{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "049ed0ad",
   "metadata": {},
   "source": [
    "# Optimization Tutorial\n",
    "\n",
    "Trey V. Wenger (c) July 2025\n",
    "\n",
    "Here we demonstrate how to optimize the number of cloud components in a `EmissionAbsorptionPhysicalModel` model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f1c46dd4",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-05T19:59:06.989214Z",
     "start_time": "2024-08-05T19:59:04.772064Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pymc version: 5.22.0\n",
      "arviz version: 0.22.0dev\n",
      "bayes_spec version: 1.9.0\n",
      "caribou_hi version: 4.1.0+3.g94a913e.dirty\n"
     ]
    }
   ],
   "source": [
    "# General imports    \n",
    "import time\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import arviz as az\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import pymc as pm\n",
    "\n",
    "print(\"pymc version:\", pm.__version__)\n",
    "print(\"arviz version:\", az.__version__)\n",
    "\n",
    "import bayes_spec\n",
    "print(\"bayes_spec version:\", bayes_spec.__version__)\n",
    "\n",
    "import caribou_hi\n",
    "print(\"caribou_hi version:\", caribou_hi.__version__)\n",
    "\n",
    "# Notebook configuration\n",
    "pd.options.display.max_rows = None"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70d808d8",
   "metadata": {},
   "source": [
    "## Model Definition and Simulated Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "da706708",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-05T19:59:10.588998Z",
     "start_time": "2024-08-05T19:59:06.991731Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from bayes_spec import SpecData\n",
    "\n",
    "# spectral axes definitions\n",
    "emission_axis = np.linspace(-60.0, 60.0, 200)  # km s-1\n",
    "absorption_axis = np.linspace(-30.0, 30.0, 100)  # km s-1\n",
    "\n",
    "# data noise can either be a scalar (assumed constant noise across the spectrum)\n",
    "# or an array of the same length as the data\n",
    "rms_emission = 0.1  # K\n",
    "rms_absorption = 0.001  # 1 - exp(-tau)\n",
    "\n",
    "# brightness data. In this case, we just throw in some random data for now\n",
    "# since we are only doing this in order to simulate some actual data.\n",
    "emission = rms_emission * np.random.randn(len(emission_axis))\n",
    "absorption = rms_absorption * np.random.randn(len(absorption_axis))\n",
    "\n",
    "dummy_data = {\n",
    "    \"emission\": SpecData(\n",
    "        emission_axis,\n",
    "        emission,\n",
    "        rms_emission,\n",
    "        xlabel=r\"$V_{\\rm LSR}$ (km s$^{-1}$)\",\n",
    "        ylabel=r\"$T_B$ (K)\",\n",
    "    ),\n",
    "    \"absorption\": SpecData(\n",
    "        absorption_axis,\n",
    "        absorption,\n",
    "        rms_absorption,\n",
    "        xlabel=r\"$V_{\\rm LSR}$ (km s$^{-1}$)\",\n",
    "        ylabel=r\"1 - exp(-$\\tau$)\",\n",
    "    ),\n",
    "}\n",
    "\n",
    "# Plot dummy data\n",
    "fig, axes = plt.subplots(2, layout=\"constrained\", sharex=True)\n",
    "axes[0].plot(dummy_data[\"emission\"].spectral, dummy_data[\"emission\"].brightness, \"k-\")\n",
    "axes[0].plot(dummy_data[\"emission\"].spectral, dummy_data[\"emission\"].noise, \"r-\")\n",
    "axes[1].plot(dummy_data[\"absorption\"].spectral, dummy_data[\"absorption\"].brightness, \"k-\", label=\"Data\")\n",
    "axes[1].plot(dummy_data[\"absorption\"].spectral, dummy_data[\"absorption\"].noise, \"r-\", label=\"Noise\")\n",
