All the Sections or Figures mentioned in this readme refer to the IST:F paper https://arxiv.org/abs/1910.09273

CONTENT OF THIS REPOSITORY

This repository contains representative Fisher matrices obtained following the recipe of the IST:F forecast paper.

One Euclid IST:F reference Fisher matrix is provided for each probe and cosmology. These matrices are in the All_results folder, divided in the optimistic and pessimistic subfolders, corresponding to the 2 sets of specifications used in this paper. These subfolders, further contain a flat and non-flat folder each. Within these, the files containing the Fisher matrices follow the naming convention

EuclidISTF_Observables_CosmoModel_SpecificationsCase.txt

For example, a Fisher matrix whose file name is

EuclidISTF_GCph_WL_XC_w0wa_flat_optimistic.txt

corresponds to the combined Fisher matrix for photometric galaxy clustering, weak lensing and their cross correlation, obtained in the flat case for the flat w0,wa cosmology, using the optimistic set of specifications. Each Fisher matrix contains a header listing the cosmological parameter of the matrix and their order.

In addition, the repository contains a set of python scripts that can be used to plot the contour ellipses and compare them with user-provided matrices.

HOW TO PRODUCE A FISHER MATRIX USING IST:F INPUT

The Euclid matrices contained in the public repository are obtained following the recipes described in section 3 for the cases analysed in section 4 and section 5.

Users who wish to validate their own code can build their Fisher matrices following these recipes, using the input files for cosmological quantities that are also included within the repository. These input files have been generated using CAMB, version August 2018.

The input files containing the cosmological quantities used to create the Fisher matrices can be found at http://pc.cd/0wJotalK . The link contains two folders: GC and WL.

GC folder:

the GC folder contains the matter power spectrum P(k,z) and growth function D(z) generated using CAMB. These quantities are available in the zip file ISTF_GC.zip. The parent folder contains the growth function D(z) and the growth rate f(z). The subfolder Pk contains the Pm(k,z), while the subfolder Pk-nw contains the Pnw(k,z) that appears in Equation 80.

Both these folders are organized as follows:

• in the fiducial folder, the P(k,z) for the fiducial cosmology are contained, with one file for each redshift at which this spectrum is computed. Each file has a suffix z_ii, where ii runs from 00 to 03 corresponding to the 4 redshift bins used for the Euclid GCsp probe z = {1.0,1.2,1.4,1.65}.
• in the par_step_eps_1p0E-2 folders, with par being the name of the parameter and step indicating a positive (pl) or negative (mn) step, the power spectra for each step in cosmological parameters are contained, following the same structure of the fiducial one (the steps amplitudes are relative; for each parameter the absolute step will be fidpar(1 + eps) with fidpar the fiducial value of the parameter and eps the value of the relative step). All the power spectrum files have the column structure

k [h/Mpc]      linear P(k,z)/sigma8^2(z) [Mpc^3/h^3]      sigma8^2(z)

while the f(z) and D(z) files have the structure

z       f(z)        D(z)

WL folder:

the WL folder contains the matter power spectrum P(k,z), generated using CAMB for the fiducial model and for each step in cosmological parameters used to compute numerical derivatives, together with a scaledmeanlum-E2Sa.dat file, which contains z (first column) and the ratio <L>(z)/L*(z) (second column) described in Equation 109.

The matter power spectra are available in two zip files:

• ISTF_WL_Flat.zip
• ISTF_WL_NonFlat.zip

The first contains the matter power spectrum P(k,z) for the flat case, while the second contains the same for the non-flat case. In each of these two zip files, the fiducial power spectrum can be found in the file pkz-Fiducial.txt, while the spectra relative to the steps in cosmological parameters are contained in subfolders whose name describe the step taken, e.g. ns_pl_eps_5p0E-2 indicates a step on ns in the positive direction of amplitude 5*10^-2 (the steps amplitudes are relative; for each parameter the absolute step will be fidpar(1 + eps) with fidpar the fiducial value of the parameter and eps the value of the relative step).

Notice that with respect to the GC input files, here many more steps for numerical derivatives are computed; this is because most of the IST:F codes for WL use the derivative scheme described in subsection 4.3.

