Initialize notebook

%pylab inline
import aquila_borg as borg
import aquila as aq
import numpy as np

Populating the interactive namespace from numpy and matplotlib
[INFO   ] libLSS version v2.0.0alpha-194-g4fdb32a5 built-in modules ares_fg;borg;dm_sheet;hades;hmclet;python
[INFO S ] Registered forward models:
[INFO S ]   - 2LPT_CIC
[INFO S ]   - 2LPT_CIC_OPENMP
[INFO S ]   - 2LPT_DOUBLE
[INFO S ]   - 2LPT_NGP
[INFO S ]   - Downgrade
[INFO S ]   - EnforceMass
[INFO S ]   - HADES_LOG
[INFO S ]   - HADES_PT
[INFO S ]   - Haar
[INFO S ]   - LPT_CIC
[INFO S ]   - LPT_CIC_OPENMP
[INFO S ]   - LPT_DOUBLE
[INFO S ]   - LPT_NGP
[INFO S ]   - PATCH_MODEL
[INFO S ]   - PM_CIC
[INFO S ]   - PM_CIC_OPENMP
[INFO S ]   - PRIMORDIAL
[INFO S ]   - PRIMORDIAL_FNL
[INFO S ]   - QLPT
[INFO S ]   - QLPT_RSD
[INFO S ]   - Softplus
[INFO S ]   - TRANSFER_EHU
[INFO S ]   - Transfer
[INFO S ]   - Upgrade
[INFO S ]   - bias::BrokenPowerLaw
[INFO S ]   - bias::DoubleBrokenPowerLaw
[INFO S ]   - bias::EFT
[INFO S ]   - bias::EFT_Thresh
[INFO S ]   - bias::Linear
[INFO S ]   - bias::ManyPower_1^1
[INFO S ]   - bias::ManyPower_1^2
[INFO S ]   - bias::ManyPower_1^4
[INFO S ]   - bias::ManyPower_2^2
[INFO S ]   - bias::Noop
[INFO S ]   - bias::PowerLaw
[INFO   ] Found MPI4PY.
[INFO   ] CPU features: MMX AVX AVX2 AVX512F SSE SSE2 SSE3 SSE4.1 SSE4.2

Chose a box and cosmological parameters

bb = borg.forward.BoxModel()
bb.N=64,64,64
cpar = borg.cosmo.CosmologicalParameters()
x = np.fft.rfftn(np.random.randn(*bb.N)/bb.Ntot**0.5)
delta_set={}

Run a 2LPT simulation

chain = borg.forward.ChainForwardModel(bb)
chain.addModel(borg.forward.models.HermiticEnforcer(bb))
chain.addModel(borg.forward.models.Primordial(bb, 1.0))
ehu = borg.forward.models.EisensteinHu(bb)
chain.addModel(ehu)
lpt = borg.forward.models.Borg2Lpt(bb, bb, ai=1.0,
                            supersampling=2)
chain.addModel(lpt)
chain.setCosmoParams(cpar)

chain.forwardModel_v2(x)
delta_2lpt=np.empty(bb.N)
chain.getDensityFinal(delta_2lpt)

imshow(delta_2lpt[:,32,:],extent=(0,bb.L[0],0,bb.L[1]),vmin=-1,vmax=1)

[STD    ] |     ___________
[STD    ] |    /-/_"/-/_/-/|     __________________________
[STD    ] |   /"-/-_"/-_//||                BORG3 model
[STD    ] |  /__________/|/|     (c) Jens Jasche 2012 - 2019
[STD    ] |  |"|_'='-]:+|/||        Guilhem Lavaux 2014 - 2019
[STD    ] |  |-+-|.|_'-"||//     __________________________
[STD    ] |  |[".[:!+-'=|//
[STD    ] |  |='!+|-:]|-|/
[STD    ] |   ----------
[STD    ] |
[STD    ] | Please acknowledge the following papers:
[STD    ] |   - Jasche & Lavaux (A&A, 2019, arXiv 1806.11117)
[STD    ] |   - Jasche & Wandelt (MNRAS, 2012, arXiv 1203.3639)
[STD    ] |   - Jasche & Kitaura (MNRAS, 2010, arXiv 0911.2496)
[STD    ] |   - And relevant papers depending on the used sub-module/contribution
[STD    ] |

