ERDF.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "0219875a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import interpolate\n",
    "\n",
    "\n",
    "def ERDF(lambda_Edd, galaxy_type = 'Blue', seed=None):\n",
    "    \"\"\"\n",
    "    ERDF for blue galaxies (radiatively-efficient, less massive)\n",
    "    \"\"\"\n",
    "    # Lbr = 10**38.1 lambda_br M_BH_br\n",
    "    # 10^41.67 = 10^38.1 * 10^x * 10^10.66\n",
    "    if galaxy_type == 'Red':\n",
    "        xi = 10**-2.13\n",
    "        lambda_br = 10**np.random.normal(-2.81, np.mean([0.22, 0.14]))\n",
    "        delta1 = np.random.normal(0.41-0.7, np.mean([0.02, 0.02])) # > -0.45 won't affect LF\n",
    "        delta2 = np.random.normal(1.22, np.mean([0.19, 0.13]))\n",
    "    \n",
    "    if galaxy_type == 'Blue': \n",
    "        xi = 10**-1.65\n",
    "        lambda_br = 10**np.random.normal(-1.84, np.mean([0.30, 0.37]))\n",
    "        delta1 = np.random.normal(0.471-0.7, np.mean([0.02, 0.02])) # > -0.45 won't affect LF\n",
    "        delta2 = np.random.normal(2.53, np.mean([0.68, 0.38]))\n",
    "\n",
    "    # https://ui.adsabs.harvard.edu/abs/2019ApJ...883..139S/abstract\n",
    "    # What sets the break? Transfer from radiatively efficient to inefficient accretion?\n",
    "\n",
    "    # parameters from this paper:\n",
    "    # https://iopscience.iop.org/article/10.3847/1538-4357/aa803b/pdf\n",
    "    print('(lambda_Edd/lambda_br)**delta1:\\n',(lambda_Edd/lambda_br)**delta1)\n",
    "    return xi * ((lambda_Edd/lambda_br)**delta1 + (lambda_Edd/lambda_br)**delta2)**-1 \n",
    "\n",
    "#based on Colin's\n",
    "def inv_trans_sampling(x, y, sampling_size = 1000):\n",
    "    #y is the pdf of x\n",
    "    dx = np.diff(x)\n",
    "    cum_values = np.zeros(x.shape)\n",
    "    cum_values[1:] = np.cumsum(y*dx)/np.sum(y*dx)\n",
    "\n",
    "    r = np.random.rand(int(sampling_size))\n",
    "    return np.interp(r, cum_values, x)\n",
    "\n",
    "#based on web (not currently used)\n",
    "def inverse_transform_sampling(data, n_bins=40, n_samples=1000):\n",
    "    hist, bin_edges = np.histogram(data, bins=n_bins, density=True)\n",
    "    cum_values = np.zeros(bin_edges.shape)\n",
    "    cum_values[1:] = np.cumsum(hist*np.diff(bin_edges))\n",
    "    inv_cdf = interpolate.interp1d(cum_values, bin_edges)\n",
    "    r = np.random.rand(n_samples)\n",
    "    return inv_cdf(r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "7c3f60ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "# parameter adopted from colin's notebook\n",
    "log_lambda_min = -8.5\n",
    "log_lambda_max = 0.5\n",
    "nbins = 1000\n",
    "lambda_ = np.logspace(log_lambda_min, log_lambda_max, nbins+1) \n",
    "dlambda = np.diff(lambda_)  #size of each bin\n",
    "#dloglambda = np.diff(np.log10(lambda_)) #not used so far\n",
    "lambda_Edd = lambda_[:-1] + dlambda/2  #middle point of each bin?  #Colin uses lambda_Edd = lambda_[1:] + dlambda/2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "7708ad93",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(lambda_Edd/lambda_br)**delta1:\n",
      " [25.19040706 25.09029589 24.99058259 24.89126556 24.79234324 24.69381405\n",
      " 24.59567643 24.49792883 24.4005697  24.30359748 24.20701066 24.11080768\n",
      " 24.01498704 23.9195472  23.82448666 23.7298039  23.63549744 23.54156576\n",
