Spartns

Spartns is a SPARse TeNSor representation library (if you don’t know what a tensor is: they are objects from Multilinear Algebra, which can be represented
as matrices, but with any number of dimensions, not just two). Spartns is distributed under the LLGPL license.

See more information on Spartns here

Features:

• No external dependencies (no BLAS or any other C or Fortran library needed). Just plain Common Lisp;
• Represents mappings from one dimension onto another using any scheme you want (there are three built-in schemes: array, hash and compressed-vector, but you can roll your own and plug it);
• Flexible: works with any data type;
• Heavily optimized: traversing the tensor can be extremely fast (in one specific situation — traversing the tensor — it was 10 times faster than a naive implementation in C++);
• Fairly portable: works with ABCL, ACL, Clisp, Clozure, CMUCL, ECL, GCL, SBCL and XCL.
• Spartns is never released without going through regression tests (if a platform breaks and can’t be supported, it will be clear in the release announcement);
• ASDF installable (thanks Slobodan Blazeski!);
• Easy to use, with introductory documentation (not only on-line);
• Comes with description of the internals of the library.

One simple example: two dimensional matrix multiplication. First, define a type for 2-dimensional matrices:

(defspartn 2dmatrix
   :representation (spartns:hash spartns:cvector)
   :non-zero       (3 4)
   :element-type   long-float
   :sparse-element 0L0)

The Spartn type “2dmatrix“ is then defined as the type for sparse tensors that map indices onto long-floats using a hashtable of compressed vectors. When they are created, the hashtables start with :size 3,
and the compressed vectors with :size 4. Now, create three matrices, X Y and Z, and multiply them:

(let ((X (make-2dmatrix))
      (Y (make-2dmatrix))
      (Z (make-2dmatrix)))
  (set-2dmatrix X 0 0 5L0)
  (set-2dmatrix Y 0 1 6L4)
  ;; set non-zeros in the rest of the matrices X and Y
  ;; and now multiply them:
  (w/fast-traversals ((2dmatrix X i j val-x)
                      (2dmatrix Y j k val-y))
    (set-2dmatrix Z i k
      (+ (get-2dmatrix Z i k) (* val-x val-y)))))