csiborgtools/notebooks/flow_calibration.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from h5py import File\n",
    "%matplotlib inline\n",
    "\n",
    "from jax import numpy as jnp\n",
    "import jax\n",
    "from tqdm import tqdm\n",
    "\n",
    "from scipy.optimize import fmin_powell\n",
    "from numpyro.infer import MCMC, NUTS, util, init_to_median\n",
    "\n",
    "import csiborgtools\n",
    "import corner\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "\n",
    "paths = csiborgtools.read.Paths(**csiborgtools.paths_glamdring)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## LOS density & radial velocity plots "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10:20:19: reading the catalogue.\n",
      "10:20:19: reading the interpolated field.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1/1 [00:00<00:00, 84.48it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10:20:19: calculating the radial velocity.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 50/50 [00:00<00:00, 21608.99it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10:20:19: reading the catalogue.\n",
      "10:20:19: reading the interpolated field.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 101/101 [00:02<00:00, 42.58it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10:20:21: calculating the radial velocity.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 50/50 [00:00<00:00, 351.66it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10:20:22: reading the catalogue.\n",
      "10:20:22: reading the interpolated field.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 20/20 [00:00<00:00, 123.83it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10:20:22: calculating the radial velocity.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 50/50 [00:00<00:00, 1285.41it/s]\n"
     ]
    }
   ],
   "source": [
    "# fpath = \"/mnt/extraspace/rstiskalek/catalogs/A2.h5\"\n",
    "fpath = \"/mnt/extraspace/rstiskalek/catalogs/PV_compilation_Supranta2019.hdf5\"\n",
    "\n",
    "loader_carrick = csiborgtools.flow.DataLoader(\"Carrick2015\", \"LOSS\", fpath, paths, ksmooth=0)\n",
    "loader_csiborg = csiborgtools.flow.DataLoader(\"csiborg1\", \"LOSS\", fpath, paths, ksmooth=0)\n",
    "loader_csiborg2 = csiborgtools.flow.DataLoader(\"csiborg2_main\", \"LOSS\", fpath, paths, ksmooth=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ks = [115,  53,  77, 105,  26,  61,  86,  29,  80,  21]\n",
    "ks = [19,  8, 15,  0, 16,  6, 48, 38, 26, 44]\n",
    "# ks = [19]\n",
    "# ks = np.random.choice(50, 10, replace=False)\n",
    "\n",
    "# k = 6\n",
    "for k in []:\n",
    "    fig, axs = plt.subplots(2, 1, figsize=(7, 7), sharex=True)\n",
    "    # Get rid of vertical spacing\n",
    "    fig.subplots_adjust(wspace=0)\n",
    "\n",
    "    # Plot CSiBORG\n",
    "    for i in range(loader_csiborg.los_density.shape[1]):\n",
    "        axs[0].plot(loader_csiborg.rdist, loader_csiborg.los_density[k, i, :], alpha=0.1, color=\"black\")\n",
    "        axs[1].plot(loader_csiborg.rdist, loader_csiborg.los_radial_velocity[k, i, :], alpha=0.1, color=\"black\")\n",
    "\n",
    "    # CSiBORG1\n",
    "    axs[0].plot(loader_csiborg.rdist, loader_csiborg.los_density[k, :, :].mean(axis=0), color=\"red\", label=\"CSiBORG1\")\n",
    "    axs[1].plot(loader_csiborg.rdist, loader_csiborg.los_radial_velocity[k, :, :].mean(axis=0), color=\"red\")\n",
    "\n",
    "    # CSiBORG2\n",
    "    axs[0].plot(loader_csiborg2.rdist, loader_csiborg2.los_density[k, :, :].mean(axis=0), color=\"violet\", label=\"CSiBORG2\")\n",
    "    axs[1].plot(loader_csiborg2.rdist, loader_csiborg2.los_radial_velocity[k, :, :].mean(axis=0), color=\"violet\")\n",
    "\n",
    "    # Plot Carrick+2015\n",
    "    axs[0].plot(loader_carrick.rdist, loader_carrick.los_density[k, 0, :], color=\"blue\", label=\"Carrick+2015\")\n",
    "    axs[1].plot(loader_carrick.rdist, loader_carrick.los_radial_velocity[k, 0, :] * 0.43, color=\"blue\")\n",
    "\n",
    "\n",
    "    # for i in range(2):\n",
    "    #     label = \"SN\"\n",
    "    #     rdist = loader_csiborg.cat[\"r_hMpc\"][k]\n",
    "    #     axs[i].axvline(rdist, color=\"violet\", linestyle=\"--\",\n",
    "    #                 zorder=0, label=label)\n",
    "\n",
    "    axs[1].set_xlabel(r\"$r ~ [\\mathrm{Mpc} / h]$\")\n",
    "    axs[0].set_ylabel(r\"$\\rho_{\\rm LOS} / \\langle \\rho_{\\rm matter} \\rangle$\")\n",
    "    axs[1].set_ylabel(r\"$v_{\\rm LOS} ~ [\\mathrm{km/s}]$\")\n",
    "\n",
    "    axs[0].set_yscale(\"log\")\n",
    "\n",
    "    axs[0].legend(loc=\"upper right\")\n",
    "    axs[0].set_xlim(0, 200)\n",
    "\n",
