code: def hungarian_single(cost):
      """Hungarian matcher for a single example."""
  
      is_transpose = cost.shape[0] > cost.shape[1]
      if is_transpose:
          cost = cost.T
  
      n, m = cost.shape
      one_hot_m = jnp.eye(m + 1)
  
      def row_scan_fn(state, i):
          """Loop over the rows of the cost matrix."""
          u, v, parent = state
  
          # parent[0] = i; note that i runs from 1 to n inclusive
          parent = jax.lax.dynamic_update_index_in_dim(
              parent, i, 0, axis=0
          )
  
          def dfs_body_fn(state):
              # Row potential, column potential, used array, support array, path array
              # column index j0.
              u, v, used, minv, way, j0 = state
  
              # Mark column as used
              # used = jax.lax.dynamic_update_index_in_dim(used, True, j0, axis=0)
              # used = jnp.logical_or(used, jnp.arange(m + 1) == j0)
              used = jnp.logical_or(used, one_hot_m[j0])
              used_slice = used[1:]
  
              # Row paired to column j0
              i0 = parent[j0]
  
              # Update minv and path to it
              cur = cost[i0 - 1, :] - u[i0] - v[1:]
              cur = jnp.where(used_slice, jnp.full_like(cur, 1e10), cur)
              way = jnp.where(cur < minv, jnp.full_like(way, j0), way)
              minv = jnp.where(cur < minv, cur, minv)
  
              # When finding an index with minimal minv, we need to mask out the visited
              # rows
              masked_minv = jnp.where(
                  used_slice, jnp.full_like(minv, 1e10), minv
              )
              j1 = jnp.argmin(masked_minv) + 1
              delta = jnp.min(
                  minv, initial=1e10, where=jnp.logical_not(used_slice)
              )
  
              # Update potentials
              indices = jnp.where(
                  used, parent, n + 1
              )  # deliberately out of bounds
              u = u.at[indices].add(delta)
              v = jnp.where(used, v - delta, v)
              minv = jnp.where(
                  jnp.logical_not(used_slice), minv - delta, minv
              )
  
              return (u, v, used, minv, way, j1)
  
          def dfs_cond_fn(state):
              _, _, _, _, _, j0 = state
              return parent[j0] != 0
  
          # Run the inner while loop (i.e. DFS)
          way = jnp.zeros((m,), dtype=jnp.int32)
          used = jnp.zeros((m + 1,), dtype=jnp.bool_)
          minv = jnp.full((m,), 1e10, dtype=jnp.float32)
          init_state = (u, v, used, minv, way, 0)
  
          state = jax.lax.while_loop(
              dfs_cond_fn, dfs_body_fn, init_state
          )
          u, v, _, _, way, j0 = state
  
          def update_parent_body_fn(state):
              """Update parents based on the DFS path."""
              parent, j0 = state
              j1 = way[j0 - 1]
              parent = jax.lax.dynamic_update_index_in_dim(
                  parent, parent[j1], j0, axis=0
              )
              return (parent, j1)
  
          def update_parent_cond_fn(state):
              """Condition function counterpart."""
              _, j0 = state
              return j0 != 0
  
          # Backtrack the DFS path
          init_state = (parent, j0)
          parent, _ = jax.lax.while_loop(
              update_parent_cond_fn, update_parent_body_fn, init_state
          )
  
          return (u, v, parent), None
  
      # Define the initial state
      u = jnp.zeros((n + 2,), dtype=jnp.float32)
      v = jnp.zeros((m + 1,), dtype=jnp.float32)
      parent = jnp.zeros((m + 1,), dtype=jnp.int32)
  
      init_state = (u, v, parent)
      (u, v, parent), _ = jax.lax.scan(
          row_scan_fn, init_state, jnp.arange(1, n + 1)
      )
  
      # -v[0] is the matching cost, but not returned to match the signature all
      # other matchers.
      if n != m:
          # This is a costly operation, so skip it when possible (i.e. for square cost
          # matrices).
          parent, indices = jax.lax.top_k(parent[1:], n)
      else:
          parent, indices = parent[1:], jnp.arange(n)
      parent = parent - 1  # Switch back to 0-based indexing.
  
      if is_transpose:
          return jnp.stack([indices, parent], axis=0)
      return jnp.stack([parent, indices], axis=0)
  
label_desc: Use image node_id 1 for calling a global function with example usage: hungarian_single(cost) and returns: jnp, u,  v,  parent,  None, jnp, u,  v,  used,  minv,  way,  j1, unknown, parent,  j1, unknown