On Tue, 5 Jul 2005, Keean Schupke wrote:
Henning Thielemann wrote:
I'm uncertain about how who want to put the different kinds of multiplication into one method, even with multi-parameter type classes. You need instances
(*) :: Matrix -> Matrix -> Matrix (*) :: RowVector -> Matrix -> RowVector (*) :: Matrix -> ColumnVector -> ColumnVector (*) :: RowVector -> ColumnVector -> Scalar (*) :: ColumnVector -> RowVector -> Matrix (*) :: Scalar -> RowVector -> RowVector (*) :: RowVector -> Scalar -> RowVector (*) :: Scalar -> ColumnVector -> ColumnVector (*) :: ColumnVector -> Scalar -> ColumnVector
but you have to make sure that it is not possible to write an expression which needs (*) :: Matrix -> RowVector -> RowVector
This was my reply to Jacques Carette who suggested to distinguish row and column vectors by their _type_. His revised suggestion was to use phantom types. Then the types changes to (*) :: Matrix -> Matrix -> Matrix (*) :: Vector Row -> Matrix -> Vector Row (*) :: Matrix -> Vector Column -> Vector Column (*) :: Vector Row -> Vector Column -> Scalar ... but the problem remains ...
Further you need transpose :: RowVector -> ColumnVector transpose :: ColumnVector -> RowVector transpose :: Matrix -> Matrix and you must forbid, say transpose :: RowVector -> RowVector
Of course if they are all of type Matrix this problem disappears.
All type problems disappear when we switch to exclusive String representation. 8-]
What is the difference between a 1xN matrix and a vector? Please explain...
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
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