[yt-users] projection results

Sam Skillman samskillman at gmail.com
Mon Jun 11 14:38:18 PDT 2012


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):
>>> [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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