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LispCookbook / cl-cookbook

The Common Lisp Cookbook
http://lispcookbook.github.io/cl-cookbook/
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Multidimensional arrays #149

Closed bendudson closed 6 years ago

bendudson commented 6 years ago

I would like to make a start at writing a page on arrays in Common Lisp, aiming at something like this https://docs.julialang.org/en/stable/manual/arrays/ . I am interested in numerical/scientific computing, mainly solving PDEs from plasma physics, but would like to help this project if possible. Topics would include:

Practical Common Lisp has a section on vectors and arrays, but does not go into much detail or cover much of this. I think most of this functionality is provided by libraries rather than the core language.

I am very new to CL, so I plan to write a guide for my own benefit anyway. This is my impression, apologies in advance for errors or omissions:

There seem to be some quite mature libraries like Antik and GSLL, though the manual link here https://www.common-lisp.net/project/antik/index.html is broken, and documentation in general seems to be sparse. The other active(ish) library seems to be matlisp ( https://github.com/matlisp/matlisp ), though I am not sure how well these packages interact.

Several other projects exist, but most seem to be abandoned. Lisplab has a manual (https://common-lisp.net/project/lisplab/) but it's not on quicklisp. Other interesting but abandoned projects include http://quickdocs.org/array-operations/ which is on github (https://github.com/tpapp/array-operations).

A relevant question on SO is: https://stackoverflow.com/questions/4116069/lisp-multidimensional-array-elementwise-operations

Is there a good guide to array operations in CL which I have missed? I understand that technical computing is not a focus for CL, but perhaps putting together a guide for new users would help consolidate the various libraries out there. Any suggestions or starting points welcome.

vindarel commented 6 years ago

Hello, I myself can absolutely not tell you if there's a good guide about this out there :] but I can encourage you to write about it, yes, please write about this and about math in CL in general (issue about math: https://github.com/LispCookbook/cl-cookbook/issues/17).

Though, is Maxima not helpful ? algebra system,

system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, sets, lists, vectors <--- \o/, matrices and tensors.

Also just stumbled across https://github.com/sjl/vex/ "yet another vector library", not ready but by an awesome CL hacker, to whom you could ask.

Also reddit/r/common_lisp is a good place for this question, you'll get more answers.

vindarel commented 6 years ago

and just in case: https://github.com/CodyReichert/awesome-cl#numerical-and-scientific

bendudson commented 6 years ago

Thanks very much; I had come across most of those but not vex. I have not tried using Maxima, though it does look quite neat. It appears to be a full DSL, mainly for symbolic manipulation, with a very different syntax to Common Lisp forms. Some posts indicate that using it as a library (combining with other lisp libraries, quicklisp etc) is somewhat clunky, and that it is not optimal for numerical calculations. I will try it out though and see.

At the moment the start of the guide is on using native arrays, with small quicklisp-loadable libraries, then link to the full systems like Maxima. Starting section currently:

Multidimensional arrays

Common Lisp has native support for multidimensional arrays, with some special treatment for 1-D arrays, called vectors. Arrays can be generalised and contain any type (element-type t), or they can be specialised to contain specific types such as single-float or integer.

There are limitations to the native arrays, in particular

Both of these problems can be solved by using CLOS to define an extended array class, with native arrays as a special case. Some libraries available through quicklisp which take this approach are:

Taking this approach further, full DSLs have been built on Common Lisp for treating mathematical objects. At the time of writing the most widely used and supported of these are:

pnathan commented 6 years ago

https://www.pvk.ca/Blog/LowLevel/ is one of the lisp numerical masters. Might be worth digging through his works or talking with him.

vindarel commented 6 years ago

https://github.com/takagi/avm ?

Efficient and expressive arrayed vector math library with multi-threading and CUDA support in Common Lisp.