On Thu, 9 Jun 2005, Keean Schupke wrote:
Hi, I have a simple matrix library (styled after MatLab's use of matrices), and was wondering if any of the standard libraries include matrix functionality.
Not more than arrays, as far as I know.
The library as stands is not suitable for general use - but it could be adapted. I guess the questions are:
- is there already a matrix library in the standard libraries?
There is a small linear algebra library of Jan Skibinski and a linear algebra part of the HaskellDSP library. I remember that this question already arose and resulted in some more interesting links.
- is anyone interested in a matrix library?
Yes.
- would people want a library like MatLab where matrices are instances of Num/Fractional/Floating and can be used in normal math equations...
I'm pretty unhappy with all these automatisms in MatLab which prevent fast detection of mistakes, e.g. treating vectors as column or row matrices, random collapses of singleton dimensions, automatic extension of singletons to vectors with equal components. What is the natural definition of matrix multiplication? The element-wise multiplication (which is commutative like the multiplication of other Num instances) or the matrix multiplication? I vote for separate functions or infix operators for matrix multiplications, linear equation system solvers, matrix-vector-multiplication, matrix and vector scaling. I wished to have an interface to LAPACK for the floating point types because you can hardly compete with algorithms you write in one afternoon. Btw. when considering the class hierarchy of the numeric prelude project http://cvs.haskell.org/darcs/numericprelude/ you would naturally put matrices and vectors in Additive, Module and VectorSpace class but not in Fractional.
- operations like cos/sin/log can be applied to a matrix (and apply to each element like in MatLab) ...
MatLab must provide these automatisms because it doesn't have proper higher functions. I think the Haskell way is to provide a 'map' for matrices. Otherwise the question is: What is the most natural 'exp' on matrices? The elementwise application of 'exp' to each element or the matrix exponentation?