types_and_complex_and(torch.bool),
             dtypesIfCPU=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.float16),
             dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.float16),
             supports_out=False,
             skips=(SkipInfo('TestOpInfo', 'test_duplicate_method_tests'),),
             sample_inputs_func=sample_inputs_tensor_split,),
      OpInfo('hsplit',
             dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.float16),
             supports_out=False,
             sample_inputs_func=sample_inputs_hsplit,),
      OpInfo('vsplit',
             dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.float16),
             supports_out=False,
             sample_inputs_func=sample_inputs_vsplit,),
      OpInfo('dsplit',
             dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.float16),
             supports_out=False,
             sample_inputs_func=sample_inputs_dsplit,),
      OpInfo('triangular_solve',
             op=torch.triangular_solve,
             dtypes=floating_and_complex_types(),
             supports_out=False,
             sample_inputs_func=sample_inputs_legacy_solve,
             check_batched_gradgrad=False,
             decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack],
             # CUDA gradchecks are slow and triangular solve backward is a composite operation
             # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
             skips=(SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)),
      UnaryUfuncInfo('trunc',
                     aliases=('fix', ),
                     ref=np.trunc,
                     dtypes=floating_types_and(torch.bfloat16),
                     dtypesIfCUDA=floating_types_and(torch.float16, torch.bfloat16),
                     assert_autodiffed=True),
      UnaryUfuncInfo('exp2',
                     aliases=('special.exp2', ),
                     ref=np_unary_ufunc_integer_promotion_wrapper(np.exp2),
                     dtypes=all_types_and(torch.bool, torch.half),
                     dtypesIfCUDA=all_types_and(torch.bool, torch.half, torch.bfloat16),
                     safe_casts_outputs=True),
      UnaryUfuncInfo('expm1',
                     aliases=('special.expm1', ),
                     ref=np_unary_ufunc_integer_promotion_wrapper(np.expm1),
                     dtypes=all_types_and(torch.bool, torch.bfloat16),
                     dtypesIfCUDA=all_types_and(torch.bool, torch.half, torch.bfloat16),
                     safe_casts_outputs=True,
                     assert_autodiffed=True,
                     skips=(
                         # Reference: https://github.com/pytorch/pytorch/pull/48926#issuecomment-739734774
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  device_type='cpu', dtypes=[torch.bfloat16]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  device_type='cpu', dtypes=[torch.bfloat16]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                  device_type='cpu', dtypes=[torch.bfloat16]),
                     )),
      UnaryUfuncInfo('nan_to_num',
                     ref=np.nan_to_num,
                     dtypes=all_types_and(torch.half, torch.bool),
                     dtypesIfCUDA=all_types_and(torch.half, torch.bool, torch.bfloat16),
                     # Passing numpy_kwargs via sample_kwargs, as numpy does comparison
                     # with BFloat16 in float, since it currently doesn't support BFloat16.
                     # Ref: https://github.com/pytorch/pytorch/issues/57982#issuecomment-839150556
                     sample_kwargs=lambda device, dtype, input: ({},
                                                                 {'posinf': torch.finfo(torch.bfloat16).max,
                                                                  'neginf': torch.finfo(torch.bfloat16).min})
                     if dtype is torch.bfloat16 else ({}, {})),
      UnaryUfuncInfo('reciprocal',
                     ref=np_unary_ufunc_integer_promotion_wrapper(np.reciprocal),
                     dtypes=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                     assert_autodiffed=True,
                     safe_casts_outputs=True,
                     skips=(
                         # Reference: https://github.com/pytorch/pytorch/issues/45690
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  dtypes=[torch.cfloat, torch.cdouble]),
                         # Reference: https://github.com/pytorch/pytorch/pull/49102#issuecomment-744604601
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  dtypes=[torch.bfloat16]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  dtypes=[torch.bfloat16]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                  dtypes=[torch.bfloat16]),
                     )),
      UnaryUfuncInfo('rsqrt',
                     ref=lambda x: np.reciprocal(np.sqrt(x)),
                     domain=(0, float('inf')),
                     dtypes=all_types_and_complex_and(torch.bool),
                     dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                     decorators=(precisionOverride({torch.half: 5e-2}),),
                     safe_casts_outputs=True,
                     assert_autodiffed=True,
                     handles_complex_extremals=False),
      UnaryUfuncInfo('sqrt',
                     ref=np.sqrt,
                     supports_sparse=True,
                     domain=(0, float('inf')),
                     dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                     dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                     assert_autodiffed=True,
                     decorators=(precisionOverride({torch.bfloat16: 7e-2}),),
                     skips=(
                         # Reference: https://github.com/pytorch/pytorch/issues/47358
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble],
                                  active_if=IS_MACOS),
                         # Reference: https://github.com/pytorch/pytorch/pull/47293#issuecomment-721774436
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  dtypes=[torch.bfloat16])),
                     safe_casts_outputs=True,
                     handles_complex_extremals=False),
      UnaryUfuncInfo('square',
                     ref=np.square,
                     dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
                     decorators=(precisionOverride({torch.complex64: 3e-4, torch.bfloat16: 3e-1}),),
                     skips=(
                         # Reference: https://github.com/pytorch/pytorch/issues/52549
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  dtypes=[torch.cfloat, torch.cdouble]),
                         # >>> t = torch.tensor(complex(-0.01, float("inf")))
                         # >>> np.square(t.numpy())
                         # (-inf-infj)
                         # >>> t.square()
                         # tensor(-inf-infj)
                         # >>> t.cuda().square()
                         # tensor(inf+nanj, device='cuda:0')
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  device_type='cuda', dtypes=[torch.cfloat, torch.cdouble]),
                         # Reference: https://github.com/pytorch/pytorch/pull/52551#issuecomment-782596181
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  dtypes=[torch.bfloat16]),
                     ),),
      OpInfo('lerp',
             dtypes=floating_and_complex_types(),
             dtypesIfCUDA=floating_and_complex_types_and(torch.half, torch.bfloat16),
             dtypesIfROCM=floating_and_complex_types_and(torch.half, torch.bfloat16),
             sample_inputs_func=sample_inputs_lerp,
             assert_autodiffed=True),
      OpInfo('linalg.inv',
             aten_name='linalg_inv',
             op=torch.linalg.inv,
             dtypes=floating_and_complex_types(),
             sample_inputs_func=sample_inputs_linalg_invertible,
             check_batched_gradgrad=False,
             gradcheck_nondet_tol=GRADCHECK_NONDET_TOL,
             decorators=[skipCUDAIfNoMagmaAndNoCusolver, skipCUDAIfRocm, skipCPUIfNoLapack],
             skips=(
                 # linalg_inv does not correctly warn when resizing out= inputs
                 SkipInfo('TestCommon', 'test_out'),
             )),
      UnaryUfuncInfo('angle',
                     ref=np.angle,
                     dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.float16),
                     dtypesIfCUDA=all_types_and_complex_and(torch.bool),
                     decorators=(precisionOverride({torch.float16: 1e-2,
                                                    torch.bfloat16: 1e-2}),),
                     safe_casts_outputs=True,
                     supports_complex_to_float=True),
      OpInfo('linalg.solve',
             aten_name='linalg_solve',
             op=torch.linalg.solve,
             dtypes=floating_and_complex_types(),
             sample_inputs_func=sample_inputs_linalg_solve,
             check_batched_gradgrad=False,
             decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack],
             skips=(SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)),
      OpInfo('linalg.matrix_rank',
             aten_name='linalg_matrix_rank',
             dtypes=floating_and_complex_types(),
             supports_autograd=False,
             sample_inputs_func=sample_inputs_linalg_invertible,
             decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack]),
      OpInfo('linalg.matrix_rank',
             aten_name='linalg_matrix_rank',
             variant_test_name='hermitian',
             dtypes=floating_and_complex_types(),
             supports_autograd=False,
             sample_inputs_func=sample_inputs_linalg_pinv_hermitian,
             decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack]),
      OpInfo('linalg.pinv',
             aten_name='linalg_pinv',
             op=torch.linalg.pinv,
             dtypes=floating_and_complex_types(),
             check_batched_grad=False,
             check_batched_gradgrad=False,
             sample_inputs_func=sample_inputs_linalg_invertible,
             decorators=[skipCUDAIfNoMagmaAndNoCusolver, skipCUDAIfRocm, skipCPUIfNoLapack],
             skips=(
                 # cuda gradchecks are slow
                 # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
                 SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)),
      OpInfo('linalg.pinv',
             aten_name='linalg_pinv',
             variant_test_name='hermitian',
             dtypes=floating_and_complex_types(),
             check_batched_grad=False,
             check_batched_gradgrad=False,
             sample_inputs_func=sample_inputs_linalg_pinv_hermitian,
             gradcheck_wrapper=gradcheck_wrapper_hermitian_input,
             decorators=[skipCUDAIfNoMagma, skipCUDAIfRocm, skipCPUIfNoLapack],