    "axes[1].set_xlabel(dummy_data[\"emission\"].xlabel)\n",
    "axes[0].set_ylabel(dummy_data[\"emission\"].ylabel)\n",
    "axes[1].set_ylabel(dummy_data[\"absorption\"].ylabel)\n",
    "_ = axes[1].legend(loc=\"lower left\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e183b304-a87b-4c53-83c6-03476a556585",
   "metadata": {},
   "outputs": [],
   "source": [
    "from caribou_hi import EmissionAbsorptionPhysicalModel\n",
    "\n",
    "# Initialize and define the model\n",
    "n_clouds = 3\n",
    "baseline_degree = 0\n",
    "model = EmissionAbsorptionPhysicalModel(\n",
    "    dummy_data,\n",
    "    n_clouds=n_clouds,\n",
    "    baseline_degree=baseline_degree,\n",
    "    bg_temp = 3.77, # assumed background temperature (K)\n",
    "    seed=1234,\n",
    "    verbose=True\n",
    ")\n",
    "model.add_priors(\n",
    "    prior_filling_factor=[2.0, 1.0],  # filling factor prior shape\n",
    "    prior_ff_NHI=1.0e21,  # filling factor * column density prior width (cm-2)\n",
    "    prior_fwhm2_thermal_fraction=[2.0, 2.0], # thermal FWHM^2 fraction prior shape\n",
    "    prior_sigma_log10_NHI=0.5, # log-normal column density distribution width\n",
    "    prior_fwhm2=200.0, # FWHM^2 prior width (km2 s-2)\n",
    "    prior_velocity=[-15.0, 15.0],  # lower and upper limit of velocity prior (km/s)\n",
    "    prior_log10_n_alpha=[-6.0, 1.0],  # log10(n_alpha) prior width (cm-3)\n",
    "    prior_nth_fwhm_1pc=[1.75, 0.25], # non-thermal FWHM at 1 pc prior mean and width (km s-1)\n",
    "    prior_depth_nth_fwhm_power=[0.3, 0.1], # non-thermal FWHM vs. depth power prior mean and width\n",
    "    prior_fwhm_L=None, # Assume Gaussian line profile\n",
    "    prior_baseline_coeffs=None, # Default baseline priors\n",
    ")\n",
    "model.add_likelihood()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "22c23708-937f-4d9b-8f16-5b640287d744",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tspin [  49.97911226  298.78900835 4259.26982821]\n",
      "fwhm2_nonthermal [  7.61461575  21.12711044 215.71459099]\n",
      "fwhm2_thermal [  2.2876605  13.725963  228.76605  ]\n",
      "fwhm2 [  9.90227625  34.85307344 444.48064099]\n",
      "fwhm2_thermal_fraction [0.2310237 0.3938236 0.5146817]\n",
      "log10_Pth [2.94897    2.47712125 3.19897   ]\n",
      "log10_NHI [20.438321   19.88729101 20.46647225]\n",
      "tau_total [3.01218479 0.14166923 0.03771258]\n",
      "wt_ff_fwhm2_thermal [1.9670751  0.07285463 0.00437128]\n"
     ]
    }
   ],
   "source": [
    "from caribou_hi import physics\n",
    "\n",
    "# Simulation parameters\n",
    "filling_factor = np.array([0.2, 0.8, 1.0])\n",
    "absorption_weight = np.array([0.9, 0.8, 1.0])\n",
    "log10_nHI = np.array([1.25, 0.0, -0.5])\n",
    "tkin = np.array([50.0, 300.0, 5000.0])\n",
    "n_alpha = np.array([1.0e-6, 2.0e-6, 3.0e-6])\n",
    "depth = np.array([5.0, 25.0, 300.0])\n",
    "nth_fwhm_1pc = np.array([2.0, 1.75, 1.5])\n",
    "depth_nth_fwhm_power = np.array([0.2, 0.3, 0.4])\n",
    "\n",
    "tspin = physics.calc_spin_temp(tkin, 10.0**log10_nHI, n_alpha).eval()\n",
    "print(\"tspin\", tspin)\n",
    "\n",
    "fwhm2_nonthermal = physics.calc_nonthermal_fwhm(depth, nth_fwhm_1pc, depth_nth_fwhm_power)**2.0\n",
    "print(\"fwhm2_nonthermal\", fwhm2_nonthermal)\n",
    "\n",
    "fwhm2_thermal = physics.calc_thermal_fwhm2(tkin)\n",
    "print(\"fwhm2_thermal\", fwhm2_thermal)\n",
    "\n",
    "fwhm2 = fwhm2_nonthermal + fwhm2_thermal\n",
    "print(\"fwhm2\", fwhm2)\n",
