1. light curve fitting.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a4adf8ae-6c6a-4861-84a5-598ab2988c6e",
   "metadata": {},
   "source": [
    "<div style=\"text-align: right\"> \n",
    "<a href = \"https://nbviewer.jupyter.org/github/siddharthchaini/Improving-Feature-Extraction-RESSPECT/blob/main/1.%20light%20curve%20fitting.ipynb\"> \n",
    "    View online on<br>\n",
    "    <img src=\"https://nbviewer.jupyter.org/static/img/nav_logo.svg\"\n",
    "         alt=\"nbviewer link\" style=\"height: 30px;\"/> \n",
    "</a>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf51ce6f-3ef0-4a6f-bfd7-219063b62188",
   "metadata": {},
   "source": [
    "# 1. Light-Curve Fitting Approaches for RESSPECT\n",
    "<a href = http://cosmostatistics-initiative.org/resspect/>\n",
    "<img src=\"https://cosmostatistics-initiative.org/wp-content/uploads/2019/04/coin_desc_3.png\" alt=\"Logo\" style=\"width: 250px;\"/>\n",
    "</a>\n",
    "\n",
    "**Authors**: Siddharth Chaini, Johann Cohen-Tanugi"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bcb2360b-e3f0-4815-adc6-1cdd4e3324cf",
   "metadata": {},
   "source": [
    "This is the first Jupyter notebook (of a total of 2) describing the different feature extraction methods explored by Siddharth and Johann in June & July, 2021.\n",
    "\n",
    "For RESSPECT, a light curve is fit to a function and then the fit parameters are then used in the RESSPECT pipeline as features for training. You can read more about this here: https://arxiv.org/pdf/2010.05941.pdf\n",
    "\n",
    "In this notebook, we will explore this model fitting based approach in detail, look at different models for fitting the curve and discuss their shortcomings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f8bac44a-8a10-41f6-ae89-963df48c939f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last Updated On: 30 July, 2021\n"
     ]
    }
   ],
   "source": [
    "import datetime\n",
    "print('Last Updated On:', datetime.datetime.now().strftime(\"%d %B, %Y\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "df72cd5a-8ef0-4ae2-94da-3e4ba386f736",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Some prerequisites\n",
    "\n",
    "import numpy as np\n",
    "np.random.seed(42)\n",
    "np.set_printoptions(suppress=True)\n",
    "from scipy.optimize import least_squares, curve_fit\n",
    "from matplotlib import pylab as plt\n",
    "import pandas as pd\n",
    "import glob\n",
    "import time\n",
    "from tqdm.notebook import tqdm\n",
    "import os\n",
    "\n",
    "import warnings\n",
    "from scipy.optimize import OptimizeWarning\n",
    "warnings.simplefilter(\"error\", OptimizeWarning)\n",
    "\n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "\n",
    "def fit1object(filename, fit_scipy, featurename):\n",
    "    '''\n",
    "    A function to fit all 6 passbands' lightcurves for a given object.\n",
    "    '''\n",
    "    d = pd.read_csv(filename)\n",
    "    feature_dict = {}\n",
    "    for filt in \"ugrizY\":\n",
    "        temp_dict = {}\n",
    "        band = d['band']==filt \n",
    "        t = np.array(d[band]['mjd'])\n",
    "        t = t-t[0]\n",
    "        f = np.array(d[band]['flux'])\n",
    "        fe = np.array(d[band]['fluxerr'])\n",
    "\n",
    "        try:\n",
    "            params_list = list(fit_scipy(t, f, fe))\n",
    "        except Exception as e:\n",
    "            params_list = [np.nan for x in featurename]\n",
    "        for num, feat in enumerate(featurename):\n",
    "            temp_dict[feat] = params_list[num]\n",
    "        feature_dict[filt] = temp_dict\n",
    "    return feature_dict\n",
    "\n",
    "def plot_fitlc(filename, feature_dict, fitfunction):\n",
    "    '''\n",
    "    A function to plot the light curve fits and the original data for all 6 passbands' for a given object.\n",
    "    '''\n",
    "    d = pd.read_csv(filename)\n",
    "    obid = int(filename.split(\"/\")[-1].split(\"_\")[0])\n",
    "    obclass = filename.split(\"_\")[-1].replace(\".csv\",\"\")\n",
    "    fig, axs = plt.subplots(2, 3, sharex=True, sharey=True, figsize=(12,8))\n",
    "    count=0\n",
    "    for filt in \"ugrizY\":\n",
    "        band = d['band']==filt \n",
    "        t = np.array(d[band]['mjd'])\n",
    "        t = t-t[0]\n",
    "        f = np.array(d[band]['flux'])\n",
    "        fe = np.array(d[band]['fluxerr'])\n",
    "        params = feature_dict[filt].values()\n",
    "        x = np.arange(t.min(), t.max(),0.001)\n",
    "        i = int(count/3)\n",
    "        j = int(count % 3)\n",
    "        axs[i,j].errorbar(t, f, fe, fmt='.')\n",
    "        axs[i,j].plot(x, fitfunction(x, *params))\n",
    "        axs[i,j].set_title(f\"Filter {filt}\")\n",
    "        axs[i,j].set_xlabel(\"Days\")\n",
    "        axs[i,j].set_ylabel(\"Flux\")\n",
    "        count+=1\n",
    "    plt.suptitle(f\"Objid: {obid} ({obclass}) - {str(fitfunction).split(' ')[1]}\")\n",
    "    return plt\n",
    "\n",
    "def plot_example(fit_scipy, fitfn, features):\n",
    "    feature_dict = fit1object(\"sample_data/plasticc/130779836_uLens.csv\",fit_scipy,features)\n",
    "    return plot_fitlc(\"sample_data/plasticc/130779836_uLens.csv\",feature_dict,fitfn)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f404763e-7cc2-41e5-b21f-cfef7980b018",
   "metadata": {},
   "source": [
    "## 1.1 Current Implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1e24d02-464d-49b9-b2e0-2002aa0f383b",
   "metadata": {},
   "source": [
    "### 1.1 Bazin - Old"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "053798bb-48f3-4db5-89c2-a552c51e681f",
   "metadata": {},
   "source": [
    "RESSPECT originally started by using the parameterisation used in [Bazin et. al. (2009)](https://arxiv.org/pdf/0904.1066.pdf) for fitting the light curves ([CODE](https://github.com/COINtoolbox/RESSPECT/blob/9950ad424314ec9391c151d9d589cc4bcc1a34f0/resspect/bazin.py#L26)). \n",
    "\n",
