[yt-users] projection results

Nathan Goldbaum goldbaum at ucolick.org
Mon Jun 11 14:30:26 PDT 2012


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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