    "\n",
    "fwhm2_thermal_fraction = fwhm2_thermal/fwhm2\n",
    "print(\"fwhm2_thermal_fraction\", fwhm2_thermal_fraction)\n",
    "\n",
    "log10_Pth = np.log10(tkin) + log10_nHI\n",
    "print(\"log10_Pth\", log10_Pth)\n",
    "\n",
    "log10_NHI = log10_nHI + np.log10(depth) + 18.489351\n",
    "print(\"log10_NHI\", log10_NHI)\n",
    "\n",
    "tau_total = physics.calc_tau_total(10.0**log10_NHI, tspin)\n",
    "print(\"tau_total\", tau_total)\n",
    "\n",
    "#wt_ff_tspin = absorption_weight / filling_factor / tspin\n",
    "#print(\"wt_ff_tspin\", wt_ff_tspin)\n",
    "wt_ff_fwhm2_thermal = absorption_weight / filling_factor / fwhm2_thermal\n",
    "print(\"wt_ff_fwhm2_thermal\", wt_ff_fwhm2_thermal)\n",
    "\n",
    "sim_params = {\n",
    "    \"wt_ff_fwhm2_thermal\": wt_ff_fwhm2_thermal,\n",
    "    \"absorption_weight\": absorption_weight,\n",
    "    \"filling_factor\": filling_factor,\n",
    "    \"log10_NHI\": log10_NHI,\n",
    "    \"tau_total\": tau_total,\n",
    "    \"tspin\": tspin,\n",
    "    \"fwhm2\": fwhm2,\n",
    "    \"fwhm2_thermal_fraction\": fwhm2_thermal_fraction,\n",
    "    \"velocity\": np.array([-5.0, 5.0, 10.0]),\n",
    "    \"n_alpha\": n_alpha,\n",
    "    \"nth_fwhm_1pc\": nth_fwhm_1pc,\n",
    "    \"depth_nth_fwhm_power\": depth_nth_fwhm_power,\n",
    "    \"baseline_emission_norm\": [0.0],\n",
    "    \"baseline_absorption_norm\": [0.0],\n",
    "}\n",
    "\n",
    "# add derived quantities to sim_params\n",
    "for key in model.cloud_deterministics:\n",
    "    if key not in sim_params.keys():\n",
    "        sim_params[key] = model.model[key].eval(sim_params, on_unused_input=\"ignore\")\n",
    "\n",
    "# Evaluate and save simulated observation\n",
    "emission = model.model[\"emission\"].eval(sim_params, on_unused_input=\"ignore\")\n",
    "absorption = model.model[\"absorption\"].eval(sim_params, on_unused_input=\"ignore\")\n",
    "\n",
    "data = {\n",
    "    \"emission\": SpecData(\n",
    "        emission_axis,\n",
    "        emission,\n",
    "        rms_emission,\n",
    "        xlabel=r\"$V_{\\rm LSR}$ (km s$^{-1}$)\",\n",
    "        ylabel=r\"$T_B$ (K)\",\n",
    "    ),\n",
    "    \"absorption\": SpecData(\n",
    "        absorption_axis,\n",
    "        absorption,\n",
    "        rms_absorption,\n",
    "        xlabel=r\"$V_{\\rm LSR}$ (km s$^{-1}$)\",\n",
    "        ylabel=r\"1 - exp(-$\\tau$)\",\n",
    "    ),\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0ecdcddd-9edc-4a57-81b1-a08663c693fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'wt_ff_fwhm2_thermal': array([1.9670751 , 0.07285463, 0.00437128]),\n",
       " 'absorption_weight': array([0.9, 0.8, 1. ]),\n",
       " 'filling_factor': array([0.2, 0.8, 1. ]),\n",
       " 'log10_NHI': array([20.438321  , 19.88729101, 20.46647225]),\n",
       " 'tau_total': array([3.01218479, 0.14166923, 0.03771258]),\n",
       " 'tspin': array([  49.97911226,  298.78900835, 4259.26982821]),\n",
       " 'fwhm2': array([  9.90227625,  34.85307344, 444.48064099]),\n",
       " 'fwhm2_thermal_fraction': array([0.2310237, 0.3938236, 0.5146817]),\n",
       " 'velocity': array([-5.,  5., 10.]),\n",
       " 'n_alpha': array([1.e-06, 2.e-06, 3.e-06]),\n",
       " 'nth_fwhm_1pc': array([2.  , 1.75, 1.5 ]),\n",
       " 'depth_nth_fwhm_power': array([0.2, 0.3, 0.4]),\n",
       " 'baseline_emission_norm': [0.0],\n",
       " 'baseline_absorption_norm': [0.0],\n",
       " 'log10_n_alpha': array([-5.75395025, -6.4990086 , -5.89087838]),\n",
