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# Source code for torch.autograd

    """
    ``torch.autograd`` provides classes and functions implementing automatic
    differentiation of arbitrary scalar valued functions. It requires minimal
    changes to the existing code - you only need to declare :class:`Tensor` s
    for which gradients should be computed with the ``requires_grad=True`` keyword.
    As of now, we only support autograd for floating point :class:`Tensor` types (
    half, float, double and bfloat16) and complex :class:`Tensor` types (cfloat, cdouble).
    """
    import warnings
    from typing import Any, Callable, cast, List, Optional, Sequence, Tuple, Union

    import torch

    from torch.types import _size, _TensorOrTensors
    from .. import _vmap_internals
    from ..overrides import handle_torch_function, has_torch_function, is_tensor_like
    from . import forward_ad, functional, graph
    from .anomaly_mode import detect_anomaly, set_detect_anomaly
    from .function import Function, NestedIOFunction
    from .grad_mode import (
        _force_original_view_tracking,
        _unsafe_preserve_version_counter,
        enable_grad,
        inference_mode,
        no_grad,
        set_grad_enabled,
        set_multithreading_enabled,
    )
    from .gradcheck import gradcheck, gradgradcheck

    from .variable import Variable

    __all__ = ["Variable", "Function", "backward", "grad_mode"]

    _OptionalTensor = Optional[torch.Tensor]
    _ShapeorNestedShape = Union[_size, Sequence[_size], torch.Tensor]

    def _calculate_shape(
        output: torch.Tensor, grad: torch.Tensor, is_grads_batched: bool
    ) -> Tuple[_ShapeorNestedShape, _ShapeorNestedShape]:
        # is_same_size ensures that both tensors are either nested or non nested
        if output.is_nested:
            if is_grads_batched:
                raise RuntimeError("Batched grads are not supported with Nested Tensor.")
            out_shape = output._nested_tensor_size()
            grad_shape = grad._nested_tensor_size()

            return out_shape, grad_shape

        reg_out_shape = output.shape
        reg_grad_shape = grad.shape if not is_grads_batched else grad.shape[1:]
        return reg_out_shape, reg_grad_shape

    def _make_grads(
        outputs: Sequence[torch.Tensor],
        grads: Sequence[_OptionalTensor],
        is_grads_batched: bool,
    ) -> Tuple[_OptionalTensor, ...]:
        new_grads: List[_OptionalTensor] = []
        for out, grad in zip(outputs, grads):
            if isinstance(grad, torch.Tensor):
                first_grad = grad if not is_grads_batched else grad[0]
                if not torch.is_same_size(out, first_grad):
                    out_shape, grad_shape = _calculate_shape(
                        out, first_grad, is_grads_batched
                    )
                    if is_grads_batched:
                        raise RuntimeError(
                            "If `is_grads_batched=True`, we interpret the first "
                            "dimension of each grad_output as the batch dimension. "
                            "The sizes of the remaining dimensions are expected to match "
                            "the shape of corresponding output, but a mismatch "
                            "was detected: grad_output["
                            + str(grads.index(grad))
                            + "] has a shape of "
                            + str(grad_shape)
                            + " and output["
                            + str(outputs.index(out))
                            + "] has a shape of "
                            + str(out_shape)
                            + ". "
                            "If you only want some tensors in `grad_output` to be considered "
                            "batched, consider using vmap."
                        )
                    else:
                        raise RuntimeError(
                            "Mismatch in shape: grad_output["
                            + str(grads.index(grad))
                            + "] has a shape of "
                            + str(grad_shape)
                            + " and output["
                            + str(outputs.index(out))
                            + "] has a shape of "
                            + str(out_shape)
                            + "."
                        )
                if out.dtype.is_complex != grad.dtype.is_complex:
                    raise RuntimeError(
                        "For complex Tensors, both grad_output and output"
                        " are required to have the same dtype."
                        " Mismatch in dtype: grad_output["
                        + str(grads.index(grad))
                        + "] has a dtype of "
                        + str(grad.dtype)
                        + " and output["
                        + str(outputs.index(out))
                        + "] has a dtype of "
                        + str(out.dtype)
                        + "."
                    )
                new_grads.append(grad)
            elif grad is None:
                if out.requires_grad:
                    if out.numel() != 1:
                        raise RuntimeError(
                            "grad can be implicitly created only for scalar outputs"
                        )
                    if not out.dtype.is_floating_point:
                        msg = (
                            "grad can be implicitly created only for real scalar outputs"
                            f" but got {out.dtype}"
                        )
                        raise RuntimeError(msg)
                    new_grads.append(
                        torch.ones_like(out, memory_format=torch.preserve_format)
                    )
                else:
                    new_grads.append(None)
            else:
                raise TypeError(
                    "gradients can be either Tensors or None, but got "
                    + type(grad).__name__
                )
        return tuple(new_grads)