             skips=(
                 # cuda gradchecks are slow
                 # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
                 SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)),
      OpInfo('eig',
             op=torch.eig,
             dtypes=floating_and_complex_types(),
             sample_inputs_func=sample_inputs_eig,
             decorators=[
                 skipCUDAIfNoMagma,
                 skipCPUIfNoLapack,
                 skipCUDAIfRocm
             ],),
      OpInfo('einsum',
             # we need this lambda because SampleInput expects tensor input as the first argument
             # TODO(@heitorschueroff) update SampleInput to handle such cases
             op=lambda tensors, equation: torch.einsum(equation, tensors),
             dtypes=all_types_and_complex_and(torch.half, torch.bfloat16),
             dtypesIfCUDA=floating_and_complex_types_and(torch.half),
             supports_out=False,
             sample_inputs_func=sample_inputs_einsum,
             skips=(
                 # test does not work with passing lambda for op
                 # there's a test `test_einsum` in `test_jit.py` to handle this case
                 SkipInfo('TestCommon', 'test_variant_consistency_jit'),
                 # The following dtypes are only supported for some inputs, ideally we should have
                 # checked this in the einsum code but to keep BC we'll just skip the tests for now.
                 SkipInfo('TestOpInfo', 'test_unsupported_dtypes',
                          dtypes=[torch.bool]),
                 SkipInfo('TestOpInfo', 'test_unsupported_dtypes',
                          device_type='cuda', dtypes=integral_types_and(torch.bfloat16)))),
      OpInfo('svd',
             op=torch.svd,
             dtypes=floating_and_complex_types(),
             sample_inputs_func=sample_inputs_svd,
             decorators=[
                 skipCUDAIfNoMagmaAndNoCusolver,
                 skipCUDAIfRocm,
                 skipCPUIfNoLapack,
                 # gradgrad checks are slow
                 DecorateInfo(slowTest, 'TestGradients', 'test_fn_gradgrad'),
             ],
             skips=(
                 # cuda gradchecks are very slow
                 # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
                 SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)),
      OpInfo('linalg.svd',
             op=torch.linalg.svd,
             aten_name='linalg_svd',
             dtypes=floating_and_complex_types(),
             sample_inputs_func=sample_inputs_linalg_svd,
             decorators=[
                 skipCUDAIfNoMagmaAndNoCusolver,
                 skipCUDAIfRocm,
                 skipCPUIfNoLapack,
                 # gradgrad checks are slow
                 DecorateInfo(slowTest, 'TestGradients', 'test_fn_gradgrad'),
             ],
             skips=(
                 # cuda gradchecks are very slow
                 # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
                 SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)),
      OpInfo('linalg.svdvals',
             op=torch.linalg.svdvals,
             aten_name='linalg_svdvals',
             dtypes=floating_and_complex_types(),
             sample_inputs_func=sample_inputs_linalg_svdvals,
             check_batched_gradgrad=False,
             decorators=[
                 skipCUDAIfNoMagmaAndNoCusolver,
                 skipCPUIfNoLapack]),
      OpInfo('polar',
             dtypes=floating_types(),
             sample_inputs_func=sample_inputs_polar),
      # TODO(@kshitij12345): Refactor similar to `mvlgamma` entries.
      # To test reference numerics against multiple values of argument `n`,
      # we make multiple OpInfo entries with each entry corresponding to different value of n (currently 0 to 4).
      # We run the op tests from test_ops.py only for `n=0` to avoid redundancy in testing.
      UnaryUfuncInfo('polygamma',
                     op=lambda x, n, **kwargs: torch.polygamma(n, x, **kwargs),
                     variant_test_name='polygamma_n_0',
                     ref=reference_polygamma if TEST_SCIPY else _NOTHING,
                     dtypes=all_types_and(torch.bool),
                     dtypesIfCUDA=all_types_and(torch.bool, torch.half),
                     safe_casts_outputs=True,
                     sample_inputs_func=sample_inputs_polygamma,
                     skips=(
                         # Probably related to the way the function is
                         # scripted for JIT tests (or maybe not).
                         # RuntimeError:
                         # Arguments for call are not valid.
                         # The following variants are available:
                         #   aten::polygamma(int n, Tensor self) -> (Tensor):
                         #   Expected a value of type 'Tensor' for argument 'self' but instead found type 'int'.
                         #   aten::polygamma.out(int n, Tensor self, *, Tensor(a!) out) -> (Tensor(a!)):
                         #   Expected a value of type 'Tensor' for argument 'self' but instead found type 'int'.
                         # The original call is:
                         #   File "<string>", line 3
                         # def the_method(i0):
                         #     return torch.polygamma(i0, 1)
                         #            ~~~~~~~~~~~~~~~ <--- HERE
                         SkipInfo('TestCommon', 'test_variant_consistency_jit'),),
                     sample_kwargs=lambda device, dtype, input: ({'n': 0}, {'n': 0})),
      UnaryUfuncInfo('polygamma',
                     op=lambda x, n, **kwargs: torch.polygamma(n, x, **kwargs),
                     variant_test_name='polygamma_n_1',
                     ref=reference_polygamma if TEST_SCIPY else _NOTHING,
                     dtypes=all_types_and(torch.bool),
                     dtypesIfCUDA=all_types_and(torch.bool, torch.half),
                     safe_casts_outputs=True,
                     sample_inputs_func=sample_inputs_polygamma,
                     skips=(
                         # Redundant tests
                         SkipInfo('TestGradients'),
                         SkipInfo('TestOpInfo'),
                         SkipInfo('TestCommon'),
                         # Mismatch: https://github.com/pytorch/pytorch/issues/55357
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal'),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard'),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal'),
                     ),
                     sample_kwargs=lambda device, dtype, input: ({'n': 1}, {'n': 1})),
      UnaryUfuncInfo('polygamma',
                     op=lambda x, n, **kwargs: torch.polygamma(n, x, **kwargs),
                     variant_test_name='polygamma_n_2',
                     ref=reference_polygamma if TEST_SCIPY else _NOTHING,
                     dtypes=all_types_and(torch.bool),
                     dtypesIfCUDA=all_types_and(torch.bool, torch.half),
                     safe_casts_outputs=True,
                     sample_inputs_func=sample_inputs_polygamma,
                     skips=(
                         # Redundant tests
                         SkipInfo('TestGradients'),
                         SkipInfo('TestOpInfo'),
                         SkipInfo('TestCommon'),
                         # Mismatch: https://github.com/pytorch/pytorch/issues/55357
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal'),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  active_if=TEST_WITH_ROCM),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                  active_if=TEST_WITH_ROCM),),
                     sample_kwargs=lambda device, dtype, input: ({'n': 2}, {'n': 2})),
      UnaryUfuncInfo('polygamma',
                     op=lambda x, n, **kwargs: torch.polygamma(n, x, **kwargs),
                     variant_test_name='polygamma_n_3',
                     ref=reference_polygamma if TEST_SCIPY else _NOTHING,
                     dtypes=all_types_and(torch.bool),
                     dtypesIfCUDA=all_types_and(torch.bool, torch.half),
                     safe_casts_outputs=True,
                     sample_inputs_func=sample_inputs_polygamma,
                     skips=(
                         # Redundant tests
                         SkipInfo('TestGradients'),
                         SkipInfo('TestOpInfo'),
                         SkipInfo('TestCommon'),
                         # Mismatch: https://github.com/pytorch/pytorch/issues/55357
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal'),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  active_if=TEST_WITH_ROCM),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                  active_if=TEST_WITH_ROCM),),
                     sample_kwargs=lambda device, dtype, input: ({'n': 3}, {'n': 3})),
      UnaryUfuncInfo('polygamma',
                     op=lambda x, n, **kwargs: torch.polygamma(n, x, **kwargs),
                     variant_test_name='polygamma_n_4',
                     ref=reference_polygamma if TEST_SCIPY else _NOTHING,
                     decorators=(precisionOverride({torch.float16: 5e-4, torch.float32: 5e-4}),),
                     dtypes=all_types_and(torch.bool),
                     dtypesIfCUDA=all_types_and(torch.bool, torch.half),
                     safe_casts_outputs=True,
                     sample_inputs_func=sample_inputs_polygamma,
                     skips=(
                         # Redundant tests
                         SkipInfo('TestGradients'),
                         SkipInfo('TestOpInfo'),
                         SkipInfo('TestCommon'),
                         # Mismatch: https://github.com/pytorch/pytorch/issues/55357
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal'),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  active_if=TEST_WITH_ROCM),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                  active_if=TEST_WITH_ROCM),),
                     sample_kwargs=lambda device, dtype, input: ({'n': 4}, {'n': 4})),
      OpInfo('ravel',
             dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             supports_out=False,
             sample_inputs_func=sample_inputs_ravel,
             ),
      OpInfo('reshape',
             dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             sample_inputs_func=sample_inputs_view_reshape,
             supports_out=False,
             ),
      OpInfo('reshape_as',
             op=lambda x, other: x.reshape_as(other),
             dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             sample_inputs_func=sample_inputs_view_as_reshape_as,
             skips=(
                 # Because reshape_as does not have a function variant.
