[yt-users] projection results

[Geoffrey So]

So the weighted projection of density would use "density" as the value and
"density * L" as the weight, and return units of Density?

From
G.S.

On Mon, Jun 11, 2012 at 2:30 PM, Nathan Goldbaum <goldbaum at ucolick.org>wrote:

> Hi Geoffrey,
>
> Well, if you look at Sam's formula and convert it into the discrete
> version, what you're really doing is:
>
> (Density1**2 * L1 + Density2**2 * L2 +...)/(Density1*L1 + Density2*L2 +
> ...) =  units of g/cm^3
>
> Unweighted projections always have column density units.  So, if you're
> projecting a field with units of T-rex, you'll get back an image with units
> of T-rex*cm.
>
> Hope that helped,
>
> Nathan Goldbaum
> Graduate Student
> Astronomy & Astrophysics, UCSC
> goldbaum at ucolick.org
> http://www.ucolick.org/~goldbaum
>
> On Jun 11, 2012, at 2:27 PM, Geoffrey So wrote:
>
> 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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