[STD    ] | This is BORG version 7647fd4efc0604e6073b38472c31486fd514667a

<matplotlib.image.AxesImage at 0x7fa75382fc40>

Run t-COLA simulation

def print_step(t,i):
    print(f" --- stepping t={t}, i={i}")

borg.console().setVerboseLevel(1)
for ff in [2,4]:
    for n in [5,10,20,40,80]:
        print(f"Running with {n} steps, ff={ff}...")
        chain = borg.forward.ChainForwardModel(bb)
        chain.addModel(borg.forward.models.HermiticEnforcer(bb))
        chain.addModel(borg.forward.models.Primordial(bb, 1.0))
        ehu = borg.forward.models.EisensteinHu(bb)
        chain.addModel(ehu)
        pm = borg.forward.models.BorgPM(bb, bb, ai=1.0,
                                        nsteps=n, supersampling=2, force_factor=ff, z_start=50., tCOLA=True)
        pm.setStepNotifier(print_step)
        pm.setAdjointRequired(False)
        chain.addModel(pm)
        chain.setCosmoParams(cpar)

        chain.forwardModel_v2(x)
        delta_set[(ff,n)]=np.empty(bb.N)
        chain.getDensityFinal(delta_set[(ff,n)])
        delta_in=np.empty(bb.N)
        ehu.getDensityFinal(delta_in)

