doc/tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "4ed4f5f8",
   "metadata": {},
   "source": [
    "# Tutorial \n",
    "\n",
    "This tutorial demonstrates the usage of the sweights package.\n",
    "\n",
    "We will first cook up a toy model with a discriminat variable (invariant mass) and a control variable (decay time) and use it to generate some toy data.\n",
    "\n",
    "Then we will use a fit to the invariant mass to obtain some component pdf estimates and use these to extract some weights which project out the signal only component in the decay time. \n",
    "\n",
    "We will demonstrate both the classic *sWeights* and the *Custom Ortogonal Weight functions* (COWs) method. See [arXiv:2112.04575](https://arxiv.org/abs/2112.04574) for more details.\n",
    "\n",
    "Finally we will fit the weighted decay time distribution and correct the covariance matrix according to the description in [arXiv:1911.01303](https://arxiv.org/abs/1911.01303)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7aa1bc84",
   "metadata": {},
   "outputs": [],
   "source": [
    "# external requirements\n",
    "import os\n",
    "from argparse import ArgumentParser\n",
    "import numpy as np\n",
    "from scipy.stats import norm, expon, uniform\n",
    "import matplotlib.pyplot as plt\n",
    "from iminuit import Minuit\n",
    "from iminuit.cost import ExtendedUnbinnedNLL\n",
    "from iminuit.pdg_format import pdg_format\n",
    "import boost_histogram as bh\n",
    "\n",
    "# from this package\n",
    "from sweights import sweight # for classic sweights\n",
    "from sweights import cow     # for custom orthogonal weight functions\n",
    "from sweights import cov_correct, approx_cov_correct # for covariance corrections\n",
    "from sweights import kendall_tau # for an independence test\n",
    "\n",
    "# set a reproducible seed\n",
    "np.random.seed(21011987)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7bae46d",
   "metadata": {},
   "source": [
    "## Make the toy model and generate some data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "eb61cca3",
   "metadata": {},
   "outputs": [],
   "source": [
    "Ns = 5000\n",
    "Nb = 5000\n",
    "ypars = [Ns,Nb]\n",
    "\n",
    "# mass\n",
    "mrange = (0,1)\n",
    "mu = 0.5\n",
    "sg = 0.1\n",
    "lb = 1\n",
    "mpars = [mu,sg,lb]\n",
    "\n",
    "# decay time\n",
    "trange = (0,1)\n",
    "tlb = 2\n",
    "tpars = [tlb]\n",
    "\n",
    "# generate the toy\n",
    "def generate(Ns,Nb,mu,sg,lb,tlb,poisson=False,ret_true=False):\n",
    "\n",
    "    Nsig = np.random.poisson(Ns) if poisson else Ns\n",
    "    Nbkg = np.random.poisson(Nb) if poisson else Nb\n",
    "\n",
    "    sigM = norm(mu,sg)\n",
    "    bkgM = expon(mrange[0], lb)\n",
    "\n",
    "    sigT = expon(trange[0], tlb)\n",
    "    bkgT = uniform(trange[0],trange[1]-trange[0])\n",
    "\n",
    "    # generate\n",
    "    sigMflt = sigM.cdf(mrange)\n",
    "    bkgMflt = bkgM.cdf(mrange)\n",
    "    sigTflt = sigT.cdf(trange) \n",
    "    bkgTflt = bkgT.cdf(trange)\n",
    "\n",
    "    sigMvals = sigM.ppf( np.random.uniform(*sigMflt,size=Nsig) )\n",
    "    sigTvals = sigT.ppf( np.random.uniform(*sigTflt,size=Nsig) )\n",
    "    \n",
    "    bkgMvals = bkgM.ppf( np.random.uniform(*bkgMflt,size=Nbkg) )\n",
    "    bkgTvals = bkgT.ppf( np.random.uniform(*bkgTflt,size=Nbkg) )\n",
    "    \n",
    "    Mvals = np.concatenate( (sigMvals, bkgMvals) )\n",
    "    Tvals = np.concatenate( (sigTvals, bkgTvals) )\n",
    "    \n",
    "    truth = np.concatenate( ( np.ones_like(sigMvals), np.zeros_like(bkgMvals) ) )\n",
    "\n",
    "    if ret_true:\n",
    "        return np.stack( (Mvals,Tvals,truth), axis=1 )\n",
    "    else:\n",
    "        return np.stack( (Mvals,Tvals), axis=1 )\n",
    "    \n",
    "toy = generate(Ns,Nb,mu,sg,lb,tlb,ret_true=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1eb58a1",
   "metadata": {},
   "source": [
