code: def conv_general_dilated(
      lhs: Array,
      rhs: Array,
      window_strides: Sequence[int],
      padding: str | Sequence[tuple[int, int]],
      lhs_dilation: Sequence[int] | None = None,
      rhs_dilation: Sequence[int] | None = None,
      dimension_numbers: ConvGeneralDilatedDimensionNumbers = None,
      feature_group_count: int = 1,
      batch_group_count: int = 1,
      precision: lax.PrecisionLike = None,
      preferred_element_type: DTypeLike | None = None,
  ) -> Array:
      """General n-dimensional convolution operator, with optional dilation.
  
      Wraps XLA's `Conv
      <https://www.tensorflow.org/xla/operation_semantics#conv_convolution>`_
      operator.
  
      Args:
        lhs: a rank `n+2` dimensional input array.
        rhs: a rank `n+2` dimensional array of kernel weights.
        window_strides: a sequence of `n` integers, representing the inter-window
          strides.
        padding: either the strings `'SAME'`, `'SAME_LOWER'`, or `'VALID'`, or a
          sequence of `n` `(low, high)` integer pairs that give the padding to apply
          before and after each spatial dimension. `'SAME'` and `'SAME_LOWER'` add
          padding to produce same output size as the input. The padding is split
          between the two sides equally or almost equally. In case the padding is an
          odd number, the extra padding is added at the end for `'SAME'` and at the
          beginning for `'SAME_LOWER'`.
        lhs_dilation: `None`, or a sequence of `n` integers, giving the dilation
          factor to apply in each spatial dimension of `lhs`. LHS dilation is also
          known as transposed convolution.
        rhs_dilation: `None`, or a sequence of `n` integers, giving the dilation
          factor to apply in each spatial dimension of `rhs`. RHS dilation is also
          known as atrous convolution.
        dimension_numbers: either `None`, a ``ConvDimensionNumbers`` object, or a
          3-tuple ``(lhs_spec, rhs_spec, out_spec)``, where each element is a string
          of length `n+2`.
        feature_group_count: integer, default 1. See XLA HLO docs.
        batch_group_count: integer, default 1. See XLA HLO docs.
        precision: Optional. Either ``None``, which means the default precision for
          the backend, a :class:`~jax.lax.Precision` enum value
          (``Precision.DEFAULT``, ``Precision.HIGH`` or ``Precision.HIGHEST``), a
          string (e.g. 'highest' or 'fastest', see the
          ``jax.default_matmul_precision`` context manager), or a tuple of two
          :class:`~jax.lax.Precision` enums or strings indicating precision of
          ``lhs`` and ``rhs``.
        preferred_element_type: Optional. Either ``None``, which means the default
          accumulation type for the input types, or a datatype, indicating to
          accumulate results to and return a result with that datatype.
  
      Returns:
        An array containing the convolution result.
  
      In the string case of ``dimension_numbers``, each character identifies by
      position:
  
      - the batch dimensions in ``lhs``, ``rhs``, and the output with the character
        'N',
      - the feature dimensions in `lhs` and the output with the character 'C',
      - the input and output feature dimensions in rhs with the characters 'I'
        and 'O' respectively, and
      - spatial dimension correspondences between lhs, rhs, and the output using
        any distinct characters.
  
      For example, to indicate dimension numbers consistent with the ``conv``
      function with two spatial dimensions, one could use ``('NCHW', 'OIHW',
      'NCHW')``. As another example, to indicate dimension numbers consistent with
      the TensorFlow Conv2D operation, one could use ``('NHWC', 'HWIO', 'NHWC')``.
      When using the latter form of convolution dimension specification, window
      strides are associated with spatial dimension character labels according to
      the order in which the labels appear in the ``rhs_spec`` string, so that
      ``window_strides[0]`` is matched with the dimension corresponding to the first
      character appearing in rhs_spec that is not ``'I'`` or ``'O'``.
  
      If ``dimension_numbers`` is ``None``, the default is ``('NCHW', 'OIHW',
      'NCHW')`` (for a 2D convolution).
      """
      dnums = conv_dimension_numbers(
          lhs.shape, rhs.shape, dimension_numbers
      )
      if lhs_dilation is None:
          lhs_dilation = (1,) * (lhs.ndim - 2)
      elif isinstance(padding, str) and not len(
          lhs_dilation
      ) == lhs_dilation.count(1):
          raise ValueError(
              "String padding is not implemented for transposed convolution "
              "using this op. Please either exactly specify the required padding or "
              "use conv_transpose."
          )
      if rhs_dilation is None:
          rhs_dilation = (1,) * (rhs.ndim - 2)
      if isinstance(padding, str):
          lhs_perm, rhs_perm, _ = dnums
          rhs_shape = np.take(rhs.shape, rhs_perm)[2:]  # type: ignore[index]
          effective_rhs_shape = [
              core.dilate_dim(k, r)
              for k, r in zip(rhs_shape, rhs_dilation)
          ]
          padding = lax.padtype_to_pads(
              np.take(lhs.shape, lhs_perm)[2:],
              effective_rhs_shape,  # type: ignore[index]
              window_strides,
              padding,
          )
      else:
          try:
              padding = tuple(
                  (operator.index(lo), operator.index(hi))
                  for lo, hi in padding
              )
          except (ValueError, TypeError) as e:
              raise ValueError(
                  "padding argument to conv_general_dilated should be a string or a "
                  f"sequence of (low, high) pairs, got {padding}"
              ) from e
  
      preferred_element_type = (
          None
          if preferred_element_type is None
          else dtypes.canonicalize_dtype(
              np.dtype(preferred_element_type)
          )
      )
      return conv_general_dilated_p.bind(
          lhs,
          rhs,
          window_strides=tuple(window_strides),
          padding=tuple(padding),
          lhs_dilation=tuple(lhs_dilation),
          rhs_dilation=tuple(rhs_dilation),
          dimension_numbers=dnums,
          feature_group_count=feature_group_count,
          batch_group_count=batch_group_count,
          precision=lax.canonicalize_precision(precision),
          preferred_element_type=preferred_element_type,
      )
  
imports: from __future__ import annotations
  from collections.abc import Sequence
  from functools import partial
  import operator
  from typing import NamedTuple, Union
  import numpy
  from jax._src import core
  from jax._src import dtypes
  from jax._src import util
  from jax._src.interpreters import ad
  from jax._src.interpreters import batching
  from jax._src.interpreters import mlir
  from jax._src.lax import lax
  from jax._src.lib.mlir.dialects import hlo
  from jax._src.typing import Array, DTypeLike
label_desc: Use image node_id 1 for calling a global function with example usage: conv_general_dilated(lhs, rhs, window_strides, padding, lhs_dilation, rhs_dilation, dimension_numbers, feature_group_count, batch_group_count, precision, preferred_element_type) and returns: conv_general_dilated_p