code: def check_kamada_kawai_costfn(self, pos, invdist, meanwt, dim):
      costfn = nx.drawing.layout._kamada_kawai_costfn
  
      cost, grad = costfn(
          pos.ravel(), np, invdist, meanweight=meanwt, dim=dim
      )
  
      expected_cost = 0.5 * meanwt * np.sum(np.sum(pos, axis=0) ** 2)
      for i in range(pos.shape[0]):
          for j in range(i + 1, pos.shape[0]):
              diff = np.linalg.norm(pos[i] - pos[j])
              expected_cost += (diff * invdist[i][j] - 1.0) ** 2
  
      assert cost == pytest.approx(expected_cost, abs=1e-7)
  
      dx = 1e-4
      for nd in range(pos.shape[0]):
          for dm in range(pos.shape[1]):
              idx = nd * pos.shape[1] + dm
              ps = pos.flatten()
  
              ps[idx] += dx
              cplus = costfn(
                  ps, np, invdist, meanweight=meanwt, dim=pos.shape[1]
              )[0]
  
              ps[idx] -= 2 * dx
              cminus = costfn(
                  ps, np, invdist, meanweight=meanwt, dim=pos.shape[1]
              )[0]
  
              assert grad[idx] == pytest.approx(
                  (cplus - cminus) / (2 * dx), abs=1e-5
              )
  
imports: import pytest
  import networkx
label_desc: Use image node_id 25 for calling the TestLayout obj's underlying member method code with example usage: obj.check_kamada_kawai_costfn(pos, invdist, meanwt, dim) without return types