Re: [ANN] GSL Shell 2.2.0 beta1 release
- From: Francesco Abbate <francesco.bbt@xxxxxxxxx>
- To: luajit@xxxxxxxxxxxxx
- Date: Mon, 17 Sep 2012 22:31:37 +0200
2012/9/17 pingon begand <sbronfion@xxxxxxxxx>:
> Is there a module/binding for your complex number library? I am interested
> in that part and I cannot find anything.
Hi,
to answer your question, the complex stuff in GSL Shell is coming from
the GSL library and from the native support in LuaJIT for complex
numbers as defined in the C99 standard.
The type gsl_complex is defined in the GSL library:
http://www.gnu.org/software/gsl/manual/html_node/Complex-Numbers.html
and many functions on complex numbers ar available as well. The only
trick here is that you can identify the gsl_complex type with C99
"double _Complex" aka "complex". So in the file "gsl.lua" you will
find the following cdef:
typedef complex gsl_complex.
With this trick all the complex numbers' functions from the GSL
library are immediately avaliable using the FFI interface. The
definitions are in the "matrix.lua" file near the function
"c_function_lookup". I admit that it is a little bit unfortunate place
to define complex numbers :/
The other trick is to define arithmetic metamethods for complex types
using the function ffi.metatype. This is also done in "matrix.lua".
Actually the reason why matrix and complex are implemented in the same
file is that they need to have common arithmetic metamethods because
in GSL shell you can add or multiply a complex numbers with a real or
complex matrix.
So, if you want to isolate the complex number stuff you have to take
the file "gsl.lua" and "matrix.lua" and keep only the stuff related to
complex numbers.
> Here are more open questions :
> Do you think that 'GSL-Shell' will offer the same function interface as in
> julia?
Unfortunately the answer to this question is negative. Julia is
designed from the beginning to support mathematical operations while
Lua is a generic purpose programming language.
For example in LuaJIT you cannot refer to an element of a matrix like
m[i, j] as it would be natural for matrices. You don't have a specific
syntax for matrix literals and, more important matrix operations are
inherently inefficient because evaluation is not delayed. So if you
write:
a + 2*b + 2*c
where a, b and c are matrices Lua will:
- create a new matrix equal to 2*b
- create a new matrix equal to 2*c
- create a new matrix to sum a + 2*b
- create a new matrix to sum (a + 2*b) with 2*c
Of course this is a disaster in term of efficiency. The evaluation
should be delayed to use BLAS operations to evaluate efficiently the
expression.
This problem exist also for the multiplication by a transpose. The
BLAS function allows to evaluate it without the need of actually
creating the transpose matrix but with Lua you cannot.
Unfortunately the "goto" statement recently implemented in LuaJIT does
not help with this problem :-)
AFAIK the only solution is to create a new language that compile to
Lua but for the moment I didn't take this direction.
> Will luajit be a dependence instead of a 'fork'?
Not now. In future who knows... :-)
Francesco
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