Thanks for the explanations, but I think I'm still confused about something
and want a bit more clarifications,
I thought when I'm projecting density, I'm doing (Density1 + Density2
+...), which is obviously wrong because I forgot about the Length
dimention, so it should be:
Density1 * L1 + Density2 * L2 + ... = units of g/cm^2
When I'm projecting density with density as weight, I would think I would
then be doing:
(Density1**2 * L1 + Density2**2 * L2 +...)/(Density1 + Density2 + ...) =
units of g/cm^2
But according to Sam, the units of weighted should be g/cm^3, where the
role of v and w is switched. "v": O(Density) is the value, and "w":
O(Density)*O(L) is the weight. And thus we get a projection weighted
Density cell value in units of g/cm^3 instead of g/cm^2. Shouldn't the
weighting not change the units, or am I confusing projection weighted
density with density weighted projection?
I've never done unweighted projections, so I kept using the units of the
field (g/cm^3 in case of Density), those units seems right or have I been
wrong all along?
From
G.S.
On Mon, Jun 11, 2012 at 1:32 PM, Sam Skillman
Geoffrey, if it helps, in the continuum limit, a weighted projection along the z direction is (v is the field, w is the weight): [image: Inline image 1] whereas unweighted is: [image: Inline image 4] For your example, the order of magnitude of your result would be O(density)**2*O(L)/O(density)*O(L) = O(density) for the weighted projection. The unweighted is just O(density)*O(L).
Sam
On Mon, Jun 11, 2012 at 2:12 PM, Matthew Turk
wrote: Hi Geoffrey,
On Mon, Jun 11, 2012 at 4:10 PM, Geoffrey So
wrote: Hi, sorry for asking a dumb question, but when I do a projection of density
field = "Density" proj = pf.h.proj(direction, field, weight_field=field)
the numbers I get are ~1e-28
but when I do proj = pf.h.proj(direction, field, weight_field=None)
the numbers become ~1e-4
this is a 64 cube simulation, if I were to multiply 64 * 1e-28 for a projection with no weighting, shouldn't I still get numbers on the order of 1e-26 or 1e-27? I'm guessing there's something I've misunderstood about pf.h.proj. Am I missing like a CGS conversion factor when I don't weight it by some field?
Nope, weighting means to take the average with respect to some other field. So when you don't weight it, you don't take an average, you get a line integral. It's probably different by a factor of roughly the same OOM as the number of centimeters your box is across.
-Matt
From G.S.
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