    "    fig.tight_layout(w_pad=0, h_pad=0)\n",
    "    fig.savefig(f\"../plots/LOSS_los_{k}.png\", dpi=500, bbox_inches=\"tight\")\n",
    "\n",
    "    fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test running a model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "16:28:25: reading the catalogue.\n",
      "16:28:25: reading the interpolated field.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 101/101 [00:21<00:00,  4.68it/s]\n",
      "/mnt/users/rstiskalek/csiborgtools/csiborgtools/flow/flow_model.py:108: UserWarning: The number of radial steps is even. Skipping the first step at 0.0 because Simpson's rule requires an odd number of steps.\n",
      "  warn(f\"The number of radial steps is even. Skipping the first \"\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "16:28:46: calculating the radial velocity.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1248/1248 [00:02<00:00, 441.14it/s]\n"
     ]
    }
   ],
   "source": [
    "fpath_data = \"/mnt/extraspace/rstiskalek/catalogs/PV_compilation_Supranta2019.hdf5\"\n",
    "# fpath_data = \"/mnt/extraspace/rstiskalek/catalogs/A2.h5\"\n",
    "\n",
    "simname = \"csiborg1\"\n",
    "catalogue = \"2MTF\"\n",
    "loader = csiborgtools.flow.DataLoader(simname, catalogue, fpath_data, paths, ksmooth=0)\n",
    "get_model_kwargs = {\"zcmb_max\": 0.06}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Maximizing the log-likelihood"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 5/5 [00:13<00:00,  2.76s/it]\n"
     ]
    }
   ],
   "source": [
    "samples, stats, fmin, logz, bic = csiborgtools.flow.optimize_model_with_jackknife(loader, 19, 5, True, get_model_kwargs=get_model_kwargs)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Log Z: \n",
      "-720.9279427394929 3.501431137265503\n",
      "BIC: \n",
      "1496.4595387739434 6.356325506551423\n",
      "beta: \n",
      "0.9214629141858417 0.2800670163219086\n"
     ]
    }
   ],
   "source": [
    "print(\"Log Z: \")\n",
    "print(np.mean(logz), np.std(logz))\n",
    "\n",
    "print(\"BIC: \")\n",
    "print(np.mean(bic), np.std(bic))\n",
    "\n",
    "print(\"beta: \")\n",
    "print(*stats[\"beta\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Running HMC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Selected 1248/1248 galaxies.\n"
     ]
    }
   ],
   "source": [
    "model = csiborgtools.flow.get_model(loader, k=30, **get_model_kwargs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [],
   "source": [
    "kernel = NUTS(model, init_strategy=init_to_median(num_samples=100))\n",
    "mcmc = MCMC(kernel, num_warmup=250, num_samples=500)\n",
    "\n",
    "rng_key = jax.random.PRNGKey(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "sample: 100%|██████████| 750/750 [03:36<00:00,  3.47it/s, 7 steps of size 4.64e-01. acc. prob=0.91]  \n"
     ]
    }
   ],
   "source": [
    "mcmc.run(rng_key, sample_alpha=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                      mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
      "          Vext_x     82.64     22.65     82.44     42.11    119.99    503.40      1.00\n",
      "          Vext_y   -195.75     24.46   -195.33   -236.00   -155.73    647.07      1.00\n",
      "          Vext_z   -306.00     25.02   -305.94   -347.13   -267.32    425.43      1.00\n",
      "               a    -22.28      0.02    -22.28    -22.30    -22.25    493.19      1.00\n",
      "           alpha      0.52      0.04      0.52      0.46      0.58    588.72      1.00\n",
      "               b     -6.31      0.09     -6.31     -6.44     -6.17    510.16      1.00\n",
      "            beta      0.95      0.05      0.95      0.87      1.03    678.00      1.00\n",
      "  e_mu_intrinsic      0.40      0.01      0.40      0.38      0.42    406.23      1.00\n",
      "         sigma_v    227.07     15.02    226.96    199.16    248.31    636.71      1.00\n",
      "\n",
      "Number of divergences: 0\n"
     ]
    }
   ],
   "source": [
    "mcmc.print_summary()\n",
    "samples = mcmc.get_samples(group_by_chain=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.hist(samples[\"beta\"], bins=\"auto\")\n",
    "plt.xlabel(r\"$\\beta$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [],
   "source": [
    "Vmag = np.sqrt(samples[\"Vext_x\"]**2 + samples[\"Vext_y\"]**2 + samples[\"Vext_z\"]**2)\n",
    "\n",
    "V = np.vstack([samples[\"Vext_x\"], samples[\"Vext_y\"], samples[\"Vext_z\"]]).T\n",
    "V = csiborgtools.cartesian_to_radec(V)\n",
    "\n",
    "l, b = csiborgtools.flow.radec_to_galactic(V[:, 1], V[:, 2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "|V|  = 373.878173828125 +- 27.086021423339844\n",