      " 23.44800738 23.35482082 23.2620046  23.16955725 23.0774773  22.9857633\n",
      " 22.89441378 22.8034273  22.71280242 22.62253769 22.5326317  22.443083\n",
      " 22.35389019 22.26505185 22.17656657 22.08843294 22.00064957 21.91321507\n",
      " 21.82612805 21.73938713 21.65299093 21.56693809 21.48122723 21.39585701\n",
      " 21.31082606 21.22613304 21.14177661 21.05775542 20.97406815 20.89071346\n",
      " 20.80769005 20.72499658 20.64263175 20.56059425 20.47888279 20.39749606\n",
      " 20.31643277 20.23569165 20.15527141 20.07517077 19.99538846 19.91592323\n",
      " 19.8367738  19.75793892 19.67941736 19.60120784 19.52330915 19.44572004\n",
      " 19.36843929 19.29146566 19.21479794 19.13843491 19.06237536 18.98661808\n",
      " 18.91116188 18.83600555 18.76114791 18.68658776 18.61232393 18.53835524\n",
      " 18.46468052 18.39129859 18.31820829 18.24540846 18.17289796 18.10067563\n",
      " 18.02874032 17.95709089 17.88572621 17.81464515 17.74384658 17.67332937\n",
      " 17.60309241 17.53313458 17.46345478 17.3940519  17.32492484 17.2560725\n",
      " 17.18749379 17.11918763 17.05115293 16.98338861 16.9158936  16.84866682\n",
      " 16.78170722 16.71501372 16.64858528 16.58242084 16.51651934 16.45087975\n",
      " 16.38550102 16.32038212 16.25552202 16.19091968 16.12657408 16.0624842\n",
      " 15.99864902 15.93506754 15.87173875 15.80866163 15.74583519 15.68325844\n",
      " 15.62093037 15.55885001 15.49701637 15.43542847 15.37408532 15.31298597\n",
      " 15.25212943 15.19151475 15.13114097 15.07100712 15.01111225 14.95145541\n",
      " 14.89203567 14.83285206 14.77390367 14.71518954 14.65670876 14.59846038\n",
      " 14.5404435  14.48265719 14.42510053 14.36777261 14.31067252 14.25379936\n",
      " 14.19715222 14.14073021 14.08453243 14.02855799 13.972806   13.91727558\n",
      " 13.86196584 13.80687592 13.75200494 13.69735202 13.6429163  13.58869692\n",
      " 13.53469302 13.48090374 13.42732822 13.37396563 13.32081511 13.26787581\n",
      " 13.21514691 13.16262756 13.11031694 13.0582142  13.00631853 12.9546291\n",
      " 12.9031451  12.8518657  12.8007901  12.74991748 12.69924703 12.64877796\n",
      " 12.59850947 12.54844074 12.498571   12.44889946 12.39942531 12.35014779\n",
      " 12.3010661  12.25217947 12.20348713 12.15498829 12.1066822  12.05856809\n",
      " 12.01064519 11.96291275 11.91537    11.8680162  11.82085059 11.77387242\n",
      " 11.72708096 11.68047545 11.63405516 11.58781935 11.54176729 11.49589825\n",
      " 11.4502115  11.40470632 11.35938199 11.31423778 11.26927298 11.22448688\n",
      " 11.17987877 11.13544794 11.09119369 11.04711531 11.0032121  10.95948338\n",
      " 10.91592844 10.87254659 10.82933716 10.78629944 10.74343277 10.70073645\n",
      " 10.65820982 10.61585219 10.5736629  10.53164128 10.48978666 10.44809838\n",
      " 10.40657578 10.36521819 10.32402497 10.28299545 10.242129   10.20142495\n",
      " 10.16088267 10.12050151 10.08028084 10.04022001 10.00031838  9.96057534\n",
      "  9.92099023  9.88156245  9.84229136  9.80317634  9.76421677  9.72541204\n",
      "  9.68676152  9.6482646   9.60992068  9.57172914  9.53368938  9.4958008\n",
      "  9.4580628   9.42047477  9.38303613  9.34574627  9.30860461  9.27161056\n",
      "  9.23476352  9.19806293  9.16150819  9.12509872  9.08883395  9.05271331\n",
