On Sun, Jun 7, 2009 at 07:20, Tom K.
Olivier Verdier-2 wrote:
There would be a much simpler solution than allowing a new operator. Just allow the numpy function dot to take more than two arguments. Then A*B*C in matrix notation would simply be: dot(A,B,C)
with arrays. Wouldn't that make everybody happy? Plus it does not break backward compatibility. Am I missing something?
That wouldn't make me happy because it is not the same syntax as a binary infix operator. Introducing a new operator for matrix multiply (and possibly matrix exponentiation) does not break backward compatibility - how could it, given that the python language does not yet support the new operator?
Going back to Alan Isaac's example: 1) beta = (X.T*X).I * X.T * Y 2) beta = np.dot(np.dot(la.inv(np.dot(X.T,X)),X.T),Y)
With a multiple arguments to dot, 2) becomes: 3) beta = np.dot(la.inv(np.dot(X.T, X)), X.T, Y)
This is somewhat better than 2) but not as nice as 1) IMO.
4) beta = la.lstsq(X, Y)[0] I really hate that example.
Seeing 1) with @'s would take some getting used but I think we would adjust.
For ".I" I would propose that ".I" be added to nd-arrays that inverts each matrix of the last two dimensions, so for example if X is 3D then X.I is the same as np.array([inv(Xi) for Xi in X]). This is also backwards compatible. With this behavior and the one I proposed for @, by adding preceding dimensions we are allowing doing matrix algebra on collections of matrices (although it looks like we might need a new .T that just swaps the last two dimensions to really pull that off). But a ".I" attribute and its behavior needn't be bundled with whatever proposal we wish to make to the python community for a new operator of course.
I am vehemently against adding .I to ndarray. I want to *discourage* the formation of explicit inverses. It is almost always a very wrong thing to do. -- Robert Kern "I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it as though it had an underlying truth." -- Umberto Eco