       " 'fwhm2_thermal': array([  2.2876605,  13.725963 , 228.76605  ]),\n",
       " 'tkin': array([  50.,  300., 5000.]),\n",
       " 'fwhm2_nonthermal': array([  7.61461575,  21.12711044, 215.71459099]),\n",
       " 'log10_depth': array([0.69897   , 1.39794001, 2.47712125]),\n",
       " 'log10_nHI': array([ 1.25,  0.  , -0.5 ]),\n",
       " 'log10_Pth': array([2.94897   , 2.47712125, 3.19897   ]),\n",
       " 'log10_Pnth': array([4.95888799, 4.1520801 , 4.66111952]),\n",
       " 'log10_Ptot': array([4.96311227, 4.16116407, 4.67585106])}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sim_params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "15c936e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot data\n",
    "fig, axes = plt.subplots(2, layout=\"constrained\", sharex=True)\n",
    "axes[0].plot(data[\"emission\"].spectral, data[\"emission\"].brightness, \"k-\")\n",
    "axes[0].plot(data[\"emission\"].spectral, data[\"emission\"].noise, \"r-\")\n",
    "axes[1].plot(data[\"absorption\"].spectral, data[\"absorption\"].brightness, \"k-\", label=\"Data\")\n",
    "axes[1].plot(data[\"absorption\"].spectral, data[\"absorption\"].noise, \"r-\", label=\"Noise\")\n",
    "axes[1].set_xlabel(data[\"emission\"].xlabel)\n",
    "axes[0].set_ylabel(data[\"emission\"].ylabel)\n",
    "axes[1].set_ylabel(data[\"absorption\"].ylabel)\n",
    "_ = axes[1].legend(loc=\"upper left\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20a2225f",
   "metadata": {},
   "source": [
    "## `Optimize`\n",
    "\n",
    "We use the `Optimize` class for optimization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "ec488d1d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-05T19:59:10.725568Z",
     "start_time": "2024-08-05T19:59:10.599441Z"
    }
   },
   "outputs": [],
   "source": [
    "from bayes_spec import Optimize\n",
    "\n",
    "# Initialize optimizer\n",
    "opt = Optimize(\n",
    "    EmissionAbsorptionPhysicalModel,  # model definition\n",
    "    data,  # data dictionary\n",
    "    max_n_clouds=5,  # maximum number of clouds\n",
    "    baseline_degree=baseline_degree,  # polynomial baseline degree\n",
    "    bg_temp=3.77,  # assumed background brightness temperature (K)\n",
    "    seed=1234,  # random seed\n",
    "    verbose=True,  # verbosity\n",
    ")\n",
    "\n",
    "# Define each model\n",
    "opt.add_priors(\n",
    "    prior_filling_factor=[2.0, 1.0],  # filling factor prior shape\n",
    "    prior_ff_NHI=1.0e21,  # filling factor * column density prior width (cm-2)\n",
    "    prior_fwhm2_thermal_fraction=[2.0, 2.0], # thermal FWHM^2 fraction prior shape\n",
    "    prior_sigma_log10_NHI=0.5, # log-normal column density distribution width\n",
    "    prior_fwhm2=200.0, # FWHM^2 prior width (km2 s-2)\n",
    "    prior_velocity=[-15.0, 15.0],  # lower and upper limit of velocity prior (km/s)\n",
    "    prior_log10_n_alpha=[-6.0, 1.0],  # log10(n_alpha) prior width (cm-3)\n",
    "    prior_nth_fwhm_1pc=[1.75, 0.25], # non-thermal FWHM at 1 pc prior mean and width (km s-1)\n",
    "    prior_depth_nth_fwhm_power=[0.3, 0.1], # non-thermal FWHM vs. depth power prior mean and width\n",
    "    prior_fwhm_L=None, # Assume Gaussian line profile\n",
    "    prior_baseline_coeffs=None, # Default baseline priors\n",
    ")\n",
    "opt.add_likelihood()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b4b0d06",
   "metadata": {},
   "source": [
