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pythontensorflow
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Reputation: 5551

What is the pattern of tensorflow fill_triangular?

I'm sure that there is some logic here, but I can't figure out what the general pattern is. If I apply tf.contrib.distributions.fill_triangular to a length (n+1)n/2 list, then in what pattern do the entries fill the upper/lower triangle of the resulting matrix?

To illustrate, here is a 5x5 matrix filled by fill_triangular:

import tensorflow as tf

foo = tf.contrib.distributions.fill_triangular(
    [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15], upper=True
)
with tf.Session('') as sesh:
    print(sesh.run(foo))

gives

[[ 1  2  3  4  5]
 [ 0  7  8  9 10]
 [ 0  0 13 14 15]
 [ 0  0  0 12 11]
 [ 0  0  0  0  6]]

OTOH, one might expect a similar behavior to np.triu_indices(5), e.g.:

import numpy as np

bar = np.zeros((5,5))
bar[np.triu_indices(5)] = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
print(bar)

which gives

array([[ 1.,  2.,  3.,  4.,  5.],
       [ 0.,  6.,  7.,  8.,  9.],
       [ 0.,  0., 10., 11., 12.],
       [ 0.,  0.,  0., 13., 14.],
       [ 0.,  0.,  0.,  0., 15.]])

What is the general fill pattern for tf.contrib.distributions.fill_triangular(list(range(int((n+1)*n/2))))?

Upvotes: 0

Views: 363

Answers (1)

zihaozhihao
zihaozhihao

Reputation: 4475

As the tf official doc mentioned, fill_triangular fills the elements in a clockwise spiral. 

import tensorflow as tf
import numpy as np

foo = tf.contrib.distributions.fill_triangular(
    np.arange(1,22), upper=True
)
with tf.Session('') as sesh:
    print(sesh.run(foo))

#[[ 1->2->3->4-> 5 -> 6]   >---->----->------->--------|
# [ 0  8->9->10->11-> 12]   >------->------>-------|   |   
# [ 0  0 15->16->17-> 18]  |   >--->--->-----|     |   |  
# [ 0  0  0  21<-20<- 19]  |  |  <---<---<---|     |   |
# [ 0  0  0  0   14<- 13]  |  <-----<------<-------|   |
# [ 0  0  0  0  0  7]]     <----<-----<-------<--------|

Upvotes: 1

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