Packing array into lower triangular of a tensor

Question

I would like to pack an array of shape (..., n * (n - 1) / 2) into the lower triangular part of a tensor with shape (..., n, n) where ... denotes an arbitrary shape. In numpy, I would implement it as

import numpy as np

# Create the array to store data in
arbitrary_shape = (10, 11, 12)
n = 5
target = np.zeros(arbitrary_shape + (n, n))
# Create the source array
source = np.random.normal(0, 1, arbitrary_shape + (n * (n - 1) / 2,))
# Create indices and set values
u, v = np.tril_indices(n, -1)
target[..., u, v] = source
# Check that everything went ok
print target[0, 0, 0]

So far, I've been able to achieve something similar in tensorflow using a combination of transpose, reshape and scatter_update but it feels clumsy.

import tensorflow as tf

# Create the source array
source = np.random.normal(0, 1, (n * (n - 1) / 2,) + arbitrary_shape)

sess = tf.InteractiveSession()

# Create a flattened representation
target = tf.Variable(np.zeros((n * n,) + arbitrary_shape))
# Assign the values
target = tf.scatter_update(target, u * n + v, source)
# Reorder the axes and reshape into a square matrix along the last dimension
target = tf.transpose(target, (1, 2, 3, 0))
target = tf.reshape(target, arbitrary_shape + (n, n))

# Initialise variables and check results
sess.run(tf.initialize_all_variables())
print target.eval()[0, 0, 0]

sess.close()

Is there a better way to achieve this?

Answer 1

I realise this is a bit late, but I've been attempting to load a lower triangular matrix, and I got it working using sparse_to_dense:

import tensorflow as tf
import numpy as np

session = tf.InteractiveSession()

n = 4 # Number of dimensions of matrix

# Get pairs of indices of positions
indices = list(zip(*np.tril_indices(n)))
indices = tf.constant([list(i) for i in indices], dtype=tf.int64)

# Test values to load into matrix
test = tf.constant(np.random.normal(0, 1, int(n*(n+1)/2)), dtype=tf.float64)

# Can pass in list of values and indices to tf.sparse_to_dense 
# and it will return a dense matrix
dense = tf.sparse_to_dense(sparse_indices=indices, output_shape=[n, n], \
                           sparse_values=test, default_value=0, \
                           validate_indices=True)

sess.close()

Answer 2

You can do this with fill_lower_triangular:

import numpy as np
import tensorflow as tf
from tensorflow.python.ops.distributions.util import fill_lower_triangular
n = 4
coeffs = tf.constant(np.random.normal(0, 1, int(n*(n+1)/2)), dtype=tf.float64)
lower_diag = fill_lower_triangular(coeffs)