# aliquot

## < a quantity that can be divided into another a whole number of time />

I am slowly updating a small Racket package for statistical analysis, which is a mix of R, LispStat and Stata actually. Don't expect too much from this package because it is mainly a proof of concept, and a way to learn Racket more seriously. Anyway, I didn't realize the (typed) math package was so complete. Beside matrices and common statistical distributions, it comes with Gram-Schmidt, QR and LU decomposition, a solver, etc. These utilities already allow to fit a simple (weighted) linear model in a few lines:

(require math)

(define T matrix-transpose)

(define (regress y x [w #f])
(matrix-solve
(matrix* (T x) (diagonal-matrix w) x) (matrix* (T x) (diagonal-matrix w) y)))


Of course, you may well prefer to rely on solid libraries for linear algebra, like LAPACK or BLAS, especially if you are going to work with large datasets or irregular design matrix ($n\ll p$ case). However, suppose you already have some C code available to estimate the parameters of such models, say the GLM routine in the snpMatrix package. Surely there are many more standalone C packages for that specific purpose, but I already used this routine in the past in a C program, so I came to appreciate it (besides its use in GWAS analysis). Being able to call the C code from Racket would alleviate the need to rewrite everything from scratch, and in the long run you could even use well-tested libraries like liblinear or wowpal.

Calling “simple C” routine code in Racket is quite easy actually, once you figured out how to map C types to Racket data structures, plus a couple of other issues discussed in the documentation. In the simplest cases, you just need to create a shared library (--shared under Linux, --dynamiclib under macOS), write a wrapper to define the C function signature in Racket, and define a Racket function that calls the C function using Racket data structures. Note that by “simple C” I refer to C procedures that do not involve pass-by-reference return values, but only parameter of the type pass-by-value or pointers to 1D array. There's a gentle tutorial that covers such simple cases. There's also a very nice tutorial available in 3 parts if you want to learn more.

Let's see a more complete example in action. Suppose your C function, qs.c, reads like this simple quick sort:

#define SWAP(x, y) do { typeof(x) SWAP = x; x = y; y = SWAP; } while (0)

void qs(int *lst, int start, int end) {
int i, j, p;
if(start < end) {
p = start;
i = start;
j = end;
while (i < j) {
while (lst[i] <= lst[p] && i < end)
i++;
while (lst[j] > lst[p])
j--;
if (i < j) {
SWAP(lst[i], lst[j]);
}
}
SWAP(lst[p], lst[j]);
qs(lst, start, j-1);
qs(lst, j+1, end);
}
}


Now, we just have to compile this using gcc or clang, depending on what's available on your OS. In my case:

~/tmp  cc -dynamiclib -o qs.dylib qs.c


You should end up with a shared (dynamic) library, ready to be used by C programs, or Racket itself. On the Racket side, let's write the corresponding functions:

(require ffi/unsafe
ffi/cvector
ffi/unsafe/define)
(define-ffi-definer define-libs (ffi-lib "qs"))
(define-libs qs (_fun (a : _cvector) _int _int -> _void -> (values a)))


That's it! Note that sorting is done in place, hence the pass-by-reference return value (*lst) that we need to tag in order to be able to refer to the captured value from Racket. You'll now just need to define a C-type vector in Racket and pass it to your function as shown below:

(define-values (a) (qs (list->cvector '(1 2 6 3 7 5 9 8 4) _int) 0 9))


And here we are finally:

> a
#<cvector>
> (cvector->list a)
'(0 1 2 3 4 5 6 7 8)


Note that Racket is using 0-base indexing, like Python. You could replace the last expression with (map add1 (cvector->list a)).