From e4060c6baf99427e58ffd6592a737dee069b7d06 Mon Sep 17 00:00:00 2001 From: Nicolas Tessore Date: Fri, 20 Oct 2023 08:41:03 +0100 Subject: [PATCH 1/5] add example for biased lognormal fields --- examples/basic/biased_lognormal.py | 166 +++++++++++++++++++++++++++++ examples/basic/cls.npy | Bin 1225352 -> 0 bytes examples/basic/cls.npz | Bin 0 -> 1226948 bytes examples/basic/shells.py | 20 ++-- 4 files changed, 174 insertions(+), 12 deletions(-) create mode 100644 examples/basic/biased_lognormal.py delete mode 100644 examples/basic/cls.npy create mode 100644 examples/basic/cls.npz diff --git a/examples/basic/biased_lognormal.py b/examples/basic/biased_lognormal.py new file mode 100644 index 0000000..a931045 --- /dev/null +++ b/examples/basic/biased_lognormal.py @@ -0,0 +1,166 @@ +""" +Biased lognormal fields +======================= + +This example shows how to compute a biased lognormal field by rescaling the +*alms* of the matter field with a biased angular power spectrum. + +""" + +# %% +# Setup +# ----- +# +# This example simulates a lognormal matter field and a biased tracer field. +# +# The precomputed angular matter power spectra from the :doc:`/basic/shells` +# example are used, so the simulation is set up in the same way. + +import numpy as np +import healpy as hp +import matplotlib.pyplot as plt + +# use the CAMB cosmology that generated the matter power spectra +import camb +from cosmology import Cosmology + +# GLASS imports +from glass.shells import distance_grid, partition, tophat_windows +from glass.fields import (discretized_cls, lognormal_gls, generate_alms, + biased_cls, rescaled_alm, alm_to_lognormal, getcl) +from glass.user import load_cls + + +# cosmology for the simulation +h = 0.7 +Oc = 0.25 +Ob = 0.05 + +# basic parameters of the simulation +nside = lmax = 256 + +# set up CAMB parameters for matter angular power spectrum +pars = camb.set_params(H0=100*h, omch2=Oc*h**2, ombh2=Ob*h**2, + NonLinear=camb.model.NonLinear_both) + +# get the cosmology from CAMB +cosmo = Cosmology.from_camb(pars) + +# shells of 200 Mpc in comoving distance spacing +zgrid = distance_grid(cosmo, 0., 1., dx=200.) + +# uniform matter weight function +shells = tophat_windows(zgrid) + +# load the previously-computed angular matter power spectra +cls = load_cls("cls.npz") + +# apply angular discretisation to cls +cls = discretized_cls(cls, nside=nside, lmax=lmax, ncorr=3) + +# %% +# Matter +# ------ +# +# The matter fields in this example are lognormal. To simulate both matter and +# the biased tracer field, we require the Gaussian *alm* array for each shell. +# We therefore use the :func:`~glass.fields.generate_alms` generator, instead +# of generating the lognormal matter fields directly. + +# compute Gaussian angular power spectra for lognormal matter fields +gls = lognormal_gls(cls) + +# generator for Gaussian random field alms +alms = generate_alms(gls, ncorr=3) + +# %% +# Biased tracer +# ------------- +# +# The biased tracer fields in this example have a single bias factor *bias*, +# but this could be an array with a different value for each shell. The +# biasing works by first applying the bias factors to the original *cls* array +# using the :func:`~glass.fields.biased_cls` function. We then compute the +# Gaussian angular power spectra for biased lognormal fields. +# +# This is just one example of how to obtained biased tracer fields. The +# Gaussian angular power spectra could be obtained in any number of ways. + +# this is the bias we want to implement +bias = 1.8 + +# apply linear bias factor to the cls +cls_b = biased_cls(cls, bias) + +# compute Gaussian cls for the biased lognormal galaxy fields +gls_b = lognormal_gls(cls_b) + +# %% +# This example will produce an integrated density for the unbiased and