gistfile1.txt

(1 0 ¯1 1 0 ¯1 1 0 ¯1)⌽"(1 0 ¯1)⊖"⊂M

Here we have a matrix M

Let's say it looks like this:

> M

 0 0 0 0 0
 0 0 0 0 0
 0 1 1 1 0
 0 0 0 0 0
 0 0 0 0 0

First we wrap it up so it appears like a scalar
 
> ⊂M

+---------+
|0 0 0 0 0|
|0 0 0 0 0|
|0 1 1 1 0|
|0 0 0 0 0|
|0 0 0 0 0|
+---------+

then we do a vertical-rotate-each
 
> (1 0 ¯1)⊖"⊂M

+---------+---------+---------+
|0 0 0 0 0|0 0 0 0 0|0 0 0 0 0|
|0 1 1 1 0|0 0 0 0 0|0 0 0 0 0|
|0 0 0 0 0|0 1 1 1 0|0 0 0 0 0|
|0 0 0 0 0|0 0 0 0 0|0 1 1 1 0|
|0 0 0 0 0|0 0 0 0 0|0 0 0 0 0|
+---------+---------+---------+

Then we do a horizonal rotate each, so we get an array of 9 matrices.

We can then multiply each member of our convolution matrix to each of these matrices

C×"(1 0 ¯1 1 0 ¯1 1 0 ¯1)⌽"(1 0 ¯1)⊖"⊂M

and then summate

+/C×"(1 0 ¯1 1 0 ¯1 1 0 ¯1)⌽"(1 0 ¯1)⊖"⊂M