hubble-fit

hubble-fit is a collection of functions to fit the Hubble diagram with a Cosmological model.

The initial version was written in Python.
This is a reimplementation in Go.

Introduction

The data/jla_lcparams.txt file contains light-curve parameters as described by the Joint Light-curve Analysis package:

name: name of the SN
zcmb: CMB frame redshift (including peculiar velocity corrections for
      nearby supernova based on the models of M.J. Hudson)
zhel: Heliocentric redshift (note both zcmb and zhel are needed
      to compute the luminosity distance)
dz: redshift error (no longer used by the plugin)
mb: B band peak magnitude
dmb: Error in mb (includes contributions from intrinsic dispersion,
     lensing, and redshift uncertainty)
x1: SALT2 shape parameter
dx1: Error in shape parameter
colour: Colour parameter
dcolour: Error in colour
3rdvar: In these files, the log_10 host stellar mass
d3rdvar: Error in 3rdvar
tmax: Date of peak brightness (mjd)
dtmax: Error in tmax
cov_m_s: The covariance between mb and x1
cov_m_c: The covariance between mb and colour
cov_s_c: The covariance between x1 and colour
set: A number indicating which sample this SN belongs to, with
   1 - SNLS, 2 - SDSS, 3 - low-z, 4 - Riess HST
ra: Right Ascension in degree (J2000)
dec: Declination in degree (J2000)
biascor: The correction for analysis bias applied to measured magnitudes
     (this correction is already applied to mb, original measurements
      can be obtained by subtracting this term to mb)

Note that you will need the covariance matrices from JLA to run the hubble-fit code.

Example

Once you have installed the Go toolchain:

$> go get github.com/lsst-lpc/hubble-fit
$> cd $GOPATH/github.com/lsst-lpc/hubble-fit
$> time hubble-fit
hubble: using method: *optimize.NelderMead (grad=false hessian=false)
Number of supernovae :  740
mean of the residuals  0.014391538550558799
mean of the absolute residuals  0.12726543895212666
hubble: initial parameters: [0.295 0.141 3.101 -19.05 -0.07]
res=&{Location:{X:[0.295 0.141 3.101 -19.05 -0.07] F:652.7606127419591 Gradient:[] Hessian:0xc429cd80c0} Stats:{MajorIterations:19 FuncEvaluations:41 GradEvaluations:0 HessEvaluations:0 Runtime:25.060160788s} Status:FunctionConvergence}
hubble: status = FunctionConvergence
hubble: func   = 652.760613
==== results ====
Omega M = +0.2950
Alpha   = +0.1410
Beta    = +3.1010
Mb      = -19.0500
Delta M = -0.0700
Hessian: ⎡ 3510.2425270080566   1167.8890228271484    181.1999397277832   -3906.792751312256  -1216.6510734558105⎤
         ⎢ 1167.8890228271484    46425.35659790039   257.57526779174805   -784.8816604614258    3034.029556274414⎥
         ⎢  181.1999397277832   257.57526779174805   302.06271743774414  -200.42919158935547   -21.88933563232422⎥
         ⎢ -3906.792751312256   -784.8816604614258  -200.42919158935547    8549.161113739014   3000.5796813964844⎥
         ⎣-1216.6510734558105    3034.029556274414   -21.88933563232422   3000.5796813964844    4887.541770935059⎦
real 0m35.845s
user 1m3.329s
sys  0m0.545s

Python reference

$> cd $GOPATH/github.com/lsst-lpc/hubble-fit
$> time python2 ./py/hubblefit.py
./py/hubblefit.py:387: InitialParamWarning: errordef is not given. Default to 1.
  limit_Mb=(-20., -18.), limit_delta_M=(-0.1, -0.0), fix_omgM=False, fix_alpha=False, fix_beta=False, fix_Mb=False, fix_delta_M=False, print_level=1)
**************************************************
*                     MIGRAD                     *
**************************************************
**********************************************************************
---------------------------------------------------------------------------------------
fval = 682.8910357476947 | total call = 90 | ncalls = 90
edm = 5.6711138504257765e-05 (Goal: 1e-05) | up = 1.0
---------------------------------------------------------------------------------------
|          Valid |    Valid Param | Accurate Covar |         Posdef |    Made Posdef |
---------------------------------------------------------------------------------------
|           True |           True |           True |           True |          False |
---------------------------------------------------------------------------------------
|     Hesse Fail |        Has Cov |      Above EDM |                |  Reach calllim |
---------------------------------------------------------------------------------------
|          False |           True |          False |            u'' |          False |
---------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------
|      |  Name   |  Value   | Para Err |   Err-   |   Err+   |  Limit-  |  Limit+  |          |
------------------------------------------------------------------------------------------------
|    0 |    omgM =  0.2951  |  0.03327 |          |          |  0.2     |  0.4     |          |
|    1 |   alpha =  0.1412  |  0.00657 |          |          |  0.1     |  0.2     |          |
|    2 |    beta =  3.102   |  0.08064 |          |          |  2       |  4       |          |
|    3 |      Mb = -19.05   |  0.02317 |          |          | -20      | -18      |          |
|    4 | delta_M = -0.07008 |  0.02216 |          |          | -0.1     | -0       |          |
------------------------------------------------------------------------------------------------
**********************************************************************
real 1m17.719s
user 1m12.372s
sys  0m4.808s