    "## Plot the toy data and generating pdfs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "45806a9e",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# useful function for plotting data points with error bars\n",
    "def myerrorbar(data, ax, bins, range, wts=None, label=None, col=None):\n",
    "    col = col or 'k'\n",
    "    nh, xe = np.histogram(data,bins=bins,range=range)\n",
    "    cx = 0.5*(xe[1:]+xe[:-1])\n",
    "    err = nh**0.5\n",
    "    if wts is not None:\n",
    "        whist = bh.Histogram( bh.axis.Regular(bins,*range), storage=bh.storage.Weight() )\n",
    "        whist.fill( data, weight = wts )\n",
    "        cx = whist.axes[0].centers\n",
    "        nh = whist.view().value\n",
    "        err = whist.view().variance**0.5\n",
    "\n",
    "    ax.errorbar(cx, nh, err, capsize=2,label=label,fmt=f'{col}o')\n",
    "\n",
    "# define the mass pdf for plotting etc.\n",
    "def mpdf(x, Ns, Nb, mu, sg, lb, comps=['sig','bkg']):\n",
    "\n",
    "    sig  = norm(mu,sg)\n",
    "    sigN = np.diff( sig.cdf(mrange) )\n",
    "\n",
    "    bkg  = expon(mrange[0], lb)\n",
    "    bkgN = np.diff( bkg.cdf(mrange) )\n",
    "\n",
    "    tot = 0\n",
    "    if 'sig' in comps: tot += Ns * sig.pdf(x) / sigN\n",
    "    if 'bkg' in comps: tot += Nb * bkg.pdf(x) / bkgN\n",
    "\n",
    "    return tot\n",
    "\n",
    "# define time pdf for plotting etc.\n",
    "def tpdf(x, Ns, Nb, tlb, comps=['sig','bkg']):\n",
    "\n",
    "    sig  = expon(trange[0],tlb)\n",
    "    sigN = np.diff( sig.cdf(trange) )\n",
    "\n",
    "    bkg  = uniform(trange[0],trange[1]-trange[0])\n",
    "    bkgN = np.diff( bkg.cdf(trange) )\n",
    "\n",
    "    tot = 0\n",
    "    if 'sig' in comps: tot += Ns * sig.pdf(x) / sigN\n",
    "    if 'bkg' in comps: tot += Nb * bkg.pdf(x) / bkgN\n",
    "\n",
    "    return tot\n",
    "\n",
    "# define plot function\n",
    "def plot(toy, draw_pdf=True):\n",
    "\n",
    "    nbins = 50\n",
    "\n",
    "    fig, ax = plt.subplots(1,2,figsize=(12,4))\n",
    "\n",
    "    myerrorbar(toy[:,0],ax[0],bins=nbins,range=mrange)\n",
    "    myerrorbar(toy[:,1],ax[1],bins=nbins,range=trange)\n",
    "\n",
    "    if draw_pdf:\n",
    "        m = np.linspace(*mrange,400)\n",
    "        mN = (mrange[1]-mrange[0])/nbins\n",
    "\n",
    "        bkgm = mpdf(m, *(ypars+mpars),comps=['bkg'])\n",
    "        sigm = mpdf(m, *(ypars+mpars),comps=['sig'])\n",
    "        totm = bkgm + sigm\n",
    "\n",
    "        ax[0].plot(m, mN*bkgm, 'r--', label='Background')\n",
    "        ax[0].plot(m, mN*sigm, 'g:' , label='Signal')\n",
    "        ax[0].plot(m, mN*totm, 'b-' , label='Total PDF')\n",
    "\n",
    "        t = np.linspace(*trange,400)\n",
    "        tN = (trange[1]-trange[0])/nbins\n",
    "\n",
    "        bkgt = tpdf(t, *(ypars+tpars),comps=['bkg'])\n",
    "        sigt = tpdf(t, *(ypars+tpars),comps=['sig'])\n",
    "        tott = bkgt + sigt\n",
    "\n",
    "        ax[1].plot(t, tN*bkgt, 'r--', label='Background')\n",
    "        ax[1].plot(t, tN*sigt, 'g:' , label='Signal')\n",
    "        ax[1].plot(t, tN*tott, 'b-' , label='Total PDF')\n",
    "\n",
    "    ax[0].set_xlabel('Invariant mass')\n",
    "    ax[0].set_ylim(bottom=0)\n",
    "    ax[0].legend()\n",
    "\n",
    "    ax[1].set_xlabel('Decay time')\n",
    "    ax[1].set_ylim(bottom=0)\n",
    "    ax[1].legend()\n",
    "\n",
    "    fig.tight_layout()\n",
    "    \n",
    "plot(toy)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "efefada1",
   "metadata": {},
   "source": [
    "## Check the independence of our data\n",
    "\n",
    "By computing the kendall rank coefficient and seeing how compatibile it is with 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f34e8376",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Kendall Tau: -0.017 ± 0.010\n"
     ]
    }
   ],
   "source": [
    "kts = kendall_tau(toy[:,0],toy[:,1])\n",
    "print('Kendall Tau:', pdg_format( kts[0], kts[1] ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06fb26fd",
