Zachary Pincus wrote:
rest of linear algebra -- e.g. that m[0] yields a matrix if m is a matrix-- it almost certainly would violate the principle of least surprise for iteration over m (intuitively understood to be choosing m [0] then m[1] and so forth) to yield anything other than a matrix.
I don't think the OP was suggesting that. Rather, I think the suggestion was that for a mXn matrix, M: M[i].shape == (n,) M[i:i+1].shape == (1,n) that is, indexing (or iterating returns a vector, and slicing returns a matrix). This is, indeed exactly how numpy arrays behave! The problem with this is: numpy matrices were created specifically to support linear algebra calculations. For linear algebra, the distinction between row vectors and column vectors is critical. By definition, a row vector has shape: (1,n), and a column vector has shape (m,1). In this case, perhaps the OP is thinking that a shape (n,) array could be considered a row vector, but in that case: M[1,:].shape == (n,) M[:,1].shape == (m,) which of these is the row and which the column? This is why matrices index this way instead: M[1,:].shape == (1, n) M[:,1].shape == (m, 1) now we know exactly what is a row and what is a column. By the way, I think with the way numpy works: M[i] == M[i,:] by definition, so those couldn't yield different shaped results. Is that right? I think we got a bit sidetracked by the example given. If I have a bunch of points I want to store, I'm going to use an (m,2) *array*, not a matrix, then then A[i] will yield a (2,) array, which makes sense for (2-d) points. In fact, I do this a LOT. If I happen to need to do some linear algebra on that array of points, I'll convert to a matrix, do the linear algebra, then convert back to an a array (or just use the linear algebra functions on the array). I hope this helps -Chris
This can't possibly be what you're asking for, right? You aren't suggesting that m[0] and list(iter(m))[0] should be different types?
There are many clear and definite use cases for m[0] being a matrix, by the way, in addition to the theoretical arguments -- these aren't hard to come by. Whether or nor there are actual good use-cases for iterating over a matrix, if you believe that m[0] should be a matrix, it's madness to suggest that list(iter(m))[0] should be otherwise.
My opinion? Don't iterate over matrices. Use matrices for linear algebra. There's no "iteration" construct in linear algebra. The behavior you find so puzzling is a necessary by-product of the fundamental behavior of the matrix class -- which has been explained and which you offered no resistance to.
Zach
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