                 SkipInfo('TestCommon', 'test_variant_consistency_jit'),),
             supports_out=False,
             ),
      OpInfo('view',
             op=lambda x, shape: x.view(shape),
             dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             supports_out=False,
             skips=(
                 # Because view does not have a function variant.
                 SkipInfo('TestCommon', 'test_variant_consistency_jit'),),
             sample_inputs_func=sample_inputs_view_reshape,
             ),
      OpInfo('view_as',
             op=lambda x, other: x.view_as(other),
             dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             supports_out=False,
             skips=(
                 # Because view_as does not have a function variant.
                 SkipInfo('TestCommon', 'test_variant_consistency_jit'),),
             sample_inputs_func=sample_inputs_view_as_reshape_as,
             ),
      OpInfo('pinverse',
             op=torch.pinverse,
             dtypes=floating_and_complex_types(),
             check_batched_grad=False,
             check_batched_gradgrad=False,
             gradcheck_nondet_tol=GRADCHECK_NONDET_TOL,
             supports_out=False,
             sample_inputs_func=sample_inputs_linalg_invertible,
             decorators=[skipCUDAIfNoMagmaAndNoCusolver, skipCUDAIfRocm, skipCPUIfNoLapack],
             skips=(
                 # cuda gradchecks are slow
                 # see discussion https://github.com/pytorch/pytorch/pull/47761#issuecomment-747316775
                 SkipInfo('TestGradients', 'test_fn_gradgrad', device_type='cuda'),)),
      OpInfo('gather',
             dtypes=all_types_and_complex_and(torch.bool, torch.float16),
             dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             sample_inputs_func=sample_inputs_gather,
             gradcheck_nondet_tol=GRADCHECK_NONDET_TOL,
             ),
      OpInfo('index_fill',
             dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             supports_inplace_autograd=False,
             skips=(SkipInfo('TestOpInfo', 'test_duplicate_method_tests'),),
             supports_out=False,
             sample_inputs_func=sample_inputs_index_fill),
      OpInfo('index_copy',
             dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             supports_inplace_autograd=False,
             supports_out=False,
             sample_inputs_func=sample_inputs_index_copy,
             gradcheck_nondet_tol=GRADCHECK_NONDET_TOL),
      OpInfo('index_select',
             dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             sample_inputs_func=sample_inputs_index_select,
             gradcheck_nondet_tol=GRADCHECK_NONDET_TOL),
      OpInfo('index_add',
             dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             supports_out=False,
             sample_inputs_func=sample_inputs_index_add,
             gradcheck_nondet_tol=GRADCHECK_NONDET_TOL),
      OpInfo('__getitem__',
             dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             supports_out=False,
             supports_inplace_autograd=False,
             op=torch.Tensor.__getitem__,
             sample_inputs_func=sample_inputs_getitem,
             skips=(SkipInfo('TestCommon', 'test_variant_consistency_jit'),)),
      OpInfo('index_put',
             dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             supports_out=False,
             supports_inplace_autograd=True,
             sample_inputs_func=sample_inputs_index_put,
             skips=(
                 SkipInfo('TestCommon', 'test_variant_consistency_jit'),
             )),
      OpInfo('sort',
             dtypes=all_types_and(torch.bool, torch.float16),
             dtypesIfCUDA=all_types_and(torch.float16),
             dtypesIfROCM=all_types_and(torch.float16),
             sample_inputs_func=sample_inputs_sort,
             skips=(
                 # sort does not correctly warn when resizing out= inputs
                 SkipInfo('TestCommon', 'test_out'),
             )),
      OpInfo('put',
             dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             supports_out=False,
             check_batched_gradgrad=False,  # vmap complains of the sizes
             sample_inputs_func=sample_inputs_put),
      OpInfo('take',
             dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             check_batched_grad=False,  # vmap complains of the sizes
             sample_inputs_func=sample_inputs_take),
      OpInfo('scatter',
             dtypes=all_types_and_complex_and(torch.bool, torch.half),
             dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
             sample_inputs_func=sample_inputs_scatter,
             supports_out=False),
      OpInfo('scatter_add',
             dtypes=all_types_and_complex_and(torch.bool, torch.half),
             dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
             sample_inputs_func=sample_inputs_scatter_add,
             supports_out=False),
      OpInfo('stack',
             dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             sample_inputs_func=sample_inputs_stack,
             assert_autodiffed=True,
             skips=(
                 # stack does not correctly warn when resizing out= inputs
                 SkipInfo('TestCommon', 'test_out'),),),
      OpInfo('hstack',
             dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             sample_inputs_func=sample_inputs_hstack_dstack_vstack,
             skips=(
                 # hstack does not correctly warn when resizing out= inputs
                 SkipInfo('TestCommon', 'test_out'),),),
      OpInfo('hypot',
             dtypes=floating_types(),
             dtypesIfCPU=floating_types_and(torch.bfloat16),
             dtypesIfCUDA=floating_types_and(torch.half, torch.bfloat16),
             sample_inputs_func=sample_inputs_hypot,
             ),
      OpInfo('vstack',
             dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             sample_inputs_func=sample_inputs_hstack_dstack_vstack,
             skips=(
                 # vstack does not correctly warn when resizing out= inputs
                 SkipInfo('TestCommon', 'test_out'),),),
      OpInfo('dstack',
             dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             sample_inputs_func=sample_inputs_hstack_dstack_vstack,
             skips=(
                 # dstack does not correctly warn when resizing out= inputs
                 SkipInfo('TestCommon', 'test_out'),),),
      OpInfo('unfold',
             op=lambda x, *args: x.unfold(*args),
             dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             supports_out=False,
             check_batched_gradgrad=False,
             skips=(
                 # torch.unfold does not exist so we get a RuntimeError.
                 SkipInfo('TestCommon', 'test_variant_consistency_jit',
                          dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16)),
                 # Skip operator schema test because this is a functional and not an operator
                 SkipInfo('TestOperatorSignatures', 'test_get_torch_func_signature_exhaustive'),
             ),
             sample_inputs_func=sample_inputs_unfold),
      OpInfo('msort',
             dtypes=all_types_and(torch.float16),
             check_batched_gradgrad=False,
             skips=(
                 #  msort does not correctly warn when resizing out= inputs.
                 SkipInfo('TestCommon', 'test_out',
                          dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16)),
                 #  msort does not raise expected Runtime Error.
                 SkipInfo('TestOpInfo', 'test_unsupported_dtypes', dtypes=[torch.bool]),
             ),
             sample_inputs_func=sample_inputs_msort),
      OpInfo('movedim',
             dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             supports_out=False,
             sample_inputs_func=sample_movedim_moveaxis),
      OpInfo('moveaxis',
             dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             supports_out=False,
             sample_inputs_func=sample_movedim_moveaxis),
      ShapeFuncInfo('repeat',
                    op=lambda x, dims: x.repeat(dims),
                    ref=np.tile,
                    dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
                    supports_out=False,
                    skips=(
                        # torch.repeat does not exist so we get a RuntimeError.
                        SkipInfo('TestCommon', 'test_variant_consistency_jit',
                                 dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16)),
                    ),
                    sample_inputs_func=sample_repeat_tile),
      OpInfo('squeeze',
             dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             supports_out=False,
             assert_autodiffed=True,
             sample_inputs_func=sample_inputs_squeeze),
      OpInfo('take_along_dim',
             dtypes=all_types_and_complex_and(torch.bool, torch.float16),
             dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             supports_inplace_autograd=False,
             sample_inputs_func=sample_inputs_take_along_dim,
             gradcheck_nondet_tol=GRADCHECK_NONDET_TOL),
      ShapeFuncInfo('tile',
                    ref=np.tile,
                    dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
                    supports_out=False,
                    sample_inputs_func=sample_repeat_tile),
      OpInfo('unsqueeze',
             dtypes=all_types_and_complex_and(torch.bool, torch.float16, torch.bfloat16),
             supports_out=False,
             assert_autodiffed=True,
             sample_inputs_func=sample_unsqueeze),
      OpInfo('var',
             dtypes=floating_and_complex_types_and(torch.half),
             dtypesIfCUDA=floating_and_complex_types_and(torch.half, torch.bfloat16),
             # var doesn't support complex autograd, https://github.com/pytorch/pytorch/issues/57358
             backward_dtypesIfCPU=floating_types_and(torch.half),
             backward_dtypesIfCUDA=floating_types_and(torch.half, torch.bfloat16),
             sample_inputs_func=sample_inputs_std_var,
             # TODO: revisit, some var signatures do support out (see std, too)
             supports_out=False,
             assert_autodiffed=True,
             ),
      OpInfo('xlogy',
             dtypes=all_types_and(torch.bool),
             dtypesIfCPU=all_types_and(torch.bool, torch.half, torch.bfloat16),
             dtypesIfCUDA=all_types_and(torch.bool, torch.half, torch.bfloat16),
             supports_inplace_autograd=True,
             safe_casts_outputs=True,
             sample_inputs_func=sample_inputs_xlogy),