   "metadata": {},
   "source": [
    "## Fit the toy in invariant mass\n",
    "\n",
    "This provides us with estimates for the component shapes and the component yields"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "76702af5",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"5\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Minimum value of function\"> FCN = -1.684e+05 </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"No. of function evaluations in last call and total number\"> Nfcn = 135 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 7.37e-05 (Goal: 0.0002) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"No. of gradient evaluations in last call and total number\">  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> No Parameters at limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix accurate?\"> Accurate </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix positive definite?\"> Pos. def. </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Was positive definiteness enforced by Minuit?\"> Not forced </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th title=\"Variable name\"> Name </th>\n",
       "        <th title=\"Value of parameter\"> Value </th>\n",
       "        <th title=\"Hesse error\"> Hesse Error </th>\n",
       "        <th title=\"Minos lower error\"> Minos Error- </th>\n",
       "        <th title=\"Minos upper error\"> Minos Error+ </th>\n",
       "        <th title=\"Lower limit of the parameter\"> Limit- </th>\n",
       "        <th title=\"Upper limit of the parameter\"> Limit+ </th>\n",
       "        <th title=\"Is the parameter fixed in the fit\"> Fixed </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 0 </th>\n",
       "        <td> Ns </td>\n",
       "        <td> 5.11e3 </td>\n",
       "        <td> 0.11e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td> 1E+04 </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 1 </th>\n",
       "        <td> Nb </td>\n",
       "        <td> 4.89e3 </td>\n",
       "        <td> 0.11e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td> 1E+04 </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 2 </th>\n",
       "        <td> mu </td>\n",
       "        <td> 0.4981 </td>\n",
       "        <td> 0.0021 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td> 1 </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 3 </th>\n",
       "        <td> sg </td>\n",
       "        <td> 0.1031 </td>\n",
       "        <td> 0.0022 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td> 1 </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 4 </th>\n",
       "        <td> lb </td>\n",
       "        <td> 1.07 </td>\n",
       "        <td> 0.06 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td> 10 </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th> Ns </th>\n",
       "        <th> Nb </th>\n",
       "        <th> mu </th>\n",
       "        <th> sg </th>\n",
       "        <th> lb </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> Ns </th>\n",
       "        <td> 1.22e+04 </td>\n",
       "        <td style=\"background-color:rgb(174,174,250);color:black\"> -7.12e+03 <strong>(-0.587)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0.00789 <strong>(-0.034)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,173,173);color:black\"> 0.124 <strong>(0.516)</strong> </td>\n",
       "        <td style=\"background-color:rgb(224,224,250);color:black\"> -1.44 <strong>(-0.203)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> Nb </th>\n",
       "        <td style=\"background-color:rgb(174,174,250);color:black\"> -7.12e+03 <strong>(-0.587)</strong> </td>\n",
       "        <td> 1.2e+04 </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 0.00788 <strong>(0.034)</strong> </td>\n",
