title: Possible tensorflow cholesky_solve inconsistency?
body: <p>I am trying to solve a linear system of equations using <a href="https://www.tensorflow.org/versions/r0.11/api_docs/python/math_ops/matrix_math_functions#cholesky_solve" rel="nofollow noreferrer">tensorflow.cholesky_solve</a> and I'm getting some unexpected results.</p>
  
  <p>I wrote a script to compare the output of a very simple linear system with simple matrix inversion a la <a href="https://www.tensorflow.org/versions/r0.11/api_docs/python/math_ops/matrix_math_functions#matrix_inverse" rel="nofollow noreferrer">tensorflow.matrix_inverse</a>, the non-cholesky based matrix equation solver <a href="https://www.tensorflow.org/versions/r0.11/api_docs/python/math_ops/matrix_math_functions#matrix_solve" rel="nofollow noreferrer">tensorflow.matrix_solve</a>, and <code>tensorflow.cholesky_solve</code>. </p>
  
  <p>According to my understanding of the docs I've linked, these three cases should all yield a solution of the identity matrix divided by 2, but this is not the case for <code>tensorflow.cholesky_solve</code>. Perhaps I'm misunderstanding the docs? </p>
  
  <pre><code>import tensorflow as tf
  
  I = tf.eye(2, dtype=tf.float32)
  X = 2 * tf.eye(2, dtype=tf.float32)
  X_inv = tf.matrix_inverse(X)
  X_solve = tf.matrix_solve(X, I)
  X_chol_solve = tf.cholesky_solve(tf.cholesky(X), I)
  
  with tf.Session() as sess:
      for x in [X_inv, X_solve, X_chol_solve]:
          print('{}:\n{}'.format(x.name, sess.run(x)))
          print
  </code></pre>
  
  <p>yielding output:</p>
  
  <pre><code>MatrixInverse:0:
  [[ 0.5  0. ]
   [ 0.   0.5]]
  
  MatrixSolve:0:
  [[ 0.5  0. ]
   [ 0.   0.5]]
  
  cholesky_solve/MatrixTriangularSolve_1:0:
  [[ 1.  0.]
   [ 0.  1.]]
  
  
  Process finished with exit code 0
  </code></pre>