      OpInfo('special.xlog1py',
             aten_name='special_xlog1py',
             dtypes=all_types_and(torch.bool, torch.half, torch.bfloat16),
             safe_casts_outputs=True,
             skips=(
                 SkipInfo('TestOpInfo', 'test_supported_backward',
                          device_type='cpu', dtypes=[torch.float16]),
             ),
             sample_inputs_func=sample_inputs_xlog1py),
      OpInfo('logsumexp',
             dtypes=floating_types_and(torch.bfloat16),
             dtypesIfCUDA=floating_types_and(torch.bfloat16, torch.half),
             assert_autodiffed=True,
             sample_inputs_func=sample_inputs_logsumexp),
      OpInfo('trace',
             dtypes=all_types_and_complex(),
             dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
             supports_inplace_autograd=False,
             supports_out=False,
             sample_inputs_func=sample_inputs_trace),
      OpInfo('transpose',
             aliases=('swapdims', 'swapaxes'),
             dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.half),
             dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.bfloat16, torch.half),
             supports_out=False,
             sample_inputs_func=sample_inputs_transpose_swapdims),
      OpInfo('kron',
             dtypes=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
             dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
             supports_inplace_autograd=False,
             sample_inputs_func=sample_inputs_kron),
      OpInfo('inner',
             dtypes=floating_and_complex_types_and(torch.half),
             dtypesIfCPU=all_types_and_complex_and(torch.half, torch.bfloat16),
             dtypesIfCUDA=floating_and_complex_types_and(torch.float16, *[torch.bfloat16] if CUDA11OrLater else []),
             dtypesIfROCM=floating_and_complex_types_and(torch.half, torch.bfloat16),
             sample_inputs_func=sample_inputs_inner),
      OpInfo('tensordot',
             dtypes=floating_and_complex_types_and(torch.half),
             dtypesIfCPU=all_types_and_complex_and(torch.half, torch.bfloat16),
             dtypesIfCUDA=floating_and_complex_types_and(torch.float16, *[torch.bfloat16] if CUDA11OrLater else []),
             dtypesIfROCM=floating_and_complex_types_and(torch.half, torch.bfloat16),
             safe_casts_outputs=True,
             sample_inputs_func=sample_inputs_tensordot,
             skips=(
                 # Currently failing due to an INTERNAL_ASSERT_FAILED error.
                 # Reference: https://github.com/pytorch/pytorch/issues/56314
                 SkipInfo("TestCommon", "test_variant_consistency_jit", dtypes=[torch.float32]),
                 # Skip operator schema test because this is a functional and not an operator.
                 # Reference: https://github.com/pytorch/pytorch/issues/54574
                 SkipInfo('TestOperatorSignatures', 'test_get_torch_func_signature_exhaustive'),
             )
             ),
      OpInfo('logcumsumexp',
             dtypes=floating_types_and(),
             dtypesIfCUDA=floating_types_and(torch.half),
             skips=(
                 # AssertionError: UserWarning not triggered : Resized a non-empty tensor but did not warn about it.
                 SkipInfo('TestCommon', 'test_out', dtypes=(torch.float32,), device_type='cuda'),
                 # logcumsumexp_backward not implemented for 'Half
                 SkipInfo('TestOpInfo', 'test_supported_backward', dtypes=(torch.float16,), device_type='cuda'),
             ),
             sample_inputs_func=sample_inputs_logcumsumexp),
      UnaryUfuncInfo('sigmoid',
                     aliases=('special.expit', ),
                     ref=reference_sigmoid if TEST_SCIPY else _NOTHING,
                     decorators=(precisionOverride({torch.float16: 1e-2,
                                                    torch.complex64: 1e-1,
                                                    torch.bfloat16: 1e-2}),),
                     skips=(
                         # Reference: https://github.com/pytorch/pytorch/issues/56012
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  device_type='cuda', dtypes=[torch.complex64]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  device_type='cuda', dtypes=[torch.complex64]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                  device_type='cpu', dtypes=[torch.cfloat, torch.cdouble])),
                     dtypes=all_types_and_complex_and(torch.bool, torch.bfloat16),
                     dtypesIfCUDA=all_types_and_complex_and(torch.bool, torch.half, torch.bfloat16),
                     # sigmoid doesn't support complex autograd, https://github.com/pytorch/pytorch/issues/48552
                     backward_dtypesIfCPU=all_types_and(torch.bool, torch.bfloat16),
                     backward_dtypesIfCUDA=all_types_and(torch.bool, torch.bfloat16),
                     safe_casts_outputs=True,
                     assert_autodiffed=True),
      UnaryUfuncInfo('digamma',
                     ref=scipy.special.digamma if TEST_SCIPY else _NOTHING,
                     decorators=(precisionOverride({torch.float16: 5e-1}),),
                     dtypes=all_types_and(torch.bool),
                     dtypesIfCUDA=all_types_and(torch.bool, torch.half),
                     safe_casts_outputs=True),
      UnaryUfuncInfo('special.entr',
                     ref=scipy.special.entr if TEST_SCIPY else _NOTHING,
                     aten_name='special_entr',
                     decorators=(precisionOverride({torch.float16: 1e-1,
                                                    torch.bfloat16: 1e-1}),),
                     dtypes=all_types_and(torch.bool, torch.bfloat16),
                     dtypesIfCUDA=all_types_and(torch.bool, torch.half, torch.bfloat16),
                     skips=(
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  dtypes=[torch.bfloat16, torch.float16]),
                     ),
                     supports_inplace_autograd=False,
                     safe_casts_outputs=True,
                     sample_inputs_func=sample_inputs_entr),
      UnaryUfuncInfo('erf',
                     ref=scipy.special.erf if TEST_SCIPY else _NOTHING,
                     aliases=('special.erf', ),
                     decorators=(precisionOverride({torch.float16: 1e-2,
                                                    torch.bfloat16: 1e-2}),),
                     dtypes=all_types_and(torch.bool, torch.bfloat16),
                     dtypesIfCUDA=all_types_and(torch.bool, torch.half, torch.bfloat16),
                     assert_autodiffed=True,
                     safe_casts_outputs=True),
      UnaryUfuncInfo('erfc',
                     ref=scipy.special.erfc if TEST_SCIPY else _NOTHING,
                     aliases=('special.erfc', ),
                     decorators=(precisionOverride({torch.float16: 1e-2,
                                                    torch.bfloat16: 1e-2}),),
                     dtypes=all_types_and(torch.bool, torch.bfloat16),
                     dtypesIfCUDA=all_types_and(torch.bool, torch.half, torch.bfloat16),
                     assert_autodiffed=True,
                     safe_casts_outputs=True),
      UnaryUfuncInfo('erfinv',
                     ref=scipy.special.erfinv if TEST_SCIPY else _NOTHING,
                     aliases=('special.erfinv', ),
                     decorators=(precisionOverride({torch.float16: 1e-2,
                                                    torch.bfloat16: 1e-2,
                                                    torch.float32: 1e-4}),),
                     dtypes=all_types_and(torch.bool, torch.bfloat16),
                     dtypesIfCUDA=all_types_and(torch.bool, torch.half),
                     safe_casts_outputs=True,
                     domain=(-1, 1),
                     skips=(
                         # Reference: https://github.com/pytorch/pytorch/pull/49155#issuecomment-742664611
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  active_if=TEST_SCIPY and distutils.version.LooseVersion(scipy.__version__) < "1.4.0"),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  active_if=TEST_SCIPY and distutils.version.LooseVersion(scipy.__version__) < "1.4.0"),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                  active_if=TEST_SCIPY and distutils.version.LooseVersion(scipy.__version__) < "1.4.0"),
                     )),
      UnaryUfuncInfo('lgamma',
                     ref=reference_lgamma if TEST_SCIPY else _NOTHING,
                     aliases=('special.gammaln', ),
                     decorators=(precisionOverride({torch.float16: 7e-1}),),
                     dtypes=all_types_and(torch.bool, torch.bfloat16),
                     dtypesIfCUDA=all_types_and(torch.bool, torch.half),
                     # "digamma" not implemented for 'BFloat16'
                     backward_dtypesIfCPU=all_types_and(torch.bool),
                     skips=(
                         # Reference: https://github.com/pytorch/pytorch/pull/50140#discussion_r552615345
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  dtypes=[torch.bfloat16]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  device_type='cpu', dtypes=[torch.bfloat16]),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                  device_type='cpu', dtypes=[torch.bfloat16]),
                         # Reference: https://github.com/pytorch/pytorch/pull/50140#issuecomment-756150214
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_extremal',
                                  dtypes=[torch.float32, torch.float64], active_if=IS_WINDOWS),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_hard',
                                  dtypes=[torch.float32, torch.float64], active_if=IS_WINDOWS),
                         SkipInfo('TestUnaryUfuncs', 'test_reference_numerics_normal',
                                  dtypes=[torch.float32, torch.float64], active_if=IS_WINDOWS),
                     ),
                     safe_casts_outputs=True),
      OpInfo(
          'logdet',
          supports_out=False,
          sample_inputs_func=sample_inputs_logdet,
          decorators=(skipCPUIfNoLapack, skipCUDAIfNoMagma, skipCUDAIfRocm)),
      UnaryUfuncInfo('logit',
                     ref=scipy.special.logit if TEST_SCIPY else _NOTHING,
                     domain=(0, 1),
                     aliases=('special.logit', ),
                     decorators=(precisionOverride({torch.bfloat16: 5e-1,
                                                    torch.float16: 5e-1}),),
                     dtypes=all_types_and(torch.bool, torch.bfloat16),
                     dtypesIfCUDA=all_types_and(torch.bool, torch.half, torch.bfloat16),
                     sample_inputs_func=sample_inputs_logit,
                     safe_casts_outputs=True),
  ]
  