    "The implemented version is:\n",
    "\n",
    "$$ F(t) = \\dfrac{e^{\\frac{-(t-t_0)}{t_\\text{fall}}}}{1+e^{\\frac{t-t_0}{t_\\text{rise}}}} $$\n",
    "\n",
    "However, there are a couple of bugs the implemented version as of May 2021. For example, a typo from the [original paper](https://arxiv.org/pdf/0904.1066.pdf) has been carried over where the numerator has the negatively signed $-(t-t_0)$ but the denominator has $(t-t_0)$\n",
    "\n",
    "The Bazin fit also fails for some PLAsTiCC objects unexpectedly. Let's look at an example: object_id: 130779836, which is an example of a µ-lens from a single lens."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8bd8e321-9cef-4db6-8df3-c9f777743aad",
   "metadata": {},
   "outputs": [],
   "source": [
    "bazinfeatures = [\"a\", \"b\", \"t0\", \"tfall\", \"trise\"]\n",
    "\n",
    "def oldbazin(time, a, b, t0, tfall, trise):\n",
    "    with np.errstate(over='ignore', invalid='ignore'):\n",
    "        X = np.exp(-(time - t0) / tfall) / (1 + np.exp((time - t0) / trise))\n",
    "        return a * X + b\n",
    "    \n",
    "def errfunc_oldbazin(params, time, flux, fluxerr):\n",
    "    return abs(flux - oldbazin(time, *params))\n",
    "\n",
    "def fit_scipy_oldbazin(time, flux, fluxerr):\n",
    "    flux = np.asarray(flux)\n",
    "    t0 = time[flux.argmax()] - time[0]\n",
    "    guess = [0, 0, t0, 40, -5]\n",
    "\n",
    "    result = least_squares(errfunc_oldbazin, guess, args=(time, flux, fluxerr), method='lm')\n",
    "\n",
    "    return result.x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5c9874ce-8a6a-4da3-a04a-914aee119720",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_example(fit_scipy_oldbazin,oldbazin,bazinfeatures).show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ae15474-830a-4b6a-a5a7-a1d17e4fbd2e",
   "metadata": {},
   "source": [
    "It's clearly not fitting well for filter u,r and z above."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3189759-1748-441d-a96a-445448cfe6ec",
   "metadata": {},
   "source": [
    "## 1.2 Alternate Implementations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2dd5b36-aa55-4c9a-ac5a-8b8f6b685c30",
   "metadata": {},
   "source": [
    "### 1.2.1 Bazin - New"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd57bf8a-f357-45da-b507-aa8d2cc796a1",
   "metadata": {},
   "source": [
    "After examining further, we realise this is mainly happening because of some bound errors, namely because the ratio of `tfall/trise` is supposed to be `>1`, as mentioned in Section 3, [Dai et. al. (2017)](https://arxiv.org/pdf/1701.05689.pdf).\n",
    "\n",
    "We can further optimise the code as well.\n",
    "\n",
    "1.  Bazin is modified to take the ratio `r=tfall/trise` instead of `trise`. This allows us to enforce the condition `r>1` on the fit.\n",
    "2.  Flux_err is used as a parameter to errfunc: `abs(flux - bazin(time, *params)) / fluxerr`\n",
    "3.  Bounds can be added to `fit_scipy()` and a better original guess was chosen to again enforce the condition `r>1`.\n",
    "\n",
    "Thus the function has been changed to,\n",
    "\n",
    "$$ F(t) = \\dfrac{e^{\\frac{-(t-t_0)}{t_\\text{fall}}}}{1+e^{\\frac{-(t-t_0)}{t_\\text{rise}}}} $$\n",
    "or, alternatively,\n",
    "$$ F(t) = \\dfrac{e^{\\frac{-(t-t_0)}{t_\\text{fall}}}}{1+e^{\\frac{-(t-t_0)}{t_\\text{fall}}r}} $$\n",
    "where $r=\\dfrac{t_\\text{fall}}{t_\\text{rise}}$.\n",
    "\n",
    "Let's code up the above changes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "edf7cc5c-58d2-42a1-9e87-c6d9b315bfd6",
   "metadata": {},
   "outputs": [],
   "source": [
    "bazinfeatures = [\"a\", \"b\", \"t0\", \"tfall\", \"trise\"]\n",
    "\n",
    "def bazin(time, a, b, t0, tfall, trise):\n",
    "    with np.errstate(over='ignore', invalid='ignore'):\n",
    "        X = np.exp(-(time - t0) / tfall) / (1 + np.exp(-(time - t0) / trise))\n",
    "        return a * X + b\n",
    "\n",
    "def bazinr(time, a, b, t0, tfall, r):\n",
    "    trise = tfall/r\n",
    "    return bazin(time, a, b, t0, tfall, trise)\n",
    "    \n",
    "def errfunc_bazin(params, time, flux, fluxerr):\n",
    "    return abs(flux - bazinr(time, *params)) / fluxerr\n",
    "\n",
    "def fit_scipy_bazin(time, flux, fluxerr):\n",
    "    flux = np.asarray(flux)\n",
    "    imax = flux.argmax()\n",
    "    flux_max = flux[imax]\n",
    "    \n",
    "    # Parameter bounds\n",
    "    a_bounds = [1.e-3, np.inf]\n",
    "    b_bounds = [-np.inf, np.inf]\n",
    "    t0_bounds = [-0.5*time.max(), 1.5*time.max()]\n",
    "    tfall_bounds = [1.e-3, np.inf]\n",
    "    r_bounds = [1, np.inf]\n",
    "\n",
    "    # Parameter guess\n",
    "    a_guess = 2*flux_max\n",
    "    b_guess = 0\n",
    "    t0_guess = time[imax]\n",
    "    \n",
    "    tfall_guess = time[imax-2:imax+2].std()/2\n",
    "    if np.isnan(tfall_guess):\n",
    "        tfall_guess = time[imax-1:imax+1].std()/2\n",
    "        if np.isnan(tfall_guess):\n",
    "            tfall_guess=50\n",
    "    if tfall_guess<1:\n",
    "        tfall_guess=50\n",
    "\n",
    "    r_guess = 2\n",
    "\n",
    "    # Clip guesses to stay in bound\n",
    "    a_guess = np.clip(a=a_guess,a_min=a_bounds[0],a_max=a_bounds[1])\n",
    "    b_guess = np.clip(a=b_guess,a_min=b_bounds[0],a_max=b_bounds[1])\n",
    "    t0_guess = np.clip(a=t0_guess,a_min=t0_bounds[0],a_max=t0_bounds[1])\n",
    "    tfall_guess = np.clip(a=tfall_guess,a_min=tfall_bounds[0],a_max=tfall_bounds[1])\n",
    "    r_guess = np.clip(a=r_guess,a_min=r_bounds[0],a_max=r_bounds[1])\n",
    "\n",
    "\n",
    "    guess = [a_guess,b_guess,t0_guess,tfall_guess,r_guess]\n",
    "\n",
    "    bounds = [[a_bounds[0], b_bounds[0], t0_bounds[0], tfall_bounds[0], r_bounds[0]],\n",
    "              [a_bounds[1], b_bounds[1], t0_bounds[1], tfall_bounds[1], r_bounds[1]]]\n",
    "    \n",
    "    result = least_squares(errfunc_bazin, guess, args=(time, flux, fluxerr), method='trf', loss='linear',bounds=bounds)\n",