All the P(k,z) files have the column structure

z     k [h=Mpc]     P(k,z) linear [Mpc^3/h^3]     P(k,z) nonlinear [Mpc^3/h^3]

HOW TO INCLUDE AN EXTERNAL MATRIX IN THE REPOSITORY

In order to compare their own Fisher code with the IST:F results, users will need to reproduce the cases described here and add their matrices in the corresponding folder. The filenames of the new matrices, must follow the convention of the repository, i.e. with a prefix stating the name of the code used, and a suffix containing the observables included in the matrix, the cosmological model used and the specifications case. The full description of the cases, with all the corresponding specifications used to obtain the matrices, can be found in section 4.

Furthermore, each matrix file provided by users must contain the header listing the cosmological parameters and their order. The matrices provided by the user must be placed in the subfolders of the corresponding cases.

HOW TO COMPARE AN EXTERNAL FISHER MATRIX

The python script performing the IST:F comparison can be launched from the parent folder using

python comparison.py [-o OBSERVABLES ] [-f USERFISHER ]

The -o and -f arguments are optional.

USERFISHER are the labels of the user provided Fisher matrices. Notice that the user's matrices must be placed in the correct folders of the repository and must follow the filename notation described above, with USERFISHER the prefix of the filename, i.e. the code name. The script will produce plots, similar to the comparison plots of section 4, only for those cases for which an external matrix to compare with is found. In case no USERFISHER argument is provided, a test matrix will be used. This test matrix is contained within the repository only for the Cross Correlation comparison cases (see subsection 4.4).

The OBSERVABLES can be one or more of the cases considered in section 4, i.e.

• GC for spectrocopic Galaxy Clustering
• WL for Weak Lensing
• XC for Probe Combination and Cross Correlation

The script can perform one, two or all cases at once. The latter is the default selection if no observable is specified. Results will be placed in results folders in each of the subcases locations, e.g.

All_results/optimistic/flat/results_XC

The comparison tool consists of:

• a common trunk, comparison.py found in the parent folder.
• 3 apps (appGC.py, appWL.py, appXC.py) found in PlottingScripts/ handling the different comparisons
• a set of plotting and analysis libraries found in PlottingScripts/

As an example, let's assume that a user wants to compare a WL matrix computed in the optimistic case, for a flat w_0,w_a cosmology. The user will add the matrix as

All_results/optimistic/flat/MyName_WL_w0wa_flat_optimistic.txt

Running the script with the command

python comparison.py -o WL -f MyName

will compare the new matrix with the Euclid IST:F for this specific case and cosmology, which will be found in

All_results/optimistic/flat/results_WL

Notice that, as said above, the script does not produce comparison results for those cases in which no external matrix is provided. In the example above, where only the WL, optimistic matrix for w_0,w_a is provided, the script will produce the results only for this specific case also running

python comparison.py -f MyName

HOW TO OBTAIN RESULTS FOR THE IST:F AND EXTERNAL MATRICES

The python script performing the IST:F ellipses plot can be launched from the parent folder using

python ellipses.py [-o OBSERVABLES ] [-f USERFISHER ] [-n USERNAME ] [-c USERCOLOR]

The -o, -f, -n and -c arguments are optional.

In case no arguments are provided, the script will reproduce Fig.10 from the paper.

With the option -o a list of OBSERVABLES can be specified, separated by spaces. Available options:

• All produces a plot like Fig.10 for different observables.
• XC produces a plot focusing on XC correlations, like Fig.11.
• GC produces a plot containing only GCs contours.
• WL produces a plot containing only WL contours.

With the option -f, a USERFISHER can be specified, which is the relative path to the Fisher matrix provided by the user. Notice that the user's matrices must be placed in the correct folders of the repository and must follow the filename notation described above. Warning: while in the comparison script case the user can provide multiple external Fisher matrices, the results scripts onle accept a single external matrix.

If an external user Fisher matrix is provided, the script will overplot it on top of the other ellipses using a color and a label name provided by the user. Default color: black, default name: USER.

The user can change the color and the label name of its Fisher matrix, with the option -c and -n, respectively.

Ellipses plots will be placed in the following folder, e.g.

All_results/optimistic/flat/results_ellipses

Additionally to the elliptical contours, the routine also produces a file called:

w0waCDM-flat-optimistic_bounds.txt

containing the relative errors on all the parameters of interest and a file

w0waCDM-flat-optimistic_FoMs.txt

containing the FoM for w_0,w_a corresponding to each of the Fisher matrices which were plotted.

The .ini files inside the directory PlottingScripts/ store all the parameters of the plot, and provide a way for the user to gain finer control of the plotting routine, if needed.