  # Common operator groupings
  unary_ufuncs = [op for op in op_db if isinstance(op, UnaryUfuncInfo)]
  spectral_funcs = [op for op in op_db if isinstance(op, SpectralFuncInfo)]
  sparse_unary_ufuncs = [op for op in op_db if isinstance(op, UnaryUfuncInfo) and op.supports_sparse is True]
  shape_funcs = [op for op in op_db if isinstance(op, ShapeFuncInfo)]
  
  def index_variable(shape, max_indices, device=torch.device('cpu')):
      if not isinstance(shape, tuple):
          shape = (shape,)
      index = torch.rand(*shape, dtype=torch.double, device=device).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, device=torch.device('cpu')):
      assert len(shape) == 2
      assert index_dim < 2
      batch_dim = 1 - index_dim
      index = torch.zeros(*shape, dtype=torch.long, device=device)
      for i in range(shape[index_dim]):
          index.select(index_dim, i).copy_(
              torch.randperm(max_indices, device=device)[: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.bool).bernoulli_()
  
  
  def mask_not_all_zeros(shape):
      assert len(shape) > 0
      while True:
          result = torch.randn(shape).gt(0)
          if result.sum() > 0:
              return result
  
  
  def uniform_scalar(offset=0, requires_grad=False):
      v = torch.rand(()) + offset
      v.requires_grad = requires_grad
      return v
  
  
  def normal_scalar_clamp(amin, amax, requires_grad=False):
      v = torch.randn(()).clamp(amin, amax)
      v.requires_grad = requires_grad
      return v
  
  
  def prod_zeros(dim_size, dim_select):
      assert len(dim_select) == 2
      result = torch.randn(dim_size, dim_size, dim_size)
      result.narrow(dim_select[0], 0, 1).narrow(dim_select[1], 1, 1).zero_()
      result.narrow(dim_select[0], 2, 1).narrow(dim_select[1], 3, 1).zero_()
      result.narrow(dim_select[0], 4, 1).narrow(dim_select[1], 3, 1).zero_()
      return result
  
  
  non_differentiable = collections.namedtuple('non_differentiable', ['tensor'])
  
  
  class dont_convert(tuple):
      pass
  
  
  class NoArgsClass(object):
      def __iter__(self):
          return self
  
      def __next__(self):
          raise StopIteration()
      next = __next__  # Python 2 compatibility
  
      def __len__(self):
          return 0
  
  NO_ARGS = NoArgsClass()
  
