Element wise computation

[divon]

Hello everyone

Suppose I have two arrays:

and


And I wanted to do calculations using this equation:


The code that I have created so far:

import numpy as np
import math as mt

G = np.array([[1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0], [1, 1, 1, 1, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 0, 0, 1, 1, 0, 0], [1, 0, 1, 0, 1, 0, 1, 0], [1, 1, 1, 1, 1, 1, 1, 1]])

r = np.array([-56.53511658, -96.6740462, -85.23212419, -90.05029513, -86.19336384, -79.31883055, -67.7323369, -86.49784743])

def boxplus(a, b):
    return 2 * aatanh(mt.tanh(a / 2) * mt.tanh(b / 2))

def aatanh(x):
    if x == 1:
        return mt.atanh(x - 0.0000001)
    elif x == -1:
        return mt.atanh(x + 0.0000001)
    else:
        return mt.atanh(x)

L = np.zeros(8)

Right now I am stuck on how to do the boxplus operation and put it into array L. And please forgive me if my post is in wrong location.

[Gribouillis]

I would try something like this:

import numpy as np
import math as mt

G = np.array([[1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0], [1, 1, 1, 1, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 0, 0, 1, 1, 0, 0], [1, 0, 1, 0, 1, 0, 1, 0], [1, 1, 1, 1, 1, 1, 1, 1]])
 
r = np.array([-56.53511658, -96.6740462, -85.23212419, -90.05029513, -86.19336384, -79.31883055, -67.7323369, -86.49784743])

def main():
    s = r.reshape((1, len(r)))
    print(s)
    M = G * s.T
    print(M)
    tmp = np.tanh(M*0.5)
    print(tmp)
    p = np.prod(tmp, axis=0)
    print(p)
    print(2 * np.arctanh(p))

if __name__ == '__main__':
    main()

The numerical result is deceiving however, due to the large values in the array r

Output:
[[-56.53511658 -96.6740462  -85.23212419 -90.05029513 -86.19336384
  -79.31883055 -67.7323369  -86.49784743]]
paillasse/pf/numbox.py:17: RuntimeWarning: divide by zero encountered in arctanh
[[-56.53511658  -0.          -0.          -0.          -0.
   -0.          -0.          -0.        ]
 [-96.6740462  -96.6740462   -0.          -0.          -0.
   -0.          -0.          -0.        ]
  print(2 * np.arctanh(p))
 [-85.23212419  -0.         -85.23212419  -0.          -0.
   -0.          -0.          -0.        ]
 [-90.05029513 -90.05029513 -90.05029513 -90.05029513  -0.
   -0.          -0.          -0.        ]
 [-86.19336384  -0.          -0.          -0.         -86.19336384
   -0.          -0.          -0.        ]
 [-79.31883055 -79.31883055  -0.          -0.         -79.31883055
  -79.31883055  -0.          -0.        ]
 [-67.7323369   -0.         -67.7323369   -0.         -67.7323369
   -0.         -67.7323369   -0.        ]
 [-86.49784743 -86.49784743 -86.49784743 -86.49784743 -86.49784743
  -86.49784743 -86.49784743 -86.49784743]]
[[-1. -0. -0. -0. -0. -0. -0. -0.]
 [-1. -1. -0. -0. -0. -0. -0. -0.]
 [-1. -0. -1. -0. -0. -0. -0. -0.]
 [-1. -1. -1. -1. -0. -0. -0. -0.]
 [-1. -0. -0. -0. -1. -0. -0. -0.]
 [-1. -1. -0. -0. -1. -1. -0. -0.]
 [-1. -0. -1. -0. -1. -0. -1. -0.]
 [-1. -1. -1. -1. -1. -1. -1. -1.]]
[1. 0. 0. 0. 0. 0. 0. 0.]
[inf  0.  0.  0.  0.  0.  0.  0.]

Note that the boxplus operator returns 0 as soon as one of the arguments is 0, and the matrix G contains many zeroes.

[divon]

I would try something like this:

import numpy as np
import math as mt

G = np.array([[1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0], [1, 1, 1, 1, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0], [1, 1, 0, 0, 1, 1, 0, 0], [1, 0, 1, 0, 1, 0, 1, 0], [1, 1, 1, 1, 1, 1, 1, 1]])
 
r = np.array([-56.53511658, -96.6740462, -85.23212419, -90.05029513, -86.19336384, -79.31883055, -67.7323369, -86.49784743])

def main():
    s = r.reshape((1, len(r)))
    print(s)
    M = G * s.T
    print(M)
    tmp = np.tanh(M*0.5)
    print(tmp)
    p = np.prod(tmp, axis=0)
    print(p)
    print(2 * np.arctanh(p))

if __name__ == '__main__':
    main()

The numerical result is deceiving however, due to the large values in the array r

Output:
[[-56.53511658 -96.6740462  -85.23212419 -90.05029513 -86.19336384
  -79.31883055 -67.7323369  -86.49784743]]
paillasse/pf/numbox.py:17: RuntimeWarning: divide by zero encountered in arctanh
[[-56.53511658  -0.          -0.          -0.          -0.
   -0.          -0.          -0.        ]
 [-96.6740462  -96.6740462   -0.          -0.          -0.
   -0.          -0.          -0.        ]
  print(2 * np.arctanh(p))
 [-85.23212419  -0.         -85.23212419  -0.          -0.
   -0.          -0.          -0.        ]
 [-90.05029513 -90.05029513 -90.05029513 -90.05029513  -0.
   -0.          -0.          -0.        ]
 [-86.19336384  -0.          -0.          -0.         -86.19336384
   -0.          -0.          -0.        ]
 [-79.31883055 -79.31883055  -0.          -0.         -79.31883055
  -79.31883055  -0.          -0.        ]
 [-67.7323369   -0.         -67.7323369   -0.         -67.7323369
   -0.         -67.7323369   -0.        ]
 [-86.49784743 -86.49784743 -86.49784743 -86.49784743 -86.49784743
  -86.49784743 -86.49784743 -86.49784743]]
[[-1. -0. -0. -0. -0. -0. -0. -0.]
 [-1. -1. -0. -0. -0. -0. -0. -0.]
 [-1. -0. -1. -0. -0. -0. -0. -0.]
 [-1. -1. -1. -1. -0. -0. -0. -0.]
 [-1. -0. -0. -0. -1. -0. -0. -0.]
 [-1. -1. -0. -0. -1. -1. -0. -0.]
 [-1. -0. -1. -0. -1. -0. -1. -0.]
 [-1. -1. -1. -1. -1. -1. -1. -1.]]
[1. 0. 0. 0. 0. 0. 0. 0.]
[inf  0.  0.  0.  0.  0.  0.  0.]

Note that the boxplus operator returns 0 as soon as one of the arguments is 0, and the matrix G contains many zeroes.

Thank you very much for your help, @Gribouillis. It gives me a new perspective on the problem. And please forgive me for being so late in replying to your post.