Create lower triangular with unit diagonal matrix in TensorFlow

Question

I would like to create a lower triangular matrix with unit diagonal elements from a vector.

From a vector

[a_21, a_31, a_32, ..., a_N1, ... , a_N(N-1)]

how to convert it into a lower triangular matrix with unit diagonal elements of the form,

[[1, 0, ..., 0], [a_21, 1, ..., 0], [a_31, a_32, 1, ..., 0], ..., [a_N1, a_N2, ... , a_N(N-1), 1]]

So far with NumPy

import numpy
A = np.eye(N)
idx = np.tril_indices(N, k=-1)
A[idx] = X

The TensorFlow, however, doesn't support item assignment. I think fill_triangular or tf.reshape help solve the problem, but I'm not sure how to do it.

Answer 1

I found the similar question and answer: Packing array into lower triangular of a tensor

Based on the page above, I made a function which transform a vector into a lower triangular with unit diagonal elements:

def flat_to_mat_TF(vector, n):
    idx = list(zip(*np.tril_indices(n, k=-1)))
    idx = tf.constant([list(i) for i in idx], dtype=tf.int64)
    values = tf.constant(vector, dtype=tf.float32)

    dense = tf.sparse_to_dense(sparse_indices=idx, output_shape=[n, n], \
                               sparse_values=values, default_value=0, \
                               validate_indices=True)
    mat = tf.matrix_set_diag(dense, tf.cast(tf.tile([1], [n]), dtype=tf.float32))
    return mat

If the input vector is already a Tensor, values = tf.constant() could be eliminated.