Henning Thielemann wrote:
- 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.
I think we can have the best of both worlds...
- 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?
MatLab has "exp" which works element wise and "expm" which does the matrix-exponentation. I have made the matrix an instance of Num/Fractional and Float. The float operations all apply element wise. I have constructors "scalar" and "vector" to produce a 1x1 and a row-matrix respectively. The '*' operator does matrix multiplication (as in MatLab) and I have a new class for matrices which defines ".*" for element wise multiplication. Like matlab, if you try to multiply a scalar (1x1 matrix) by another matrix you get element wise multiplication instead of matrix multiplication... (as a scalar can only really be multiplied by another scalar this is unabiguous). What about implementation? At the moment I am coding the vector operations in Haskell (a foreign interface to lapack or Intel MKL can come later)... and am using a UArray - is this portable enough - or should I parameterise by array type (using IArray) even though this might result in type ambiguities? Keean.