    "`Optimize` has created `max_n_clouds` models, where `opt.models[1]` has `n_clouds=1`, `opt.models[2]` has `n_clouds=2`, etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e66910c3",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-05T19:59:10.730059Z",
     "start_time": "2024-08-05T19:59:10.727121Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<caribou_hi.emission_absorption_physical_model.EmissionAbsorptionPhysicalModel object at 0x716ae0200c30>\n",
      "4\n"
     ]
    }
   ],
   "source": [
    "print(opt.models[4])\n",
    "print(opt.models[4].n_clouds)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3cc17df3",
   "metadata": {},
   "source": [
    "By default (`approx=True`), the optimization algorithm first loops over every model and approximates the posterior distribution using variational inference. This is generally a bad idea, since VI is only an approximation and tends to struggle with complex models. Instead we use `approx=False` to sample every model with MCMC. This is slower but more robust.\n",
    "\n",
    "We can supply arguments to `fit` and `sample` via dictionaries. Whichever model is the first to have a BIC within `bic_threshold` of the minimum BIC is the \"best\" model. The algorithm will terminate early if successive models have increasing BICs or fail to converge."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "cf08c08c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-05T19:59:59.141293Z",
     "start_time": "2024-08-05T19:59:10.731559Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Null hypothesis BIC = 1.433e+06\n",
      "Sampling n_cloud = 1 posterior...\n",
      "Initializing NUTS using custom advi+adapt_diag strategy\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f2d56b2462d544f4bbf20c636e1b73a7",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Convergence achieved at 46600\n",
      "Interrupted at 46,599 [23%]: Average Loss = 5.0785e+05\n",
      "Multiprocess sampling (8 chains in 8 jobs)\n",
      "NUTS: [baseline_emission_norm, baseline_absorption_norm, fwhm2_norm, velocity_norm, log10_n_alpha_norm, nth_fwhm_1pc, depth_nth_fwhm_power, ff_NHI_norm, fwhm2_thermal_fraction, filling_factor, wt_ff_tkin]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d5b4c03bde1e4167a6624a0eb03b24ee",
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       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 8 chains for 1_000 tune and 1_000 draw iterations (8_000 + 8_000 draws total) took 157 seconds.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Adding log-likelihood to trace\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0256023393fe4485a70e6571a08952c6",
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       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GMM converged to unique solution\n",
      "n_cloud = 1 solution = 0 BIC = 1.680e+05\n",
      "\n",
      "Sampling n_cloud = 2 posterior...\n",
      "Initializing NUTS using custom advi+adapt_diag strategy\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e9689852190a43b287aa0cc5fe6d703b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Convergence achieved at 85200\n",
      "Interrupted at 85,199 [42%]: Average Loss = 2.7226e+05\n",
      "Multiprocess sampling (8 chains in 8 jobs)\n",
