[yt-users] projection results

[John ZuHone]

Ugh, sorry about that. 

On Jun 11, 2012, at 5:38 PM, Sam Skillman wrote:

> Wait.  No, I think the correct terminology is:
> 
> Density is the value (v).  Density is the weight (w).  L comes in through the dz.
> 
> The units of a density-weighted projection of density is density. 
> 
> Sam
> 
> On Mon, Jun 11, 2012 at 3:36 PM, John ZuHone <jzuhone at gmail.com> wrote:
> Yes, that's right. For myself, I prefer to weigh density by volume or by "ones", depending on the situation.
> 
> On Jun 11, 2012, at 5:32 PM, Geoffrey So wrote:
> 
>> 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):
>>> 
>>> whereas unweighted is:
>>> 
>>> 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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