       "        <td style=\"background-color:rgb(182,182,250);color:black\"> -0.124 <strong>(-0.520)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,219,219);color:black\"> 1.44 <strong>(0.205)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> mu </th>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0.00789 <strong>(-0.034)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 0.00788 <strong>(0.034)</strong> </td>\n",
       "        <td> 4.46e-06 </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -2.09e-07 <strong>(-0.045)</strong> </td>\n",
       "        <td style=\"background-color:rgb(218,218,250);color:black\"> -3.35e-05 <strong>(-0.247)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> sg </th>\n",
       "        <td style=\"background-color:rgb(250,173,173);color:black\"> 0.124 <strong>(0.516)</strong> </td>\n",
       "        <td style=\"background-color:rgb(182,182,250);color:black\"> -0.124 <strong>(-0.520)</strong> </td>\n",
       "        <td style=\"background-color:rgb(244,244,250);color:black\"> -2.09e-07 <strong>(-0.045)</strong> </td>\n",
       "        <td> 4.72e-06 </td>\n",
       "        <td style=\"background-color:rgb(228,228,250);color:black\"> -2.39e-05 <strong>(-0.172)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> lb </th>\n",
       "        <td style=\"background-color:rgb(224,224,250);color:black\"> -1.44 <strong>(-0.203)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,219,219);color:black\"> 1.44 <strong>(0.205)</strong> </td>\n",
       "        <td style=\"background-color:rgb(218,218,250);color:black\"> -3.35e-05 <strong>(-0.247)</strong> </td>\n",
       "        <td style=\"background-color:rgb(228,228,250);color:black\"> -2.39e-05 <strong>(-0.172)</strong> </td>\n",
       "        <td> 0.00411 </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = -1.684e+05                 │              Nfcn = 135              │\n",
       "│ EDM = 7.37e-05 (Goal: 0.0002)    │                                      │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │        No Parameters at limit        │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│ Below EDM threshold (goal x 10)  │           Below call limit           │\n",
       "├───────────────┬──────────────────┼───────────┬─────────────┬────────────┤\n",
       "│  Covariance   │     Hesse ok     │ Accurate  │  Pos. def.  │ Not forced │\n",
       "└───────────────┴──────────────────┴───────────┴─────────────┴────────────┘\n",
       "┌───┬──────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼──────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ Ns   │  5.11e3   │  0.11e3   │            │            │    0    │  10000  │       │\n",
       "│ 1 │ Nb   │  4.89e3   │  0.11e3   │            │            │    0    │  10000  │       │\n",
       "│ 2 │ mu   │  0.4981   │  0.0021   │            │            │    0    │    1    │       │\n",
       "│ 3 │ sg   │  0.1031   │  0.0022   │            │            │    0    │    1    │       │\n",
       "│ 4 │ lb   │   1.07    │   0.06    │            │            │    0    │   10    │       │\n",
       "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌────┬───────────────────────────────────────────────────┐\n",
       "│    │        Ns        Nb        mu        sg        lb │\n",
       "├────┼───────────────────────────────────────────────────┤\n",
       "│ Ns │  1.22e+04 -7.12e+03  -0.00789     0.124     -1.44 │\n",
       "│ Nb │ -7.12e+03   1.2e+04   0.00788    -0.124      1.44 │\n",
       "│ mu │  -0.00789   0.00788  4.46e-06 -2.09e-07 -3.35e-05 │\n",
       "│ sg │     0.124    -0.124 -2.09e-07  4.72e-06 -2.39e-05 │\n",
       "│ lb │     -1.44      1.44 -3.35e-05 -2.39e-05   0.00411 │\n",
       "└────┴───────────────────────────────────────────────────┘"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# define mass pdf for iminuit fitting\n",
    "def mpdf_min(x, Ns, Nb, mu, sg, lb):\n",
    "    return (Ns+Nb, mpdf(x, Ns, Nb, mu, sg, lb) )\n",
    "\n",
    "mi = Minuit( ExtendedUnbinnedNLL(toy[:,0], mpdf_min), Ns=Ns, Nb=Nb, mu=mu, sg=sg, lb=lb )\n",
    "mi.limits['Ns'] = (0,Ns+Nb)\n",