    "    \n",
    "    a_fit,b_fit,t0_fit,tfall_fit,r_fit = result.x\n",
    "    trise_fit = tfall_fit/r_fit\n",
    "    final_result = np.array([a_fit,b_fit,t0_fit,tfall_fit,trise_fit])\n",
    "    \n",
    "    return final_result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "eba97302-c876-422f-a12d-70b34c80c7f8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_example(fit_scipy_bazin,bazin,bazinfeatures).show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ffd9b51-d439-4d2a-94bd-5c156663dc99",
   "metadata": {},
   "source": [
    "And voila! We have a better fit.\n",
    "\n",
    "There is a clear improvement in the fit for the \"u\", \"r\" and \"z\" bands. This change has been incorporated into Pull Request #49 for RESSPECT - https://github.com/COINtoolbox/RESSPECT/pull/49\n",
    "\n",
    "Let us look at more functions for similar curve fitting parameterisations."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7347916a-7bf2-470a-b08b-faa0f565ea35",
   "metadata": {},
   "source": [
    "### 1.2.2 FRED"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6352d69c-36ce-452c-aa9f-432afbca6c36",
   "metadata": {},
   "source": [
    "This parameterisation is based on the equation 3 from [Peng et. al. (2009)](https://iopscience.iop.org/article/10.1088/0004-637X/698/1/417):\n",
    "$$\n",
    "F(t)=F_{m}\\left(\\frac{t+t_{0}}{t_{m}+t_{0}}\\right)^{r}\\left[\\frac{d}{d+r}+\\frac{r}{d+r}\\left(\\frac{t+t_{0}}{t_{m}+t_{0}}\\right)^{(r+1)}\\right]^{-\\frac{r + d}{r+1}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "83aa9a0a-ca98-4715-8f86-1fce48572510",
   "metadata": {},
   "outputs": [],
   "source": [
    "fredfeatures = [\"tm\", \"r\", \"d\", \"Fm\", \"b\"]\n",
    "\n",
    "def fred(time, tm, r, d, Fm, b):\n",
    "    t0 = 0 # No trigger time in our case and timestamps are arbitrary, so t0 = 0\n",
    "    x = (time+t0)/(tm+t0)\n",
    "    val = Fm * (x)**r * ((d)/(d+r) + (r)/(d+r) * (x)**(r+1) )**(-(r+d)/(r+1)) + b\n",
    "    return val\n",
    "\n",
    "def errfunc_fred(params, time, flux, fluxerr):\n",
    "    return abs(flux - fred(time, *params))/ fluxerr\n",
    "\n",
    "\n",
    "def fit_scipy_fred(time, flux, fluxerr):\n",
    "    flux = np.asarray(flux)\n",
    "    imax = flux.argmax()\n",
    "    flux_max = flux[imax]\n",
    "    \n",
    "    tm_bounds = [-0.5*time.max(), 1.5*time.max()]\n",
    "    r_bounds = [1.e-3,np.inf]\n",
    "    d_bounds = [1.e-3,np.inf]\n",
    "    Fm_bounds = [-np.inf,np.inf]\n",
    "    b_bounds = [-np.inf,np.inf]\n",
    "    \n",
    "    # Parameter guess\n",
    "    tm_guess = time[imax]\n",
    "    r_guess = 30\n",
    "    d_guess = 30\n",
    "    Fm_guess = flux_max\n",
    "    b_guess = time[0]\n",
    "    \n",
    "    guess = [tm_guess, r_guess, d_guess, Fm_guess, b_guess]\n",
    "\n",
    "    result = least_squares(errfunc_fred, guess, args=(time, flux, fluxerr), method='trf', loss='linear',\\\n",
    "                                  bounds=([tm_bounds[0], r_bounds[0], d_bounds[0], Fm_bounds[0], b_bounds[0]],\n",
    "                                          [tm_bounds[1], r_bounds[1], d_bounds[1], Fm_bounds[1], b_bounds[1]])\n",
    "                          )\n",
    "    \n",
    "    return result.x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "236f05d3-580d-46d7-888c-d7922e81bffb",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-7-df6b65c3b3bb>:6: RuntimeWarning: overflow encountered in power\n",
      "  val = Fm * (x)**r * ((d)/(d+r) + (r)/(d+r) * (x)**(r+1) )**(-(r+d)/(r+1)) + b\n",
      "<ipython-input-7-df6b65c3b3bb>:6: RuntimeWarning: invalid value encountered in multiply\n",
      "  val = Fm * (x)**r * ((d)/(d+r) + (r)/(d+r) * (x)**(r+1) )**(-(r+d)/(r+1)) + b\n",
      "<ipython-input-7-df6b65c3b3bb>:6: RuntimeWarning: invalid value encountered in power\n",
      "  val = Fm * (x)**r * ((d)/(d+r) + (r)/(d+r) * (x)**(r+1) )**(-(r+d)/(r+1)) + b\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_example(fit_scipy_fred,fred,fredfeatures).show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb81e349-dbcb-4557-831c-2f79e69d6a69",
   "metadata": {},
   "source": [
    "### 1.2.3 Karpenka"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70834548-599e-4bd9-90d2-38be0f02958f",
   "metadata": {},
   "source": [
    "This parameterisation is based on the equation 1 from [Karpenka et. al. (2013)](https://academic.oup.com/mnras/article/429/2/1278/1038192), where an offset parameter c has been added:\n",
    "\n",
    "$$\n",
    "f(t)=A\\left[1+B\\left(t-t_{1}\\right)^{2}\\right] \\frac{e^{-\\left(t-t_{0}\\right) / t_{\\text {fall }}}}{1+e^{-\\left(t-t_{0}\\right) / t_{\\text {rise }}}} + c\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c69ba7c7-66a1-42ca-8652-406d95157f4a",
   "metadata": {},
   "outputs": [],
   "source": [
    "karpenkafeatures = [\"a\", \"b\", \"t0\", \"tfall\", \"trise\", \"t1\", \"c\"]\n",
    "\n",
    "def karpenka(time, a, b, t0, tfall, trise, t1, c):\n",
    "    val = a*(1+b*(time-t1)**2)* (np.exp(-(time-t0)/tfall))/(1+np.exp(-(time-t0)/trise))\n",
    "    return val + c\n",
    "\n",
    "def karpenkar(time, a, b, t0, tfall, r, t1, c):\n",
    "    trise = tfall/r\n",
    "    return karpenka(time, a, b, t0, tfall, trise, t1, c)\n",
    "\n",
    "def errfunc_karpenka(params, time, flux, fluxerr):\n",
    "    return abs(flux - karpenkar(time, *params)) / fluxerr\n",
    "\n",
    "def fit_scipy_karpenka(time, flux, fluxerr):\n",
    "    flux = np.asarray(flux)\n",
    "    imax = flux.argmax()\n",
    "    flux_max = flux[imax]\n",
    "    \n",
    "    # Parameter guess\n",
    "    a_guess = 2*flux_max\n",
    "    b_guess = 0\n",
    "    t0_guess = time[imax]\n",
    "    t1_guess = time[imax]\n",
    "    c_guess = 0\n",
    "    \n",
    "    tfall_guess = time[imax-2:imax+2].std()/2\n",
    "    if np.isnan(tfall_guess):\n",
    "        tfall_guess = time[imax-1:imax+1].std()/2\n",