    def _tensor_or_tensors_to_tuple(
        tensors: Optional[_TensorOrTensors], length: int
    ) -> Tuple[_OptionalTensor, ...]:
        if tensors is None:
            return (None,) * length
        if isinstance(tensors, torch.Tensor):
            return (tensors,)
        return tuple(tensors)

    def backward(
        tensors: _TensorOrTensors,
        grad_tensors: Optional[_TensorOrTensors] = None,
        retain_graph: Optional[bool] = None,
        create_graph: bool = False,
        grad_variables: Optional[_TensorOrTensors] = None,
        inputs: Optional[_TensorOrTensors] = None,
    ) -> None:
        r"""Computes the sum of gradients of given tensors with respect to graph
        leaves.

        The graph is differentiated using the chain rule. If any of ``tensors``
        are non-scalar (i.e. their data has more than one element) and require
        gradient, then the Jacobian-vector product would be computed, in this
        case the function additionally requires specifying ``grad_tensors``.
        It should be a sequence of matching length, that contains the "vector"
        in the Jacobian-vector product, usually the gradient of the differentiated
        function w.r.t. corresponding tensors (``None`` is an acceptable value for
        all tensors that don't need gradient tensors).

        This function accumulates gradients in the leaves - you might need to zero
        ``.grad`` attributes or set them to ``None`` before calling it.
        See :ref:`Default gradient layouts<default-grad-layouts>`
        for details on the memory layout of accumulated gradients.

        .. note::
            Using this method with ``create_graph=True`` will create a reference cycle
            between the parameter and its gradient which can cause a memory leak.
            We recommend using ``autograd.grad`` when creating the graph to avoid this.
            If you have to use this function, make sure to reset the ``.grad`` fields of your
            parameters to ``None`` after use to break the cycle and avoid the leak.

        .. note::

            If you run any forward ops, create ``grad_tensors``, and/or call ``backward``
            in a user-specified CUDA stream context, see
            :ref:`Stream semantics of backward passes<bwd-cuda-stream-semantics>`.

        .. note::

            When ``inputs`` are provided and a given input is not a leaf,
            the current implementation will call its grad_fn (even though it is not strictly needed to get this gradients).
            It is an implementation detail on which the user should not rely.
            See https://github.com/pytorch/pytorch/pull/60521#issuecomment-867061780 for more details.

        Args:
            tensors (Sequence[Tensor] or Tensor): Tensors of which the derivative will be
                computed.
            grad_tensors (Sequence[Tensor or None] or Tensor, optional): The "vector" in
                the Jacobian-vector product, usually gradients w.r.t. each element of
                corresponding tensors. None values can be specified for scalar Tensors or
                ones that don't require grad. If a None value would be acceptable for all
                grad_tensors, then this argument is optional.
            retain_graph (bool, optional): If ``False``, the graph used to compute the grad
                will be freed. Note that in nearly all cases setting this option to ``True``
                is not needed and often can be worked around in a much more efficient
                way. Defaults to the value of ``create_graph``.
            create_graph (bool, optional): If ``True``, graph of the derivative will
                be constructed, allowing to compute higher order derivative products.
                Defaults to ``False``.
            inputs (Sequence[Tensor] or Tensor, optional): Inputs w.r.t. which the gradient
                be will accumulated into ``.grad``. All other Tensors will be ignored. If
                not provided, the gradient is accumulated into all the leaf Tensors that
                were used to compute the attr::tensors.
        """
        if torch._C._are_functorch_transforms_active():
            raise RuntimeError(
                "backward() called inside a functorch transform. This is not "
                "supported, please use functorch.grad or functorch.vjp instead "
                "or call backward() outside of functorch transforms."
            )

        if grad_variables is not None:
            warnings.warn("'grad_variables' is deprecated. Use 'grad_tensors' instead.")
            if grad_tensors is None:
                grad_tensors = grad_variables
            else:
                raise RuntimeError(
                    "'grad_tensors' and 'grad_variables' (deprecated) "
                    "arguments both passed to backward(). Please only "
                    "use 'grad_tensors'."
                )
        if inputs is not None and len(inputs) == 0:
            raise RuntimeError("'inputs' argument to backward() cannot be empty.")

        tensors = (tensors,) if isinstance(tensors, torch.Tensor) else tuple(tensors)
        inputs = (
            (inputs,)
            if isinstance(inputs, torch.Tensor)
            else tuple(inputs)
            if inputs is not None
            else tuple()
        )

        grad_tensors_ = _tensor_or_tensors_to_tuple(grad_tensors, len(tensors))
        grad_tensors_ = _make_grads(tensors, grad_tensors_, is_grads_batched=False)
        if retain_graph is None:
            retain_graph = create_graph