      "  9.01673621  8.9809021   8.94521039  8.90966053  8.87425195  8.83898409\n",
      "  8.8038564   8.7688683   8.73401926  8.69930871  8.66473611  8.6303009\n",
      "  8.59600255  8.5618405   8.52781422  8.49392317  8.4601668   8.42654459\n",
      "  8.393056    8.3597005   8.32647757  8.29338666  8.26042726  8.22759885\n",
      "  8.19490091  8.16233291  8.12989435  8.0975847   8.06540346  8.03335011\n",
      "  8.00142414  7.96962506  7.93795235  7.90640551  7.87498404  7.84368745\n",
      "  7.81251524  7.78146692  7.75054198  7.71973995  7.68906032  7.65850263\n",
      "  7.62806637  7.59775108  7.56755626  7.53748145  7.50752615  7.4776899\n",
      "  7.44797223  7.41837266  7.38889073  7.35952596  7.33027789  7.30114606\n",
      "  7.27213001  7.24322927  7.21444338  7.1857719   7.15721436  7.12877032\n",
      "  7.10043931  7.0722209   7.04411464  7.01612007  6.98823676  6.96046426\n",
      "  6.93280214  6.90524995  6.87780725  6.85047362  6.82324862  6.79613181\n",
      "  6.76912277  6.74222107  6.71542629  6.68873798  6.66215575  6.63567915\n",
      "  6.60930778  6.58304122  6.55687904  6.53082083  6.50486619  6.47901469\n",
      "  6.45326593  6.4276195   6.402075    6.37663201  6.35129014  6.32604898\n",
      "  6.30090813  6.2758672   6.25092579  6.2260835   6.20133993  6.1766947\n",
      "  6.15214741  6.12769768  6.10334512  6.07908934  6.05492996  6.03086659\n",
      "  6.00689885  5.98302636  5.95924875  5.93556563  5.91197664  5.88848139\n",
      "  5.86507952  5.84177064  5.81855441  5.79543043  5.77239836  5.74945782\n",
      "  5.72660845  5.70384989  5.68118177  5.65860375  5.63611545  5.61371652\n",
      "  5.59140661  5.56918536  5.54705243  5.52500745  5.50305009  5.48117999\n",
      "  5.4593968   5.43770019  5.4160898   5.39456529  5.37312633  5.35177257\n",
      "  5.33050367  5.3093193   5.28821912  5.26720279  5.24626999  5.22542038\n",
      "  5.20465363  5.18396941  5.16336739  5.14284725  5.12240865  5.10205129\n",
      "  5.08177483  5.06157895  5.04146333  5.02142766  5.00147161  4.98159487\n",
      "  4.96179713  4.94207806  4.92243736  4.90287472  4.88338982  4.86398236\n",
      "  4.84465203  4.82539852  4.80622152  4.78712074  4.76809587  4.74914661\n",
      "  4.73027266  4.71147371  4.69274947  4.67409965  4.65552395  4.63702206\n",
      "  4.61859371  4.6002386   4.58195643  4.56374692  4.54560978  4.52754471\n",
      "  4.50955144  4.49162968  4.47377915  4.45599955  4.43829061  4.42065206\n",
      "  4.4030836   4.38558496  4.36815586  4.35079603  4.33350519  4.31628307\n",
      "  4.29912939  4.28204389  4.26502628  4.24807631  4.2311937   4.21437818\n",
      "  4.19762949  4.18094736  4.16433153  4.14778174  4.13129771  4.1148792\n",
      "  4.09852594  4.08223766  4.06601412  4.04985506  4.03376021  4.01772933\n",
      "  4.00176216  3.98585844  3.97001793  3.95424037  3.93852552  3.92287312\n",
      "  3.90728292  3.89175468  3.87628815  3.86088309  3.84553926  3.8302564\n",
      "  3.81503428  3.79987265  3.78477128  3.76972993  3.75474835  3.73982631\n",
      "  3.72496357  3.7101599   3.69541507  3.68072883  3.66610096  3.65153122\n",
      "  3.63701938  3.62256522  3.6081685   3.593829    3.57954648  3.56532072\n",
      "  3.5511515   3.53703859  3.52298177  3.50898082  3.4950355   3.48114561\n",