    "        if np.isnan(tfall_guess):\n",
    "            tfall_guess=50\n",
    "    if tfall_guess<1:\n",
    "        tfall_guess=50\n",
    "\n",
    "    r_guess = 2\n",
    "\n",
    "    guess = [a_guess,b_guess,t0_guess,tfall_guess,r_guess,t1_guess,c_guess]\n",
    "\n",
    "    # Parameter bounds\n",
    "    a_bounds = [1.e-3, np.inf]\n",
    "    b_bounds = [-np.inf, np.inf]\n",
    "    t0_bounds = [-0.5*time.max(), 1.5*time.max()]\n",
    "    t1_bounds = [-0.5*time.max(), 1.5*time.max()]\n",
    "    tfall_bounds = [1.e-3, np.inf]\n",
    "    r_bounds = [1, np.inf]\n",
    "    c_bounds = [-np.inf, np.inf]\n",
    "    \n",
    "    bounds = [[a_bounds[0], b_bounds[0], t0_bounds[0], tfall_bounds[0], r_bounds[0], t1_bounds[0], c_bounds[0]],\n",
    "              [a_bounds[1], b_bounds[1], t0_bounds[1], tfall_bounds[1], r_bounds[1], t1_bounds[1], c_bounds[1]]]\n",
    "    \n",
    "    result = least_squares(errfunc_karpenka, guess, args=(time, flux, fluxerr), method='trf', loss='linear',bounds=bounds)\n",
    "    \n",
    "    a_fit,b_fit,t0_fit,tfall_fit,r_fit,t1_fit,c_fit = result.x\n",
    "    trise_fit = tfall_fit/r_fit\n",
    "    final_result = np.array([a_fit,b_fit,t0_fit,tfall_fit,trise_fit,t1_fit,c_fit])\n",
    "    \n",
    "    return final_result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e9b59aef-f414-4645-a3e0-f3318dd7acc0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_example(fit_scipy_karpenka,karpenka,karpenkafeatures).show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ebe3b55-636f-4c5e-adef-10bbc6c602c5",
   "metadata": {},
   "source": [
    "### 1.2.4 Villar"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "431ba1ff-d86b-4c95-99e5-016c3b37da6a",
   "metadata": {},
   "source": [
    "This parameterisation is based on the equation 1 from [Villar et. al. (2019)](https://iopscience.iop.org/article/10.3847/1538-4357/ab418c):\n",
    "\n",
    "$$\n",
    "F= \\begin{cases}\\frac{A+\\beta\\left(t-t_{0}\\right)}{1+e^{-\\left(t-t_{0}\\right) / t_\\text{rise}}} & t<t_{1} \\\\ \\frac{\\left(A+\\beta\\left(t_{1}-t_{0}\\right)\\right) e^{-\\left(t-t_{1}\\right) / t_{\\text {fall }}}}{1+e^{-\\left(t_{0}-t_{0}\\right) / t_{\\text {rise }}}} & t \\geq t_{1}\\end{cases}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b84f5acc-fff3-4081-bcc9-faa99d480967",
   "metadata": {},
   "outputs": [],
   "source": [
    "villarfeatures = [\"a\", \"beta\", \"t0\", \"gamma\", \"t_fall\", \"t_rise\"]\n",
    "\n",
    "def villarupper(time,a,beta,t0,t1,tfall,trise):\n",
    "    val = (a + beta*(time-t0))/(1+np.exp(-(time-t0)/trise))\n",
    "    return val\n",
    "\n",
    "def villarlower(time,a,beta,t0,t1,tfall,trise):\n",
    "    val = ((a+beta*(t1-t0))*np.exp(-(time-t1)/tfall))/(1+np.exp(-(time-t0)/trise))\n",
    "    return val\n",
    "\n",
    "def villar(time,a,beta,t0,gamma,tfall,trise):\n",
    "    t1 = t0 + gamma\n",
    "    val = np.piecewise(time, [time < t1, time >= t1], [lambda time: villarupper(time,a,beta,t0,t1,tfall,trise), lambda time: villarlower(time,a,beta,t0,t1,tfall,trise)])\n",
    "    return val\n",
    "\n",
    "def errfunc_villar(params, time, flux, fluxerr):\n",
    "    return abs(flux - villar(time, *params))/ fluxerr\n",
    "\n",
    "def fit_scipy_villar(time, flux, fluxerr):\n",
    "    flux = np.asarray(flux)\n",
    "    imax = flux.argmax()\n",
    "    t0 = time[imax]\n",
    "    max_flux = flux[imax]\n",
    "    if max_flux>0:\n",
    "        a_bounds = [max_flux / 3.0, max_flux * 3.0]\n",
    "    else:\n",
    "        a_bounds = [-np.inf, np.inf]\n",
    "    beta_bounds = [0.0, 1.0]\n",
    "    t0_bounds = [-0.5*time.max(), 1.5*time.max()]\n",
    "    gamma_bounds = [1.0, 100.0]\n",
    "    tfall_bounds = [1.0, 100.0]\n",
    "    trise_bounds = [1.0, 100.0]\n",
    "\n",
    "    \n",
    "    a_guess = np.clip(1.5 * max_flux, a_bounds[0], a_bounds[1])\n",
    "    beta_guess = 0\n",
    "    t0_guess = np.clip(time[imax] * 2.0 / 3.0, t0_bounds[0], t0_bounds[1])\n",
    "    gamma_guess = np.clip(time[imax], gamma_bounds[0], gamma_bounds[1])\n",
    "    tfall_guess = 50\n",
    "    trise_guess = 45\n",
    "    \n",
    "    guess = [a_guess, beta_guess, t0_guess, gamma_guess, tfall_guess, trise_guess]\n",
    "    \n",
    "    result = least_squares(errfunc_villar, guess, args=(time, flux, fluxerr), method='trf', loss='linear',\\\n",
    "                                  bounds=([a_bounds[0], beta_bounds[0], t0_bounds[0], gamma_bounds[0], tfall_bounds[0], trise_bounds[0]],\n",
    "                                         [a_bounds[1], beta_bounds[1], t0_bounds[1], gamma_bounds[1], tfall_bounds[1], trise_bounds[1]])\n",
    "                          )\n",
    "    return result.x\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "69a57246-a3be-42e7-a59a-8cb43e3a81dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_example(fit_scipy_villar,villar,villarfeatures).show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e2a95b3-6765-47af-839d-9d6dfaab5056",
   "metadata": {},
   "source": [
    "### 1.2.5 ALERCE v1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "125c0758-4d57-4113-beed-dfa13544907a",
   "metadata": {},
   "source": [
    "This parameterisation is based on the equation A4 from [Sanchez-Sael et. al. (2021)](https://iopscience.iop.org/article/10.3847/1538-4357/ab418c).\n",
    "\n",
    "$$\n",
    "F=\\left\\{\\begin{array}{c}\n",
    "\\frac{A\\left(1-\\beta^{\\prime} \\frac{t-t_{0}}{t_{1}-t_{0}}\\right)}{1+\\exp \\left(-\\frac{t-t_{0}}{\\tau_{\\text {rise }}}\\right)} \\quad \\text { if } t<t_{1} \\\\\n",
    "\\frac{A\\left(1-\\beta^{\\prime}\\right) \\exp \\left(-\\frac{t-t_{1}}{\\tau_{\\text {fall }}}\\right)}{1+\\exp \\left(-\\frac{t-t_{0}}{\\tau_{\\text {rise }}}\\right)} \\text { if } t \\geq t_{1}\n",
    "\\end{array}\\right.\n",
    "$$\n",
    "\n",