      "l    = 342.21601176361986 +- 4.145220888130849\n",
      "b    = -27.483255950082246 +- 3.1987615901961264\n",
      "beta = 0.9494613409042358 +- 0.05187663435935974\n"
     ]
    }
   ],
   "source": [
    "print(f\"|V|  = {np.mean(Vmag)} +- {np.std(Vmag)}\")\n",
    "print(f\"l    = {np.mean(l)} +- {np.std(l)}\")\n",
    "print(f\"b    = {np.mean(b)} +- {np.std(b)}\")\n",
    "print(f\"beta = {np.mean(samples['beta'])} +- {np.std(samples['beta'])}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAkwAAAGxCAYAAACQgOmZAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/H5lhTAAAACXBIWXMAAA9hAAAPYQGoP6dpAACBoElEQVR4nO2de3wU5b3/P5uQBBLIjQAbFJGLt8glwKkSoSqIGgXBtvb8ROtdrIqnlHoh1FIRjlKqLforFhWVeo4K9ZyCICo/oFBbIQgVA4SbBLk1JCAENhAgxGR+f8RZdjdzeea2M7P5vF+vvCDZmdlnnp2d5zPfa0CSJAmEEEIIIUSVJLcHQAghhBDidSiYCCGEEEJ0oGAihBBCCNGBgokQQgghRAcKJkIIIYQQHSiYCCGEEEJ0oGAihBBCCNGhjdsDSBSamppw8OBBdOjQAYFAwO3hEEIIIUQASZJw4sQJdO3aFUlJ6nYkCiabOHjwILp16+b2MAghhBBiggMHDuD8889XfZ2CySY6dOgAoHnCMzMzXR4NIYQQQkSora1Ft27dwuu4GhRMNiG74TIzMymYCCGEEJ+hF07DoG9CCCGEEB0omAghhBBCdKBgIoQQQgjRgYKJEEIIIUQHCiZCCCGEEB0omAghhBBCdKBgIoQQQgjRgYKJEEIIIUQHCiZCCCGEEB1Y6ZsQQhKYxiYJ6/fU4PCJM+jcoS2u6JGL5CQ2CCfEKBRMhBCSoCwrr8KzH25DVehM+G/5WW3xzC0FKO6T7+LICPEfdMkRQkgCsqy8Co+8szFKLAFAdegMHnlnI5aVV7k0MkL8CQUTIYQkGI1NEp79cBskhdfkvz374TY0NiltQQhRgoKJEEISjPV7alpYliKRAFSFzmD9npr4DYoQn8MYJkKIKgwY9ieHT6iLJTPbEUIomAghKjBg2L907tDW8HYUx4RoQ8FECGmBHDAcG+EiBwzP+clAiiYPc0WPXORntUV16IxiHFMAQDCrWRQBFMeEiMAYJkJIFH4OGG5sklC6+ygWl1WidPdRT44xHiQnBfDMLQUAmsVRJPLvz9xSgOSkALPpCBGEFiZCSBRGAoaLenWM38B0oJUkmuI++Zjzk4Et5iQYMSd64jiAZnF8fUGQ7jnS6qFgIoRE4ceAYboQlSnuk4/rC4KqsUl+FceEuAEFEyEkCjMBw25CK4k2yUkBVbHjR3FMiFswhokQEoUcMKwmLQJodnXJAcNuw5pD5vGbOCbETSiYCCFRGAkY9gK0kpjHb+KYEDehYCKEtEAOGA5mRVsWglltPRcPRCuJefwmjglxE8YwEdJK0StUqBcw7BWM1hwi0Yhk0xFCgIAkSa2zUInN1NbWIisrC6FQCJmZmW4PhxBNEi0FX86SAxAlmmRp5zWrmBdhpW/SWhFdvymYbIKCifgFtRR8v4uLRBOBhJD4ILp++yaGae/evXjggQfQo0cPtGvXDr169cIzzzyDs2fPRm23efNmfP/730fbtm3RrVs3/Pa3v9U99v79+zFy5Eikp6ejc+fOePLJJ/Htt986dSqEuIafq3jrUdwnH59NGo754wbj5dsLMX/cYHw2aTjFEiHEFnwTw7Rjxw40NTXhtddeQ+/evVFeXo5x48ahrq4OL774IoBmlXjDDTdgxIgRePXVV7Flyxbcf//9yM7OxkMPPaR43MbGRowcORLBYBBr165FVVUV7r77bqSkpOD555+P5ykS4jiJXqhQq+YQIYRYwdcuuRdeeAFz5szB119/DQCYM2cOnn76aVRXVyM1NRUAUFJSgg8++AA7duxQPMYnn3yCUaNG4eDBg+jSpQsA4NVXX8WkSZPwzTffhI+jB11yxA8sLqvEhAVlutu9fHshxhSe5/yACCHEZRLOJadEKBRCbu65zJfS0lJcffXVUSLnxhtvxM6dO3Hs2DHFY5SWlqJv375hsSTvU1tbi61bt6q+d319PWpra6N+CPE6TMEnhBBz+FYwVVRU4A9/+AN++tOfhv9WXV0dJXwAhH+vrq5WPI6ZfQBgxowZyMrKCv9069bN1HkQEk9YqJAQQszhumAqKSlBIBDQ/Il1p1VWVqK4uBg//vGPMW7cOFfGPXnyZIRCofDPgQMHXBkHIUZgoUJCCDGH60Hfjz/+OO69917NbXr27Bn+/8GDBzFs2DBcddVVeP3116O2CwaDOHToUNTf5N+DwaDisYPBINavX29oHwBIS0tDWlqa5rgJ8SIsVEgIIcZxXTB16tQJnTp1Etq2srISw4YNw6BBgzBv3jwkJUUbyIqKivD000+joaEBKSkpAIAVK1bgkksuQU5OjuIxi4qK8Nxzz+Hw4cPo3LlzeJ/MzEwUFBRYODNC7MPuooJ+qeJNCCFewTdZcpWVlbj22mvRvXt3vP3220hOTg6/JluCQqEQLrnkEtxwww2YNGkSysvLcf/992PWrFnhsgKLFi3C5MmTw26+xsZGFBYWomvXrvjtb3+L6upq3HXXXXjwwQcNlRVglhxxChZkJIQQ5xBdv123MImyYsUKVFRUoKKiAueff37Ua7Lmy8rKwvLlyzF+/HgMGjQIeXl5+PWvfx1VgykUCmHnzp3h35OTk7F06VI88sgjKCoqQkZGBu655x5MmzYtPidGiAZqVbmrQ2fwyDsbfVuVmxA3YPsXYgXfWJi8Di1MxG4amyQMnblKtdCk3FT2s0nDedMnRAdaaokaraIOEyFepbFJQunuo1hcVonS3UdNtRoxUpWbEKKObKmN/T7Jltpl5VUujYz4Cd+45AjxC3Y9yR4+oS6WzGxH4gddP95Br39iAM39E68vCPIzIppQMBFiI3bGHLEqtz+h68dbJHr/RBI/6JIjxCb0nmSB5idZUfccq3L7j0R1/djhYnYLWmqJXdDCRIhN2P0kK1flfuSdjQgAUUKMVbmt4YTLLFFdP363mNFSS+yCgokQm3DiSdbPVbm9GsfjlABIRNdPIpS1kC211aEzimJWzjalpZboQcFEiE049STrx6rcXrVKOCkAEs31kygWM1pqiV0whokQm3Ay5ig5KYCiXh0xpvA8FPXq6Ombu1fjeOyOMYsl0Vw/iVTWQrbUBrOi5z6Y1dYXVjLiDWhhIsQm+CTrbauE0y6zRHP9JJrFzI+WWuItaGEixEZa05OsUuaUl60STgsAWTADaGFl9KNgTjSLGeAvSy3xHrQwEWIzreFJVi1G6eY+QaH93bBKiC7see3TULr7qKnPLl5B+vEIqE80ixkhVmEvOZtgLznSWlALnI51Q2oxf9zguGeKyb35tARAdnoK0tokobq2Pvx3M8HqTgqaeAbUy581oOxiVrKaejU7khA1RNdvCiaboGAirQG9hsAAkBQAJElZPLndMFhLAKjdCLXEgdPEio9jdWcx/j1lsao1RisixohA82p2JCFaUDDFGQom0hoo3X0UY+euE9pWLfDd7VgutUX9dEMjjp9qUNzHDaGnNM6kAKCWxKc2RjtEjIjg0rI8Au5/7oSoIbp+M4aJECKMaOzR/UMuxCfl1XErtmnEgqIUY9bUJOHONz9XPX68i06qiQ+tigdKY7Sr7pQcLK2Gl7MjCbELCiZCiDCigdPXFwTx9MiCuMSymLGgxAqAxWWVQu8Vj2B1LfEhgjzGeIqYRKxyTkgsLCtACBHGSHHOeKRw21Uk00sp9HriQw95jPEs8ZBoNZsIUYKCiRAijJdqDdlZudvJKu1GMSsqYscYTxHjJcFJiFNQMBFCDOGV4px2WlC8JATNiAqlMcZTxHhJcBLiFIxhIoQYxgvFOe22oJgpOulEzSG9gpFAy2w5pTHGs/Ak2wKR1gAFEyHEFHqZU07jhAXFiBB0quaQiPiYPXYAcjLSNMcYDxETKxhfuWMgpn/kbJVz4m/8XNiUdZhsgnWYCIkvIkU08x2qnRSPmkN2CTKnhJ3acaeMvExXzJHWiVcLm7JwZZyhYCIk/sz4eBte+/se1dd/enUPTL65wNb31BNqdha5tOtp3O6nehapJEbx8jXDwpWEEFeIl8m9sUnCkk3aZQOWbKrCU8WX2fr+8aw5ZJfb0073KYtUEqMkyjV
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.scatter(l, b)\n",
    "plt.xlabel(r\"$l$\")\n",
    "plt.ylabel(r\"$b$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.hist(V[:, 0], bins=\"auto\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [],