      "  3.46731091  3.4535312   3.43980625  3.42613585  3.41251978  3.39895782\n",
      "  3.38544975  3.37199537  3.35859446  3.34524681  3.3319522   3.31871043\n",
      "  3.30552128  3.29238455  3.27930003  3.26626751  3.25328678  3.24035764\n",
      "  3.22747988  3.2146533   3.20187769  3.18915286  3.1764786   3.16385471\n",
      "  3.15128098  3.13875723  3.12628325  3.11385885  3.10148382  3.08915797\n",
      "  3.0768811   3.06465303  3.05247355  3.04034248  3.02825961  3.01622477\n",
      "  3.00423776  2.99229838  2.98040645  2.96856179  2.95676419  2.94501349\n",
      "  2.93330948  2.92165198  2.91004082  2.8984758   2.88695674  2.87548346\n",
      "  2.86405577  2.85267351  2.84133647  2.8300445   2.81879739  2.80759499\n",
      "  2.79643711  2.78532357  2.7742542   2.76322882  2.75224725  2.74130933\n",
      "  2.73041488  2.71956373  2.70875569  2.69799062  2.68726832  2.67658864\n",
      "  2.6659514   2.65535643  2.64480357  2.63429265  2.6238235   2.61339596\n",
      "  2.60300986  2.59266504  2.58236132  2.57209856  2.56187658  2.55169523\n",
      "  2.54155434  2.53145375  2.5213933   2.51137283  2.50139219  2.49145121\n",
      "  2.48154974  2.47168762  2.46186469  2.4520808   2.4423358   2.43262952\n",
      "  2.42296182  2.41333253  2.40374152  2.39418862  2.38467369  2.37519657\n",
      "  2.36575712  2.35635518  2.3469906   2.33766324  2.32837295  2.31911958\n",
      "  2.30990299  2.30072302  2.29157954  2.2824724   2.27340144  2.26436654\n",
      "  2.25536755  2.24640431  2.2374767   2.22858457  2.21972778  2.21090618\n",
      "  2.20211965  2.19336803  2.1846512   2.17596901  2.16732132  2.158708\n",
      "  2.15012891  2.14158391  2.13307287  2.12459566  2.11615214  2.10774218\n",
      "  2.09936563  2.09102238  2.08271228  2.07443521  2.06619104  2.05797963\n",
      "  2.04980085  2.04165458  2.03354068  2.02545902  2.01740949  2.00939194\n",
      "  2.00140626  1.99345232  1.98552998  1.97763913  1.96977964  1.96195139\n",
      "  1.95415424  1.94638809  1.93865279  1.93094824  1.92327431  1.91563087\n",
      "  1.90801782  1.90043501  1.89288235  1.88535969  1.87786694  1.87040396\n",
      "  1.86297064  1.85556687  1.84819251  1.84084747  1.83353161  1.82624483\n",
      "  1.81898701  1.81175803  1.80455778  1.79738614  1.79024301  1.78312827\n",
      "  1.7760418   1.76898349  1.76195324  1.75495092  1.74797643  1.74102966\n",
      "  1.7341105   1.72721884  1.72035456  1.71351756  1.70670774  1.69992498\n",
      "  1.69316917  1.68644022  1.67973801  1.67306243  1.66641338  1.65979076\n",
      "  1.65319445  1.64662436  1.64008038  1.63356241  1.62707034  1.62060408\n",
      "  1.61416351  1.60774853  1.60135905  1.59499497  1.58865617  1.58234257\n",
      "  1.57605406  1.56979054  1.56355191  1.55733808  1.55114894  1.5449844\n",
      "  1.53884435  1.53272871  1.52663738  1.52057025  1.51452723  1.50850823\n",
      "  1.50251315  1.49654189  1.49059437  1.48467048  1.47877014  1.47289324\n",
      "  1.4670397   1.46120942  1.45540232  1.44961829  1.44385725  1.4381191\n",
      "  1.43240376  1.42671113  1.42104113  1.41539366  1.40976863  1.40416596\n",
      "  1.39858555  1.39302732  1.38749119  1.38197705  1.37648483  1.37101443\n",
      "  1.36556577  1.36013877  1.35473334  1.34934939  1.34398683  1.33864559\n",