      "NUTS: [baseline_emission_norm, baseline_absorption_norm, fwhm2_norm, velocity_norm, log10_n_alpha_norm, nth_fwhm_1pc, depth_nth_fwhm_power, ff_NHI_norm, fwhm2_thermal_fraction, filling_factor, wt_ff_tkin]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1237173e8c5a4a4b99c4e36a5d9e3f76",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 8 chains for 1_000 tune and 1_000 draw iterations (8_000 + 8_000 draws total) took 191 seconds.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Adding log-likelihood to trace\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "56b8688e5cac45dbb324944e8edf6c7c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GMM converged to unique solution\n",
      "n_cloud = 2 solution = 0 BIC = 5.528e+03\n",
      "\n",
      "Sampling n_cloud = 3 posterior...\n",
      "Initializing NUTS using custom advi+adapt_diag strategy\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "56c497ac7d8941cfad64178fa3b3b941",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Convergence achieved at 104000\n",
      "Interrupted at 103,999 [51%]: Average Loss = 2.7689e+05\n",
      "Multiprocess sampling (8 chains in 8 jobs)\n",
      "NUTS: [baseline_emission_norm, baseline_absorption_norm, fwhm2_norm, velocity_norm, log10_n_alpha_norm, nth_fwhm_1pc, depth_nth_fwhm_power, ff_NHI_norm, fwhm2_thermal_fraction, filling_factor, wt_ff_tkin]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "66f8850102984c3589fea29f5284229d",
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       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 8 chains for 1_000 tune and 1_000 draw iterations (8_000 + 8_000 draws total) took 196 seconds.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Adding log-likelihood to trace\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5493bcc8339448cb92aca6f85574e58c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GMM converged to unique solution\n",
      "n_cloud = 3 solution = 0 BIC = -1.299e+03\n",
      "\n",
      "Sampling n_cloud = 4 posterior...\n",
      "Initializing NUTS using custom advi+adapt_diag strategy\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c2482459db21401989fc946723dde71a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Convergence achieved at 87300\n",
      "Interrupted at 87,299 [43%]: Average Loss = 4.4508e+05\n",
      "Multiprocess sampling (8 chains in 8 jobs)\n",
      "NUTS: [baseline_emission_norm, baseline_absorption_norm, fwhm2_norm, velocity_norm, log10_n_alpha_norm, nth_fwhm_1pc, depth_nth_fwhm_power, ff_NHI_norm, fwhm2_thermal_fraction, filling_factor, wt_ff_tkin]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5427ec1aac584355b7dd78dcb9394c51",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 8 chains for 1_000 tune and 1_000 draw iterations (8_000 + 8_000 draws total) took 406 seconds.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Adding log-likelihood to trace\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "05489b88c0da41158e5588936aa1593b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There were 245 divergences in converged chains.\n",
      "GMM converged to unique solution\n",
      "5 of 8 chains appear converged.\n",
      "Label order mismatch in solution 0\n",
      "Chain 1 order: [1 0 2 3]\n",
      "Chain 2 order: [1 0 2 3]\n",
      "Chain 3 order: [1 0 3 2]\n",
      "Chain 4 order: [1 0 2 3]\n",
      "Chain 5 order: [1 0 2 3]\n",
      "Adopting (first) most common order: [1 0 2 3]\n",
      "n_cloud = 4 solution = 0 BIC = -1.247e+03\n",
      "\n",
      "Stopping criteria met.\n",
      "Sampling n_cloud = 5 posterior...\n",
      "Initializing NUTS using custom advi+adapt_diag strategy\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "380f8db52f63426d95f092d15e665c7f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Convergence achieved at 168500\n",
