code: def forward(self, inputs):
      self.retain_inputs(())
      x = inputs[0]
      xp = backend.get_array_module(x)
      x_shape = x.shape
      b, c = x_shape[:2]
      g = self.groups
      C = c // g
      spatial_axis, m = _calc_axis_and_m(x_shape, b)
  
      # (g, C, m)
      x_hat = x.transpose((1, 0) + spatial_axis).reshape(g, C, m)
      mean = x_hat.mean(axis=2, keepdims=True)
      x_hat = x_hat - mean
      self.eps = x.dtype.type(self.eps)
  
      eps_matrix = self.eps * xp.eye(C, dtype=x.dtype)
      cov = (
          _matmul(x_hat, x_hat.transpose(0, 2, 1), xp) / x.dtype.type(m)
          + eps_matrix
      )
      # (g, C), (g, C, C)
      self.eigvals, self.eigvectors = _eigh(cov, xp)
      U = _matmul(
          _diag(self.eigvals**-0.5, xp),
          self.eigvectors.transpose(0, 2, 1),
          xp,
      )
      self.y_hat_pca = _matmul(U, x_hat, xp)  # PCA whitening
      # ZCA whitening
      y_hat = _matmul(self.eigvectors, self.y_hat_pca, xp)
  
      y = y_hat.reshape((c, b) + x_shape[2:]).transpose(
          (1, 0) + spatial_axis
      )
  
      # Update running statistics
      if self.running_mean is not None:
          mean = mean.squeeze(axis=2)
          self.running_mean *= self.decay
          self.running_mean += (1 - self.decay) * mean
      if self.running_projection is not None:
          adjust = m / max(m - 1.0, 1.0)  # unbiased estimation
          self.running_projection *= self.decay
          projection = _matmul(self.eigvectors, U, xp)
          self.running_projection += (
              (1 - self.decay) * adjust * projection
          )
  
      return (y,)
  
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 3 for calling the DecorrelatedBatchNormalization obj's underlying member method code with example usage: obj.forward(inputs) and returns: y