  def ident(x):
      return x
  
  # Do NOT add to this list. Method tests are being DEPRECATED and replaced by OpInfos.
  # See https://github.com/pytorch/pytorch/wiki/Writing-tests-in-PyTorch-1.8
  #
  # (
  #   method name,
  #   input size/constructing fn,
  #   args (tuple represents shape of a tensor arg),
  #   test variant name (will be used at test name suffix),    // optional
  #   (should_autodiff_node[bool], nonfusible_nodes, fusible_nodes) for autodiff, // optional
  #   indices for possible dim arg,                            // optional
  #   fn mapping output to part that should be gradcheck'ed,   // optional
  #   kwargs                                                   // optional
  # )
  # Note: some functions have separate schema for (Tensor other) and (Scalar other),
  #       and it's possible that we only support AD for Scalar version but not Tensor
  #       version, and vice versa.
  #       When writing tests, only scalar(float/int) input triggers the Scalar schema.
  #       uniform_scalar produces a scalar **Tensor** which won't match Scalar input.
  def method_tests():
      set_rng_seed(SEED)
      return [
          ('div', (S, S, S), (torch.rand(S, S, S) + 0.1,), '', (True,)),
          ('div', (S, S, S), (torch.rand(S, S) + 0.1,), 'broadcast_rhs', (True,)),
          ('div', (S, S), (torch.rand(S, S, S) + 0.1,), 'broadcast_lhs', (True,)),
          ('div', (S, 1, S), (torch.rand(M, S) + 0.1,), 'broadcast_all', (True,)),
          ('div', (), (uniform_scalar(0.1),), 'scalar', (True,)),
          ('div', (S, S, S), (uniform_scalar(0.1),), 'scalar_broadcast_rhs', (True,)),
          ('div', (), (uniform_scalar(0.1),), 'scalar_broadcast_lhs', (True,)),
          ('div', torch.rand(S, S, S) + 1e-1, (3.14,), 'constant', (True,)),
          ('div', uniform_scalar(1e-1, requires_grad=True), (3.14,), 'scalar_constant', (True,)),
          ('true_divide', (S, S, S), (torch.rand(S, S, S) + 0.1,), '', (True,)),
          ('true_divide', (S, S, S), (torch.rand(S, S) + 0.1,), 'broadcast_rhs', (True,)),
          ('true_divide', (S, S), (torch.rand(S, S, S) + 0.1,), 'broadcast_lhs', (True,)),
          ('true_divide', (S, 1, S), (torch.rand(M, S) + 0.1,), 'broadcast_all', (True,)),
          ('true_divide', (), (uniform_scalar(0.1),), 'scalar', (True,)),
          ('true_divide', (S, S, S), (uniform_scalar(0.1),), 'scalar_broadcast_rhs', (True,)),
          ('true_divide', (), (uniform_scalar(0.1),), 'scalar_broadcast_lhs', (True,)),
          ('true_divide', torch.rand(S, S, S) + 1e-1, (3.14,), 'constant', (True,)),
          ('true_divide', uniform_scalar(1e-1, requires_grad=True), (3.14,), 'scalar_constant', (True,)),
          ('div', (S, S, S), (torch.rand(S, S, S, dtype=torch.cdouble) + 0.1,), 'complex', (True,)),
          ('div', (S, S, S), (torch.rand(S, S, dtype=torch.cdouble) + 0.1,), 'complex_broadcast_rhs', (True,)),
          ('div', (S, S), (torch.rand(S, S, S, dtype=torch.cdouble) + 0.1,), 'complex_broadcast_lhs', (True,)),
          ('div', (S, 1, S), (torch.rand(M, S, dtype=torch.cdouble) + 0.1,), 'complex_broadcast_all', (True,)),
          ('div', (), (uniform_scalar(0.1j),), 'complex_scalar', (True,)),
          ('div', (S, S, S), (uniform_scalar(0.1j),), 'complex_scalar_broadcast_rhs', (True,)),
          ('div', (), (uniform_scalar(0.1j),), 'complex_scalar_broadcast_lhs', (True,)),
          ('div', torch.rand(S, S, S, dtype=torch.cdouble) + 1e-1, (3.14j,), 'complex_constant', (True,)),
          ('div', uniform_scalar(1e-1j, requires_grad=True), (3.14j,), 'complex_scalar_constant', (True,)),
          ('t', (1, 2), NO_ARGS, '', (False,)),
          ('fmod', (S, S, S), (1.5,), '', (True,)),
          ('fmod', (), (1.5,), 'scalar', (True,)),
          ('fmod', (S, S, S), (non_differentiable(torch.rand(S, S, S) + 1.5),), 'tensor'),
          ('fmod', (S,), (non_differentiable(torch.rand(S, S, S) + 1.5),), 'tensor_broadcast_lhs'),
          ('fmod', (S, S, S), (non_differentiable(torch.rand(S) + 1.5),), 'tensor_broadcast_rhs'),
          ('fmod', (S, 1, S), (non_differentiable(torch.rand(S, S) + 1.5),), 'tensor_broadcast_all'),
          ('fmod', (), (non_differentiable(uniform_scalar(1.5)),), 'scalar_tensor'),
          ('fmod', (), (non_differentiable(torch.rand(S, S, S) + 1.5),), 'scalar_tensor_broadcast_lhs'),
          ('fmod', (S, S, S), (non_differentiable(uniform_scalar(1.5)),), 'scalar_tensor_broadcast_rhs'),
          ('remainder', (S, S, S), (1.5,), '', (True,)),
          ('remainder', (), (1.5,), 'scalar', (True,)),
          ('remainder', (S, S, S), (non_differentiable(torch.rand(S, S, S) + 1.5),), 'tensor'),
          ('remainder', (S,), (non_differentiable(torch.rand(S, S, S) + 1.5),), 'tensor_broadcast_lhs'),
          ('remainder', (S, 1, S), (non_differentiable(torch.rand(S, S) + 1.5),), 'tensor_broadcast_all'),
          ('remainder', (), (non_differentiable(uniform_scalar(1.5)),), 'scalar_tensor'),
          ('remainder', (), (non_differentiable(torch.rand(S, S, S) + 1.5),), 'scalar_tensor_broadcast_lhs'),
          ('kthvalue', (S, S, S), (2,)),
          ('kthvalue', (S, S, S), (2, 1,), 'dim', (), [1]),
          ('kthvalue', (S, S, S), (2, 1, True,), 'keepdim_dim', (), [1]),
          ('kthvalue', (S,), (2, 0,), 'dim_1d', (), [1]),
          ('kthvalue', (S,), (2, 0, True,), 'keepdim_dim_1d', (), [1]),
          ('kthvalue', (), (1,), 'scalar', (), ()),
          ('kthvalue', (), (1, 0,), 'scalar_dim', (), [1]),
          ('kthvalue', (), (1, 0, True), 'scalar_keepdim_dim', (), [1]),
          ('median', (S, S, S), NO_ARGS),
          ('median', (S, S, S), (1,), 'dim', (), [0]),
          ('median', (S, S, S), (1, True,), 'keepdim_dim', (), [0]),
          ('median', (), NO_ARGS, 'scalar'),
          ('median', (), (0,), 'scalar_dim', (), [0]),
          ('median', (), (0, True,), 'scalar_keepdim_dim', (), [0]),
          ('nanmedian', (S, S, S), NO_ARGS),
          ('nanmedian', (S, S, S), (1,), 'dim', (), [0]),
          ('nanmedian', (S, S, S), (1, True,), 'keepdim_dim', (), [0]),
          ('nanmedian', (), NO_ARGS, 'scalar'),
          ('nanmedian', (), (0,), 'scalar_dim', (), [0]),
          ('nanmedian', (), (0, True,), 'scalar_keepdim_dim', (), [0]),
          ('var_mean', (S, S, S), NO_ARGS, ''),
          ('var_mean', (S, S, S), (1,), 'dim', [0]),
          ('var_mean', (S, S, S), (1, True, True), 'keepdim_dim', [0]),
          ('var_mean', (S,), (0,), 'dim_1d', [0]),
          ('var_mean', (S,), (0, True, True), 'keepdim_dim_1d', [0]),
          ('std_mean', (S, S, S), NO_ARGS, ''),
          ('std_mean', (S, S, S), (1,), 'dim', [0]),
          ('std_mean', (S, S, S), (1, True, True), 'keepdim_dim', [0]),
          ('std_mean', (S,), (0,), 'dim_1d', [0]),
          ('std_mean', (S,), (0, True, True), 'keepdim_dim_1d', [0]),
          ('renorm', (S, S, S), (2, 1, 0.5), 'dim', (), [1]),
          ('renorm', (S, S, S), (1, 2, 3), 'norm_1'),
          ('renorm', (S, S, S), (inf, 2, 0.5), 'norm_inf'),
          ('log_softmax', (S, S, S), (1, torch.float64,), 'kwarg_dtype_would_break_jit_loader', (True,)),
          ('zero_', (S, S, S), NO_ARGS),
          ('zero_', (), NO_ARGS, 'scalar'),
          ('norm', (S, S), (), 'default'),
          ('norm', (S, S), (2,), '2'),
          ('norm', (S, S), (0,), '0'),
          ('norm', (S, S), (0.5,), '0_5'),
          ('norm', (S, S), (1,), '1'),
          ('norm', (S, S), (3,), '3'),
          ('norm', (S, S), (inf,), 'inf'),
          ('norm', (S, S), (-inf,), '-inf'),
          ('norm', (S, S), ('fro',), 'fro_default'),
          ('norm', (S, S), ('fro', [0, 1],), 'fro'),
          ('norm', (S, S), ('nuc',), 'nuc', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
          ('norm', (S, S, S), ('nuc', [1, 2]), 'nuc_batched', (), NO_ARGS, [skipCPUIfNoLapack, skipCUDAIfNoMagma]),
          ('norm', (S, S), (-1,), 'neg_1'),
          ('norm', (S, S), (-2,), 'neg_2'),
          ('norm', (S, S), (-0.5,), 'neg_0_5'),
          ('norm', (S, S), (-1.5,), 'neg_1_5'),
          ('norm', (S, S), (-2, 1,), 'neg_2_2_dim', (), [1]),
          ('norm', (S, S), (-1, 1,), 'neg_1_2_dim', (), [1]),
          ('norm', (S, S), (0, 1,), '0_2_dim', (), [1]),
          ('norm', (S, S), (1, 1,), '1_2_dim', (), [1]),
          ('norm', (S, S), (2, 1,), '2_2_dim', (), [1]),
          ('norm', (S, S), (3, 1,), '3_2_dim', (), [1]),
          ('norm', (S, S), (inf, 1,), 'inf_2_dim'),
          ('norm', torch.rand(S, S, S) + 5e-2, (1.5,), '1_5_default'),
          ('norm', (S, S, S), (2, 1), '2_dim', (), [1]),
          ('norm', (S, S, S), (3, 1), '3_dim', (), [1]),
          ('norm', torch.rand(S, S, S) + 5e-2, (1.5, 1), '1_5_dim', (), [1]),
          ('norm', (S, S, S), (2, 1, True), 'keepdim_2_dim', (), [1]),
          ('norm', (S, S, S), (3, 1, True), 'keepdim_3_dim', (), [1]),
          ('norm', torch.rand(S, S, S) + 5e-2, (1.5, 1, True), 'keepdim_1_5_dim', (), [1]),
          ('norm', (), (2, 0), '2_dim_scalar', (), [1]),
          ('norm', (), (3, 0), '3_dim_scalar', (), [1]),
          ('norm', (), (2, 0, True), 'keepdim_2_dim_scalar', (), [1]),
          ('norm', (), (3, 0, True), 'keepdim_3_dim_scalar', (), [1]),
          ('clone', (S, M, S), NO_ARGS),
          ('clone', (), NO_ARGS, 'scalar'),
          ('contiguous', (S, S), NO_ARGS, '', (True,)),
          ('contiguous', torch.randn(S, S).transpose(0, 1), NO_ARGS, 'not_contiguous', (True,)),
          ('diag_embed', (S, S), NO_ARGS),
          ('diagonal', (M, M), NO_ARGS, '2d'),
          ('diagonal', (3, 5), NO_ARGS, '2d_wide'),
          ('diagonal', (3, 5), (2,), '2d_wide_pos'),
          ('diagonal', (3, 5), (-2,), '2d_wide_neg'),
          ('diagonal', (5, 3), NO_ARGS, '2d_tall'),
          ('diagonal', (5, 3), (2,), '2d_tall_pos'),
          ('diagonal', (5, 3), (-2,), '2d_tall_neg'),
          ('diagonal', (M, M), (1,), '2d_1'),
          ('diagonal', (M, M), (2,), '2d_2'),
          ('diagonal', (M, M, M), (1, 1, 2), '3d_1'),
          ('diagonal', (M, M, M), (2, 0, 1), '3d_2'),
          ('diagonal', (M, M, M), (-2, 0, 1), '3d_3'),
          ('tril', (M, M), NO_ARGS),
          ('tril', (M, M), (2,), 'idx'),
          ('tril', (S, M, M), NO_ARGS, 'batched'),
          ('tril', (S, M, M), (2,), 'batched_idx'),
          ('tril', (3, 3, S, S), NO_ARGS, 'more_batched'),
          ('triu', (M, M), NO_ARGS),
          ('triu', (M, M), (2,), 'idx'),
          ('triu', (S, M, M), NO_ARGS, 'batched'),
          ('triu', (S, M, M), (2,), 'batched_idx'),
          ('triu', (3, 3, S, S), NO_ARGS, 'more_batched'),
          ('cross', (S, 3), ((S, 3),)),
          ('cross', (S, 3, S), ((S, 3, S), 1), 'dim'),
          ('fill_', (S, S, S), (1,), 'number'),
          ('fill_', (), (1,), 'number_scalar'),
          ('fill_', (S, S, S), ((),), 'variable'),
          ('split', (S, S, S), (2,), '', (True,)),
          ('split', (S, S, S), (S, 1), 'dim', (True,), [1]),
          ('split', (S, S, S), ([int(S / 3), S - int(S / 3) * 2, int(S / 3)],), 'size_list',
              (True, 'aten::split_with_sizes')),
          ('split', (S, S, S), ([int(S / 2), S - int(S / 2) * 2, int(S / 2)], 2), 'size_list_dim',
              (True, 'aten::split_with_sizes'), [1]),
          ('split_with_sizes', (S, S, S), ([int(S / 3), S - int(S / 3) * 2, int(S / 3)],), '', (True,)),
          ('split_with_sizes', (S, S, S), ([int(S / 3), S - int(S / 3), 0],), 'size_0', (True, )),
          ('split_with_sizes', (S, S, S), ([int(S / 3), S - int(S / 3) * 2, int(S / 3)],), 'dim', (True, ), [1]),
          ('tensor_split', (S, S, S), (3,), 'sections', (False,)),
          ('tensor_split', (S, S, S), (3, 1), 'sections_dim', (False,), [1]),
          ('tensor_split', (S, S, S), ([2, 4],), 'indices', (False,)),
          ('tensor_split', (S, S, S), ([2, 4], 1), 'indices_dim', (False,), [1]),
          ('resize_', (S, S, S), (torch.Size([S * S, S])), 'fewer_dims'),
          ('resize_', (), (dont_convert(()),), 'scalar'),
          ('resize_', (), (torch.Size([1, 1, 1])), 'scalar_to_dims'),
          ('resize_as_', (), (non_differentiable(torch.tensor(5.)),), 'scalar'),
          ('resize_as_', (), (non_differentiable(torch.randn((1, 1, 1))),), 'scalar_to_dims'),
          ('resize_as_', (S, S, S), (non_differentiable(torch.randn(S * S, S)),)),
          ('where', (M, M), (mask_not_all_zeros((M, M)), (M, M)), '', (True,)),
          ('where', (M, 1, M), (mask_not_all_zeros((M, M)), (M, M, 1)), 'broadcast_all', (True,)),
          ('where', (), (bernoulli_scalar(), ()), 'scalar', (True,)),
          ('where', (M, 1, M), (bernoulli_scalar(), (M, M, 1)), 'scalar_broadcast_mask', (True,)),
          ('where', (), (mask_not_all_zeros((M, M)), ()), 'scalar_broadcast_non_mask', (True,)),
          ('to_sparse', (S, S), (), '', (), (), [], lambda x: x.to_dense())
      ]
  
