
Flouring the loaf
Now heres a task that cries out for a simple solution: put a border round a matrix. My matrix is boolean and represents a QR code (yes, well come to that) but its the same problem as, say, putting a 1px border on an image.
So lets examine it as wrapping a char matrix in spaces. Well use
3 4#"ABCDEGHIJKL"
.Amend At
Our first strategy is to manipulate indexes, which is often an efficient approach in q. We make a larger blank matrix for the result and write the original matrix in the right place.
Start with the shape of the matrix; that is, count the rows and columns. (Shape is a concept that q did not inherit from its ancestor APL, but is easy enough to calculate.) We use the Zen monks for a pointfree expression.
q)show M:3 4#"ABCDEFGHIJKL" "ABCD" "EFGH" "IJKL" q)count each 1 first M / shape of M 3 4
So the result shape is 5 6, and here is our blank template:
q){n:2+count each 1 firstx; n#" "}M " " " " " " " " " "
For the last move we could use Amend Each
.'
to map each item ofM
to a rowcolumn pair in the result. But it should be more efficient to razeM
and use Amend At@
to map all its items to the vectorprd[n]#" "
and then reshape it. Something likeq){n:2+s:count each 1 firstx; n#@[prd[n]#" "; ??? ;:;raze x]}M " " " ABCD " " EFGH " " IJKL " " "
Above,
???
is some expression that returns the target indices for the items ofM
. Lets start with an easy expression wrong, but easy. Well write the items ofM
into the first positions of the result.q){n:2+s:count each 1 firstx; n#@[prd[n]#" ";til prd s;:;raze x]}M "ABCDEF" "GHIJKL" " " " " " "
Next we come to an oftenoverlooked overload of
vs
andsv
: they encode and decode different (and variable) arithmetic bases. English pounds have 100 pennies (once known as New Pence) but once had 240, of which 12 made a shilling; and 20 shillings a pound.q)240*4.50 / 4.50 in old pence 1080f q)100 20 12 vs 240*4.50 / 4.50 was 4 10s 0d. 4 10 0f q)%[;240]100 20 12 sv 4 10 0 / 4/10/ in decimal coinage 4.5 q)%[;240]100 20 12 sv 4 17 6 / not every sterling amount has an exact equivalent 4.875
We can use
vs
andsv
to convert between rowcol pairs and equivalent vector indices.q){n:2+s:count each 1 firstx; n#@[prd[n]#" ";n sv flip 1 1+/:s vs/:til prd s;:;raze x]}M " " " ABCD " " EFGH " " IJKL " " "
The above has a certain elegance in that it is probably efficient for a large matrix, but it does seem a lot of code for a simple task. If our matrices are small, perhaps we can see a simpler way?
Join
Join
,
looks like an obvious candidate. (And it will lead us to something aboutflip
we might not have known; but well come to that.) We have to apply it to each of four sides, but we have decided we dont necessarily need the fastest expression for this.Looks straightforward: Join for top and bottom, Join Each for the sides.
q),[;" "] " ",'" ",M,'" " " " " ABCD " " EFGH " " IJKL " " "
Ah, not quite that straightforward. Joining an atom doesnt use scalar extension the same way Join Each does. We could count the first row
q){row:enlist(count first x)#" ";" ",'(row,x,row),'" "}M " " " ABCD " " EFGH " " IJKL " " "
Better, but the refactoring itch remains.
The simplest operation is the Join Each, which exploits scalar extension.
When I flour an unbaked loaf, I dont daub flour over it, I roll it in the flour.
q)reverse flip ,'[" "] M "DHL" "CGK" "BFJ" "AEI" " " q)reverse flip ,'[" "] reverse flip ,'[" "] M "LKJI " "HGFE " "DCBA " " " q)4{reverse flip ,'[" "] x}/M " " " ABCD " " EFGH " " IJKL " " "
I dont need the (admittedly tiny) overhead of a lambda to apply a series of unaries. I can use a composition.
q)4(reverse flip ,'[" "]@)/M " " " ABCD " " EFGH " " IJKL " " "
Now heres a surprise: we dont need the Each.
q)4(reverse flip ,[" "]@)/M " " " ABCD " " EFGH " " IJKL " " "
How does that work? It turns out that
flip
uses scalar extension. The items of its argument must conform; that is, they must be samelength lists or atoms. But the result will have samelength lists.q)flip M "AEI" "BFJ" "CGK" "DHL" q)flip M,enlist "XYZ" / must conform! 'length [0] flip M,enlist "XYZ" ^ q)flip M,"X" "AEIX" "BFJX" "CGKX" "DHLX" q)
Loaf floured! And the QR code? Watch this space.
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