    "This is a small modification of the one used by [Villar et. al. (2019)](https://iopscience.iop.org/article/10.3847/1538-4357/ab418c)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "83629be0-8cfe-411a-b77a-3021cf4abbc6",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "alercev1features = [\"a\", \"beta\", \"t0\", \"gamma\", \"t_fall\", \"t_rise\"]\n",
    "\n",
    "def upperfn(time,a,beta,t0,t1,tfall,trise):\n",
    "    val = (a*(1 - beta*(time-t0)/(t1-t0)))/(1+np.exp(-(time-t0)/trise))\n",
    "    return val\n",
    "def lowerfn(time,a,beta,t0,t1,tfall,trise):\n",
    "    val = (a*(1-beta)*np.exp(-(time-t1)/tfall))/(1+np.exp(-(time-t0)/trise))\n",
    "    return val\n",
    "def alercev1(time,a,beta,t0,gamma,tfall,trise):\n",
    "    t1 = t0 + gamma\n",
    "    val = np.piecewise(time, [time < t1, time >= t1], [lambda time: upperfn(time,a,beta,t0,t1,tfall,trise), lambda time: lowerfn(time,a,beta,t0,t1,tfall,trise)])\n",
    "    return val\n",
    "\n",
    "def errfunc_alercev1(params, time, flux, fluxerr):\n",
    "    return abs(flux - alercev1(time, *params))/ fluxerr\n",
    "\n",
    "def fit_scipy_alercev1(time, flux, fluxerr):\n",
    "    flux = np.asarray(flux)\n",
    "    imax = flux.argmax()\n",
    "    t0 = time[imax]\n",
    "    max_flux = flux[imax]\n",
    "    if max_flux>0:\n",
    "        a_bounds = [max_flux / 3.0, max_flux * 3.0]\n",
    "    else:\n",
    "        a_bounds = [-np.inf, np.inf]\n",
    "    beta_bounds = [0.0, 1.0]\n",
    "    t0_bounds = [-0.5*time.max(), 1.5*time.max()]\n",
    "    gamma_bounds = [1.0, 100.0]\n",
    "    tfall_bounds = [1.0, 100.0]\n",
    "    trise_bounds = [1.0, 100.0]\n",
    "\n",
    "    \n",
    "    a_guess = np.clip(1.5 * max_flux, a_bounds[0], a_bounds[1])\n",
    "    beta_guess = 0\n",
    "    t0_guess = np.clip(time[imax] * 2.0 / 3.0, t0_bounds[0], t0_bounds[1])\n",
    "    gamma_guess = np.clip(time[imax], gamma_bounds[0], gamma_bounds[1])\n",
    "    tfall_guess = 50\n",
    "    trise_guess = 45\n",
    "    \n",
    "    guess = [a_guess, beta_guess, t0_guess, gamma_guess, tfall_guess, trise_guess]\n",
    "    \n",
    "    result = least_squares(errfunc_alercev1, guess, args=(time, flux, fluxerr), method='trf', loss='linear',\\\n",
    "                                  bounds=([a_bounds[0], beta_bounds[0], t0_bounds[0], gamma_bounds[0], tfall_bounds[0], trise_bounds[0]],\n",
    "                                         [a_bounds[1], beta_bounds[1], t0_bounds[1], gamma_bounds[1], tfall_bounds[1], trise_bounds[1]])\n",
    "                          )\n",
    "    return result.x\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "2b1e8be3-ed98-4222-84ed-eb11541dabdb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_example(fit_scipy_alercev1,alercev1,alercev1features).show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ae9f0e6-3a45-4863-a739-ede8cd366888",
   "metadata": {},
   "source": [
    "### 1.2.6 Sánchez-Sáez (ALERCE v2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fea7d360-dbcd-4542-8047-9af5e2f181e2",
   "metadata": {},
   "source": [
    "This parameterisation is based on the equation A5 from [Sanchez-Sael et. al. (2021)](https://iopscience.iop.org/article/10.3847/1538-4357/ab418c).\n",
    "\n",
    "$$\n",
    "F=\\frac{A\\left(1-\\beta^{\\prime} \\frac{t-t_{0}}{t_{1}-t_{0}}\\right)}{1+\\exp \\left(-\\frac{t-t_{0}}{\\tau_{\\text {rise }}}\\right)} \\cdot\\left[1-\\sigma\\left(\\frac{t-t_{1}}{3}\\right)\\right]+\\frac{A\\left(1-\\beta^{\\prime}\\right) \\exp \\left(-\\frac{t-t_{1}}{\\tau_{\\text {fall }}}\\right)}{1+\\exp \\left(-\\frac{t-t_{0}}{\\tau_{\\text {rise }}}\\right)} \\cdot\\left[\\sigma\\left(\\frac{t-t_{1}}{3}\\right)\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "1752e560-a625-407d-9821-b042da93ea8c",
   "metadata": {},
   "outputs": [],
   "source": [
    "alercev2features = [\"A\", \"t0\", \"gamma\", \"beta\", \"t_rise\", \"t_fall\"]\n",
    "\n",
    "def alercev2(times, A, t0, gamma, beta, t_rise, t_fall):\n",
    "    sigmoid_factor = 1.0 / 3.0\n",
    "    t1 = t0 + gamma\n",
    "\n",
    "    sigmoid = 1.0 / (1.0 + np.exp(-sigmoid_factor * (times - t1)))\n",
    "    den = 1 + np.exp(-(times - t0) / t_rise)\n",
    "    flux = ((1 - beta) * np.exp(-(times - t1) / t_fall)\n",
    "            * sigmoid\n",
    "            + (1. - beta * (times - t0) / gamma)\n",
    "            * (1 - sigmoid)) * A / den\n",
    "    return flux\n",
    "\n",
    "def fit_scipy_alercev2(times, fluxpsf, obs_errors):\n",
    "    '''\n",
    "    Adapted from:\n",
    "    https://github.com/alercebroker/lc_classifier/blob/main/lc_classifier/features/extractors/sn_parametric_model_computer.py#L113\n",
    "    '''\n",
    "    # Parameter bounds\n",
    "    argmax_fluxpsf = np.argmax(fluxpsf)\n",
    "    max_fluxpsf = fluxpsf[argmax_fluxpsf]\n",
    "    A_bounds = [max_fluxpsf / 5, max_fluxpsf * 5]\n",
    "    t0_bounds = [-0.5*times.max(), times.max()]\n",
    "    gamma_bounds = [1.0, 50]  # (1,50/100)\n",
    "    beta_bounds = [0.0, 1.0]\n",
    "    trise_bounds = [1.0, 100.0]\n",
    "    tfall_bounds = [1.0, 100.0]\n",
    "    \n",
    "    \n",
    "    # Parameter guess\n",
    "    A_guess = np.clip(1.5 * max_fluxpsf, A_bounds[0], A_bounds[1])\n",
    "    t0_guess = np.clip(times[argmax_fluxpsf] * 2.0 / 3.0, t0_bounds[0], t0_bounds[1])\n",
    "    gamma_guess = np.clip(times[argmax_fluxpsf], gamma_bounds[0], gamma_bounds[1])\n",
    "#     gamma_guess = 50\n",
    "    beta_guess = 0\n",
    "    trise_guess = np.clip(times[argmax_fluxpsf] / 2.0, trise_bounds[0], trise_bounds[1])\n",
    "#     print(f\"trise_gess = np.clip({times[argmax_fluxpsf] / 2.0},{trise_bounds[0]},{trise_bounds[1]})\")\n",
    "#     trise_guess = 45\n",
    "    tfall_guess = 40\n",
    "        \n",
    "    p0 = [A_guess, t0_guess, gamma_guess,\n",
    "          beta_guess, trise_guess, tfall_guess]\n",
    "    # get parameters\n",
    "    try:\n",
    "        pout, pcov = curve_fit(\n",
    "            f=alercev2,\n",