    "mi.limits['Nb'] = (0,Ns+Nb)\n",
    "mi.limits['mu'] = mrange\n",
    "mi.limits['sg'] = (0,mrange[1]-mrange[0])\n",
    "mi.limits['lb'] = (0,10)\n",
    "\n",
    "mi.migrad()\n",
    "mi.hesse()\n",
    "display(mi) # only valid for ipython notebooks"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6261600a",
   "metadata": {},
   "source": [
    "### Construct the sweighter\n",
    "\n",
    "Note that this will run much quicker if `verbose=False` and `checks=False`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b09cc060",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initialising sweight with the summation method:\n",
      "    PDF normalisations:\n",
      "\t 0 5107.224408977729\n",
      "\t 1 4892.156810093505\n",
      "    W-matrix:\n",
      "\t[[1.38699027e-04 5.96207082e-05]\n",
      "\t [5.96207082e-05 1.42184207e-04]]\n",
      "    A-matrix:\n",
      "\t[[ 8795.16287156 -3687.98933236]\n",
      "\t [-3687.98933236  8579.57828096]]\n",
      "    Integral of w*pdf matrix (should be close to the identity):\n",
      "\t[[ 1.00011709e+00 -1.32635071e-04]\n",
      "\t [-1.57992838e-04  1.00004886e+00]]\n",
      "    Check of weight sums (should match yields):\n",
      "\tComponent  | sWeightSum |   Yield    |   Diff    |\n",
      "\t---------------------------------------------------\n",
      "\t  0        |  5107.2244 |  5107.2244 |    -0.00% |\n",
      "\t  1        |  4892.1568 |  4892.1568 |     0.00% |\n"
     ]
    }
   ],
   "source": [
    "# define estimated functions\n",
    "spdf = lambda m: mpdf(m,*mi.values,comps=['sig'])\n",
    "bpdf = lambda m: mpdf(m,*mi.values,comps=['bkg'])\n",
    "\n",
    "# make the sweighter\n",
    "sweighter = sweight( toy[:,0], [spdf,bpdf], [mi.values['Ns'],mi.values['Nb']], (mrange,), method='summation', compnames=('sig','bkg'), verbose=True, checks=True )\n",
    "\n",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db8c3132",
   "metadata": {},
   "source": [
    "### Construct the COW\n",
    "\n",
    "Note that COW pdfs are always normalised in the COW numerator so that the W and A matrices tend to come out with elements of order one. This example uses a variance function of unity, I(m)=1, but also codes the case where I(m) = g(m), which is equiavalent to sweights."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "57f2f1f7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initialising COW:\n",
      "    W-matrix:\n",
      "\t[[2.73492037 0.97050271]\n",
      "\t  [0.97050271 1.07239023]]\n",
      "    A-matrix:\n",
      "\t[[ 0.53861176 -0.48743839]\n",
      "\t  [-0.48743839  1.37362336]]\n"
     ]
    }
   ],
   "source": [
    "# unity\n",
    "Im = 1 \n",
    "# sweight equiavlent\n",
    "# Im = lambda m: mpdf(m,*mi.values) / (mi.values['Ns'] + mi.values['Nb'] )\n",
    "\n",
    "# make the cow\n",
    "cw = cow(mrange, spdf, bpdf, Im, verbose=True)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85b6c197",
   "metadata": {},
   "source": [
    "## Comparison of the sweight and COW methods"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bbb12e0",
   "metadata": {},
   "source": [
    "### Compare the weight distributoins"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "2d8eff72",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_wts(x, sw, bw, title=None):\n",
    "    fig,ax = plt.subplots()\n",
    "    ax.plot(x, sw, 'b--', label='Signal')\n",
    "    ax.plot(x, bw, 'r:' , label='Background')\n",
    "    ax.plot(x, sw+bw, 'k-', label='Sum')\n",
    "    ax.set_xlabel('Mass')\n",
    "    ax.set_ylabel('Weight')\n",
    "    if title: ax.set_title(title)\n",
    "    fig.tight_layout()\n",
    "\n",
    "for meth, cls in zip( ['SW','COW'], [sweighter,cw] ):\n",
    "\n",
    "    # plot weights\n",
    "    x = np.linspace(*mrange,400)\n",
    "    swp = cls.getWeight(0,x)\n",
    "    bwp = cls.getWeight(1,x)\n",
    "    plot_wts(x, swp, bwp, meth)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6383d0e5",
