Shouldn't max([])=-inf ?
Matlab seems to follow a rule that iterative reduction operators give appropriate non-empty values to empty inputs. Examples include,
sum([])
prod([])
all([])
any([])
Is it an oversight not to do something similar for min and max?
max([])
For non-empty A and B,
max([A,B])= max(max(A), max(B))
The extension to B=[] should therefore satisfy,
max(A)=max(max(A),max([]))
for any A, which will only be true if we define max([])=-inf.
6 Comments
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I believe that would be inconsistent with this -
norm([])
det([])
Given that
norm([])
I would expect that max(svd([])) == 0, yet
max(svd([]))
It makes sense to me that
svd([]) % svd(blkdiag(A,B)) == sort([svd(A);svd(B)]) == svd(A) w/ B = []
But then to satisfy norm([]) == 0 we'd have to have max(double.empty(0,1)) == 0, which would be troubling.
I wonder why norm([]) == 0, keeping in mind that [] is a matrix, not a vector.
[isvector([]), ismatrix([])]
de Boor states (reference) that "Further, any norm of an empty matrix is zero, as the supremum of the empty set of nonnegative numbers." which seems like a tautological statement (and should "supremum" be replaced "infimum"?)
Wouldn't the identity hold if max([]) returned realmin (of the precision of the input)?
What should max(empty) return if the empty input is of a datatype that doesn't support inf, like int32 for example?
int32(-inf) % == intmin("int32")
max(int32.empty) % should return -2147483648
My preference would be to cast -inf to the requisit type, as is done in concatenation.
cast(-inf,'like',int8([]))
cast(-inf,'like',uint8([]))
cast(-inf,'like',double([]))
cast(-inf,'like',single([]))
Perhaps because max is often also used to calculate indices? Even though for the last decades you can use find with more arguments.
Just a minor note: I only understood what you meant by iterative reduction when you showed your example definition at the end. With that in mind, suddently the other outputs also make sense. I can't say I can see a pattern that would explain the results for sum, prod, all, and any, and also explains why max([]) would return an empty answer.
The index returned from max is empty for an empty input
[m,index] = max([])
which seems like a reasonable outcome even if m is returned non-empty.
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