      "Interrupted at 168,499 [84%]: Average Loss = 3.0913e+05\n",
      "Multiprocess sampling (8 chains in 8 jobs)\n",
      "NUTS: [baseline_emission_norm, baseline_absorption_norm, fwhm2_norm, velocity_norm, log10_n_alpha_norm, nth_fwhm_1pc, depth_nth_fwhm_power, ff_NHI_norm, fwhm2_thermal_fraction, filling_factor, wt_ff_tkin]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c7b32f82cb2a4e148a551ba742e10155",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 8 chains for 1_000 tune and 1_000 draw iterations (8_000 + 8_000 draws total) took 425 seconds.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Adding log-likelihood to trace\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "37c3686eae994fd4b55bdbd7b4e3d2ea",
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       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There were 277 divergences in converged chains.\n",
      "No solution found!\n",
      "0 of 8 chains appear converged.\n",
      "\n",
      "Stopping criteria met.\n",
      "Stopping early.\n"
     ]
    }
   ],
   "source": [
    "fit_kwargs = {\n",
    "    \"rel_tolerance\": 0.005,\n",
    "    \"abs_tolerance\": 0.005,\n",
    "    \"learning_rate\": 0.001,\n",
    "}\n",
    "sample_kwargs = {\n",
    "    \"chains\": 8,\n",
    "    \"cores\": 8,\n",
    "    \"n_init\": 200_000,\n",
    "    \"init_kwargs\": fit_kwargs,\n",
    "    \"nuts_kwargs\": {\"target_accept\": 0.9},\n",
    "}\n",
    "solve_kwargs = {\n",
    "    \"init_params\": \"random_from_data\",\n",
    "    \"n_init\": 10,\n",
    "    \"max_iter\": 1_000,\n",
    "    \"kl_div_threshold\": 0.1,\n",
    "}\n",
    "opt.optimize(\n",
    "    bic_threshold=10.0,\n",
    "    sample_kwargs=sample_kwargs,\n",
    "    fit_kwargs=fit_kwargs,\n",
    "    solve_kwargs=solve_kwargs,\n",
    "    approx=False,\n",
    "    start_spread = {\"velocity_norm\": [0.1, 0.9]},\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "0486ae8b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt.best_model.n_clouds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ba72835b",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: [absorption, emission]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c3f5e7e578c140a6b8902815bafb1498",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from bayes_spec.plots import plot_predictive\n",
    "\n",
    "posterior = opt.best_model.sample_posterior_predictive(\n",
    "    thin=100, # keep one in {thin} posterior samples\n",
    ")\n",
    "axes = plot_predictive(opt.best_model.data, posterior.posterior_predictive)\n",
    "axes.ravel()[0].sharex(axes.ravel()[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "99a89912-b4ae-4f25-a1af-8005328aed12",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'BIC')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(opt.bics.keys(), opt.bics.values(), 'ko')\n",
    "plt.xlabel(\"Number of Components\")\n",
    "plt.ylabel(\"BIC\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "0e0e67f9-1d97-4249-9592-785dd5ab870b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-2000.0, 0.0)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(opt.bics.keys(), opt.bics.values(), 'ko')\n",
    "plt.xlabel(\"Number of Components\")\n",
    "plt.ylabel(\"BIC\")\n",
    "plt.ylim(-2000, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b7fc966b-4fdf-449f-8701-bd5b90869830",
   "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": "3.13.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}