Q80 Multi Dim Solution

[Hemanth21k]

Following upon previous conversation, this PR follows on resolve #215 and an added solution for creating a centered subpart.

Question 80: Consider an arbitrary array, write a function that extracts a subpart with a fixed shape and centered on a given element (pad with a fill value when necessary)

Previous Conversation for Context:

Me:

      "
      I have to say I do not quite understand the question nor the solution.
      The existing solution is also not centered.
      So, I am adding my solution according to my understanding of the question.
      step 1: extract a subpart of given shape from an array.
      step 2: pad the subpart so that it can be centered across all existing dimensions.
      Please let me know if this is the correct solution or the correct understanding of the question.
      Thank you. 
      "

---

Current solution output by author:

Arbitrary array Z: 
      [  [5 7 7 1 6 6 2 6 3 7]
         [3 7 0 1 0 8 5 0 5 7]
         [8 8 8 9 6 8 6 5 8 4]
         [3 7 1 9 2 6 5 9 0 8]
         [4 8 3 6 5 3 8 9 5 1]
         [9 3 6 2 7 7 2 5 1 7]
         [3 2 6 5 3 1 9 7 2 6]
         [5 1 1 3 5 3 8 7 6 2]
         [9 9 7 7 9 8 8 3 0 2]
         [1 9 4 8 2 7 6 7 3 1]  ]

Output centered subpart of the array, R:

    [  [0 0 0 0 0]
       [0 5 7 7 1]
       [0 3 7 0 1]
       [0 8 8 8 9]
       [0 3 7 1 9]  ]    (padded with fill value 0)

---

As you can see above the output sub array array is clearly not centered and is also fixed, meaning no matter how many times you run you always take the same subpart of the array (indices wise, of course Z is randomly generated every time).

Updated solution (showing multi dimensional array):

Random array of shape (5,5,5):
[[[0.41318587, 0.02686425, 0.27634727, 0.34828896, 0.53552608],
[0.54426485, 0.40573159, 0.32785901, 0.95110226, 0.74314067],
[0.20954932, 0.28623217, 0.70648967, 0.8790684 , 0.58088525],
[0.93627437, 0.9338704 , 0.26930749, 0.28473462, 0.57721401],
[0.26036955, 0.2339317 , 0.41383287, 0.32453434, 0.5999981 ]],

[[0.17264282, 0.09969286, 0.54365084, 0.24587597, 0.63170746],
[0.73230861, 0.61695342, 0.33547145, 0.32364859, 0.30090559],
[0.82022138, 0.25265008, 0.20509734, 0.79525084, 0.69119536],
[0.37488242, 0.70970922, 0.49893688, 0.76578014, 0.82251079],
[0.02927624, 0.5578041 , 0.72246968, 0.23032316, 0.82340544]],

[[0.52939221, 0.35862534, 0.68652225, 0.17703581, 0.79556611],
[0.628605 , 0.49367779, 0.92209193, 0.30016312, 0.64213181],
[0.04117666, 0.2536342 , 0.70921765, 0.00874844, 0.50106527],
[0.47607017, 0.61145768, 0.85605809, 0.3551498 , 0.15807602],
[0.08091961, 0.02181234, 0.35937453, 0.2406722 , 0.05558978]],

[[0.62017971, 0.64246925, 0.28136912, 0.30680361, 0.80700583],
[0.01607795, 0.30556255, 0.84313362, 0.21627144, 0.81764976],
[0.12892675, 0.14246595, 0.59990127, 0.88475525, 0.4042635 ],
[0.07722488, 0.07539892, 0.65651728, 0.19927838, 0.73940527],
[0.89474121, 0.24049369, 0.97836756, 0.21814119, 0.09843175]],

[[0.31122096, 0.82433984, 0.3487815 , 0.34754057, 0.60063218],
[0.99627488, 0.21458165, 0.10521583, 0.31445038, 0.94451234],
[0.95148131, 0.60257491, 0.18610522, 0.87703271, 0.62835079],
[0.35963395, 0.69448514, 0.47953283, 0.64439803, 0.5633606 ],
[0.17343141, 0.69441931, 0.02642798, 0.92214243, 0.65579668]]]

Output - a random centered subpart of shape (2,3,2):
[[[0. 0. 0. 0. ]
[0. 0. 0. 0. ]
[0. 0. 0. 0. ]
[0. 0. 0. 0. ]
[0. 0. 0. 0. ]]

[[0. 0. 0. 0. ]
[0. 0.17264282 0.09969286 0. ]
[0. 0.73230861 0.61695342 0. ]
[0. 0.82022138 0.25265008 0. ]
[0. 0. 0. 0. ]]

[[0. 0. 0. 0. ]
[0. 0.52939221 0.35862534 0. ]
[0. 0.628605 0.49367779 0. ]
[0. 0.04117666 0.2536342 0. ]
[0. 0. 0. 0. ]]

[[0. 0. 0. 0. ]
[0. 0. 0. 0. ]
[0. 0. 0. 0. ]
[0. 0. 0. 0. ]
[0. 0. 0. 0. ]]] (padded with fill value 0)

---

The updated solution not only takes a random subpart of a given shape, but also centers it evenly across multiple dimensions.

Please correct me if I am wrong but this was my understanding of the given question.

Thank you.

[rougier]

I've edited your comment to ease reading of outputs. Can you also update the second part using only integers because it make things easier to read and debug.

For the first example you give, can you five the full script in another comment?