Running with 5 steps, ff=2...
 --- stepping t=0.14215686274509803, i=2097152
 --- stepping t=0.38725490196078427, i=2097152
 --- stepping t=0.6323529411764706, i=2097152
 --- stepping t=0.8774509803921569, i=2097152
Running with 10 steps, ff=2...
 --- stepping t=0.07407407407407407, i=2097152
 --- stepping t=0.1830065359477124, i=2097152
 --- stepping t=0.29193899782135074, i=2097152
 --- stepping t=0.40087145969498905, i=2097152
 --- stepping t=0.5098039215686274, i=2097152
 --- stepping t=0.6187363834422658, i=2097152
 --- stepping t=0.7276688453159041, i=2097152
 --- stepping t=0.8366013071895424, i=2097152
 --- stepping t=0.9455337690631808, i=2097152
Running with 20 steps, ff=2...
 --- stepping t=0.04540763673890609, i=2097152
 --- stepping t=0.09700722394220845, i=2097152
 --- stepping t=0.14860681114551083, i=2097152
 --- stepping t=0.2002063983488132, i=2097152
 --- stepping t=0.2518059855521156, i=2097152
 --- stepping t=0.30340557275541796, i=2097152
 --- stepping t=0.3550051599587203, i=2097152
 --- stepping t=0.40660474716202266, i=2097152
 --- stepping t=0.45820433436532504, i=2097152
 --- stepping t=0.5098039215686274, i=2097152
 --- stepping t=0.5614035087719298, i=2097152
 --- stepping t=0.6130030959752322, i=2097152
 --- stepping t=0.6646026831785345, i=2097152
 --- stepping t=0.7162022703818369, i=2097152
 --- stepping t=0.7678018575851393, i=2097152
 --- stepping t=0.8194014447884417, i=2097152
 --- stepping t=0.8710010319917441, i=2097152
 --- stepping t=0.9226006191950464, i=2097152
 --- stepping t=0.9742002063983487, i=2097152
Running with 40 steps, ff=2...
 --- stepping t=0.03217697335344394, i=2097152
 --- stepping t=0.05731523378582202, i=2097152
 --- stepping t=0.0824534942182001, i=2097152
 --- stepping t=0.10759175465057817, i=2097152
 --- stepping t=0.13273001508295626, i=2097152
 --- stepping t=0.15786827551533433, i=2097152
 --- stepping t=0.1830065359477124, i=2097152
 --- stepping t=0.20814479638009048, i=2097152
 --- stepping t=0.23328305681246855, i=2097152
 --- stepping t=0.2584213172448466, i=2097152
 --- stepping t=0.28355957767722473, i=2097152
 --- stepping t=0.3086978381096028, i=2097152
 --- stepping t=0.3338360985419809, i=2097152
 --- stepping t=0.3589743589743589, i=2097152
 --- stepping t=0.384112619406737, i=2097152
 --- stepping t=0.40925087983911507, i=2097152
 --- stepping t=0.43438914027149317, i=2097152
 --- stepping t=0.45952740070387127, i=2097152
 --- stepping t=0.4846656611362493, i=2097152
 --- stepping t=0.5098039215686274, i=2097152
 --- stepping t=0.5349421820010055, i=2097152
 --- stepping t=0.5600804424333835, i=2097152
 --- stepping t=0.5852187028657616, i=2097152
 --- stepping t=0.6103569632981397, i=2097152
 --- stepping t=0.6354952237305178, i=2097152
 --- stepping t=0.6606334841628959, i=2097152
 --- stepping t=0.6857717445952739, i=2097152
 --- stepping t=0.710910005027652, i=2097152
 --- stepping t=0.7360482654600301, i=2097152
 --- stepping t=0.7611865258924082, i=2097152
 --- stepping t=0.7863247863247862, i=2097152
 --- stepping t=0.8114630467571643, i=2097152
 --- stepping t=0.8366013071895424, i=2097152
 --- stepping t=0.8617395676219205, i=2097152
 --- stepping t=0.8868778280542986, i=2097152
 --- stepping t=0.9120160884866766, i=2097152
 --- stepping t=0.9371543489190547, i=2097152
 --- stepping t=0.9622926093514328, i=2097152
 --- stepping t=0.9874308697838109, i=2097152
Running with 80 steps, ff=2...
 --- stepping t=0.025812856788284932, i=2097152
 --- stepping t=0.038222884090344994, i=2097152
 --- stepping t=0.05063291139240506, i=2097152
 --- stepping t=0.06304293869446512, i=2097152
 --- stepping t=0.07545296599652519, i=2097152