        # The reason we repeat the same comment below is that
        # some Python versions print out the first line of a multi-line function
        # calls in the traceback and some print out the last line
        Variable._execution_engine.run_backward(  # Calls into the C++ engine to run the backward pass
            tensors,
            grad_tensors_,
            retain_graph,
            create_graph,
            inputs,
            allow_unreachable=True,
            accumulate_grad=True,
        )  # Calls into the C++ engine to run the backward pass

    def grad(
        outputs: _TensorOrTensors,
        inputs: _TensorOrTensors,
        grad_outputs: Optional[_TensorOrTensors] = None,
        retain_graph: Optional[bool] = None,
        create_graph: bool = False,
        only_inputs: bool = True,
        allow_unused: Optional[bool] = None,
        is_grads_batched: bool = False,
        materialize_grads: bool = False,
    ) -> Tuple[torch.Tensor, ...]:
        r"""Computes and returns the sum of gradients of outputs with respect to
        the inputs.

        ``grad_outputs`` should be a sequence of length matching ``output``
        containing the "vector" in vector-Jacobian product, usually the pre-computed
        gradients w.r.t. each of the outputs. If an output doesn't require_grad,
        then the gradient can be ``None``).

        .. note::

            If you run any forward ops, create ``grad_outputs``, and/or call ``grad``
            in a user-specified CUDA stream context, see
            :ref:`Stream semantics of backward passes<bwd-cuda-stream-semantics>`.

        .. note::

            ``only_inputs`` argument is deprecated and is ignored now (defaults to ``True``).
            To accumulate gradient for other parts of the graph, please use
            ``torch.autograd.backward``.

        Args:
            outputs (sequence of Tensor): outputs of the differentiated function.
            inputs (sequence of Tensor): Inputs w.r.t. which the gradient will be
                returned (and not accumulated into ``.grad``).
            grad_outputs (sequence of Tensor): The "vector" in the vector-Jacobian product.
                Usually gradients w.r.t. each output. None values can be specified for scalar
                Tensors or ones that don't require grad. If a None value would be acceptable
                for all grad_tensors, then this argument is optional. Default: None.
            retain_graph (bool, optional): If ``False``, the graph used to compute the grad
                will be freed. Note that in nearly all cases setting this option to ``True``
                is not needed and often can be worked around in a much more efficient
                way. Defaults to the value of ``create_graph``.
            create_graph (bool, optional): If ``True``, graph of the derivative will
                be constructed, allowing to compute higher order derivative products.
                Default: ``False``.
            allow_unused (Optional[bool], optional): If ``False``, specifying inputs
                that were not used when computing outputs (and therefore their grad is
                always zero) is an error. Defaults to the value of ``materialize_grads``.
            is_grads_batched (bool, optional): If ``True``, the first dimension of each
                tensor in ``grad_outputs`` will be interpreted as the batch dimension.
                Instead of computing a single vector-Jacobian product, we compute a
                batch of vector-Jacobian products for each "vector" in the batch.
                We use the vmap prototype feature as the backend to vectorize calls
                to the autograd engine so that this computation can be performed in a
                single call. This should lead to performance improvements when compared
                to manually looping and performing backward multiple times. Note that
                due to this feature being experimental, there may be performance
                cliffs. Please use ``torch._C._debug_only_display_vmap_fallback_warnings(True)``
                to show any performance warnings and file an issue on github if warnings exist
                for your use case. Defaults to ``False``.
            materialize_grads (bool, optional): If ``True``, set the gradient for unused inputs
                to zero instead of None. This is useful when computing higher-order derivatives.
                If ``materialize_grads`` is ``True`` and ``allow_unused`` is ``False``, an error
                will be raised. Defaults to ``False``.

        """
        if materialize_grads and allow_unused is False:
            raise ValueError(
                "Expected allow_unused to be True or not passed when materialize_grads=True, "
                "but got: allow_unused=False."
            )
        if allow_unused is None:
            allow_unused = materialize_grads
        t_outputs = cast(
            Tuple[torch.Tensor, ...],
            (outputs,) if is_tensor_like(outputs) else tuple(outputs),
        )
        t_inputs = cast(
            Tuple[torch.Tensor, ...], (inputs,) if is_tensor_like(inputs) else tuple(inputs)
        )
        overridable_args = t_outputs + t_inputs
        if has_torch_function(overridable_args):
            return handle_torch_function(
                grad,
                overridable_args,
                t_outputs,
                t_inputs,
                grad_outputs=grad_outputs,
                retain_graph=retain_graph,
                create_graph=create_graph,
                only_inputs=only_inputs,
                allow_unused=allow_unused,
                is_grads_batched=is_grads_batched,
                materialize_grads=materialize_grads,
            )