    "            xdata=times,\n",
    "            ydata=fluxpsf,\n",
    "            p0=p0,\n",
    "            sigma=5+obs_errors,\n",
    "            bounds=[[A_bounds[0], t0_bounds[0], gamma_bounds[0], beta_bounds[0], trise_bounds[0], tfall_bounds[0]],\n",
    "                    [A_bounds[1], t0_bounds[1], gamma_bounds[1], beta_bounds[1], trise_bounds[1], tfall_bounds[1]]],\n",
    "            ftol=1e-8,\n",
    "            # verbose=2\n",
    "        )\n",
    "    except (ValueError, RuntimeError, OptimizeWarning):\n",
    "        try:\n",
    "            # print('First fit of SPM failed. Attempting second fit.')\n",
    "            pout, pcov = curve_fit(\n",
    "                f=alercev2,\n",
    "                xdata=times,\n",
    "                ydata=fluxpsf,\n",
    "                p0=p0,\n",
    "                sigma=5+obs_errors,\n",
    "                bounds=[[A_bounds[0], t0_bounds[0], gamma_bounds[0], beta_bounds[0], trise_bounds[0], tfall_bounds[0]],\n",
    "                        [A_bounds[1], t0_bounds[1], gamma_bounds[1], beta_bounds[1], trise_bounds[1], tfall_bounds[1]]],\n",
    "                ftol=0.1,\n",
    "                # verbose=2\n",
    "            )\n",
    "        except (ValueError, RuntimeError, OptimizeWarning):\n",
    "            # print('Two fits of SPM failed. Returning NaN.')\n",
    "            pout = np.array([np.nan, np.nan, np.nan, np.nan, np.nan, np.nan])    \n",
    "    return pout\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "505e9986-4436-43f0-946c-5b5f34592c93",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_example(fit_scipy_alercev2,alercev2,alercev2features).show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0811469e-565c-4774-9b34-ff7e6cd0d0f2",
   "metadata": {},
   "source": [
    "### 1.2.7 Summary of Alternate Approaches\n",
    "\n",
    "Table 1: A comparison of the different parameterisations for full light curve fitting.\n",
    "\n",
    "|    | Parameterisation Used      |   Average Time per Object for all 6 passbands (s) |   Average F1 Score for RFC (n=150) |   Total objects (of 480) where fit failed (for ≥ 1 passband) |\n",
    "|---:|:---------------------------|--------------------------------------------------:|-----------------------------------:|-------------------------------------------------------------:|\n",
    "|  0 | Bazin - old implementation |                                        0.00814443 |                           0.567551 |                                                            0 |\n",
    "|  1 | Bazin - new implementation |                                        0.0370185  |                           0.61107  |                                                           11 |\n",
    "|  2 | FRED                       |                                        0.0515021  |                           0.453149 |                                                           54 |\n",
    "|  3 | Karpenka                   |                                        0.140439   |                           0.423564 |                                                           12 |\n",
    "|  4 | Villar                     |                                        0.0427893  |                           0.425545 |                                                            0 |\n",
    "|  5 | Alercev1                   |                                        0.0547328  |                           0.490861 |                                                            0 |\n",
    "|  6 | Alercev2                   |                                        0.0950013  |                           0.481691 |                                                           10 |\n",
    "\n",
    "\n",
    "---\n",
    "\n",
    "\n",
    "Table 1 is based on the results of a Random Forest Classifier (10-fold CV, n=150), which I trained on the following 8 extragalactic DDF classes, 60 samples  each, from PLAsTiCC:\n",
    "- SNIa (WD detonation Type Ia SN)\n",
    "- SNIa-91bg (Peculiar type Ia: 91bg)\n",
    "- SNIax (Peculiar SNIax)\n",
    "- SNII (Core Collapse Type II SN)\n",
    "- SNIbc (Core Collapse Type Ibc SN)\n",
    "- SLSN-I (Super-Lum. SN - magnetar)\n",
    "- TDE (Tidal Disruption Event)\n",
    "- AGN (Active Galactic Nuclei)\n",
    "\n",
    "I chose 60 samples as that was the maximum number of TDE samples available in some given set of PLAsTiCC, and I wanted to keep it a balanced class problem. All parameterisations were calculated by fitting the full light curve. The comparative score is the F1 Score for the above RFC.\n",
    "\n",
    "The time taken here is not representative of the time it would take for RESSPECT, for example, because I was working on my personal laptop. Further, as the dataset was small, the comparative (F1) score is not in any means representative of how well it will work for RESSPECT. But since everything was identical, it does provide a way to compare the which one works better.\n",
    "\n",
    "The code for generating the above table can be found on this GitHub repository: https://github.com/siddharthchaini/comparing-parameterisations\n",
    "\n",
    "**(NOTE: This will be ported over to the current repository soon. ToDo)**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b59b36e3-8794-4e63-b07a-6c38d960fd0e",
   "metadata": {},
   "source": [
    "## 1.3 Further Improvements"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e9b9054-30b3-4245-930b-4ca44e6fd543",
   "metadata": {},
   "source": [
    "### 1.3.1 Less Than 5 Points\n",
    "\n",
    "Because the primary goal of RESSPECT is as a recommendation system, it's imperative to properly handle early light curves - when there aren't enough observations.\n",
    "\n",
    "Now, we saw that for each passband, the Bazin function (Sec 1.2.1) has 5 free parameters: (a, b, t0, tfall, trise) and so it will need at least 5 points to fit the function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "1e661d16-1b3d-462b-bfb5-8de9f35e5882",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv(\"sample_data/plasticc/130779836_uLens.csv\")\n",