      "  1.33332557  1.3280267   1.32274888  1.31749205  1.3122561   1.30704096\n",
      "  1.30184654  1.29667277  1.29151957  1.28638684  1.28127451  1.27618249\n",
      "  1.27111072  1.2660591   1.26102755  1.256016    1.25102437  1.24605258\n",
      "  1.24110054  1.23616819  1.23125544  1.22636221  1.22148843  1.21663401\n",
      "  1.21179889  1.20698299  1.20218622  1.19740852  1.1926498   1.18791\n",
      "  1.18318904  1.17848683  1.17380332  1.16913841  1.16449205  1.15986415\n",
      "  1.15525464  1.15066345  1.14609051  1.14153574  1.13699908  1.13248044\n",
      "  1.12797976  1.12349697  1.11903199  1.11458476  1.1101552   1.10574325\n",
      "  1.10134883  1.09697187  1.09261231  1.08827007  1.08394509  1.0796373\n",
      "  1.07534663  1.07107301  1.06681638  1.06257666  1.05835379  1.0541477\n",
      "  1.04995833  1.04578561  1.04162947  1.03748985  1.03336668  1.0292599\n",
      "  1.02516944  1.02109523  1.01703722  1.01299533  1.00896951  1.00495968\n",
      "  1.00096579  0.99698778  0.99302557  0.98907911  0.98514833  0.98123318\n",
      "  0.97733358  0.97344948  0.96958082  0.96572753  0.96188956  0.95806684\n",
      "  0.95425931  0.95046692  0.94668959  0.94292728  0.93917992  0.93544745\n",
      "  0.93172981  0.92802695  0.92433881  0.92066532  0.91700643  0.91336209\n",
      "  0.90973222  0.90611678  0.90251572  0.89892896  0.89535645  0.89179815\n",
      "  0.88825398  0.8847239   0.88120785  0.87770578  0.87421762  0.87074332\n",
      "  0.86728283  0.86383609  0.86040306  0.85698366  0.85357785  0.85018558\n",
      "  0.8468068   0.84344143  0.84008945  0.83675078  0.83342539  0.8301132\n",
      "  0.82681419  0.82352828  0.82025543  0.81699559  0.8137487   0.81051472\n",
      "  0.80729359  0.80408526  0.80088969  0.79770681  0.79453658  0.79137895\n",
      "  0.78823387  0.78510129  0.78198115  0.77887342  0.77577804  0.77269496\n",
      "  0.76962413  0.76656551  0.76351904  0.76048468  0.75746238  0.75445209\n",
      "  0.75145376  0.74846735  0.74549281  0.74253009  0.73957914  0.73663992\n",
      "  0.73371238  0.73079648  0.72789216  0.72499939  0.72211811  0.71924829\n",
      "  0.71638987  0.7135428   0.71070706  0.70788258  0.70506933  0.70226726\n",
      "  0.69947632  0.69669648  0.69392768  0.69116989  0.68842306  0.68568714\n",
      "  0.6829621   0.68024789  0.67754446  0.67485178  0.6721698   0.66949848\n",
      "  0.66683777  0.66418764  0.66154804  0.65891893  0.65630027  0.65369201\n",
      "  0.65109412  0.64850656  0.64592928  0.64336224  0.6408054   0.63825873\n",
      "  0.63572218  0.6331957   0.63067927  0.62817284  0.62567637  0.62318982\n",
      "  0.62071315  0.61824633  0.61578931  0.61334205  0.61090452  0.60847667\n",
      "  0.60605848  0.6036499   0.60125088  0.59886141  0.59648142  0.5941109\n",
      "  0.5917498   0.58939808  0.58705571  0.58472264  0.58239885  0.58008429\n",
      "  0.57777893  0.57548274  0.57319567  0.57091769  0.56864876  0.56638884\n",
      "  0.56413791  0.56189593  0.55966286  0.55743866  0.5552233   0.55301674\n",
      "  0.55081895  0.5486299   0.54644955  0.54427786  0.5421148   0.53996034\n",
      "  0.53781444  0.53567707  0.5335482   0.53142778  0.52931579  0.5272122\n",
      "  0.52511696  0.52303005  0.52095144  0.51888108  0.51681896  0.51476503\n",