        if not only_inputs:
            warnings.warn(
                "only_inputs argument is deprecated and is ignored now "
                "(defaults to True). To accumulate gradient for other "
                "parts of the graph, please use torch.autograd.backward."
            )

        grad_outputs_ = _tensor_or_tensors_to_tuple(grad_outputs, len(t_outputs))
        grad_outputs_ = _make_grads(
            t_outputs, grad_outputs_, is_grads_batched=is_grads_batched
        )

        if retain_graph is None:
            retain_graph = create_graph

        # The reason we repeat the same comment several times below is because
        # some Python versions print out the first line of multi-line function
        # calls in the traceback and some print out the last line
        if is_grads_batched:

            def vjp(gO):
                return Variable._execution_engine.run_backward(  # Calls into the C++ engine to run the backward pass
                    t_outputs,
                    gO,
                    retain_graph,
                    create_graph,
                    t_inputs,
                    allow_unused,
                    accumulate_grad=False,
                )  # Calls into the C++ engine to run the backward pass

            result = _vmap_internals._vmap(vjp, 0, 0, allow_none_pass_through=True)(
                grad_outputs_
            )
        else:
            result = Variable._execution_engine.run_backward(  # Calls into the C++ engine to run the backward pass
                t_outputs,
                grad_outputs_,
                retain_graph,
                create_graph,
                t_inputs,
                allow_unused,
                accumulate_grad=False,
            )  # Calls into the C++ engine to run the backward pass
        if materialize_grads:
            result = tuple(
                output
                if output is not None
                else torch.zeros_like(input, requires_grad=True)
                for (output, input) in zip(result, t_inputs)
            )
        return result

    # This function applies in case of gradient checkpointing for memory
    # optimization. Currently, gradient checkpointing is supported only if the
    # execution engine is invoked through torch.autograd.backward() and its
    # inputs argument is not passed. It is not supported for torch.autograd.grad().
    # This is because if inputs are specified, the gradient won't be calculated for
    # anything else e.g. model parameters like weights, bias etc.
    #
    # This function returns whether the checkpointing is valid i.e. torch.autograd.backward
    # or not i.e. torch.autograd.grad. The implementation works by maintaining a thread
    # local variable in torch/csrc/autograd/engine.cpp which looks at the NodeTask
    # in the stack and before a NodeTask is executed in evaluate_function, it
    # checks for whether reentrant backwards is imperative or not.
    # See https://github.com/pytorch/pytorch/pull/4594 for more discussion/context
    def _is_checkpoint_valid():
        return Variable._execution_engine.is_checkpoint_valid()

    def variable(*args, **kwargs):
        raise RuntimeError(
            "torch.autograd.variable(...) is deprecated, use torch.tensor(...) instead"
        )

    # Monkey patching variable.Variable to fix FX codegen. FX generates a call by roughly doing
    # f"{fn.__module__}.{fn.__name__}(...). This yields torch.autograd.variable.Variable(...) in the
    # output of an FX graph.  Unfortunately the module name torch.autograd.variable is shadowed by the
    # deprecated function - variable(...).
    variable.Variable = Variable  # type: ignore[attr-defined]

    if not torch._C._autograd_init():
        raise RuntimeError("autograd initialization failed")

    # Import all native method/classes
    from torch._C._autograd import (
        _add_metadata_json,
        _disable_profiler,
        _disable_profiler_legacy,
        _enable_profiler,
        _enable_profiler_legacy,
        _enable_record_function,
        _get_sequence_nr,
        _kineto_step,
        _KinetoEvent,
        _pop_saved_tensors_default_hooks,
        _prepare_profiler,
        _profiler_enabled,
        _ProfilerResult,
        _push_saved_tensors_default_hooks,
        _record_function_with_args_enter,
        _record_function_with_args_exit,
        _set_empty_test_observer,
        _supported_activities,
        DeviceType,
        kineto_available,
        ProfilerEvent,
        SavedTensor,
    )

    from torch._C._profiler import ProfilerActivity, ProfilerConfig, ProfilerState

    from . import profiler

    def _register_py_tensor_class_for_device(device, cls):
        if not isinstance(cls, type):
            raise RuntimeError("cls isn't a typeinfo object")
        torch._C._register_py_class_for_device(device, cls)

    is_multithreading_enabled = torch._C._is_multithreading_enabled
    torch._C._add_docstr(
        is_multithreading_enabled, "Returns True if multithreading is currently enabled."
    )

    is_view_replay_enabled = torch._C._is_view_replay_enabled
    torch._C._add_docstr(
        is_view_replay_enabled, "Returns True if view-replay is currently enabled."
    )

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