   "source": [
    "if \"alpha\" in samples:\n",
    "    data = np.vstack([samples[\"alpha\"], samples[\"beta\"], l, b, Vmag]).T\n",
    "    labels = [r\"$\\alpha$\", r\"$\\beta$\", r\"$l$\", r\"$b$\", r\"$|\\bf{V}_{\\rm ext}|$\"]\n",
    "else:\n",
    "    data = np.vstack([samples[\"beta\"], l, b, Vmag]).T\n",
    "    labels = [r\"$\\beta$\", r\"$l$\", r\"$b$\", r\"$|\\bf{V}_{\\rm ext}|$\"]\n",
    "\n",
    "# keys = samples.keys()\n",
    "# data = np.vstack([samples[key] for key in keys]).T\n",
    "# labels = list(keys)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 1180x1180 with 25 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = corner.corner(data, labels=labels, show_titles=True, title_fmt=\".3f\", title_kwargs={\"fontsize\": 12}, smooth=1)\n",
    "fig.savefig(f\"../plots/corner.png\", dpi=300, bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vizualize the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 20/20 [00:00<00:00, 113.74it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<KeysViewHDF5 ['Vext_x', 'Vext_y', 'Vext_z', 'alpha', 'alpha_cal', 'beta', 'beta_cal', 'e_mu_intrinsic', 'mag_cal', 'sigma_v']>\n"
     ]
    }
   ],
   "source": [
    "paths = csiborgtools.read.Paths(**csiborgtools.paths_glamdring)\n",
    "catalogue = \"LOSS\"\n",
    "simname = \"csiborg2_random\"\n",
    "\n",
    "nsims = paths.get_ics(simname)\n",
    "\n",
    "Vx = []\n",
    "Vy = []\n",
    "Vz = []\n",
    "beta = []\n",
    "sigma_v = []\n",
    "alpha = []\n",
    "\n",
    "alpha_cal = []\n",
    "beta_cal = []\n",
    "mag_cal = []\n",
    "e_mu_intrinsic = []\n",
    "\n",
    "\n",
    "with File(f\"/mnt/extraspace/rstiskalek/csiborg_postprocessing/peculiar_velocity/flow_samples_{catalogue}_{simname}_smooth_0.hdf5\", 'r') as f:\n",
    "    for i, nsim in enumerate(tqdm(nsims)):\n",
    "        if i == 0:\n",
    "            print(f[f\"sim_{nsim}\"].keys())\n",
    "\n",
    "        Vx.append(f[f\"sim_{nsim}/Vext_x\"][:])\n",
    "        Vy.append(f[f\"sim_{nsim}/Vext_y\"][:])\n",
    "        Vz.append(f[f\"sim_{nsim}/Vext_z\"][:])\n",
    "        alpha.append(f[f\"sim_{nsim}/alpha\"][:])\n",
    "        beta.append(f[f\"sim_{nsim}/beta\"][:])\n",
    "        sigma_v.append(f[f\"sim_{nsim}/sigma_v\"][:])\n",
    "\n",
    "        alpha_cal.append(f[f\"sim_{nsim}/alpha_cal\"][:])\n",
    "        beta_cal.append(f[f\"sim_{nsim}/beta_cal\"][:])\n",
    "        mag_cal.append(f[f\"sim_{nsim}/mag_cal\"][:])\n",
    "        e_mu_intrinsic.append(f[f\"sim_{nsim}/e_mu_intrinsic\"][:])\n",
    "\n",
    "Vx = np.hstack(Vx)\n",
    "Vy = np.hstack(Vy)\n",
    "Vz = np.hstack(Vz)\n",
    "alpha = np.hstack(alpha)\n",
    "beta = np.hstack(beta)\n",
    "sigma_v = np.hstack(sigma_v)\n",
    "\n",
    "alpha_cal = np.hstack(alpha_cal)\n",
    "beta_cal = np.hstack(beta_cal)\n",
    "mag_cal = np.hstack(mag_cal)\n",
    "e_mu_intrinsic = np.hstack(e_mu_intrinsic)\n",
    "\n",
    "Vmag = np.sqrt(Vx**2 + Vy**2 + Vz**2)\n",
    "\n",
    "V = np.vstack([Vx, Vy, Vz]).T\n",
    "V = csiborgtools.cartesian_to_radec(V)\n",
    "l, b = csiborgtools.flow.radec_to_galactic(V[:, 1], V[:, 2])\n",
    "\n",
    "\n",
    "data = np.vstack([alpha, beta, Vmag, l, b, sigma_v, alpha_cal, beta_cal, mag_cal, e_mu_intrinsic]).T\n",
    "labels = [r\"$\\alpha$\", r\"$\\beta$\", r\"$|\\bf{V}_{\\rm ext}|$\", r\"$l$\", r\"$b$\", r\"$\\sigma_v$\", r\"$\\alpha_{\\rm cal}$\", r\"$\\beta_{\\rm cal}$\", r\"$M$\", r\"$\\sigma_\\mu$\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 2230x2230 with 100 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = corner.corner(data, labels=labels, show_titles=True, title_fmt=\".3f\", title_kwargs={\"fontsize\": 12})\n",
    "fig.suptitle(f\"{catalogue}, {simname}\")\n",
    "fig.savefig(f\"../plots/corner_{catalogue}_{simname}.png\", dpi=300, bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "294.53874356626227"
      ]
     },
     "execution_count": 210,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(l)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 299,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.38958"
      ]
     },
     "execution_count": 299,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0.906 * 0.43"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.hist(V[:, 0], bins=\"auto\", density=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.61461765 0.095553815\n",
      "198.02641 36.928383\n",
      "294.53874356626227 -5.542468825545464\n"
     ]
    }
   ],
   "source": [
    "print(beta.mean(), beta.std())\n",
    "print(np.mean(V[:, 0]), np.std(V[:, 0]))\n",
