@Silvia A very formal name for the bottom part is frustrum. In this case it would be an oblique frustrum whereas it would have been a right frustrum if the cut were parallel to the base. The other part would be the apical part, that is, "the part next to the apex". I have not heard of a simple name for this part.

@Szabolcs I don't know, but I'd be curious the answer if you asked on the main site

@WReach Well, that's my new knowledge for the day

@WReach but be sure to check out footnote 1 en.wikipedia.org/wiki/Frustum#endnote_1

;-)

@ChrisK Yikes, I fell into that trap. My mind thinks frustum by my finger muscle memory types frustrum @Silvia: please take note: it is "frustum".

ArgMax[] itself should be what I'm looking for, but I can't seem to get it

@Axoren (probably) fastest way: Pick[Range[Length[array]], array, Max[array]]

Will that work on the output of Grad[]?

What is the output of Grad?

A vector

Then yes

The only issue arises when you have multi-dimensional arrays, in which case the Range spec needs to be your full array of indices

I keep getting "not found" when I use TakeLargest and then FirstPosition

If you need to do this many times, prebuild your indices

What are you doing with TakeLargest and FirstPosition?

It's not working

Same problems

I know I can do it by using Partial Derivatives instead

But I already have gradients and I'm being stubborn

Dude you need to use :=

Ugh, is that the slip up?

Otherwise Max[g[x, y]] isn't numerical

I'm so used to not using := from other languages

So I've made that mistake a bunch

f[x_, y_] := 1 - ((20 - x)/20)^y;
g[x_, y_] = Grad[f[x, y], {x, y}]

{20^-y (20 - x)^(-1 + y) y, 20^-y (20 - x)^y Log[20] - 20^-y (20 - x)^y Log[20 - x]}

h[x_, y_] = Max[g[x, y]]

Max[20^-y (20 - x)^(-1 + y) y, 20^-y (20 - x)^y Log[20] - 20^-y (20 - x)^y Log[20 - x]]

= will immediately evaluate the RHS

:= will wait until the function is called

h[x_, y_] should not be the Max, it should be the index of the largest component

I basically never use raw = when defining functions

I know but it's immediately evaluating that expression

Okay, so it's working. That was it.

Yup

It gives the result as {2} and {1}, is there a way to get those out of there?

Easiest is to put a [[1]] at the end

The way I'm doing it when I see it requires I save the value as a variable first

Thanks

If there are multiple indices which have the max value it'll return all of them, hence the list wrapping

I see, of course. I wasn't thinking about that because in my application it's not possible for both to be equal

I'm trying to only consider the domain of integers

And it very quickly deviates in the range I'm looking at

That split in the middle is supposed to be where the colors split.

That while line is supposed to bisect the colors, but it just draws the colors down the middle.

@Axoren set ColorFunctionScaling -> False

@b3m2a1 That did it. Is there a reason why that option's default behavior doesn't work out of the box for a discrete values? There's some obvious funk at the point where the colors blend, but I'd be willing to accept that if that funk was at least in the right place.

It's because ColorFunction expects values from [0, 1] by default so Mathematica scales everything into that range.

You have to explicitly turn that off if you want to do something different

@WReach Nice! I knew there would be names for them! (And yes I noticed the spelling :) Many thanks!

I tend to believe there is magic in true names :)

From medRxiv(line 221): "About 30% of recovered patients generated very low titers of SARS-CoV-2-specific NAbs"

They have a very small sample set (175 patients). But if their finding is true, then herd immunity might be harder to achieve than people had thought.

Here NAbs is short for neutralizing antibodies.

CodeParser is a full-fledged WL parser, and CodeInspector is a linter for WL

Please check them out and play around with them and let me know what you think!