 --- stepping t=0.08786299329858525, i=2097152
 --- stepping t=0.10027302060064532, i=2097152
 --- stepping t=0.11268304790270538, i=2097152
 --- stepping t=0.12509307520476545, i=2097152
 --- stepping t=0.13750310250682551, i=2097152
 --- stepping t=0.14991312980888558, i=2097152
 --- stepping t=0.16232315711094564, i=2097152
 --- stepping t=0.1747331844130057, i=2097152
 --- stepping t=0.18714321171506576, i=2097152
 --- stepping t=0.19955323901712582, i=2097152
 --- stepping t=0.21196326631918588, i=2097152
 --- stepping t=0.22437329362124595, i=2097152
 --- stepping t=0.236783320923306, i=2097152
 --- stepping t=0.24919334822536607, i=2097152
 --- stepping t=0.26160337552742613, i=2097152
 --- stepping t=0.2740134028294862, i=2097152
 --- stepping t=0.28642343013154625, i=2097152
 --- stepping t=0.29883345743360634, i=2097152
 --- stepping t=0.3112434847356664, i=2097152
 --- stepping t=0.32365351203772647, i=2097152
 --- stepping t=0.3360635393397865, i=2097152
 --- stepping t=0.3484735666418466, i=2097152
 --- stepping t=0.3608835939439066, i=2097152
 --- stepping t=0.3732936212459667, i=2097152
 --- stepping t=0.38570364854802675, i=2097152
 --- stepping t=0.39811367585008683, i=2097152
 --- stepping t=0.41052370315214687, i=2097152
 --- stepping t=0.42293373045420696, i=2097152
 --- stepping t=0.43534375775626705, i=2097152
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 --- stepping t=0.46016381236038717, i=2097152
 --- stepping t=0.4725738396624472, i=2097152
 --- stepping t=0.4849838669645073, i=2097152
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 --- stepping t=0.5098039215686274, i=2097152
 --- stepping t=0.5222139488706875, i=2097152
 --- stepping t=0.5346239761727475, i=2097152
 --- stepping t=0.5470340034748076, i=2097152
 --- stepping t=0.5594440307768677, i=2097152
 --- stepping t=0.5718540580789278, i=2097152
 --- stepping t=0.5842640853809877, i=2097152
 --- stepping t=0.5966741126830478, i=2097152
 --- stepping t=0.6090841399851079, i=2097152
 --- stepping t=0.621494167287168, i=2097152
 --- stepping t=0.6339041945892281, i=2097152
 --- stepping t=0.6463142218912881, i=2097152
 --- stepping t=0.6587242491933482, i=2097152
 --- stepping t=0.6711342764954082, i=2097152
 --- stepping t=0.6835443037974683, i=2097152
 --- stepping t=0.6959543310995283, i=2097152
 --- stepping t=0.7083643584015884, i=2097152
 --- stepping t=0.7207743857036485, i=2097152
 --- stepping t=0.7331844130057086, i=2097152
 --- stepping t=0.7455944403077686, i=2097152
 --- stepping t=0.7580044676098286, i=2097152
 --- stepping t=0.7704144949118887, i=2097152
 --- stepping t=0.7828245222139488, i=2097152
 --- stepping t=0.7952345495160088, i=2097152
 --- stepping t=0.8076445768180689, i=2097152
 --- stepping t=0.820054604120129, i=2097152
 --- stepping t=0.8324646314221891, i=2097152
 --- stepping t=0.8448746587242492, i=2097152
 --- stepping t=0.8572846860263091, i=2097152
 --- stepping t=0.8696947133283692, i=2097152
 --- stepping t=0.8821047406304293, i=2097152
 --- stepping t=0.8945147679324894, i=2097152
 --- stepping t=0.9069247952345494, i=2097152
 --- stepping t=0.9193348225366095, i=2097152
 --- stepping t=0.9317448498386696, i=2097152
 --- stepping t=0.9441548771407297, i=2097152
 --- stepping t=0.9565649044427896, i=2097152
 --- stepping t=0.9689749317448497, i=2097152
 --- stepping t=0.9813849590469098, i=2097152
 --- stepping t=0.9937949863489699, i=2097152
Running with 5 steps, ff=4...
 --- stepping t=0.14215686274509803, i=2097152
 --- stepping t=0.38725490196078427, i=2097152
 --- stepping t=0.6323529411764706, i=2097152
 --- stepping t=0.8774509803921569, i=2097152
Running with 10 steps, ff=4...