    "print(l.mean(), b.mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAj8AAAGxCAYAAACN/tcCAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/H5lhTAAAACXBIWXMAAA9hAAAPYQGoP6dpAADSsElEQVR4nOydd5wV1fn/P+fMzC3blw6CgFhBsfcCKoqCYEGIsUTRGBNLBNF8YxJjEpOoERXFFrvJL8aICtIRQVEUqSIgCoqA9Lp9b5mZc35/zMyt03b3bj/vvAh472fPnLl39s5zz3me50M45xwCgUAgEAgE7QTa3BMQCAQCgUAgaEpE8CMQCAQCgaBdIYIfgUAgEAgE7QoR/AgEAoFAIGhXiOBHIBAIBAJBu0IEPwKBQCAQCNoVIvgRCAQCgUDQrpCbewItDcYYdu7cicLCQhBCmns6AoFAIBAIfMA5R1VVFXr06AFK3dd2RPCTwc6dO9GrV6/mnoZAIBAIBIJ6sG3bNvTs2dNVI4KfDAoLCwEYL15RUVEzz0YgEAgEAoEfKisr0atXr8R93A0R/GRgbXUVFRWJ4EcgEAgEglaGn5QVkfAsEAgEAoGgXSGCH4FAIBAIBO0KEfwIBAKBQCBoV4jgRyAQCAQCQbtCBD8CgUAgEAjaFSL4EQgEAoFA0K4QwY9AIBAIBIJ2hQh+BAKBQCAQtCtE8CMQCAQCgaBdITo8CwQCgQDxmIqP/rsYi6cuxalDT8RFNw5COD/U3NMSCBoFwjnnzT2JlkRlZSWKi4tRUVEh7C0EAkGbp3xfBWa+MB9Tn56NygNVIJSAc468wjBG/mooLr/zEnQ6pGNzT1Mg8KQu928R/GQggh+BQNBemP3Sh5h81yvQNR2cZd8KqGRkRtz4l5/g2vuvaurpCQR1oi73b5HzIxAIBO2ULxeuha7aBz4AwHQGpjMsm72qiWcmEDQuIvgRCASC9oy3AbZA0OYQwY9AIBAIBIJ2hQh+BAKBoD3jK+1TLA8J2hYi+BEIBIJ2ypDrz0PHHh0AJJObLQg1Ap6ijoW47LaLmnxuAkFjIqq9MhDVXgKBoD2hazoWT12GKROnY8Py70EpAWMcvfv3xJj7Lsfga85GIKg09zQFAk9EqXsDEMGPQCBor6z/YiM+e28pTrnkBJxw/rEgRGx3CVoPdbl/iw7PAoFAIAAA9D/jSPQ/48jmnoZA0OiInB+BQCAQCATtCrHyIxAIBK2YWCSGBf9ZjCUzluOM4SdjyA3nIRgONve0BIIWjcj5yUDk/AgEgtZA2Z5yTH9uHqZNnoPq8hrDk4tx5Bfn4Yo7L8XIO4aiQ7fS5p6mQNBkiITnBiCCH4FA0NKZ9swcvHDPG+CMgzGW9TyVKAgBbn30Bowaf1kzzFAgaHqEt5dAIBC0YVZ9uAa6ptsGPoDhyaVrDCvmrW7aiQkErQQR/AgEAoFAIGhXiOBHIBAIBAJBu0JUewkEggbDOcdXH3+NWS/NR5denXH5nZegS69OjXasrz/fgBnPz0Npl2Jcftel6N63a6Mcq9UjehTasvfHfXj/mbnYt/0Aht92EQae1180dGxniOBHIBDUGzWu4uO3PsfbE9/HlnXbEv5QUx6fjkFjzsTV40fgqFMPz8mxNFXDp+8uxZSJ0/Hdqh8Sx3rvqdk46/JTcfWEERhw1lHt4iZ28Y2D8e2y71G2uzxhR2FhVX2VdCnGJTdf2IyzbHl8s/Q7vPvEDHzy7heJ6+Sjtz5D3+MOxZj7LsegMWdCCQgrj/aAqPbKQFR7CQT++H71Zvx26F9Rsa8yccNNRZIpdI3hxAuOxaPz/9igoGT7xp2494I/4cDOsqybfeqxjjnjSDyx6M+Qlbb/vU5TNXzyzhd4+7H3sWn1lsTrctjA3hhz3+U4b/QZ4kZuwhjDfRf+GWsWrU9cK6mkBoyPfvAADhvYu5lmKmgIwt5CIBA0Ot+v2oyKfZUAkBX4AEjcYL5cuA6aqjXoRvzDmq04sLMMALICn9RjffPFRtRU1KK4U9v/4iIrMi746Tk4/5qz8fVn32LJ9BU4/bKTcdy5x7SL1a+6EI+qWLNoPQBkBT5A8vot31uB77/cLIKfdoAIfgQCgaAVQwjBseccg2PPOaa5pyIQtBpEtZdAIBAIBIJ2hVj5EQgEaZTvq8DMF+Zj01ebcfGN5+P04SeB0ub7nlRdXoMl01c02/HrQ6QmivlvLMLyeV/inCtPx/k/PQeBoMi/yTW6pmPx1GVY+OanGHDWURh26xAUlOQ397QErQAR/AgEAgDA1vXb8O6kWZj/r0XQNR0EBIvfW4Zufbvg6ntG4OKbBiOcH0rojz9/AI4+/XB8u/R7xyRSSaIYfttF9cr32blpN6Y+NRuzX/4Q8ajqqrXsHC762SAUdiio87Fyxf4dB/D+M3Mx/fl5qK2KgBCCL2asxIv3/RtX/noYLvvlRSjpXNxs82sr1FTUYPbLC/HupJk4sOMgCCVYMmMF3njwfxj28yG48u5h6NGvW0IfDAcw4lcXY/ZLC8AZc0yY73/mkTh+8ICmPh1BMyCqvTIQ1V6C9sg/bnoG8/+1yD6IIQQcHHmFYfxxygScfNHxac9/u+w7vPPkTHwyZQkIIWA6Q2GHAvNmfzFKu9T9Zv/8Pa/jvadmgVIKpttbOFjkF+dh5O1DMfKOS9CpR4c6HytX/PeRqXj9gbcAwHbOhBJIsoS7Jt+CYbcOaerptRk+fW8pHr3hacSjKuxuX1SiYIzhyl8Pw+1Pjk17rmxPOWY8/wGmTZ6NqrIaUImCc57ztgyC5kFUewkEgjrxxQxjW8m2Esa8wURrYlj/+cas4Ofo047AH/47HnsfvR7zXvsYnQ/thAt+ejYCoUDD5sPtgwgLQggGDuqPv868H6G8YL2PlSuWzfnSdb6cceiqhlUL1ojgpwGs/WQ91LhmG/gAyWtmyfQVWcFPadcS/OxPY3DNb6/Agv98iv07DmLo2PMbrSGnoOUigh+BQOALQt3Lp7sc2hk3PDi6iWZjbFX0PfbQFhH4+EaUoOcESgmYXv+fD4QCuPQW0QCyPSOqvQQCgUAgELQrxMqPoE3TGqtBGGNYPudLzH39Ixx2bG9c9qvsvBnGGFbM+wpzX1uI3sf0xMjbh6K0a0kDjuq9IqGrOlZ9uAaX3HIBOvfsmPZcrry9OOdYt/hbHNxT4anVVB1rP/0Guzbvqbe31zdLv8P05+aioDgfl991KXoe0T1Ls2H593j/ubnIKwjjirsuRc8je2RpNq7chO0bd3oejzOOjSt/wNb129C7f696zXnz2q2Y9sxccM5x5V2Xou9x9WvIt3X9Nkx7Zi60uIrL77gUh5/Yt17j5Iqdm3bj/WfmomJ/JUbePhT9zzzKUeuVB9ZUWAnuuzbvwbBbL8KJFxwrGky2EkTCcwYi4bltYFcNAgBKQLatBmkJRGtjmP+vRZjy+HTs2rQHVCIANxI4h9wwCKPGX4buh3XBh//+BG9PnI6d3+82/K24sSU15PpzMWr8ZfW6Gb759/fw5t/fQzwSd8ylAIzjEEIwaMxZuPqey9D3uENtvb3qmkSqqRo+mbIEb0+cjk2rt9jaZdhBKQHnqJO3l67p+GzaMkyZOB3fLvvemDMxbqhnDD/ZGOfso/HFjBV4e+J0fLNkIySZggNgGsNpw07E6Akjcey5x2DpzJWY8vh0fP3ZhjrNmTGOky8aiNH3jsRJQwZ6ztkKdqdMnI7VH62DJFPzXBhOOP9YjL53JE4ZerxnSwLOOVZ9uAZTJk7Hyvlr0sY57txjMPrekU3a2sAKdt95YgY+n74clBpVe7rGcOQp/TDm3pE456rTIclS4mfWLf4Gj419Fjs37TGSm1MCodTk/LEP/RRX3HVpo8x748pNeOeJmVj09ueJx5jO0Lt/T4y+d6RobdBM1OX+LYKfDETw0/ppSDVIc/HVx1/jwSv/gZrKWuOBjGlbVViyIkFTdRACZJ6apTn36jPwx7cn1HkONRU1mPPKQrz75Ezs33HQVZs1nwZ4e21dvw33DfmLrUmnX/x6e+3avAcTBj+IfdsOuHqEyQEZWlzLurk
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.hexbin(l, b, gridsize=50, mincnt=1)\n",
    "plt.xlabel(r\"$l$\")\n",
    "plt.ylabel(r\"$b$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "for i in range(len(x)):\n",
    "    plt.hist(x[i], bins=\"auto\", density=True, histtype=\"step\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test bias"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 437,
   "metadata": {},
   "outputs": [],
   "source": [
    "from jax.lax import cond"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 488,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "def bias(rho_norm, b):\n",
