In [1]:
%matplotlib inline
import matplotlib.pyplot as plt
from matplotlib import rc
from scipy.stats import norm, lognorm
import pandas as pd
import numpy as np
import seaborn as sns
import itertools
rc('text', usetex=True)
sns.set_style("whitegrid")
# we will work with datasets of 2000 samples
tmp = pd.read_csv('mock_data.csv')
mass = tmp.mass_h.as_matrix()
z = tmp.z.as_matrix()
# np.random.seed(0)
# alpha1 = norm(10.709, 0.022).rvs()
# alpha2 = norm(0.359, 0.009).rvs()
# alpha3 = 2.35e14
# alpha4 = norm(1.10, 0.06).rvs()
# S = norm(0.155, 0.0009).rvs()
# sigma_L = 0.05
# mu_li = np.exp(alpha1) * ((mass / alpha3) ** (alpha2))* ((1+z) ** (alpha4))
# li = lognorm(S, scale=mu_li).rvs()
# observed = lognorm(sigma_L, scale=li).rvs()
# tmp['lum'] =
In [2]:
tmp.drop('Unnamed: 0', axis=1, inplace=True)
In [3]:
np.random.seed(0)
alpha1 = norm(10.709, 0.022).rvs()
alpha2 = norm(0.359, 0.009).rvs()
alpha3 = 2.35e14
alpha4 = norm(1.10, 0.06).rvs()
S = norm(0.155, 0.0009).rvs()
sigma_L = 0.05
mu_li = np.exp(alpha1) * ((mass / alpha3) ** (alpha2))* ((1+z) ** (alpha4))
li = lognorm(S, scale=mu_li).rvs()
observed = lognorm(sigma_L, scale=li).rvs()
tmp['mass'] = tmp['mass_h']
tmp['lum'] = li
tmp['lum_obs'] = observed
tmp.drop('mass_h', axis=1).to_csv('mock_data.csv')
In [4]:
tmp
Out[4]:
gal_id
z
mass_h
ra
dec
lum
lum_obs
mass
0
22005657000031
2.07709
1.005246e+11
-108.623172
-101.696113
13777.036439
13748.793557
1.005246e+11
1
23003396000121
2.00452
9.989612e+10
-106.131150
-104.863309
8553.898485
8259.738500
9.989612e+10
2
23003339006170
1.99264
3.945599e+11
-105.764686
-102.987674
18963.368661
18382.304954
3.945599e+11
3
23003385000769
1.99573
1.432479e+11
-105.287527
-101.737709
11060.429382
11510.690346
1.432479e+11
4
22000106000031
2.04182
1.344521e+11
-105.776374
-102.895886
11085.593094
12059.614847
1.344521e+11
5
489020438001227
2.12403
3.062861e+12
-107.538907
-104.584507
38500.816256
35905.873192
3.062861e+12
6
23005411000031
2.01065
6.471282e+10
-107.512780
-102.343440
8735.401794
8726.686673
6.471282e+10
7
489020448004718
2.14909
1.262842e+11
-108.392843
-102.238933
14405.812397
14915.361990
1.262842e+11
8
22000106000306
2.04232
9.738346e+10
-106.649906
-103.290196
11297.504338
11609.498789
9.738346e+10
9
489020438013554
2.12085
1.011532e+11
-106.629967
-103.928585
10670.604639
9932.444944
1.011532e+11
10
23003331032688
1.97194
3.706852e+10
-105.134891
-102.794129
7370.070293
7135.366056
3.706852e+10
11
23003339009419
1.99453
7.514255e+11
-105.130422
-101.295615
21759.307213
22347.824551
7.514255e+11
12
23003339012562
1.99308
1.865990e+11
-107.446432
-101.609138
15745.834820
13544.178225
1.865990e+11
13
23003334013157
2.03242
1.206296e+11
-107.873056
-101.492942
10451.207326
10514.498134
1.206296e+11
14
23003339014535
1.98944
1.124623e+11
-105.593142
-102.989737
10871.301611
11056.979460
1.124623e+11
15
23003331037591
1.97385
5.283835e+11
-105.580423
-103.554902
15765.466881
16591.973900
5.283835e+11
16
489020517000263
2.10828
1.589546e+11
-106.462205
-101.378808
8221.382866
8353.804189
1.589546e+11
17
22004397000031
2.08523
1.652377e+11
-106.450516
-102.725718
13676.265269
14017.038305
1.652377e+11
18
23003675000174
2.01170
1.093204e+11
-108.069007
-102.400163
11834.539246
12092.872682
1.093204e+11
19
23005110000031
2.01723
1.200010e+11
-108.045975
-101.793401
9532.293118
8826.989692
1.200010e+11
20
489020448001768
2.14908
7.979119e+10
-108.037036
-101.556540
13862.595120
14071.799044
7.979119e+10
21
23003331013748
1.97491
6.408451e+10
-108.739368
-103.838516
6679.421052
6892.031867
6.408451e+10
22
23004504000031
1.98738
2.877521e+11
-107.932529
-102.690996
14643.738159
14536.083254
2.877521e+11
23
23003334023784
2.02952
9.612713e+10
-107.996127
-103.134122
9641.738331
9188.549870
9.612713e+10
24
22004259000031
2.09194
2.381180e+11
-108.011941
-102.476825
17970.112504
19243.524955
2.381180e+11
25
23003339008071
1.99263
1.671226e+11
-105.009757
-101.750085
15067.634606
16431.649986
1.671226e+11
26
489020440007032
2.14665
1.413630e+11
-105.275494
-103.993215
12226.647968
12885.988070
1.413630e+11
27
23003334015778
2.03251
9.926832e+10
-105.723777
-104.821024
10672.525773
11567.896090
9.926832e+10
28
23003339007672
1.98870
1.086926e+11
-106.592151
-104.371367
8889.961199
9025.298145
1.086926e+11
29
489020492001498
2.14307
1.162321e+11
-106.609684
-104.005591
8133.363440
7537.693881
1.162321e+11
...
