Reconstruction (Log Binning) Results

In this post I discussed trying different binning to get the reconstruction to overlap more with the actual correlation functions.

Here is the binning I am using. The binning is log in theta (for 2d correlation function) and rlos (for 3d correlation function), but the binning in redshift is such that each bin has the same number of galaxies.

Here are the arrays:

rbins = array([ 4.592407, 136.86079 , 170.595585, 194.675063, 211.888514,

227.822058, 242.439338, 254.738113, 267.180894, 277.596667,

287.557931, 297.031654, 305.563449, 314.144417, 322.061375,

329.842934, 337.956897, 345.179652, 352.14308 , 359.026505,

365.954462, 372.052363, 378.261215, 384.175881, 389.837465,

395.409799, 400.562692, 405.823926, 411.006328, 416.036745,

420.853707, 425.608283, 430.068758, 434.598696, 438.968533,

443.201263, 447.527471, 451.469393, 455.440266, 459.405314,

463.13316 , 466.657868, 470.378975, 474.188462, 478.033728,

481.934477, 485.61191 , 489.252768, 492.81945 , 496.462536,

499.999607]

theta = array([ 1.12201850e-03, 1.41253750e-03, 1.77827940e-03,

2.23872110e-03, 2.81838290e-03, 3.54813390e-03,

4.46683590e-03, 5.62341330e-03, 7.07945780e-03,

8.91250940e-03, 1.12201845e-02, 1.41253754e-02,

1.77827941e-02, 2.23872114e-02, 2.81838293e-02,

3.54813389e-02, 4.46683592e-02, 5.62341325e-02,

7.07945784e-02, 8.91250938e-02, 1.12201845e-01,

1.41253754e-01, 1.77827941e-01, 2.23872114e-01,

2.81838293e-01, 3.54813389e-01, 4.46683592e-01,

5.62341325e-01, 7.07945784e-01, 8.91250938e-01,

1.12201845e+00, 1.41253754e+00, 1.77827941e+00,

2.23872114e+00, 2.81838293e+00, 3.54813389e+00,

4.46683592e+00, 5.62341325e+00, 7.07945784e+00,

8.91250938e+00])

rlos = array([ 0.52962686, 0.59425111, 0.66676072, 0.74811783,

0.83940201, 0.94182454, 1.05674452, 1.18568685,

1.33036253, 1.49269131, 1.6748272 , 1.87918702,

2.10848252, 2.36575629, 2.65442222, 2.97831072,

3.34171959, 3.74947105, 4.20697571, 4.72030438,

5.29626863, 5.94251114, 6.66760716, 7.48117828,

8.39402009, 9.41824545, 10.5674452 , 11.85686853,

13.3036253 , 14.92691309, 16.74827196, 18.79187021,

21.08482517, 23.65756295, 26.54422221, 29.78310718,

33.41719588, 37.49471047, 42.06975708, 47.20304381])

Here are plots of the 2D and 3D correlation functions:

I've found it hard to find phibin spacing that doesn't go below the limits of the correlation function. I get the following error with a lot of binning:

sximat=crl.getximat(th,rlos,phibins,rs,xispec,xierr)

0.000505647568659 is less than minimum r_ss 0.000529627

refusing to extrapolate

Perhaps I should allow it to extrapolate to smaller angles....

but the following phibins works:

phibins = array([ 0.01 , 0.03578947, 0.06157895, 0.08736842, 0.11315789,

0.13894737, 0.16473684, 0.19052632, 0.21631579, 0.24210526,

0.26789474, 0.29368421, 0.31947368, 0.34526316, 0.37105263,

0.39684211, 0.42263158, 0.44842105, 0.47421053, 0.5 ])

Here is what the xi and sximat plots look like, as you can see they overlap more now:

But the reconstruction isn't so great:

If I change the binning (here is 50 bins):

phibins =

array([ 0.00459241, 0.13686079, 0.17059558, 0.19467506, 0.21188851,

0.22782206, 0.24243934, 0.25473811, 0.26718089, 0.27759667,

0.28755793, 0.29703165, 0.30556345, 0.31414442, 0.32206137,

0.32984293, 0.3379569 , 0.34517965, 0.35214308, 0.3590265 ,

0.36595446, 0.37205236, 0.37826121, 0.38417588, 0.38983746,

0.3954098 , 0.40056269, 0.40582393, 0.41100633, 0.41603674,

0.42085371, 0.42560828, 0.43006876, 0.4345987 , 0.43896853,

0.44320126, 0.44752747, 0.45146939, 0.45544027, 0.45940531,

0.46313316, 0.46665787, 0.47037898, 0.47418846, 0.47803373,

0.48193448, 0.48561191, 0.48925277, 0.49281945, 0.49646254,

0.49999961])

Another thing is that now I have so many theta, rlos, r bins the crl.getCoeff takes a long time to run.

I suppose this looks better. At this point I need to either try a different binning, or re-write the crl.getximat to allow extrapolation to smaller angles / separations to that I can try different reconstructions. Opinions Alexia?