    "df['mjd'] = df['mjd'] - df['mjd'][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "64c039ca-6f61-4b72-bbc1-5bc9a310e87f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mjd</th>\n",
       "      <th>band</th>\n",
       "      <th>flux</th>\n",
       "      <th>fluxerr</th>\n",
       "      <th>detected_bool</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>134.5768</td>\n",
       "      <td>z</td>\n",
       "      <td>16366.390625</td>\n",
       "      <td>130.593475</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>148.6704</td>\n",
       "      <td>Y</td>\n",
       "      <td>27343.818359</td>\n",
       "      <td>199.967590</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>157.6125</td>\n",
       "      <td>r</td>\n",
       "      <td>31437.089844</td>\n",
       "      <td>362.050262</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>353.9913</td>\n",
       "      <td>i</td>\n",
       "      <td>1288.216431</td>\n",
       "      <td>29.758102</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>57</th>\n",
       "      <td>429.7003</td>\n",
       "      <td>u</td>\n",
       "      <td>90.714111</td>\n",
       "      <td>40.501080</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>435.7362</td>\n",
       "      <td>g</td>\n",
       "      <td>100.993713</td>\n",
       "      <td>19.232201</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         mjd band          flux     fluxerr  detected_bool\n",
       "24  134.5768    z  16366.390625  130.593475              1\n",
       "25  148.6704    Y  27343.818359  199.967590              1\n",
       "27  157.6125    r  31437.089844  362.050262              1\n",
       "40  353.9913    i   1288.216431   29.758102              1\n",
       "57  429.7003    u     90.714111   40.501080              0\n",
       "59  435.7362    g    100.993713   19.232201              0"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[df.groupby('band').cumcount()==5]\n",
    "# 5th observation point for each passband"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "16cbce2c-df2e-4748-935e-9c2164306ae5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['a', 'b', 't0', 'tfall', 'trise']\n",
      "For 1 points:\n",
      "[1518.112182    0.         42.7361     50.         25.      ]\n",
      "For 2 points:\n",
      "[6055.97429468   72.3408057   100.21519702   49.51047521   17.40910436]\n",
      "For 3 points:\n",
      "[7161.40892332  711.1533556   113.30038404   14.71355816    7.19815851]\n",
      "For 4 points:\n",
      "[8332.91600013  707.36564169  113.73084279   56.68522276   11.20965019]\n",
      "For 5 points:\n",
      "[6376188.88504908     442.10926313     307.71176356       3.85079507\n",
      "       3.36590785]\n",
      "For 6 points:\n",
      "[21194.04931367   -67.97237323   175.78290762    53.88005217\n",
      "    23.29678792]\n",
      "For 7 points:\n",
      "[26115.87334379    -1.82948357   183.12615738    47.30264901\n",
      "    21.58630401]\n",
      "For 8 points:\n",
      "[25127.2333485    -11.47287818   181.7816997     48.39120652\n",
      "    21.87050166]\n",
      "For 9 points:\n",
      "[22752.00583769   -29.64755383   177.84248123    51.33084511\n",
      "    22.54410001]\n"
     ]
    }
   ],
   "source": [
    "print(bazinfeatures)\n",
    "for i in range(1,10):\n",
    "    df_g = df[df[\"band\"] == \"g\"].iloc[:i]\n",
    "    print(f\"For {i} points:\")\n",
    "    print(fit_scipy_bazin(df_g[\"mjd\"].to_numpy(),df_g[\"flux\"].to_numpy(),df_g[\"fluxerr\"].to_numpy()))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85d36883-b906-4346-9444-715e687178e7",
   "metadata": {},
   "source": [
    "This essentially implies that it might take a long time for some bands to have a proper fit. For example, in the above case it takes 134 days for 5 observations in the z band, but takes 435 days for 5 observations in g band. \n",
    "\n",
    "But, we know that all light parameters are not equally important. For example, b is just the offset from the x axis (i.e difference from template image), and not nearly as important as trise or tfall, as it does not necessarily tell us anything about the light curve's astronomical source.\n",
    "\n",
    "From the above example, we can see that the value of becomes somewhat absurd (707)\n",
    "\n",
    "Thus, an alternative approach is to set these values manually."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "1df39222-12a4-4fac-8da9-439ca647d3ac",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Same as before:\n",
    "bazinfeatures = [\"a\", \"b\", \"t0\", \"tfall\", \"trise\"]\n",
    "\n",
    "def bazin(time, a, b, t0, tfall, trise):\n",
    "    with np.errstate(over='ignore', invalid='ignore'):\n",
    "        X = np.exp(-(time - t0) / tfall) / (1 + np.exp(-(time - t0) / trise))\n",
    "        return a * X + b\n",
    "\n",
    "def bazinr(time, a, b, t0, tfall, r):\n",
    "    trise = tfall/r\n",
    "    return bazin(time, a, b, t0, tfall, trise)\n",
    "    \n",
    "def errfunc_bazin(params, time, flux, fluxerr):\n",
    "    return abs(flux - bazinr(time, *params)) / fluxerr\n",
    "\n",
    "# Changed\n",
    "def errfunc_bazin4pts(params, time, flux, fluxerr):\n",
    "    a,t0,tfall,r = params\n",
    "    b=0 #HARDCODED\n",
    "    return abs(flux - bazinr(time, a, b, t0, tfall, r)) / fluxerr\n",
    "\n",
    "def errfunc_bazin3pts(params, time, flux, fluxerr):\n",
    "    a,t0,tfall = params\n",
    "    b=0 #HARDCODED\n",
    "    trise=10 #HARDCODED\n",
    "    r = tfall/trise\n",
    "    return abs(flux - bazinr(time, a, b, t0, tfall, r)) / fluxerr\n",
    "\n",
    "def fit_scipy_bazin_early(time, flux, fluxerr):\n",
    "    flux = np.asarray(flux)\n",
    "    imax = flux.argmax()\n",
