Add fill_triangular_inverse, which flattens a triangular matrix in a way such that:

# Lower triangular matrix
x = tf.matrix_band_part(x, -1, 0)
x == fill_triangular(fill_triangular_inverse(x))
Code by srvasude@ which I'm submitting on his behalf.

PiperOrigin-RevId: 198623887

tensorflow/contrib/distributions/__init__.py

@@ -32,6 +32,7 @@ from tensorflow.contrib.distributions.python.ops.conditional_distribution import
 from tensorflow.contrib.distributions.python.ops.conditional_transformed_distribution import *
 from tensorflow.contrib.distributions.python.ops.deterministic import *
 from tensorflow.contrib.distributions.python.ops.distribution_util import fill_triangular
+from tensorflow.contrib.distributions.python.ops.distribution_util import fill_triangular_inverse
 from tensorflow.contrib.distributions.python.ops.distribution_util import matrix_diag_transform
 from tensorflow.contrib.distributions.python.ops.distribution_util import reduce_weighted_logsumexp
 from tensorflow.contrib.distributions.python.ops.distribution_util import softplus_inverse
@@ -156,6 +157,7 @@ _allowed_symbols = [
     'kl_divergence',
     'RegisterKL',
     'fill_triangular',
+    'fill_triangular_inverse',
     'matrix_diag_transform',
     'reduce_weighted_logsumexp',
     'softplus_inverse',

tensorflow/python/kernel_tests/distributions/util_test.py

@@ -814,6 +814,30 @@ class FillTriangularTest(test.TestCase):
     self._run_test(self._rng.randn(2, 3, int(7*8/2)), upper=True)
 
 
+class FillTriangularInverseTest(FillTriangularTest):
+
+  def _run_test(self, x_, use_deferred_shape=False, **kwargs):
+    x_ = np.asarray(x_)
+    with self.test_session() as sess:
+      static_shape = None if use_deferred_shape else x_.shape
+      x_pl = array_ops.placeholder_with_default(x_, shape=static_shape)
+      zeros_like_x_pl = (x_pl * array_ops.stop_gradient(x_pl - 1.)
+                         - array_ops.stop_gradient(x_pl * (x_pl - 1.)))
+      x = x_pl + zeros_like_x_pl
+      actual = du.fill_triangular(x, **kwargs)
+      inverse_actual = du.fill_triangular_inverse(actual, **kwargs)
+
+      inverse_actual_ = sess.run(
+          inverse_actual,
+          feed_dict={x_pl: x_})
+
+    if use_deferred_shape:
+      self.assertEqual(None, inverse_actual.shape)
+    else:
+      self.assertAllEqual(x_.shape, inverse_actual.shape)
+    self.assertAllEqual(x_, inverse_actual_)
+
+
 class ReduceWeightedLogSumExp(test.TestCase):
 
   def _reduce_weighted_logsumexp(self, logx, w, axis, keep_dims=False):

tensorflow/python/ops/distributions/util.py

@@ -824,8 +824,8 @@ def fill_triangular(x, upper=False, name=None):
   Triangular matrix elements are filled in a clockwise spiral. See example,
   below.
 
-  If `x.get_shape()` is `[b1, b2, ..., bK, d]` then the output shape is `[b1,
+  If `x.get_shape()` is `[b1, b2, ..., bB, d]` then the output shape is
-  b2, ..., bK, n, n]` where `n` is such that `d = n(n+1)/2`, i.e.,
+  `[b1, b2, ..., bB, n, n]` where `n` is such that `d = n(n+1)/2`, i.e.,
   `n = int(np.sqrt(0.25 + 2. * m) - 0.5)`.
 
   Example:
@@ -914,7 +914,7 @@ def fill_triangular(x, upper=False, name=None):
     #   = 2 (n**2 / 2 + n / 2) - n**2
     #   = n**2 + n - n**2
     #   = n
-    ndims = array_ops.rank(x) if x.shape.ndims is None else x.shape.ndims
+    ndims = prefer_static_rank(x)
     if upper:
       x_list = [x, array_ops.reverse(x[..., n:], axis=[ndims - 1])]
     else:
@@ -932,6 +932,74 @@ def fill_triangular(x, upper=False, name=None):
     return x
 
 
+def fill_triangular_inverse(x, upper=False, name=None):
+  """Creates a vector from a (batch of) triangular matrix.
+
+  The vector is created from the lower-triangular or upper-triangular portion
+  depending on the value of the parameter `upper`.
+
+  If `x.shape` is `[b1, b2, ..., bB, n, n]` then the output shape is
+  `[b1, b2, ..., bB, d]` where `d = n (n + 1) / 2`.
+
+  Example:
+
+  ```python
+  fill_triangular_inverse(
+    [[4, 0, 0],
+     [6, 5, 0],
+     [3, 2, 1]])
+
+  # ==> [1, 2, 3, 4, 5, 6]
+
+  fill_triangular_inverse(
+    [[1, 2, 3],
+     [0, 5, 6],
+     [0, 0, 4]], upper=True)
+
+  # ==> [1, 2, 3, 4, 5, 6]
+  ```
+
+  Args:
+    x: `Tensor` representing lower (or upper) triangular elements.
+    upper: Python `bool` representing whether output matrix should be upper
+      triangular (`True`) or lower triangular (`False`, default).
+    name: Python `str`. The name to give this op.
+
+  Returns:
+    flat_tril: (Batch of) vector-shaped `Tensor` representing vectorized lower
+      (or upper) triangular elements from `x`.
+  """
+
+  with ops.name_scope(name, "fill_triangular_inverse", values=[x]):
+    x = ops.convert_to_tensor(x, name="x")
+    if x.shape.with_rank_at_least(2)[-1].value is not None:
+      n = np.int32(x.shape[-1].value)
+      m = np.int32((n * (n + 1)) // 2)
+      static_final_shape = x.shape[:-2].concatenate([m])
+    else:
+      n = array_ops.shape(x)[-1]
+      m = (n * (n + 1)) // 2
+      static_final_shape = x.shape.with_rank_at_least(2)[:-2].concatenate(
+          [None])
+    ndims = prefer_static_rank(x)
+    if upper:
+      initial_elements = x[..., 0, :]
+      triangular_portion = x[..., 1:, :]
+    else:
+      initial_elements = array_ops.reverse(x[..., -1, :], axis=[ndims - 2])
+      triangular_portion = x[..., :-1, :]
+    rotated_triangular_portion = array_ops.reverse(
+        array_ops.reverse(triangular_portion, axis=[ndims - 1]),
+        axis=[ndims - 2])
+    consolidated_matrix = triangular_portion + rotated_triangular_portion
+    end_sequence = array_ops.reshape(
+        consolidated_matrix,
+        array_ops.concat([array_ops.shape(x)[:-2], [n * (n - 1)]], axis=0))
+    y = array_ops.concat([initial_elements, end_sequence[..., :m - n]], axis=-1)
+    y.set_shape(static_final_shape)
+    return y
+
+
 def tridiag(below=None, diag=None, above=None, name=None):
   """Creates a matrix with values set above, below, and on the diagonal.