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tf.contrib.distributions.fill_triangular

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

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.

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.

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

ValueError if x cannot be mapped to a triangular matrix.