code: def forward(self, inputs):
      self.retain_inputs(())
      x, mean, projection, gy = inputs
      xp = backend.get_array_module(x)
      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)
  
      gy_hat = gy.transpose((1, 0) + spatial_axis).reshape(g, C, m)
      x_hat = x.transpose((1, 0) + spatial_axis).reshape(g, C, m)
      gy_hat_pca = _matmul(projection.transpose(0, 2, 1), gy_hat, xp)
      gx = gy_hat_pca.reshape((c, b) + gy_shape[2:]).transpose(
          (1, 0) + spatial_axis
      )
      rhs = x_hat - xp.expand_dims(mean, axis=2)
      gprojection = _matmul(
          (x_hat - rhs).transpose(0, 2, 1), gy_hat, xp
      )
      gmean = -gy_hat_pca[..., 0]
      self.retain_outputs(())
      return gx, gmean, gprojection
  
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 FixedDecorrelatedBatchNormalizationGrad obj's underlying member method code with example usage: obj.forward(inputs) and returns: gx,  gmean,  gprojection