      "  0.51271926  0.51068162  0.50865208  0.50663061  0.50461717  0.50261173\n",
      "  0.50061426  0.49862473  0.49664311  0.49466936  0.49270345  0.49074536\n",
      "  0.48879505  0.48685249  0.48491766  0.48299051  0.48107102  0.47915915\n",
      "  0.47725489  0.4753582   0.47346904  0.47158739]\n"
     ]
    }
   ],
   "source": [
    "xi_blue = ERDF(lambda_Edd) #xi_blue = ERDF(np.log10(lambda_Edd)) ?\n",
    "#using colin's\n",
    "sampling = inv_trans_sampling(lambda_, xi_blue, 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "4ea5f9ac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x28cb953a0>]"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.plot(lambda_Edd, xi_blue)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "b5151c79",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 7.67393795, 12.78989659, 10.67042801, 10.45117264,  7.96627845,\n",
       "         5.84680987,  4.60436277,  2.77723469,  1.90021321,  1.90021321,\n",
       "         1.2424471 ,  0.9501066 ,  0.65776611,  0.21925537,  0.29234049,\n",
       "         0.58468099,  0.51159586,  0.14617025,  0.14617025,  0.        ,\n",
       "         0.29234049,  0.14617025,  0.14617025,  0.07308512,  0.14617025,\n",
       "         0.07308512,  0.07308512,  0.07308512,  0.07308512,  0.        ,\n",
       "         0.14617025,  0.07308512,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.07308512,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ,  0.07308512,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.07308512,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ,  0.07308512,\n",
       "         0.        ,  0.        ,  0.07308512,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ,  0.07308512]),\n",
       " array([6.03120870e-05, 1.37429872e-02, 2.74256623e-02, 4.11083375e-02,\n",
       "        5.47910126e-02, 6.84736877e-02, 8.21563629e-02, 9.58390380e-02,\n",
       "        1.09521713e-01, 1.23204388e-01, 1.36887063e-01, 1.50569739e-01,\n",
       "        1.64252414e-01, 1.77935089e-01, 1.91617764e-01, 2.05300439e-01,\n",
       "        2.18983114e-01, 2.32665789e-01, 2.46348464e-01, 2.60031140e-01,\n",
       "        2.73713815e-01, 2.87396490e-01, 3.01079165e-01, 3.14761840e-01,\n",
       "        3.28444515e-01, 3.42127190e-01, 3.55809865e-01, 3.69492541e-01,\n",
       "        3.83175216e-01, 3.96857891e-01, 4.10540566e-01, 4.24223241e-01,\n",
       "        4.37905916e-01, 4.51588591e-01, 4.65271267e-01, 4.78953942e-01,\n",
       "        4.92636617e-01, 5.06319292e-01, 5.20001967e-01, 5.33684642e-01,\n",
       "        5.47367317e-01, 5.61049992e-01, 5.74732668e-01, 5.88415343e-01,\n",
       "        6.02098018e-01, 6.15780693e-01, 6.29463368e-01, 6.43146043e-01,\n",
       "        6.56828718e-01, 6.70511393e-01, 6.84194069e-01, 6.97876744e-01,\n",
       "        7.11559419e-01, 7.25242094e-01, 7.38924769e-01, 7.52607444e-01,\n",
       "        7.66290119e-01, 7.79972795e-01, 7.93655470e-01, 8.07338145e-01,\n",
       "        8.21020820e-01, 8.34703495e-01, 8.48386170e-01, 8.62068845e-01,\n",
       "        8.75751520e-01, 8.89434196e-01, 9.03116871e-01, 9.16799546e-01,\n",
       "        9.30482221e-01, 9.44164896e-01, 9.57847571e-01, 9.71530246e-01,\n",
       "        9.85212922e-01, 9.98895597e-01, 1.01257827e+00, 1.02626095e+00,\n",
       "        1.03994362e+00, 1.05362630e+00, 1.06730897e+00, 1.08099165e+00,\n",