 --- stepping t=0.07407407407407407, i=2097152
 --- stepping t=0.1830065359477124, i=2097152
 --- stepping t=0.29193899782135074, i=2097152
 --- stepping t=0.40087145969498905, i=2097152
 --- stepping t=0.5098039215686274, i=2097152
 --- stepping t=0.6187363834422658, i=2097152
 --- stepping t=0.7276688453159041, i=2097152
 --- stepping t=0.8366013071895424, i=2097152
 --- stepping t=0.9455337690631808, i=2097152
Running with 20 steps, ff=4...
 --- stepping t=0.04540763673890609, i=2097152
 --- stepping t=0.09700722394220845, i=2097152
 --- stepping t=0.14860681114551083, i=2097152
 --- stepping t=0.2002063983488132, i=2097152
 --- stepping t=0.2518059855521156, i=2097152
 --- stepping t=0.30340557275541796, i=2097152
 --- stepping t=0.3550051599587203, i=2097152
 --- stepping t=0.40660474716202266, i=2097152
 --- stepping t=0.45820433436532504, i=2097152
 --- stepping t=0.5098039215686274, i=2097152
 --- stepping t=0.5614035087719298, i=2097152
 --- stepping t=0.6130030959752322, i=2097152
 --- stepping t=0.6646026831785345, i=2097152
 --- stepping t=0.7162022703818369, i=2097152
 --- stepping t=0.7678018575851393, i=2097152
 --- stepping t=0.8194014447884417, i=2097152
 --- stepping t=0.8710010319917441, i=2097152
 --- stepping t=0.9226006191950464, i=2097152
 --- stepping t=0.9742002063983487, i=2097152
Running with 40 steps, ff=4...
 --- stepping t=0.03217697335344394, i=2097152
 --- stepping t=0.05731523378582202, i=2097152
 --- stepping t=0.0824534942182001, i=2097152
 --- stepping t=0.10759175465057817, i=2097152
 --- stepping t=0.13273001508295626, i=2097152
 --- stepping t=0.15786827551533433, i=2097152
 --- stepping t=0.1830065359477124, i=2097152
 --- stepping t=0.20814479638009048, i=2097152
 --- stepping t=0.23328305681246855, i=2097152
 --- stepping t=0.2584213172448466, i=2097152
 --- stepping t=0.28355957767722473, i=2097152
 --- stepping t=0.3086978381096028, i=2097152
 --- stepping t=0.3338360985419809, i=2097152
 --- stepping t=0.3589743589743589, i=2097152
 --- stepping t=0.384112619406737, i=2097152
 --- stepping t=0.40925087983911507, i=2097152
 --- stepping t=0.43438914027149317, i=2097152
 --- stepping t=0.45952740070387127, i=2097152
 --- stepping t=0.4846656611362493, i=2097152
 --- stepping t=0.5098039215686274, i=2097152
 --- stepping t=0.5349421820010055, i=2097152
 --- stepping t=0.5600804424333835, i=2097152
 --- stepping t=0.5852187028657616, i=2097152
 --- stepping t=0.6103569632981397, i=2097152
 --- stepping t=0.6354952237305178, i=2097152
 --- stepping t=0.6606334841628959, i=2097152
 --- stepping t=0.6857717445952739, i=2097152
 --- stepping t=0.710910005027652, i=2097152
 --- stepping t=0.7360482654600301, i=2097152
 --- stepping t=0.7611865258924082, i=2097152
 --- stepping t=0.7863247863247862, i=2097152
 --- stepping t=0.8114630467571643, i=2097152
 --- stepping t=0.8366013071895424, i=2097152
 --- stepping t=0.8617395676219205, i=2097152
 --- stepping t=0.8868778280542986, i=2097152
 --- stepping t=0.9120160884866766, i=2097152
 --- stepping t=0.9371543489190547, i=2097152
 --- stepping t=0.9622926093514328, i=2097152
 --- stepping t=0.9874308697838109, i=2097152
Running with 80 steps, ff=4...
 --- stepping t=0.025812856788284932, i=2097152
 --- stepping t=0.038222884090344994, i=2097152
 --- stepping t=0.05063291139240506, i=2097152
 --- stepping t=0.06304293869446512, i=2097152
 --- stepping t=0.07545296599652519, i=2097152
 --- stepping t=0.08786299329858525, i=2097152
 --- stepping t=0.10027302060064532, i=2097152
 --- stepping t=0.11268304790270538, i=2097152
 --- stepping t=0.12509307520476545, i=2097152
 --- stepping t=0.13750310250682551, i=2097152