biased +# fields. Here, we are making an example *dndz* distribution, and computing +# its contribution to each matter shell. + +# localised redshift distribution +# the actual density per arcmin2 does not matter here, it is never used +z = np.linspace(0, 1, 101) +dndz = np.exp(-(z - 0.5)**2/(0.1)**2) + +# partition the dndz function into a ngal value for each shell +ngal = partition(z, dndz, shells) + +# %% +# Simulation +# ---------- +# The simulation generates the Gaussian *alm* for each matter shell and +# computes its lognormal matter field. The *alm* array is rescaled with the +# biased *gls* to compute the biased lognormal tracer field. Both are then +# added to an integrated number density field, using the shell's contribution +# *ngal* to the total redshift distribution. + +# initialise maps for biased and unbiased total number densities +ntot = np.zeros(12 * nside**2) +ntot_b = np.zeros(12 * nside**2) + +# main loop to simulate the matter fields iteratively +for i, alm in enumerate(alms): + + # first, compute the lognormal matter field + delta = alm_to_lognormal(alm, nside) + + # now rescale the alm to the biased lognormal field for galaxies + alm_b = rescaled_alm(alm, getcl(gls_b, i), getcl(gls, i)) + + # compute the biased lognormal galaxies field + delta_b = alm_to_lognormal(alm_b, nside) + + # add both fields to number density + ntot += ngal[i] * (1 + delta) + ntot_b += ngal[i] * (1 + delta_b) + +# %% +# Analysis +# -------- +# To make sure the biased tracer field works as expected, we compute the +# density contrast of the unbiased and biased integrated fields, then compare +# their bias to the linear bias factor we used above. + +# this is the mean number density over the entire distribution +nbar = np.trapz(dndz, z) + +# compute the integrated density contrasts +delta_tot = (ntot - nbar)/nbar +delta_tot_b = (ntot_b - nbar)/nbar + +# get the angular power spectra of the number density maps +sim_cls = hp.anafast([delta_tot, delta_tot_b], + pol=False, lmax=lmax, use_pixel_weights=True) + +# plot the unbiased and biased cls +l = np.arange(lmax+1) +plt.plot(l, (sim_cls[1]/sim_cls[0])**0.5, "-k", lw=2, label="simulated bias") +plt.axhline(bias, c="r", ls="-", lw=1, label="bias factor") +plt.xscale("log") +plt.xlabel(r"angular mode number $l$") +plt.ylabel(r"bias factor") +plt.legend(frameon=False) +plt.show() diff --git a/examples/basic/cls.npy b/examples/basic/cls.npy deleted file mode 100644 index f7b3db9b6a1359f8e979c54e48fec0dd115b1ae0..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 1225352 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define the shells for these examples, and use CAMB to compute the # angular matter power spectra for the shell definitions. -import numpy as np import camb from cosmology import Cosmology -import glass.shells -import glass.ext.camb +from glass.shells import distance_grid, tophat_windows +from glass.ext.camb import matter_cls, camb_tophat_weight +from glass.user import save_cls # cosmology for the simulation @@ -41,18 +41,14 @@ cosmo = Cosmology.from_camb(pars) # shells of 200 Mpc in comoving distance spacing -zb = glass.shells.distance_grid(cosmo, 0., 1., dx=200.) +zgrid = distance_grid(cosmo, 0., 1., dx=200.) # uniform matter weight function # CAMB requires linear ramp for low redshifts -ws = glass.shells.tophat_windows(zb, weight=glass.ext.camb.camb_tophat_weight) +shells = tophat_windows(zgrid, weight=camb_tophat_weight) # compute angular matter power spectra with CAMB -cls = glass.ext.camb.matter_cls(pars, lmax, ws) +cls = matter_cls(pars, lmax, shells) - -# %% -# Save -# ---- -# We save the shell definitions to file, for use in other examples. -np.save('cls.npy', cls) +# save the angular power spectra to file, to use in other examples +save_cls("cls.npz", cls) From 90bf85642df7438af9491f65ade56283dca9a61d Mon Sep 17 00:00:00 2001 From: Nicolas Tessore Date: Fri, 20 Oct 2023 09:18:48 +0100 Subject: [PATCH 2/5] update ReadTheDocs config --- .readthedocs.yml | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/.readthedocs.yml b/.readthedocs.yml index 8076f03..7e47f55 100644 --- a/.readthedocs.yml +++ b/.readthedocs.yml @@ -1,5 +1,10 @@ version: 2 +build: + os: ubuntu-22.04 + tools: + python: "3.11" + python: install: - requirements: requirements.txt From 8e7cea5dc944b3e962c7680307b78711c4ce797f Mon Sep 17 00:00:00 2001 From: Nicolas Tessore Date: Fri, 20 Oct 2023 11:09:11 +0100 Subject: [PATCH 3/5] updates to existing examples --- examples/advanced/plot_s4_galaxies.py | 13 ++++++++----- examples/advanced/plot_shears.py | 18 +++++++++++------- .../basic/{plot_density.py => galaxies.py} | 10 +++++++--- examples/basic/{plot_lensing.py => lensing.py} | 12 ++++++++---- examples/basic/matter.py | 10 +++++++--- 5 files changed, 41 insertions(+), 22 deletions(-) rename examples/basic/{plot_density.py => galaxies.py} (93%) rename examples/basic/{plot_lensing.py => lensing.py} (94%) diff --git a/examples/advanced/plot_s4_galaxies.py b/examples/advanced/plot_s4_galaxies.py index 2227cdd..afc3266 100644 --- a/examples/advanced/plot_s4_galaxies.py +++ b/examples/advanced/plot_s4_galaxies.py @@ -2,9 +2,9 @@ Stage IV Galaxy Survey ====================== -This example simulates a galaxy catalogue from a Stage IV Space Satellite Galaxy -Survey such as *Euclid* and *Roman* combining the :doc:`/basic/plot_density` and -:doc:`/basic/plot_lensing` examples with galaxy ellipticities and galaxy shears, +This example simulates a galaxy catalogue from a Stage IV Space Satellite +Galaxy Survey such as *Euclid* and *Roman* combining the :doc:`/basic/galaxies` +and :doc:`/basic/lensing` examples with galaxy ellipticities and galaxy shears, as well as using some auxiliary functions. The focus in this example is mock catalogue generation using auxiliary functions @@ -71,9 +71,12 @@ # compute the angular matter power spectra of the shells with CAMB cls = glass.ext.camb.matter_cls(pars, lmax, ws) -# compute Gaussian cls for lognormal fields for 3 correlated shells +# angular discretisation with 3 correlated shells # putting nside here means that the HEALPix pixel window function is applied -gls = glass.fields.lognormal_gls(cls, nside=nside, lmax=lmax, ncorr=3) +cls = glass.fields.discretized_cls(cls, nside=nside, lmax=lmax, ncorr=3) + +# compute Gaussian cls for lognormal fields +gls = glass.fields.lognormal_gls(cls) # generator for lognormal matter fields matter = glass.fields.generate_lognormal(gls, nside, ncorr=3) diff --git a/examples/advanced/plot_shears.py b/examples/advanced/plot_shears.py index 8ed3781..2988e69 100644 --- a/examples/advanced/plot_shears.py +++ b/examples/advanced/plot_shears.py @@ -3,8 +3,8 @@ ============ This example simulates a galaxy catalogue with shears affected by weak lensing, -combining the :doc:`/basic/plot_density` and :doc:`/basic/plot_lensing` examples -with generators for the intrinsic galaxy ellipticity and the resulting shear. +combining the :doc:`/basic/galaxies` and :doc:`/basic/lensing` examples with +generators for the intrinsic galaxy ellipticity and the resulting shear. ''' @@ -31,6 +31,7 @@ import glass.shapes import glass.lensing import glass.galaxies +import glass.user from glass.core.constants import ARCMIN2_SPHERE @@ -56,15 +57,18 @@ ws = glass.shells.tophat_windows(zb) # load the angular matter power spectra previously computed with CAMB -cls = np.load('../basic/cls.npy') +cls = glass.user.load_cls('../basic/cls.npz') + +# angular discretisation with 3 correlated shells +# putting nside here means that the HEALPix pixel window function