    "    def bias_small(rho_norm, b):\n",
    "        return jnp.log((1 + jnp.exp((1 - b + b * rho_norm))) / (1 + jnp.exp((1 - b))))\n",
    "\n",
    "    def bias_large(rho_norm, b):\n",
    "        return 1 - b + b * rho_norm - jnp.log(1 + jnp.exp(1 - b))\n",
    "\n",
    "    return jnp.where(rho_norm < 3, \n",
    "                     bias_small(rho_norm, b), \n",
    "                     bias_large(rho_norm, b))\n",
    "\n",
    "     "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 489,
   "metadata": {},
   "outputs": [],
   "source": [
    "rho_norm = jnp.linspace(0, 100, 100)\n",
    "b = 2\n",
    "y = bias(rho_norm, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 490,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([  0.       ,   1.0148089,   2.7738497,   4.7473445,   6.767546 ,\n",
       "         8.787747 ,  10.80795  ,  12.828152 ,  14.848353 ,  16.868557 ,\n",
       "        18.888758 ,  20.90896  ,  22.929163 ,  24.949364 ,  26.969566 ,\n",
       "        28.989767 ,  31.00997  ,  33.03017  ,  35.050373 ,  37.07057  ,\n",
       "        39.090775 ,  41.110977 ,  43.13118  ,  45.151382 ,  47.171585 ,\n",
       "        49.191784 ,  51.211987 ,  53.23219  ,  55.25239  ,  57.272594 ,\n",
       "        59.292793 ,  61.312996 ,  63.3332   ,  65.3534   ,  67.373604 ,\n",
       "        69.39381  ,  71.41401  ,  73.43421  ,  75.45441  ,  77.47461  ,\n",
       "        79.49481  ,  81.515015 ,  83.53522  ,  85.55542  ,  87.57562  ,\n",
       "        89.595825 ,  91.61603  ,  93.63623  ,  95.65643  ,  97.67663  ,\n",
       "        99.69683  , 101.71703  , 103.737236 , 105.75744  , 107.77764  ,\n",
       "       109.797844 , 111.81805  , 113.83825  , 115.85845  , 117.87865  ,\n",
       "       119.89885  , 121.91905  , 123.939255 , 125.95946  , 127.97966  ,\n",
       "       129.99986  , 132.02007  , 134.04027  , 136.06047  , 138.08067  ,\n",
       "       140.10088  , 142.12108  , 144.14128  , 146.16148  , 148.18169  ,\n",
       "       150.20187  , 152.22208  , 154.24228  , 156.26248  , 158.28268  ,\n",
       "       160.30289  , 162.32309  , 164.34329  , 166.3635   , 168.3837   ,\n",
       "       170.4039   , 172.4241   , 174.4443   , 176.46451  , 178.48471  ,\n",
       "       180.50491  , 182.52512  , 184.54532  , 186.56552  , 188.58572  ,\n",
       "       190.60593  , 192.62613  , 194.64632  , 196.66652  , 198.68674  ],      dtype=float32)"
      ]
     },
     "execution_count": 490,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 485,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([ 0.       ,  1.0148089,  2.7738497,  4.753666 ,  6.768387 ,\n",
       "        8.787859 , 10.807965 , 12.828154 , 14.848354 , 16.868557 ,\n",
       "       18.888758 , 20.90896  , 22.929163 , 24.949364 , 26.969566 ,\n",
       "       28.989767 , 31.00997  , 33.03017  , 35.050373 , 37.07057  ,\n",
       "       39.090775 , 41.110977 , 43.13118  , 45.151382 , 47.171585 ,\n",
       "       49.191784 , 51.211987 , 53.23219  , 55.25239  , 57.272594 ,\n",
       "       59.292793 , 61.312996 , 63.3332   , 65.3534   , 67.373604 ,\n",
       "       69.39381  , 71.41401  , 73.43421  , 75.45441  , 77.47461  ,\n",
       "       79.49481  , 81.515015 , 83.53522  , 85.55542  , 87.57562  ,\n",
       "              inf,        inf,        inf,        inf,        inf,\n",
       "              inf,        inf,        inf,        inf,        inf,\n",
       "              inf,        inf,        inf,        inf,        inf,\n",
       "              inf,        inf,        inf,        inf,        inf,\n",
       "              inf,        inf,        inf,        inf,        inf,\n",
       "              inf,        inf,        inf,        inf,        inf,\n",
       "              inf,        inf,        inf,        inf,        inf,\n",
       "              inf,        inf,        inf,        inf,        inf,\n",
       "              inf,        inf,        inf,        inf,        inf,\n",
       "              inf,        inf,        inf,        inf,        inf,\n",
       "              inf,        inf,        inf,        inf,        inf],      dtype=float32)"
      ]
     },
     "execution_count": 485,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bias_small(rho_norm, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 487,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(rho_norm, y)\n",
    "plt.plot(rho_norm, bias_small(rho_norm, b), ls=\"--\")\n",
    "plt.plot(rho_norm, bias_large(rho_norm, b), ls=\"dotted\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 462,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([[1.3646735 , 1.434935  , 1.5887474 , 1.6949235 , 1.7769545 ,\n",