   "metadata": {},
   "source": [
    "### Fit the weighted data in decay time and correct the covariance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d9f5711a",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Method: SW\n",
      "Method: SW - covariance corrected 1.71 +/- 0.14 ---> 1.71 +/- 0.19\n",
      "Method: COW\n",
      "Method: COW - covariance corrected 1.64 +/- 0.13 ---> 1.64 +/- 0.18\n"
     ]
    }
   ],
   "source": [
    "# define weighted nll\n",
    "def wnll(tlb, tdata, wts):\n",
    "    sig  = expon(trange[0],tlb)\n",
    "    sigN = np.diff( sig.cdf(trange) )\n",
    "    return -np.sum( wts * np.log( sig.pdf( tdata ) / sigN ) )\n",
    "\n",
    "# define signal only time pdf for cov corrector\n",
    "def tpdf_cor(x, tlb):\n",
    "    return tpdf(x,1,0,tlb,['sig'])\n",
    "\n",
    "flbs=[]\n",
    "for meth, cls in zip( ['SW','COW'], [sweighter,cw] ):\n",
    "    \n",
    "    print('Method:', meth)\n",
    "    # get the weights\n",
    "    wts = cls.getWeight(0,toy[:,0])\n",
    "    \n",
    "    # define the nll\n",
    "    nll = lambda tlb: wnll(tlb, toy[:,1], wts)\n",
    "\n",
    "    # do the minimisation\n",
    "    tmi = Minuit( nll, tlb=tlb )\n",
    "    tmi.limits['tlb'] = (1,3)\n",
    "    tmi.errordef = Minuit.LIKELIHOOD\n",
    "    tmi.migrad()\n",
    "    tmi.hesse()\n",
    "\n",
    "    # and do the correction\n",
    "    fval = np.array(tmi.values)\n",
    "    flbs.append(fval[0])\n",
    "    fcov = np.array( tmi.covariance.tolist() )\n",
    "\n",
    "    # first order correction\n",
    "    ncov = approx_cov_correct(tpdf_cor, toy[:,1], wts, fval, fcov, verbose=False)\n",
    "\n",
    "    # second order correction\n",
    "    hs  = tpdf_cor\n",
    "    ws  = lambda m: cls.getWeight(0,m)\n",
    "    W   = cls.Wkl\n",
    "\n",
    "    # these derivatives can be done numerically but for the sweights / COW case it's straightfoward to compute them\n",
    "    ws = lambda Wss, Wsb, Wbb, gs, gb: (Wbb*gs - Wsb*gb) / ((Wbb-Wsb)*gs + (Wss-Wsb)*gb)\n",
    "    dws_Wss = lambda Wss, Wsb, Wbb, gs, gb: gb * ( Wsb*gb - Wbb*gs ) / (-Wss*gb + Wsb*gs + Wsb*gb - Wbb*gs)**2\n",
    "    dws_Wsb = lambda Wss, Wsb, Wbb, gs, gb: ( Wbb*gs**2 - Wss*gb**2 ) / (Wss*gb - Wsb*gs - Wsb*gb + Wbb*gs)**2\n",
    "    dws_Wbb = lambda Wss, Wsb, Wbb, gs, gb: gs * ( Wss*gb - Wsb*gs ) / (-Wss*gb + Wsb*gs + Wsb*gb - Wbb*gs)**2\n",
    "\n",
    "    tcov = cov_correct(hs, [spdf,bpdf], toy[:,1], toy[:,0], wts, [mi.values['Ns'],mi.values['Nb']], fval, fcov, [dws_Wss,dws_Wsb,dws_Wbb],[W[0,0],W[0,1],W[1,1]], verbose=False)\n",
    "    print('Method:', meth, f'- covariance corrected {fval[0]:.2f} +/- {fcov[0,0]**0.5:.2f} ---> {fval[0]:.2f} +/- {tcov[0,0]**0.5:.2f}')\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "857bddaf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Plot the weighted decay distributions and the fit result\n",
    "def plot_tweighted(x, wts, wtnames=[], funcs=[]):\n",
    "\n",
    "    fig, ax = plt.subplots()\n",
    "\n",
    "    t = np.linspace(*trange,400)\n",
    "    N = (trange[1]-trange[0])/50\n",
    "\n",
    "    for i, wt in enumerate(wts):\n",
    "        label = None\n",
    "        if i<len(wtnames): label = wtnames[i]\n",
    "        myerrorbar(x, ax, bins=50, range=trange, wts=wt, label=label, col=f'C{i}')\n",
    "        if i<len(funcs):\n",
    "            ax.plot(t,N*funcs[i](t),f'C{i}-')\n",
    "\n",
    "    ax.legend()\n",
    "    ax.set_xlabel('Time')\n",
    "    ax.set_ylabel('Weighted Events')\n",
    "    fig.tight_layout()\n",
    "\n",
    "swf  = lambda t: tpdf(t, mi.values['Ns'], 0, flbs[0], comps=['sig'] )\n",
    "cowf = lambda t: tpdf(t, mi.values['Ns'], 0, flbs[1], comps=['sig'] )\n",
    "sws  = sweighter.getWeight(0, toy[:,0])\n",
    "scow = cw.getWeight(0, toy[:,0])\n",
    "\n",
    "plot_tweighted(toy[:,1], [sws,scow], ['SW','COW'], funcs=[swf,cowf] )\n",
    "\n"
   ]
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