Re: [Haskell-cafe] matrix computations based on the GSL

Henning Thielemann wrote:

My objections to making everything a matrix were the objections I sketched for MatLab.

The example, again: If you write some common expression like

transpose x * a * x

Which just goes to show why haskell limits the '*' operator to multiplying the same types. Keep this to Matrix-times-Matrix operators. Surely a vector is a 1xN matrix? And in terms of matrices a 1x1 matrix and a scalar are the same? I don't see the point of having separate matix and vector types... just have 'matrix constructors: matrix :: [[a]] -> Matrix a vector :: [a] -> Matrix a scalar :: a -> Matrix a I don't see any problems with this, and it lets you define the matrix exponential: instance Floating a => Floating (Matrix a) where exp = undefined Type of exp in Floating is (a -> a -> a), so substituting the class parameter gives: exp :: Matrix a -> Matrix a -> Matrix a, however you can only compute the matrix exponential (x^y) for "scalar-x matrix-y" or "matrix-x scalar-y"... I feel using separate types for vectors and scalars just overcomplicates things...

then both the human reader and the compiler don't know whether x is a "true" matrix or if it simulates a column or a row vector. It may be that 'x' is a row vector and 'a' a 1x1 matrix, then the expression denotes a square matrix of the size of the vector simulated by 'x'. It may be that 'x' is a column vector and 'a' a square matrix. Certainly in most cases I want the latter one and I want to have a scalar as a result. But if everything is a matrix then I have to check at run-time if the result is a 1x1 matrix and then I have to extract the only element from this matrix. If I omit the 1x1 test mistakes can remain undiscovered. I blame the common notation x^T * A * x for this trouble since the alternative notation can be immediately transcribed into computer language code while retaining strong distinction between a vector and a matrix type.

If x is a matrix and y is a matrix then x * y can only be interpreted in one simple way - no special cases. Sometimes you may need to transpose a 1xN into an Nx1 but at least you will get an 'error' if you try to use the wrong type...

More examples? More theory?

More complexity? Keean.