...
...
...
...
...
...
...
...
115889
127016819000036
3.03286
1.086926e+11
-119.645276
-110.286698
14315.341869
13571.901017
1.086926e+11
115890
154012642001049
3.17510
2.167567e+11
-118.837062
-110.060150
19845.531114
19001.082643
2.167567e+11
115891
131003555070522
3.08358
6.785423e+10
-119.661433
-108.975198
9258.001351
9493.968473
6.785423e+10
115892
127016102000104
3.04269
1.470176e+11
-119.478889
-112.091171
15191.511017
16528.606424
1.470176e+11
115893
131003555040466
3.09984
6.911078e+10
-119.005511
-106.677751
10290.137419
10297.270659
6.911078e+10
115894
131003555039564
3.10047
1.137187e+11
-119.000698
-106.456360
12579.171357
11963.993162
1.137187e+11
115895
128000002009906
2.99064
6.892229e+11
-119.020294
-105.916290
32551.998886
31005.010183
6.892229e+11
115896
289000366000035
2.84549
1.137187e+11
-89.779851
-113.219783
17078.054226
15657.830180
1.137187e+11
115897
289000147000179
2.87487
1.652377e+11
-89.396542
-113.230440
13001.474551
12855.690953
1.652377e+11
115898
289000953000035
2.87505
1.206296e+11
-89.440202
-116.122961
15638.008391
16159.031398
1.206296e+11
115899
294001497000086
2.89482
3.267057e+10
-89.833824
-115.281056
8643.156429
8533.088527
3.267057e+10
115900
294001194000468
2.93028
1.306824e+11
-86.980837
-115.130827
15230.707827
13504.234213
1.306824e+11
115901
289000147000035
2.87565
2.814690e+11
-89.169307
-112.778033
22596.962193
23415.017152
2.814690e+11
115902
294001150002253
2.94287
6.973902e+10
-86.572089
-114.226012
11099.456197
11325.810672
6.973902e+10
115903
289000451000035
2.86855
3.700567e+11
-87.598601
-115.240835
22057.698120
20356.659578
3.700567e+11
115904
294001497000120
2.89598
1.972796e+11
-89.906360
-115.581172
17143.196571
18003.320684
1.972796e+11
115905
289000212000035
2.87128
2.525683e+11
-87.654292
-114.474561
20107.707367
18876.353496
2.525683e+11
115906
289001462000035
2.84460
1.030380e+11
-87.700014
-113.171999
17422.167163
17759.578980
1.030380e+11
115907
294001522000035
2.93074
1.451328e+11
-86.291225
-113.679754
13600.906702
14261.624933
1.451328e+11
115908
294001150002370
2.94288
1.137187e+11
-86.789011
-114.943813
15530.533164
15623.516584
1.137187e+11
115909
294001422000035
2.90749
9.801126e+10
-88.278931
-113.928647
14151.860591
13839.037172
9.801126e+10
115910
289000193000147
2.81032
3.769676e+10
-87.295391
-111.342430
11300.310106
10480.906947
3.769676e+10
115911
289000037005179
2.88232
3.361300e+11
-88.427098
-110.789984
23981.064809
22403.320152
3.361300e+11
115912
294002054000035
2.92923
2.525683e+11
-87.772207
-118.405968
14234.588200
14285.396718
2.525683e+11
115913
294001194000115
2.93078
1.878553e+11
-87.795240
-116.497331
14470.491858
14279.630544
1.878553e+11
115914
289000217000035
2.84022
3.644021e+11
-89.583899
-116.869983
19098.012484
18561.440351
3.644021e+11
115915
294002202000035
2.94070
9.612713e+10
-87.618883
-119.025794
13678.508971
13842.939986
9.612713e+10
115916
131004218000036
3.08036
1.671226e+11
-119.445543
-110.464086
18504.595929
19165.509454
1.671226e+11
115917
131003555070726
3.08397
6.106881e+11
-119.474076
-109.414542
26433.179858
28743.105812
6.106881e+11
115918
154012673000342
3.17980
1.589546e+11
-116.335070
-111.939910
17296.712819
17474.887424
1.589546e+11
115919 rows × 8 columns
Content source: davidthomas5412/PanglossNotebooks
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