code: def create_sinusoidal_positions(num_pos, dim):
      inv_freq = 1.0 / (10000 ** (np.arange(0, dim, 2) / dim))
      sinusoid_inp = np.einsum(
          "i , j -> i j", np.arange(num_pos), inv_freq
      ).astype("float32")
      sin, cos = np.sin(sinusoid_inp), np.cos(sinusoid_inp)
  
      sentinel = dim // 2 + dim % 2
      out = np.zeros((num_pos, dim))
      out[:, 0:sentinel] = sin
      out[:, sentinel:] = cos
  
      return jnp.array(out)
  
imports: from functools import partial
  from typing import Optional, Tuple
  import flax.linen
  import jax
  import jax.numpy
  import numpy
  from flax.core.frozen_dict import FrozenDict, freeze, unfreeze
  from flax.linen import combine_masks, make_causal_mask
  from flax.linen.attention import dot_product_attention_weights
  from flax.traverse_util import flatten_dict, unflatten_dict
  from jax import lax
  from ...modeling_flax_outputs import FlaxBaseModelOutput, FlaxCausalLMOutput
  from ...modeling_flax_utils import ACT2FN, FlaxPreTrainedModel, append_call_sample_docstring
  from ...utils import add_start_docstrings, add_start_docstrings_to_model_forward, logging
  from .configuration_gptj import GPTJConfig
label_desc: Use image node_id 1 for calling a global function with example usage: create_sinusoidal_positions(num_pos, dim) and returns: jnp