       "        1.8709289 , 2.0290222 , 2.1513133 , 2.2334485 , 2.329708  ,\n",
       "        2.444497  , 2.5160108 , 2.5457559 , 2.5692239 , 2.608365  ,\n",
       "        2.6157517 , 2.5902514 , 2.5320826 , 2.4516525 , 2.3783646 ,\n",
       "        2.3570633 , 2.2927842 , 2.235333  , 2.1849432 , 2.131144  ,\n",
       "        2.1050715 , 2.1284485 , 2.1777897 , 2.2121887 , 2.2108288 ,\n",
       "        2.2272425 , 2.2835732 , 2.2929268 , 2.2634182 , 2.241768  ,\n",
       "        2.2274647 , 2.1347542 , 2.0022526 , 1.8764566 , 1.757152  ,\n",
       "        1.5877327 , 1.4179734 , 1.2245289 , 1.0326    , 0.83725584,\n",
       "        0.9779409 , 0.8560009 , 0.7459278 , 0.64249325, 0.5510863 ,\n",
       "        0.4705007 , 0.40490875, 0.3523176 , 0.3036849 , 0.25979096,\n",
       "        0.22670034, 0.2001784 , 0.17650758, 0.15544249, 0.1421564 ,\n",
       "        0.1319982 , 0.12369715, 0.11719201, 0.11655279, 0.1178802 ,\n",
       "        0.12243555, 0.12922992, 0.13944156, 0.15134403, 0.16509394,\n",
       "        0.1822752 , 0.20241688, 0.22445495, 0.24860011, 0.2747241 ,\n",
       "        0.3021833 , 0.32956758, 0.3581138 , 0.38779044, 0.4175948 ,\n",
       "        0.44733912, 0.47730353, 0.5037043 , 0.5280483 , 0.54990727,\n",
       "        0.5693671 , 0.5882731 , 0.5948174 , 0.59384704, 0.5889778 ,\n",
       "        0.581055  , 0.5679292 , 0.5492731 , 0.5233676 , 0.4954697 ,\n",
       "        0.46466196, 0.43128756, 0.39837906, 0.36807328, 0.34046337,\n",
       "        0.31282854, 0.2916725 , 0.2727041 , 0.25453895, 0.24449702,\n",
       "        0.24894878, 0.25541925, 0.2639165 , 0.27725202, 0.30834335,\n",
       "        0.35066515, 0.39812556, 0.45682377, 0.5331358 , 0.6178547 ,\n",
       "        0.71351516, 0.82063544, 0.93213975, 0.7524649 , 0.91292727,\n",
       "        1.0464138 , 1.1508375 , 1.251418  , 1.3491758 , 1.380678  ,\n",
       "        1.4025079 , 1.4121331 , 1.3930808 , 1.3075174 , 1.2249244 ,\n",
       "        1.1454424 , 1.0572306 , 0.92409194, 0.79356396, 0.99048895,\n",
       "        0.90620065, 0.828229  , 0.76082796, 0.698414  , 0.6505554 ,\n",
       "        0.61402965, 0.5859119 , 0.5657008 , 0.5566434 , 0.553449  ,\n",
       "        0.5563643 , 0.5653806 , 0.58270925, 0.6048739 , 0.6295522 ,\n",
       "        0.65922254, 0.69377667, 0.7332983 , 0.7763519 , 0.8221179 ,\n",
       "        0.8646504 , 0.9119135 , 0.9640299 , 0.7129375 , 0.7891277 ,\n",
       "        0.8571147 , 0.9190582 , 0.9803752 , 1.0396756 , 1.0979573 ,\n",
       "        1.1553053 , 1.1901921 , 1.2196769 , 1.2462472 , 1.2697977 ,\n",
       "        1.2838    , 1.2984327 , 1.3102382 , 1.3194026 , 1.3225473 ,\n",
       "        1.3196949 , 1.3108543 , 1.306914  , 1.3042039 , 1.294299  ,\n",
       "        1.2772909 , 1.260877  , 1.2417816 , 1.2328533 , 1.2146448 ,\n",
       "        1.1977972 , 1.1745423 , 1.1424965 , 1.1101197 , 1.101576  ,\n",
       "        1.0878228 , 1.0645813 , 1.0333818 , 0.9999348 , 0.9850849 ,\n",
       "        0.97065103, 0.9509536 , 0.92941177, 0.90072215, 0.8717872 ,\n",
       "        0.89219344, 0.91042507, 0.92014444, 0.9214734 , 0.9279727 ,\n",
       "        0.9602722 , 1.0090538 , 1.0460545 , 1.0889293 , 1.1205827 ,\n",
       "        1.1391929 , 1.1663109 , 1.1970347 , 1.209669  , 1.2047967 ,\n",
       "        1.187488  , 1.1674637 , 1.1264628 , 1.0695738 , 1.0057136 ,\n",
       "        0.938321  , 0.8566655 , 0.7593492 , 0.9830673 , 0.91409945,\n",
       "        0.8435176 , 0.7711419 , 0.70559967, 0.6515862 , 0.5985839 ,\n",
       "        0.54632187, 0.502273  , 0.45877022, 0.42054328, 0.3934341 ,\n",
       "        0.37144205, 0.34999198, 0.3290352 , 0.31012294, 0.30171677,\n",
       "        0.2962771 , 0.29083773, 0.28842846, 0.28969994, 0.2920595 ,\n",
       "        0.2989802 , 0.31210732, 0.3281337 , 0.34449434, 0.36123806,\n",
       "        0.3927679 , 0.4286105 , 0.4655993 , 0.5053859 , 0.5691393 ,\n",
       "        0.6362327 , 0.7067257 , 0.78761345, 0.8970398 , 0.6997818 ,\n",
       "        0.8535489 , 1.0259563 , 1.2127107 , 1.3874727 , 1.5501367 ,\n",
       "        1.7126855 , 1.867709  , 2.001937  , 2.1140966 , 2.1916142 ,\n",
       "        2.2460651 , 2.2813406 , 2.297223  , 2.2536044 , 2.196093  ,\n",
       "        2.1253767 , 2.03259   , 1.8823694 , 1.7347625 , 1.6018292 ,\n",
       "        1.4532942 , 1.283286  , 1.1178659 , 0.9570924 , 0.8172244 ,\n",
       "        0.6897191 , 0.9147335 , 0.8344159 , 0.7673473 , 0.7086063 ,\n",
       "        0.6641469 , 0.6225449 , 0.5973549 , 0.57440835, 0.5516249 ,\n",
