tf.contrib.distributions.fill_triangular

Creates a (batch of) triangular matrix from a vector of inputs.

tf.contrib.distributions.fill_triangular(
    x, upper=False, name=None
)

Created matrix can be lower- or upper-triangular. (It is more efficient to create the matrix as upper or lower, rather than transpose.)

Triangular matrix elements are filled in a clockwise spiral. See example, below.

If x.get_shape() is [b1, b2, ..., bB, d] then the output shape is [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:

fill_triangular([1, 2, 3, 4, 5, 6])
# ==> [[4, 0, 0],
#      [6, 5, 0],
#      [3, 2, 1]]

fill_triangular([1, 2, 3, 4, 5, 6], upper=True)
# ==> [[1, 2, 3],
#      [0, 5, 6],
#      [0, 0, 4]]

For comparison, a pure numpy version of this function can be found in util_test.py, function _fill_triangular.

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
tril	Tensor with lower (or upper) triangular elements filled from x.

Raises
ValueError	if x cannot be mapped to a triangular matrix.