code: def reduce_dm(
      density_matrix, indices, check_state=False, c_dtype="complex128"
  ):
      """Compute the density matrix from a state represented with a density matrix.
  
      Args:
          density_matrix (tensor_like): 2D or 3D density matrix tensor. This tensor should be of size ``(2**N, 2**N)`` or
              ``(batch_dim, 2**N, 2**N)``, for some integer number of wires``N``.
          indices (list(int)): List of indices in the considered subsystem.
          check_state (bool): If True, the function will check the state validity (shape and norm).
          c_dtype (str): Complex floating point precision type.
  
      Returns:
          tensor_like: Density matrix of size ``(2**len(indices), 2**len(indices))`` or ``(batch_dim, 2**len(indices), 2**len(indices))``
  
      .. seealso:: :func:`pennylane.math.reduce_statevector`, and :func:`pennylane.density_matrix`
  
      **Example**
  
      >>> x = np.array([[1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]])
      >>> reduce_dm(x, indices=[0])
      [[1.+0.j 0.+0.j]
       [0.+0.j 0.+0.j]]
  
      >>> y = [[0.5, 0, 0.5, 0], [0, 0, 0, 0], [0.5, 0, 0.5, 0], [0, 0, 0, 0]]
      >>> reduce_dm(y, indices=[0])
      [[0.5+0.j 0.5+0.j]
       [0.5+0.j 0.5+0.j]]
  
      >>> reduce_dm(y, indices=[1])
      [[1.+0.j 0.+0.j]
       [0.+0.j 0.+0.j]]
  
      >>> z = tf.Variable([[1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]], dtype=tf.complex128)
      >>> reduce_dm(x, indices=[1])
      tf.Tensor(
      [[1.+0.j 0.+0.j]
       [0.+0.j 0.+0.j]], shape=(2, 2), dtype=complex128)
  
      >>> x = np.array([[[1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]],
      ...               [[0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]])
      >>> reduce_dm(x, indices=[1])
      array([[[1.+0.j, 0.+0.j],
              [0.+0.j, 0.+0.j]],
             [[0.+0.j, 0.+0.j],
              [0.+0.j, 1.+0.j]]])
      """
      density_matrix = cast(density_matrix, dtype=c_dtype)
  
      if check_state:
          _check_density_matrix(density_matrix)
  
      if len(np.shape(density_matrix)) == 2:
          batch_dim, dim = None, density_matrix.shape[0]
      else:
          batch_dim, dim = density_matrix.shape[:2]
  
      num_indices = int(np.log2(dim))
      consecutive_indices = list(range(num_indices))
  
      # Return the full density matrix if all the wires are given, potentially permuted
      if len(indices) == num_indices:
          return _permute_dense_matrix(
              density_matrix, consecutive_indices, indices, batch_dim
          )
  
      if batch_dim is None:
          density_matrix = qml.math.stack([density_matrix])
  
      # Compute the partial trace
      traced_wires = [
          x for x in consecutive_indices if x not in indices
      ]
      density_matrix = _batched_partial_trace(
          density_matrix, traced_wires
      )
  
      if batch_dim is None:
          density_matrix = density_matrix[0]
  
      # Permute the remaining indices of the density matrix
      return _permute_dense_matrix(
          density_matrix, sorted(indices), indices, batch_dim
      )
  
imports: import itertools
  import functools
  from string import ascii_letters
  from autoray import numpy
  from numpy import float64
  import pennylane
  from .None import single_dispatch
  from .multi_dispatch import diag, dot, scatter_element_add, einsum, get_interface
  from .utils import is_abstract, allclose, cast, convert_like, cast_like
  from .matrix_manipulation import _permute_dense_matrix
label_desc: Use image node_id 3 for calling a global function with example usage: reduce_dm(density_matrix, indices, check_state, c_dtype) and returns: _permute_dense_matrix, _permute_dense_matrix