[Numpy-discussion] matrix default to column vector?
Tom K.
tpk at kraussfamily.org
Sun Jun 7 08:20:17 EDT 2009
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.
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.
Regards,
Tom K.
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