Rotation summation

Question

Take a square matrix containing positive integers as input, and calculate the "rotated sum" of the matrix.

Rotated sum:

Take the sum of the original matrix and the same matrix rotated 90, 180 and 270 degrees.

Suppose the matrix is:

 2    5    8
 3   12    8
 6    6   10

then the rotated sum will be:

2    5    8     8    8   10    10    6    6     6    3    2
3   12    8  +  5   12    6  +  8   12    3  +  6   12    5  = 
6    6   10     2    3    6     8    5    2    10    8    8   

26   22   26
22   48   22
26   22   26

Test cases:

Input and output separated by dashes, different test cases separated by a newline. Test cases in more convenient formats can be found here.

1
-------------
4

1 3
2 4
-------------
10   10 
10   10    

14    6    7   14
 6   12   13   13
 6    2    3   10
 5    1   12   12
-------------
45   37   24   45
24   30   30   37
37   30   30   24
45   24   37   45    

14    2    5   10    2
18    9   12    1    9
 3    1    5   11   14
13   20    7   19   12
 2    1    9    5    6
-------------
24   29   31   41   24
41   49   31   49   29
31   31   20   31   31
29   49   31   49   41
24   41   31   29   24

Shortest code in bytes in each language wins. Explanations are highly encouraged!

Answer 1

Factor + combinators.extras math.matrices, 49 48 bytes

[ [ dup flip [ reverse ] map ] thrice m+ m+ m+ ]

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• [ ... ] thrice Call [ ... ] 3 times.
• dup Make a copy of the top of the stack.
• flip [ reverse ] map Rotate a matrix 90 degrees.
• m+ m+ m+ Add 4 matrices together.

Answer 2

Perl 5, 92 bytes

sub f{@t=@_;map{//;[map$t[$'-1][$_-1]+$t[$_-1][-$']+$t[-$'][-$_]+$t[-$_][$'-1],1..@t]}1..@t}

Try it online!

Answer 3

Burlesque, 38 bytes

SP{{}{tp<-}{<-)<-}{tp)<-}}M-r{q?+Z]}sp

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SP        # Read input as array
{
 {}       # Original
 {tp<-}   # 90deg 
 {<-)<-}  # 180deg
 {tp)<-}  # 270deg
}
M-        # Return an array of maps
r{        # Reduce by
 q?+      # Vectorised addition
 Z]       # Zip, push, map
}
sp        # Pretty print as array

Answer 4

GolfScript, 64 bytes

4/{.(,\;[]:w;{[]:t;{(t\+:t;}%t{+}*w\+:w;}\*; w.,(!!3*)*.4/,/~}%`

I cheated, I cheated. Kinda. Though there are typical, standardized ways to take in Matrix input, I decided to take it in a... less conventional method. GolfScript is fucking terrible at rotational mathematics, so I knew I had to try. Below is the array-matrix method I used.

So yeah. You might notice a bit of convenient symmetry in this format, and I abused the hell out of it.

Input is taken in as an array of circular-ordered arrays, such as

[ [1 2 3 4][5 6 7 8][9 10 11 12][13 14 15 16][17 18][19 20][21 22][23 24][25] ]

for a 5x5 array.

1  2  3  4  5
16 17 18 19 6
15 24 25 20 7
14 23 22 21 8
13 12 11 10 9

It returns in identical output.

Teehee.

Maybe one day I'll make a program that takes an array of this format and turns it into nice formatting and vice-versa.

Then my program will no longer be an abomination.

I mean, it still would be, the I/O would just be more conventional.

God, should I even write an explanation for this hot garbage?

Try it online, if you dare.

Answer 5

Haskell, 84 bytes

import Data.List
s=foldl1(zipWith(zipWith(+))).take 4.iterate(transpose.map reverse)

Try it online!