  def create_input(call_args, requires_grad=True, non_contiguous=False, call_kwargs=None, dtype=torch.double, device=None):
      if not isinstance(call_args, tuple):
          call_args = (call_args,)
  
      def map_arg(arg):
          def maybe_non_contig(tensor):
              return tensor if not non_contiguous else make_non_contiguous(tensor)
  
          if isinstance(arg, torch.Size) or isinstance(arg, dont_convert):
              return arg
          elif isinstance(arg, tuple) and len(arg) == 0:
              var = torch.randn((), dtype=dtype, device=device)
              var.requires_grad = requires_grad
              return var
          elif isinstance(arg, tuple) and not isinstance(arg[0], torch.Tensor):
              return Variable(maybe_non_contig(torch.randn(*arg, dtype=dtype, device=device)), requires_grad=requires_grad)
          # double check casting
          elif isinstance(arg, non_differentiable):
              if isinstance(arg.tensor, torch.Tensor):
                  if arg.tensor.dtype == torch.float:
                      return maybe_non_contig(arg.tensor.to(dtype=torch.double, device=device))
                  if arg.tensor.dtype == torch.cfloat:
                      return maybe_non_contig(arg.tensor.to(dtype=torch.cdouble, device=device))
                  return maybe_non_contig(arg.tensor.to(device=device))
              return maybe_non_contig(arg.tensor.to(device=device))
          elif isinstance(arg, torch.Tensor):
              if arg.dtype == torch.float:
                  arg = arg.double()
              if arg.dtype == torch.cfloat:
                  arg = arg.to(torch.cdouble)
              if arg.is_complex() != dtype.is_complex:
                  raise RuntimeError("User provided tensor is real for a test that runs with complex dtype, ",
                                     "which is not supported for now")
              # NOTE: We do clone() after detach() here because we need to be able to change size/storage of v afterwards
              v = maybe_non_contig(arg).detach().to(device=device).clone()
              v.requires_grad = requires_grad and (v.is_floating_point() or v.is_complex())
              return v
          elif callable(arg):
              return map_arg(arg(dtype=dtype, device=device))
          else:
              return arg
      args_out = tuple(map_arg(arg) for arg in call_args)
      kwargs_out = {k: map_arg(v) for k, v in call_kwargs.items()} if call_kwargs else {}
      return args_out, kwargs_out
  
  
  def _compare_trilu_indices(
          self, row, col, offset=0, dtype=torch.long, device='cpu'):
      if row == 0 or col == 0:
          # have to handle this separately as tril and triu does not take
          # empty matrix as input
          self.assertEqual(
              torch.empty(0, 2, dtype=dtype, device=device).transpose(0, 1),
              torch.tril_indices(row, col, offset, dtype=dtype, device=device))
  
          self.assertEqual(
              torch.empty(0, 2, dtype=dtype, device=device).transpose(0, 1),
              torch.triu_indices(row, col, offset, dtype=dtype, device=device))
  
      else:
          # TODO(#38095): Replace assertEqualIgnoreType. See issue #38095
          self.assertEqualIgnoreType(
              torch.ones(row, col, device='cpu')
                   .tril(offset).nonzero().to(dtype).transpose(0, 1),
              torch.tril_indices(row, col, offset, dtype=dtype, device=device))
  