is applied +cls = glass.fields.discretized_cls(cls, nside=nside, lmax=lmax, ncorr=3) # %% # Matter # ------ -# compute Gaussian cls for lognormal fields for 3 correlated shells -# putting nside here means that the HEALPix pixel window function is applied -gls = glass.fields.lognormal_gls(cls, nside=nside, lmax=lmax, ncorr=3) +# compute Gaussian cls for lognormal fields +gls = glass.fields.lognormal_gls(cls) # generator for lognormal matter fields matter = glass.fields.generate_lognormal(gls, nside, ncorr=3) @@ -136,7 +140,7 @@ # apply the shear fields to the ellipticities gal_she = glass.galaxies.galaxy_shear(gal_lon, gal_lat, gal_eps, - kappa_i, gamm1_i, gamm2_i) + kappa_i, gamm1_i, gamm2_i) # map the galaxy shears to a HEALPix map; this is opaque but works gal_pix = hp.ang2pix(nside, gal_lon, gal_lat, lonlat=True) diff --git a/examples/basic/plot_density.py b/examples/basic/galaxies.py similarity index 93% rename from examples/basic/plot_density.py rename to examples/basic/galaxies.py index 190d84d..1ecc96c 100644 --- a/examples/basic/plot_density.py +++ b/examples/basic/galaxies.py @@ -28,6 +28,7 @@ import glass.fields import glass.points import glass.galaxies +import glass.user # cosmology for the simulation @@ -52,14 +53,17 @@ ws = glass.shells.tophat_windows(zb) # load the angular matter power spectra previously computed with CAMB -cls = np.load('cls.npy') +cls = glass.user.load_cls('cls.npz') + +# angular discretisation with 3 correlated shells +cls = glass.fields.discretized_cls(cls, nside=nside, lmax=lmax, ncorr=3) # %% # Matter # ------ -# compute Gaussian cls for lognormal fields for 3 correlated shells -gls = glass.fields.lognormal_gls(cls, nside=nside, lmax=lmax, ncorr=3) +# compute Gaussian cls for lognormal fields +gls = glass.fields.lognormal_gls(cls) # generator for lognormal matter fields matter = glass.fields.generate_lognormal(gls, nside, ncorr=3) diff --git a/examples/basic/plot_lensing.py b/examples/basic/lensing.py similarity index 94% rename from examples/basic/plot_lensing.py rename to examples/basic/lensing.py index 7489639..4190fe0 100644 --- a/examples/basic/plot_lensing.py +++ b/examples/basic/lensing.py @@ -36,6 +36,7 @@ import glass.fields import glass.lensing import glass.galaxies +import glass.user # cosmology for the simulation @@ -60,15 +61,18 @@ ws = glass.shells.tophat_windows(zb) # load the angular matter power spectra previously computed with CAMB -cls = np.load('cls.npy') +cls = glass.user.load_cls('cls.npz') + +# angular discretisation with 3 correlated shells +# putting nside here means that the HEALPix pixel window function is applied +cls = glass.fields.discretized_cls(cls, nside=nside, lmax=lmax, ncorr=3) # %% # Matter # ------ -# compute Gaussian cls for lognormal fields for 3 correlated shells -# putting nside here means that the HEALPix pixel window function is applied -gls = glass.fields.lognormal_gls(cls, nside=nside, lmax=lmax, ncorr=3) +# compute Gaussian cls for lognormal fields +gls = glass.fields.lognormal_gls(cls) # generator for lognormal matter fields matter = glass.fields.generate_lognormal(gls, nside, ncorr=3) diff --git a/examples/basic/matter.py b/examples/basic/matter.py index b6a52d2..8d4cfa5 100644 --- a/examples/basic/matter.py +++ b/examples/basic/matter.py @@ -26,6 +26,7 @@ # these are the GLASS imports: matter and random fields import glass.shells import glass.fields +import glass.user # cosmology for the simulation @@ -48,10 +49,13 @@ zb = glass.shells.distance_grid(cosmo, 0., 1., dx=200.) # load precomputed angular matter power spectra -cls = np.load('cls.npy') +cls = glass.user.load_cls('cls.npz') -# compute Gaussian cls for lognormal fields with 3 correlated shells -gls = glass.fields.lognormal_gls(cls, ncorr=3, nside=nside) +# angular