How to construct a matrix that contains all pairs of rows of a matrix in tensorflow

user_7934786 0
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I need to construct a matrix z that would contain combinations of pairs of rows of a matrix x.

x = tf.constant([[1, 3],
                 [2, 4],
                 [0, 2],
                 [0, 1]], dtype=tf.int32)

z=[[[1,2],
    [1,0],
    [1,0],
    [2,0],
    [2,0],
    [0,0]],
    [3,4],
    [3,2], 
    [3,1],
    [4,2],
    [4,1],
    [2,1]]]

It pairs each value with the rest of the values on that row.

I could not find any function or come up with a good idea to do that.

Update 1

So I need the final shape be 2*6*2 like the z above.

tensorflow python
2 Answers

Unfortunately, it's a bit more complex than one would like using tensorflow operators only. I would go with creating the indices for all combinations with a while_loop then use tf.gather to collect values:

import tensorflow as tf
x = tf.constant([[1, 3],
                 [2, 4],
                 [3, 2],
                 [0, 1]], dtype=tf.int32)
m = tf.constant([], shape=(0,2), dtype=tf.int32)
_, idxs = tf.while_loop(
  lambda i, m: i < tf.shape(x)[0] - 1,
  lambda i, m: (i + 1, tf.concat([m, tf.stack([tf.tile([i], (tf.shape(x)[0] - 1 - i,)), tf.range(i + 1, tf.shape(x)[0])], axis=1)], axis=0)),
  loop_vars=(0, m),
  shape_invariants=(tf.TensorShape([]), tf.TensorShape([None, 2])))
z = tf.reshape(tf.transpose(tf.gather(x, idxs), (2,0,1)), (-1, 2))

# <tf.Tensor: shape=(12, 2), dtype=int32, numpy=
# array([[1, 2],
#        [1, 3],
#        [1, 0],
#        [2, 3],
#        [2, 0],
#        [3, 0],
#        [3, 4],
#        [3, 2],
#        [3, 1],
#        [4, 2],
#        [4, 1],
#        [2, 1]])>

This should work in both TF1 and TF2.

If the length of x is known in advance, you don't need the while_loop and could simply precompute the indices in python then place them in a constant.

user_17350030

Here is a way to do that without a loop:

import tensorflow as tf

x = tf.constant([[1, 3],
                 [2, 4],
                 [0, 2],
                 [0, 1]], dtype=tf.int32)
# Number of rows
n = tf.shape(x)[0]
# Grid of indices
ri = tf.range(0, n - 1)
rj = ri + 1
ii, jj = tf.meshgrid(ri, rj, indexing='ij')
# Stack together
grid = tf.stack([ii, jj], axis=-1)
# Get upper triangular part
m = ii < jj
idx = tf.boolean_mask(grid, m)
# Get values
g = tf.gather(x, idx, axis=0)
# Rearrange result
result = tf.transpose(g, [2, 0, 1])
print(result.numpy())
# [[[1 2]
#   [1 0]
#   [1 0]
#   [2 0]
#   [2 0]
#   [0 0]]
# 
#  [[3 4]
#   [3 2]
#   [3 1]
#   [4 2]
#   [4 1]
#   [2 1]]]
user_17827920
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