          # TODO(#38095): Replace assertEqualIgnoreType. See issue #38095
          self.assertEqualIgnoreType(
              torch.ones(row, col, device='cpu')
                   .tril(offset).nonzero().to(dtype).transpose(0, 1),
              torch.tril_indices(row, col, offset, dtype=dtype, device=device))
  
  
  def _compare_large_trilu_indices(
          self, row, col, offset=0, dtype=torch.long, device='cpu'):
      l = torch.ones(row, col, dtype=dtype, device='cpu').tril(offset) \
               .nonzero()[-100:-1, :].transpose(0, 1).to(device)
      torch.cuda.empty_cache()
  
      r = torch.tril_indices(
          row, col, offset, dtype=dtype, device=device)[:, -100:-1]
      self.assertEqual(l, r)
      torch.cuda.empty_cache()
  
      l = torch.ones(row, col, dtype=dtype, device='cpu').triu(offset) \
               .nonzero()[-100:-1, :].transpose(0, 1).to(device)
      torch.cuda.empty_cache()
  
      r = torch.triu_indices(
          row, col, offset, dtype=dtype, device=device)[:, -100:-1]
      self.assertEqual(l, r)
      torch.cuda.empty_cache()
  
  # (
  #   row
  #   col
  #   offset (optional)
  #   dtype (optional)
  # )
  tri_tests_args = [
      (1, 1),
      (3, 3),
      (3, 3, 1),
      (3, 3, 2),
      (3, 3, 200),
      (3, 3, -1),
      (3, 3, -2),
      (3, 3, -200),
      (0, 3, 0),
      (0, 3, 1),
      (0, 3, -1),
      (3, 0, 0),
      (3, 0, 1),
      (3, 0, -1),
      (0, 0, 0),
      (0, 0, 1),
      (0, 0, -1),
      (3, 6, 0),
      (3, 6, 1),
      (3, 6, 3),
      (3, 6, 9),
      (3, 6, -1),
      (3, 6, -3),
      (3, 6, -9),
      (6, 3, 0),
      (6, 3, 1),
      (6, 3, 3),
      (6, 3, 9),
      (6, 3, -1),
      (6, 3, -3),
      (6, 3, -9),
      (258, 253, 1, torch.float32),
      (257, 258, 1, torch.float64),
      (258, 258, 1, torch.short),
      (3, 513, 1, torch.long),
      (513, 3, 1, torch.int),
      (513, 0, 1, torch.double),
      (1024, 1024),
      (1024, 1024, 500, torch.float32),
      (1024, 1024, 1023),
      (1024, 1024, -500),
      (1023, 1025),
      (1025, 1023, 1022),
      (1024, 1024, -500),
      (3, 2028),
      (3, 2028, 1),
      (3, 2028, -1),
      (2028, 3),
      (2028, 1),
      (2028, 1, -1)
  ]
  
  tri_large_tests_args: List[Tuple[int, ...]] = [
      # Large test cases below are deliberately commented out to speed up CI
      # tests and to avoid OOM error. When modifying implementations of
      # tril_indices and triu_indices, please enable these tests and make sure
      # they pass.
      #
      # (1, 268435455),
      # (5000, 5000),
      # (10000, 10000),
      # (268435455, 1),
      # (134217727, 2, 1),
      # (2, 134217727, 1),
      # (536870901, 1),
      # (1, 536870901),
      # (268435455, 2, 1),
      # (2, 268435455, 1)
  ]
  
  
  def run_additional_tri_tests(self, device):
      x = torch.ones(
          3, 3, dtype=torch.long, device=device, layout=torch.strided)
      l = x.tril(0).nonzero().transpose(0, 1)
      u = x.triu(0).nonzero().transpose(0, 1)
      self.assertEqual(l, torch.tril_indices(3, 3, device=device))
      self.assertEqual(
          l, torch.tril_indices(3, 3, device=device, layout=torch.strided))
  
      self.assertEqual(u, torch.triu_indices(3, 3, device=device))
      self.assertEqual(
          u, torch.triu_indices(3, 3, device=device, layout=torch.strided))
  
      self.assertRaises(
          RuntimeError,
          lambda: torch.triu_indices(
              1, 1, device=device, layout=torch.sparse_coo))
  
      self.assertRaises(
          RuntimeError,
          lambda: torch.tril_indices(
              1, 1, device=device, layout=torch.sparse_coo))
  
  
  def unpack_variables(args):
      if isinstance(args, tuple):
          return tuple(unpack_variables(elem) for elem in args)
      else:
          return args
  
  
  EXCLUDE_FUNCTIONAL = {
      'addmm',
      'addmm_',
      'reshape',
      'where'  # argument order
  }
  EXCLUDE_GRADCHECK: Dict[str, Any] = {
  }
  EXCLUDE_GRADGRADCHECK: Dict[str, Any] = {
  }
  EXCLUDE_GRADGRADCHECK_BY_TEST_NAME = {
      # `other` expand_as(self, other) is not used in autograd.
      'test_expand_as',
      'test_cdist',
  }
  
  
  def exclude_tensor_method(name, test_name):
      # there are no tensor equivalents for these (inplace or out)
      exclude_all_tensor_method_by_test_name = {
          'test_slice',
          'test_where',
          'test_where_broadcast_all',
          'test_where_scalar',
          'test_where_scalar_broadcast_mask',
          'test_where_scalar_broadcast_non_mask',
          'test_var_mean_keepdim_dim_1d',
          'test_var_mean_keepdim_dim',
          'test_var_mean_dim_1d',
          'test_var_mean_dim',
          'test_var_mean',
          'test_std_mean_keepdim_dim_1d',
          'test_std_mean_keepdim_dim',
          'test_std_mean_dim_1d',
          'test_std_mean_dim',
          'test_std_mean',
      }
      # there are no out-of-place tensor equivalents for these
      exclude_outplace_tensor_method = {
          'index_fill',
          'scatter',
          'scatter_add',
      }
      if test_name in exclude_all_tensor_method_by_test_name:
          return True
      is_magic_method = name[:2] == '__' and name[-2:] == '__'
      is_inplace = name[-1] == "_" and not is_magic_method
      if not is_inplace and name in exclude_outplace_tensor_method:
          return True
      return False
  
apis: torch.empty torch.get_default_dtype torch.testing._internal.common_utils.random_symmetric_matrix torch.rand torch.no_grad torch.tril_indices torch.testing._internal.common_utils.make_tensor torch.cuda.empty_cache torch.testing._internal.common_utils.random_hermitian_pd_matrix torch.testing.floating_types torch.randn torch.repeat_interleave torch.testing._internal.common_utils.is_iterable_of_tensors numpy.abs numpy.random.choice torch.testing._internal.common_utils.random_symmetric_pd_matrix numpy.sinc torch.testing.floating_types_and torch.device torch.testing.integral_types_and torch.triu_indices torch.testing._internal.common_utils._wrap_warn_once torch.testing.floating_and_complex_types_and torch.ones torch.testing._internal.common_utils.random_symmetric_psd_matrix numpy.sqrt torch.testing.floating_and_complex_types torch.testing.make_non_contiguous torch.empty_strided torch.tensor torch.testing._internal.common_utils.set_rng_seed torch.linalg.cholesky torch.testing.all_types_and_complex torch.testing._internal.common_device_type.skipIf torch.einsum torch.testing.all_types_and_complex_and torch.testing._internal.common_utils.random_well_conditioned_matrix torch.testing.complex_types torch.polygamma torch.testing._internal.common_device_type.precisionOverride numpy.sign torch.testing.all_types torch.Size numpy.modf numpy.exp torch.testing._internal.common_utils.random_fullrank_matrix_distinct_singular_value torch.linalg.svd torch.finfo torch.randperm torch.zeros torch.LongTensor torch.testing.all_types_and