Comparison with other libraries

There are two main asdf systems:

• numericals is designed to work with cl:array so that interfacing with the rest of the lisp ecosystem is trivial.
• dense-numericals is designed to work with dense-arrays:array

Each of these has a number of systems and corresponding packages:

• utils
• basic-math
• transcendental
• statistics
• linalg
• random

These can be loaded individually. For example (asdf:load-system "numericals/random").

Native CL arrays

As of this writing,

• The only libraries that offer broadcasted operations on arrays are this and numcl
• numcl does not yet have a focus on high performance - though, it should be possible to implement the current einsum based backend using BLAS and BMAS; instead the focus there is on functionality; by contrast, the focus here is on performance first, and functionality second. Users do not have to choose. :mix option of uiop:define-package can be useful for mixing the two libraries as per user preferences
• Other minor differences wrt numcl include:
  • Both (ones 2 3 :type 'single-float) and (ones '(2 3) :type 'single-float) are legal in numericals; while only the latter is legal in numcl/numpy
  • numericals provides a *array-element-type-alist* similar to swank:*readtable-alist* to provide a package local way of specifying the default element-type for arrays. This can be further overriden by binding *array-element-type*. This does impose performance penalties however.
  • numcl relies on JIT backed by specialized-function, while numericals relies on AOT backed by polymorphic-functions. Again, these are not either-or, high level user functions can (in theory) utilize specialized-function, while the innards can use static-dispatch either by polymorphic-functions or static-dispatch or fast-generic-functions.
• In addition to these two, another performant library operating on CL arrays includes lla. Again, uiop:define-package with :mix and :local-nicknames can be used suitably.

The author of numericals did not find other libraries operating on native CL arrays.

Non-native CL arrays

There are quite a few libraries in Common Lisp in this domain. I have only managed to take a peak at femlisp-matlisp.

That said, the goal of numericals is not to replace python ecosystems, at least not in the short run, but instead to overcome the limitations of libraries like py4cl/2 of sub-10,000 instructions per second. However, now there's also py4cl2-cffi which is about a 10 times slower than CPython itself.

Foreign function interfaces

gsll

A number of functions in gsl and gsll operate on double precision floats, while some applications appreciate operators working on single precision floats without a conversion overhead. Thus, while extremely featureful, gsll is insufficient for everyone's needs.

eigen

eigen has wonderful documentation. I have only ever done a basic course in linear algebra, and often feel as if I am missing out on something when people work on linear algebra, but I found eigen's documentation to be superb! For instance, see

• this QuickRef page,
• or this Linear Algebra tutorial comparing different decompositions,
• or this linked page on benchmark comparison of various decompositions.

So, if eigen and C++ suit your needs, you might as well use it! That said, it isn't the fastest in everything - SLEEF can often be faster in areas where it is specifically designed for.