class_docstr: Linear mixing of the latent GPs to form the output.
class_docstr_tok: ["Linear","mixing","of","the","latent","GPs","to","form","the","output","."]
code: def K(
      self,
      X: TensorType,
      X2: Optional[TensorType] = None,
      full_output_cov: bool = True,
  ) -> tf.Tensor:
      Kxx = self.Kgg(X, X2)
      if X2 is None:
          cs(Kxx, "[L, batch..., N, N]")
          rank = tf.rank(X) - 1
          ones = tf.ones((rank + 1,), dtype=tf.int32)
          P = tf.shape(self.W)[0]
          L = tf.shape(self.W)[1]
          W_broadcast = cs(
              tf.reshape(self.W, tf.concat([[P, L], ones], 0)),
              "[P, L, broadcast batch..., 1, 1]",
          )
          KxxW = cs(
              Kxx[None, ...] * W_broadcast, "[P, L, batch..., N, N]"
          )
          if full_output_cov:
              # return tf.einsum('lnm,kl,ql->nkmq', Kxx, self.W, self.W)
              WKxxW = cs(
                  tf.tensordot(self.W, KxxW, [[1], [1]]),
                  "[P, P, batch..., N, N]",
              )
              perm = tf.concat(
                  [
                      2 + tf.range(rank),
                      [0, 2 + rank, 1],
                  ],
                  0,
              )
              return cs(
                  tf.transpose(WKxxW, perm), "[batch..., N, P, N, P]"
              )
      else:
          cs(Kxx, "[L, batch..., N, batch2..., N2]")
          rank = tf.rank(X) - 1
          rank2 = tf.rank(X2) - 1
          ones12 = tf.ones((rank + rank2,), dtype=tf.int32)
          P = tf.shape(self.W)[0]
          L = tf.shape(self.W)[1]
          W_broadcast = cs(
              tf.reshape(self.W, tf.concat([[P, L], ones12], 0)),
              "[P, L, broadcast batch..., 1, broadcast batch2..., 1]",
          )
          KxxW = cs(
              Kxx[None, ...] * W_broadcast,
              "[P, L, batch..., N, batch2..., N2]",
          )
          if full_output_cov:
              # return tf.einsum('lnm,kl,ql->nkmq', Kxx, self.W, self.W)
              WKxxW = cs(
                  tf.tensordot(self.W, KxxW, [[1], [1]]),
                  "[P, P, batch..., N, batch2..., N2]",
              )
              perm = tf.concat(
                  [
                      2 + tf.range(rank),
                      [0],
                      2 + rank + tf.range(rank2),
                      [1],
                  ],
                  0,
              )
              return cs(
                  tf.transpose(WKxxW, perm),
                  "[batch..., N, P, batch2..., N2, P]",
              )
      # return tf.einsum('lnm,kl,kl->knm', Kxx, self.W, self.W)
      return tf.reduce_sum(W_broadcast * KxxW, axis=1)
  
imports: import abc
  from typing import Optional, Sequence, Tuple
  import tensorflow
  from check_shapes import check_shape
  from check_shapes import check_shapes, inherit_check_shapes
  from ...base import Parameter, TensorType
  from ..base import Combination, Kernel
label_desc: Use image node_id 5 for calling the LinearCoregionalization obj's underlying member method code with example usage: obj.K(X, X2, full_output_cov) and returns: tf, cs, cs