code: def forward(self, inputs):
      self.retain_inputs(())
      gy = inputs[0]
      xp = backend.get_array_module(gy)
      gy_shape = gy.shape
      b, c = gy_shape[:2]
      g = self.groups
      C = c // g
      spatial_axis, m = _calc_axis_and_m(gy_shape, b)
      arange_C = numpy.arange(C)
      diag_indices = slice(None), arange_C, arange_C
  
      gy_hat = gy.transpose((1, 0) + spatial_axis).reshape(g, C, m)
  
      eigvectors = self.eigvectors
      eigvals = self.eigvals
      y_hat_pca = self.y_hat_pca
      gy_hat_pca = _matmul(eigvectors.transpose(0, 2, 1), gy_hat, xp)
      f = gy_hat_pca.mean(axis=2, keepdims=True)
  
      K = eigvals[:, :, None] - eigvals[:, None, :]
      valid = (
          K != 0
      )  # to avoid nan, use eig_i != eig_j instead of i != j
      K[valid] = xp.reciprocal(K[valid])
  
      V = _diag(eigvals, xp)
      V_sqrt = _diag(eigvals**0.5, xp)
      V_invsqrt = _diag(eigvals**-0.5, xp)
  
      F_c = _matmul(
          gy_hat_pca, y_hat_pca.transpose(0, 2, 1), xp
      ) / gy.dtype.type(m)
      M = xp.zeros_like(F_c)
      M[diag_indices] = F_c[diag_indices]
  
      mat = K.transpose(0, 2, 1) * (
          _matmul(V, F_c.transpose(0, 2, 1), xp)
          + _matmul(_matmul(V_sqrt, F_c, xp), V_sqrt, xp)
      )
      S = mat + mat.transpose(0, 2, 1)
      R = (
          gy_hat_pca
          - f
          + _matmul((S - M).transpose(0, 2, 1), y_hat_pca, xp)
      )
      gx_hat = _matmul(
          _matmul(R.transpose(0, 2, 1), V_invsqrt, xp),
          eigvectors.transpose(0, 2, 1),
          xp,
      ).transpose(0, 2, 1)
  
      gx = gx_hat.reshape((c, b) + gy_shape[2:]).transpose(
          (1, 0) + spatial_axis
      )
  
      self.retain_outputs(())
      return (gx,)
  
imports: import numpy
  from chainer import backend
  from chainer import function_node
  from chainer.utils import argument
  from chainer.utils import type_check
label_desc: Use image node_id 2 for calling the DecorrelatedBatchNormalizationGrad obj's underlying member method code with example usage: obj.forward(inputs) and returns: gx