[yt-users] projection results

[Geoffrey So]

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 <samskillman at gmail.com> wrote:

> 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 <matthewturk at gmail.com>wrote:
>
>> Hi Geoffrey,
>>
>> On Mon, Jun 11, 2012 at 4:10 PM, Geoffrey So <gsiisg at gmail.com> 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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