       "        0.5317883 , 0.53176755, 0.52977276, 0.5252905 , 0.5225403 ,\n",
       "        0.5306233 , 0.537339  , 0.5404994 , 0.5452957 , 0.5526741 ,\n",
       "        0.55304235, 0.5479818 , 0.55197227, 0.55319256, 0.5490432 ,\n",
       "        0.53936017, 0.5228505 , 0.51295424, 0.51168084, 0.5088841 ,\n",
       "        0.5002767 , 0.4915954 , 0.48361063, 0.49827686, 0.515961  ,\n",
       "        0.5374632 , 0.5629945 , 0.5906428 , 0.6248773 , 0.68398076,\n",
       "        0.7490516 , 0.81219375, 0.8711733 , 0.93306047, 0.70086324,\n",
       "        0.7925049 , 0.8672184 , 0.9352511 , 0.9940311 , 1.0134267 ,\n",
       "        1.0167335 , 1.0081466 , 0.98725164, 0.94359004, 0.88869536,\n",
       "        0.8169855 , 0.7289902 , 0.968997  , 0.90388423, 0.8363196 ,\n",
       "        0.7754801 , 0.7210487 , 0.6658874 , 0.6120377 , 0.5709876 ,\n",
       "        0.5380987 , 0.5059658 , 0.47608382, 0.45786625, 0.4429148 ,\n",
       "        0.42846784, 0.41462535, 0.40961948, 0.40622896, 0.40261546,\n",
       "        0.39951095, 0.3999179 , 0.40015367, 0.40194058, 0.40492177,\n",
       "        0.41054347, 0.4160852 , 0.42165357, 0.43058476, 0.44315138,\n",
       "        0.45663595, 0.47077337, 0.49090838, 0.5150634 , 0.53872305,\n",
       "        0.56145823, 0.58853346, 0.6170561 , 0.64647895, 0.67653644,\n",
       "        0.69559836, 0.71325165, 0.7297187 , 0.74179244, 0.74279547,\n",
       "        0.7412879 , 0.73549235, 0.72251487, 0.7011512 , 0.6794939 ,\n",
       "        0.6576475 , 0.634315  , 0.62078434, 0.6265948 , 0.6586482 ,\n",
       "        0.75736463, 0.86079174, 0.94762903, 0.99869275]], dtype=float32)"
      ]
     },
     "execution_count": 462,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bias(loader._los_density[0], 2.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 436,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "b = 1.4\n",
    "\n",
    "rho = np.linspace(0, 3, 100)\n",
    "\n",
    "def bias(rho, b):\n",
    "    return np.log((1 + np.exp((1 - b + b * rho))) / (1 + np.exp((1 - b))))\n",
    "\n",
    "def linear_bias(rho, b):\n",
    "    return (1 - b + b * rho)\n",
    "\n",
    "plt.figure()\n",
    "cols = plt.rcParams['axes.prop_cycle'].by_key()['color']\n",
    "for i, b in enumerate([0.5, 1, 1.5, 3]):\n",
    "    plt.plot(rho, bias(rho, b), label=f\"b = {b}\", c=cols[i])\n",
    "    plt.plot(rho, 1 - b + b * rho - np.log(1 + np.exp(1 - b)), ls=\"--\", c=cols[i])\n",
    "    # plt.plot(rho, linear_bias(rho, b), ls=\"--\", c=cols[i])\n",
    "    \n",
    "\n",
    "plt.axline((1, 1), slope=1, color=\"red\", linestyle=\"dotted\")\n",
    "plt.axhline(0, color=\"black\", linestyle=\"--\")\n",
    "plt.xlabel(r\"$\\rho / \\langle \\rho \\rangle$\")\n",
    "plt.ylabel(r\"$1 + \\delta_g$\")\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [],
   "source": [
    " def get_field(kind):\n",
    "    folder = \"/mnt/extraspace/rstiskalek/catalogs\"\n",
    "    from os.path import join\n",
    "    if kind == \"density\":\n",
    "        fpath = join(folder, \"twompp_density_carrick2015.npy\")\n",
    "        return np.load(fpath).astype(np.float32)\n",
    "    elif kind == \"velocity\":\n",
    "        fpath = join(folder, \"twompp_velocity_carrick2015.npy\")\n",
    "        field = np.load(fpath).astype(np.float32)\n",
    "\n",
    "        # Because the Carrick+2015 data is in the following form:\n",
    "        # \"The velocities are predicted peculiar velocities in the CMB\n",
    "        # frame in Galactic Cartesian coordinates, generated from the\n",
    "        # \\(\\delta_g^*\\) field with \\(\\beta^* = 0.43\\) and an external\n",
    "        # dipole \\(V_\\mathrm{ext} = [89,-131,17]\\) (Carrick et al Table 3)\n",
    "        # has already been added.\"\"\n",
    "        field[0] -= 89\n",
    "        field[1] -= -131\n",
    "        field[2] -= 17\n",
    "        field /= 0.43\n",
    "\n",
    "        return field"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [],
   "source": [
    "density = get_field(\"density\")\n",
    "velocity = get_field(\"velocity\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [],
   "source": [
    "from h5py import File"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [],
   "source": [
    "with File(\"/mnt/extraspace/rstiskalek/catalogs/Carrick2015_unscaled.hdf5\", 'w') as f:\n",
    "    f.create_dataset(\"density\", data=density)\n",
    "    f.create_dataset(\"velocity\", data=velocity)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
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   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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