 --- stepping t=0.14991312980888558, i=2097152
 --- stepping t=0.16232315711094564, i=2097152
 --- stepping t=0.1747331844130057, i=2097152
 --- stepping t=0.18714321171506576, i=2097152
 --- stepping t=0.19955323901712582, i=2097152
 --- stepping t=0.21196326631918588, i=2097152
 --- stepping t=0.22437329362124595, i=2097152
 --- stepping t=0.236783320923306, i=2097152
 --- stepping t=0.24919334822536607, i=2097152
 --- stepping t=0.26160337552742613, i=2097152
 --- stepping t=0.2740134028294862, i=2097152
 --- stepping t=0.28642343013154625, i=2097152
 --- stepping t=0.29883345743360634, i=2097152
 --- stepping t=0.3112434847356664, i=2097152
 --- stepping t=0.32365351203772647, i=2097152
 --- stepping t=0.3360635393397865, i=2097152
 --- stepping t=0.3484735666418466, i=2097152
 --- stepping t=0.3608835939439066, i=2097152
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 --- stepping t=0.38570364854802675, i=2097152
 --- stepping t=0.39811367585008683, i=2097152
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 --- stepping t=0.42293373045420696, i=2097152
 --- stepping t=0.43534375775626705, i=2097152
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 --- stepping t=0.4849838669645073, i=2097152
 --- stepping t=0.4973938942665673, i=2097152
 --- stepping t=0.5098039215686274, i=2097152
 --- stepping t=0.5222139488706875, i=2097152
 --- stepping t=0.5346239761727475, i=2097152
 --- stepping t=0.5470340034748076, i=2097152
 --- stepping t=0.5594440307768677, i=2097152
 --- stepping t=0.5718540580789278, i=2097152
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 --- stepping t=0.5966741126830478, i=2097152
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 --- stepping t=0.6959543310995283, i=2097152
 --- stepping t=0.7083643584015884, i=2097152
 --- stepping t=0.7207743857036485, i=2097152
 --- stepping t=0.7331844130057086, i=2097152
 --- stepping t=0.7455944403077686, i=2097152
 --- stepping t=0.7580044676098286, i=2097152
 --- stepping t=0.7704144949118887, i=2097152
 --- stepping t=0.7828245222139488, i=2097152
 --- stepping t=0.7952345495160088, i=2097152
 --- stepping t=0.8076445768180689, i=2097152
 --- stepping t=0.820054604120129, i=2097152
 --- stepping t=0.8324646314221891, i=2097152
 --- stepping t=0.8448746587242492, i=2097152
 --- stepping t=0.8572846860263091, i=2097152
 --- stepping t=0.8696947133283692, i=2097152
 --- stepping t=0.8821047406304293, i=2097152
 --- stepping t=0.8945147679324894, i=2097152
 --- stepping t=0.9069247952345494, i=2097152
 --- stepping t=0.9193348225366095, i=2097152
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 --- stepping t=0.9565649044427896, i=2097152
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 --- stepping t=0.9813849590469098, i=2097152
 --- stepping t=0.9937949863489699, i=2097152

imshow(delta_set[(4,80)][:,32,:],extent=(0,bb.L[0],0,bb.L[1]),vmin=-1,vmax=1)

<matplotlib.image.AxesImage at 0x7fa6e42ec2b0>

Compute power spectra

H_set={}

for k in delta_set:
    bc, H = aq.clustering.power.compute_power_spectrum(delta_set[k], bb.L[0],logk=False)
    #print(k)
    H_set[k] = H
bc, H_in = aq.clustering.power.compute_power_spectrum(delta_in, bb.L[0],logk=False)
_, H_2lpt = aq.clustering.power.compute_power_spectrum(delta_2lpt, bb.L[0],logk=False)

axhline(1.0,color='k')
for n,ff in [(4,20),(2,10)]:#H_set:
    semilogx(bc,H_set[(n,ff)]/H_set[(4,80)],label=f'PM n={n}, ff={ff}')
semilogx(bc,H_2lpt/H_set[(4,80)],label=f'2lpt')
legend(frameon=False,ncol=2)
ylim(0.9,1.2)

/home/lavaux/.local/lib/python3.8/site-packages/PyAquila-1.0-py3.8.egg/aquila/clustering/power.py:53: RuntimeWarning: invalid value encountered in true_divide

(0.9, 1.2)