discretisation with 3 correlated shells +cls = glass.fields.discretized_cls(cls, nside=nside, ncorr=3) + +# compute Gaussian cls for lognormal fields +gls = glass.fields.lognormal_gls(cls) # this generator will yield the matter fields in each shell matter = glass.fields.generate_lognormal(gls, nside, ncorr=3) From 8ba32e515e51d7feb1313be9411f5228a35ee6c1 Mon Sep 17 00:00:00 2001 From: Nicolas Tessore Date: Fri, 20 Oct 2023 13:09:01 +0100 Subject: [PATCH 4/5] add warning about biased lognormal tracers --- examples/basic/biased_lognormal.py | 28 ++++++++++++++++++++++------ 1 file changed, 22 insertions(+), 6 deletions(-) diff --git a/examples/basic/biased_lognormal.py b/examples/basic/biased_lognormal.py index a931045..558f367 100644 --- a/examples/basic/biased_lognormal.py +++ b/examples/basic/biased_lognormal.py @@ -5,6 +5,8 @@ This example shows how to compute a biased lognormal field by rescaling the *alms* of the matter field with a biased angular power spectrum. +**WARNING**: This model has a major caveat. See below. + """ # %% @@ -157,10 +159,24 @@ # plot the unbiased and biased cls l = np.arange(lmax+1) -plt.plot(l, (sim_cls[1]/sim_cls[0])**0.5, "-k", lw=2, label="simulated bias") -plt.axhline(bias, c="r", ls="-", lw=1, label="bias factor") -plt.xscale("log") -plt.xlabel(r"angular mode number $l$") -plt.ylabel(r"bias factor") -plt.legend(frameon=False) +fig, ax = plt.subplots(2, 1, sharex=True, sharey=True, layout="constrained") +ax[0].plot(l, (sim_cls[1]/sim_cls[0])**0.5, "-k", lw=2, label="simulated bias (biased $\\times$ biased)") +ax[0].axhline(bias, c="r", ls="-", lw=1, label="bias factor") +ax[0].legend(frameon=False) +ax[0].set_ylabel(r"bias factor") +ax[1].plot(l, sim_cls[2]/sim_cls[0], "-k", lw=2, label="simulated bias (biased $\\times$ unbiased)") +ax[1].axhline(bias, c="r", ls="-", lw=1, label="bias factor") +ax[1].legend(frameon=False) +ax[1].set_ylabel(r"bias factor") +ax[1].set_xscale("log") +ax[1].set_xlabel(r"angular mode number $l$") +ax[1].set_ylim(bias - 0.25, bias + 0.25) plt.show() + +# %% +# The results show that the biased lognormal tracer is able to capture the +# linear bias in the auto-correlation of the biased tracer reasonably well. +# **However, there is a significant deviation from the linear model in the +# cross-correlation between biased tracer and unbiased field.** The biased +# lognormal tracer model should therefore only be used where this defect is +# acceptable. From 69725e031da0177218cb740ebf8e044859de9774 Mon Sep 17 00:00:00 2001 From: Nicolas Tessore Date: Sat, 21 Oct 2023 10:51:59 +0100 Subject: [PATCH 5/5] add some potential causes to the biased lognormal caveat --- examples/basic/biased_lognormal.py | 8 +++++--- 1 file changed, 5 insertions(+), 3 deletions(-) diff --git a/examples/basic/biased_lognormal.py b/examples/basic/biased_lognormal.py index 558f367..7e4dc20 100644 --- a/examples/basic/biased_lognormal.py +++ b/examples/basic/biased_lognormal.py @@ -177,6 +177,8 @@ # The results show that the biased lognormal tracer is able to capture the # linear bias in the auto-correlation of the biased tracer reasonably well. # **However, there is a significant deviation from the linear model in the -# cross-correlation between biased tracer and unbiased field.** The biased -# lognormal tracer model should therefore only be used where this defect is -# acceptable. +# cross-correlation between biased tracer and unbiased field.** The "defect" +# in the model is roughly a function of the amplitude of the spectrum, and +# hence tendentially worse for lower redshifts, higher :math:`sigma_8` values, +# and higher bias values. The biased lognormal tracer model should therefore +# only be used where this defect is acceptable.

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