       "        1.09467432e+00, 1.10835700e+00, 1.12203967e+00, 1.13572235e+00,\n",
       "        1.14940502e+00, 1.16308770e+00, 1.17677037e+00, 1.19045305e+00,\n",
       "        1.20413572e+00, 1.21781840e+00, 1.23150107e+00, 1.24518375e+00,\n",
       "        1.25886642e+00, 1.27254910e+00, 1.28623177e+00, 1.29991445e+00,\n",
       "        1.31359712e+00, 1.32727980e+00, 1.34096247e+00, 1.35464515e+00,\n",
       "        1.36832783e+00]),\n",
       " <BarContainer object of 100 artists>)"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(sampling, bins=100, density=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "0b849cec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3.16227766e-09, 8.91250938e-09, 2.51188643e-08, 7.07945784e-08,\n",
       "       1.99526231e-07, 5.62341325e-07, 1.58489319e-06, 4.46683592e-06,\n",
       "       1.25892541e-05, 3.54813389e-05, 1.00000000e-04, 2.81838293e-04,\n",
       "       7.94328235e-04, 2.23872114e-03, 6.30957344e-03, 1.77827941e-02,\n",
       "       5.01187234e-02, 1.41253754e-01, 3.98107171e-01, 1.12201845e+00,\n",
       "       3.16227766e+00])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lambda_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "a5003aa6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6.03739352e-09, 1.70156868e-08, 4.79567214e-08, 1.35160405e-07,\n",
       "       3.80933778e-07, 1.07361726e-06, 3.02586456e-06, 8.52804502e-06,\n",
       "       2.40352965e-05, 6.77406695e-05, 1.90919147e-04, 5.38083264e-04,\n",
       "       1.51652469e-03, 4.27414729e-03, 1.20461838e-02, 3.39507587e-02,\n",
       "       9.56862389e-02, 2.69680463e-01, 7.60062812e-01, 2.14214806e+00])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lambda_Edd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "44c124e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.e+01, 1.e+02, 1.e+03, 1.e+04, 1.e+05, 1.e+06, 1.e+07, 1.e+08,\n",
       "       1.e+09, 1.e+10])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.logspace(1, 10, 10) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "b9088747",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3.16227766e-09, 8.91250938e-09, 2.51188643e-08, 7.07945784e-08,\n",
       "       1.99526231e-07, 5.62341325e-07, 1.58489319e-06, 4.46683592e-06,\n",
       "       1.25892541e-05, 3.54813389e-05, 1.00000000e-04, 2.81838293e-04,\n",
       "       7.94328235e-04, 2.23872114e-03, 6.30957344e-03, 1.77827941e-02,\n",
       "       5.01187234e-02, 1.41253754e-01, 3.98107171e-01, 1.12201845e+00,\n",
       "       3.16227766e+00])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lambda_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "a52a68de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5.75023172e-09, 1.62063549e-08, 4.56757141e-08, 1.28731653e-07,\n",
       "       3.62815094e-07, 1.02255187e-06, 2.88194273e-06, 8.12241820e-06,\n",
       "       2.28920848e-05, 6.45186611e-05, 1.81838293e-04, 5.12489942e-04,\n",
       "       1.44439290e-03, 4.07085231e-03, 1.14732207e-02, 3.23359293e-02,\n",
       "       9.11350311e-02, 2.56853416e-01, 7.23911284e-01, 2.04025921e+00])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dlambda"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9cf56b1a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}