    "    flux_max = flux[imax]\n",
    "        \n",
    "    # Parameter bounds\n",
    "    a_bounds = [1.e-3, np.inf]\n",
    "    b_bounds = [-np.inf, np.inf]\n",
    "    t0_bounds = [-0.5*time.max(), 1.5*time.max()]\n",
    "    tfall_bounds = [1.e-3, np.inf]\n",
    "    r_bounds = [1, np.inf]\n",
    "\n",
    "    # Parameter guess\n",
    "    a_guess = 2*flux_max\n",
    "    b_guess = 0\n",
    "    t0_guess = time[imax]\n",
    "    \n",
    "    tfall_guess = time[imax-2:imax+2].std()/2\n",
    "    if np.isnan(tfall_guess):\n",
    "        tfall_guess = time[imax-1:imax+1].std()/2\n",
    "        if np.isnan(tfall_guess):\n",
    "            tfall_guess=50\n",
    "    if tfall_guess<1:\n",
    "        tfall_guess=50\n",
    "\n",
    "    r_guess = 2\n",
    "\n",
    "    # Clip guesses to stay in bound\n",
    "    a_guess = np.clip(a=a_guess,a_min=a_bounds[0],a_max=a_bounds[1])\n",
    "    b_guess = np.clip(a=b_guess,a_min=b_bounds[0],a_max=b_bounds[1])\n",
    "    t0_guess = np.clip(a=t0_guess,a_min=t0_bounds[0],a_max=t0_bounds[1])\n",
    "    tfall_guess = np.clip(a=tfall_guess,a_min=tfall_bounds[0],a_max=tfall_bounds[1])\n",
    "    r_guess = np.clip(a=r_guess,a_min=r_bounds[0],a_max=r_bounds[1])\n",
    "\n",
    "    \n",
    "    if len(flux)>=5:\n",
    "        # Full fit\n",
    "        guess = [a_guess,b_guess,t0_guess,tfall_guess,r_guess]\n",
    "        bounds = [[a_bounds[0], b_bounds[0], t0_bounds[0], tfall_bounds[0], r_bounds[0]],\n",
    "                  [a_bounds[1], b_bounds[1], t0_bounds[1], tfall_bounds[1], r_bounds[1]]]\n",
    "        result = least_squares(errfunc_bazin, guess, args=(time, flux, fluxerr), method='trf', loss='linear',bounds=bounds)\n",
    "        a_fit,b_fit,t0_fit,tfall_fit,r_fit = result.x\n",
    "        trise_fit = tfall_fit/r_fit\n",
    "    elif len(flux)==4:\n",
    "        b_fit=0 #HARDCODED\n",
    "        guess = [a_guess,t0_guess,tfall_guess,r_guess]\n",
    "        bounds = [[a_bounds[0], t0_bounds[0], tfall_bounds[0], r_bounds[0]],\n",
    "                  [a_bounds[1], t0_bounds[1], tfall_bounds[1], r_bounds[1]]]\n",
    "        result = least_squares(errfunc_bazin4pts, guess, args=(time, flux, fluxerr), method='trf', loss='linear',bounds=bounds)\n",
    "        a_fit,t0_fit,tfall_fit,r_fit = result.x\n",
    "        trise_fit = tfall_fit/r_fit\n",
    "    else:\n",
    "        b_fit=0 #HARDCODED\n",
    "        trise_fit=10 #HARDCODED\n",
    "        guess = [a_guess,t0_guess,tfall_guess]\n",
    "        tfall_bounds[0] = trise_fit # CHANGE tfall lower bound to ensure tfall>trise as no r>1 bound here\n",
    "        bounds = [[a_bounds[0], t0_bounds[0], tfall_bounds[0]],\n",
    "                  [a_bounds[1], t0_bounds[1], tfall_bounds[1]]]\n",
    "        result = least_squares(errfunc_bazin3pts, guess, args=(time, flux, fluxerr), method='trf', loss='linear',bounds=bounds)\n",
    "        a_fit,t0_fit,tfall_fit = result.x\n",
    "    \n",
    "    final_result = np.array([a_fit,b_fit,t0_fit,tfall_fit,trise_fit])\n",
    "    \n",
    "    return final_result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "daa56194-3e5f-4ee6-a9fd-913ee70f1932",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['a', 'b', 't0', 'tfall', 'trise']\n",
      "For 1 points:\n",
      "[1518.112182    0.         42.7361     50.         10.      ]\n",
      "For 2 points:\n",
      "[7504.23140932    0.           84.87364817   21.75060696   10.        ]\n",
      "For 3 points:\n",
      "[11718.16303967     0.           152.41515       13.32731027\n",
      "    10.        ]\n",
      "For 4 points:\n",
      "[133760.88244624      0.            250.76082905     18.60814792\n",
      "     12.7213767 ]\n",
      "For 5 points:\n",
      "[6376188.88504908     442.10926313     307.71176356       3.85079507\n",
      "       3.36590785]\n",
      "For 6 points:\n",
      "[21194.04931367   -67.97237323   175.78290762    53.88005217\n",
      "    23.29678792]\n",
      "For 7 points:\n",
      "[26115.87334379    -1.82948357   183.12615738    47.30264901\n",
      "    21.58630401]\n",
      "For 8 points:\n",
      "[25127.2333485    -11.47287818   181.7816997     48.39120652\n",
      "    21.87050166]\n",
      "For 9 points:\n",
      "[22752.00583769   -29.64755383   177.84248123    51.33084511\n",
      "    22.54410001]\n"
     ]
    }
   ],
   "source": [
    "print(bazinfeatures)\n",
    "for i in range(1,10):\n",
    "    df_g = df[df[\"band\"] == \"g\"].iloc[:i]\n",
    "    print(f\"For {i} points:\")\n",
    "    print(fit_scipy_bazin_early(df_g[\"mjd\"].to_numpy(),df_g[\"flux\"].to_numpy(),df_g[\"fluxerr\"].to_numpy()))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d635cf5c-c4ae-4d1a-a1c6-0effea478887",
   "metadata": {},
   "source": [
    "Thus we see that for >=5 points, this becomes the same as the old approach. Only the early light curve fits have been modified.\n",
    "\n",
    "What remains to be seen is whether this gives a better performance for RESSPECT."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65f0b6fb-6450-490f-93c1-541f86ea3fb9",
   "metadata": {},
   "source": [
    "## 1.4 Limitations of all curve fitting approaches\n",
    "1. Slow - As it involves fitting 6 functions (so 30-40 free parameters) for each object.\n",
    "2. Greedy - Each passband is treated and fit independently.\n",
    "3. Data intensive - Each fit needs 5 points per light-curve per passband. This is not ideal for early light curve classification, which is important for RESSPECT.\n",
    "4. Not very robust - Designed for SNIa & SNII \n",
    "\n",
    "Because of the above reasons, we are interested in other modern deep-learning based approaches, like GP-VAE.\n",
    "\n",
    "You can find more about GP-VAE in the next notebook [here](https://github.com/siddharthchaini/Improving-Feature-Extraction-RESSPECT/blob/main/2.%20gp-vae.ipynb)."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}