code: def initialize_einmix(
      self,
      pattern: str,
      weight_shape: str,
      bias_shape: Optional[str],
      axes_lengths: dict,
  ):
      left_pattern, right_pattern = pattern.split("->")
      left = ParsedExpression(left_pattern)
      right = ParsedExpression(right_pattern)
      weight = ParsedExpression(weight_shape)
      _report_axes(
          set.difference(
              right.identifiers,
              {*left.identifiers, *weight.identifiers},
          ),
          "Unrecognized identifiers on the right side of EinMix {}",
      )
  
      if left.has_ellipsis or right.has_ellipsis or weight.has_ellipsis:
          raise EinopsError(
              "Ellipsis is not supported in EinMix (right now)"
          )
      if any(
          x.has_non_unitary_anonymous_axes
          for x in [left, right, weight]
      ):
          raise EinopsError(
              "Anonymous axes (numbers) are not allowed in EinMix"
          )
      if "(" in weight_shape or ")" in weight_shape:
          raise EinopsError(
              f"Parenthesis is not allowed in weight shape: {weight_shape}"
          )
  
      pre_reshape_pattern = None
      pre_reshape_lengths = None
      post_reshape_pattern = None
      if any(len(group) != 1 for group in left.composition):
          names: List[str] = []
          for group in left.composition:
              names += group
          composition = " ".join(names)
          pre_reshape_pattern = f"{left_pattern}->{composition}"
          pre_reshape_lengths = {
              name: length
              for name, length in axes_lengths.items()
              if name in names
          }
  
      if any(len(group) != 1 for group in right.composition):
          names = []
          for group in right.composition:
              names += group
          composition = " ".join(names)
          post_reshape_pattern = f"{composition}->{right_pattern}"
  
      self._create_rearrange_layers(
          pre_reshape_pattern,
          pre_reshape_lengths,
          post_reshape_pattern,
          {},
      )
  
      for axis in weight.identifiers:
          if axis not in axes_lengths:
              raise EinopsError(
                  "Dimension {} of weight should be specified".format(
                      axis
                  )
              )
      _report_axes(
          set.difference(
              set(axes_lengths),
              {*left.identifiers, *weight.identifiers},
          ),
          "Axes {} are not used in pattern",
      )
      _report_axes(
          set.difference(
              weight.identifiers,
              {*left.identifiers, *right.identifiers},
          ),
          "Weight axes {} are redundant",
      )
      if len(weight.identifiers) == 0:
          warnings.warn(
              "EinMix: weight has no dimensions (means multiplication by a number)"
          )
  
      _weight_shape = [
          axes_lengths[axis] for axis, in weight.composition
      ]
      # single output element is a combination of fan_in input elements
      _fan_in = _product(
          [
              axes_lengths[axis]
              for axis, in weight.composition
              if axis not in right.identifiers
          ]
      )
      if bias_shape is not None:
          if not isinstance(bias_shape, str):
              raise EinopsError(
                  "bias shape should be string specifying which axes bias depends on"
              )
          bias = ParsedExpression(bias_shape)
          _report_axes(
              set.difference(bias.identifiers, right.identifiers),
              "Bias axes {} not present in output",
          )
          _report_axes(
              set.difference(bias.identifiers, set(axes_lengths)),
              "Sizes not provided for bias axes {}",
          )
  
          _bias_shape = []
          for axes in right.composition:
              for axis in axes:
                  if axis in bias.identifiers:
                      _bias_shape.append(axes_lengths[axis])
                  else:
                      _bias_shape.append(1)
      else:
          _bias_shape = None
  
      weight_bound = (3 / _fan_in) ** 0.5
      bias_bound = (1 / _fan_in) ** 0.5
      self._create_parameters(
          _weight_shape, weight_bound, _bias_shape, bias_bound
      )
  
      # rewrite einsum expression with single-letter latin identifiers so that
      # expression will be understood by any framework
      mapped_identifiers = {
          *left.identifiers,
          *right.identifiers,
          *weight.identifiers,
      }
      mapping2letters = {
          k: letter
          for letter, k in zip(
              string.ascii_lowercase, mapped_identifiers
          )
      }
  
      def write_flat(axes: list):
          return "".join(mapping2letters[axis] for axis in axes)
  
      self.einsum_pattern: str = "{},{}->{}".format(
          write_flat(left.flat_axes_order()),
          write_flat(weight.flat_axes_order()),
          write_flat(right.flat_axes_order()),
      )
  
file_path: einops/einops/layers/_einmix.py
imports: from typing import Any, List, Optional, Dict
  from einops import EinopsError
  from einops.parsing import ParsedExpression
  import warnings
  import string
  from ..einops import _product
label_desc: Use image node_id 2 for calling the _EinmixMixin obj's underlying member method code with example usage: obj.initialize_einmix(pattern, weight_shape, bias_shape, axes_lengths) and returns: str