discrete profiling.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from iminuit import Minuit\n",
    "from iminuit.cost import ExtendedBinnedNLL\n",
    "from scipy.stats import norm, expon\n",
    "from scipy.interpolate import BPoly\n",
    "import numpy as np\n",
    "from pyik.mplext import plot_hist\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def scaled_cdf_bernstein(x, pars):\n",
    "    pars = np.atleast_1d(pars)\n",
    "    c = BPoly(pars[..., np.newaxis], xrange).antiderivative()\n",
    "    return c(x)\n",
    "\n",
    "\n",
    "def scaled_cdf_expon(x, a, b):\n",
    "    return a * (1 - np.exp(-b * x))\n",
    "\n",
    "\n",
    "def model1(x, a, b, c):\n",
    "    sig = a * norm(0.5, 0.05).cdf(x)\n",
    "    bkg = scaled_cdf_expon(x, b, c)\n",
    "    return bkg + sig\n",
    "\n",
    "\n",
    "def model2(x, par):\n",
    "    sig = par[0] * norm(0.5, 0.05).cdf(x)\n",
    "    bkg = scaled_cdf_bernstein(x, par[1:])\n",
    "    return bkg + sig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x131c4c5b0>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.default_rng(1)\n",
    "xrange = np.array((0, 1))\n",
    "x_bkg = rng.exponential(0.4, size=10000)\n",
    "x_sig = norm(0.5, 0.05).rvs(5000)\n",
    "x = np.append(x_bkg, x_sig)\n",
    "x = x[(x > xrange[0]) & (x < xrange[1])]\n",
    "n, xe = np.histogram(x, bins=50, range=xrange)\n",
    "plot_hist(xe, n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 50.68 </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"No. of function evaluations in last call and total number\"> Nfcn = 98 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 4e-06 (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 style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Parameters </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> a </td>\n",
       "        <td> 5.01e3 </td>\n",
       "        <td> 0.08e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 1 </th>\n",
       "        <td> b </td>\n",
       "        <td> 10.06e3 </td>\n",
       "        <td> 0.13e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 2 </th>\n",
       "        <td> c </td>\n",
       "        <td> 2.46 </td>\n",
       "        <td> 0.04 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th> a </th>\n",
       "        <th> b </th>\n",
       "        <th> c </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> a </th>\n",
       "        <td> 7.23e+03 </td>\n",
       "        <td style=\"background-color:rgb(214,214,250);color:black\"> -3.09e+03 <strong>(-0.280)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,222,222);color:black\"> 0.703 <strong>(0.186)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> b </th>\n",
       "        <td style=\"background-color:rgb(214,214,250);color:black\"> -3.09e+03 <strong>(-0.280)</strong> </td>\n",
       "        <td> 1.68e+04 </td>\n",
       "        <td style=\"background-color:rgb(191,191,250);color:black\"> -2.61 <strong>(-0.454)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> c </th>\n",
       "        <td style=\"background-color:rgb(250,222,222);color:black\"> 0.703 <strong>(0.186)</strong> </td>\n",
       "        <td style=\"background-color:rgb(191,191,250);color:black\"> -2.61 <strong>(-0.454)</strong> </td>\n",
       "        <td> 0.00196 </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌──────────────────────────────────┬──────────────────────────────────────┐\n",
       "│ FCN = 50.68                      │              Nfcn = 98               │\n",
       "│ EDM = 4e-06 (Goal: 0.0002)       │                                      │\n",
       "├───────────────┬──────────────────┼──────────────────────────────────────┤\n",
       "│ Valid Minimum │ Valid Parameters │        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 │ a    │  5.01e3   │  0.08e3   │            │            │    0    │         │       │\n",
       "│ 1 │ b    │  10.06e3  │  0.13e3   │            │            │    0    │         │       │\n",
       "│ 2 │ c    │   2.46    │   0.04    │            │            │    0    │         │       │\n",
       "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌───┬───────────────────────────────┐\n",
       "│   │         a         b         c │\n",
       "├───┼───────────────────────────────┤\n",
       "│ a │  7.23e+03 -3.09e+03     0.703 │\n",
       "│ b │ -3.09e+03  1.68e+04     -2.61 │\n",
       "│ c │     0.703     -2.61   0.00196 │\n",
       "└───┴───────────────────────────────┘"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m1 = Minuit(ExtendedBinnedNLL(n, xe, model1), 500, 1000, 1)\n",
    "m1.limits = (0, None)\n",
    "m1.migrad()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1320eaeb0>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_hist(xe, n)\n",
    "plot_hist(xe, np.diff(model1(xe, *m1.values)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 65.9 </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"No. of function evaluations in last call and total number\"> Nfcn = 126 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 1.1e-06 (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 style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Parameters </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> x0 </td>\n",
       "        <td> 4.95e3 </td>\n",
       "        <td> 0.09e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 1 </th>\n",
       "        <td> x1 </td>\n",
       "        <td> 23.0e3 </td>\n",
       "        <td> 0.4e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 2 </th>\n",
       "        <td> x2 </td>\n",
       "        <td> 2.2e3 </td>\n",
       "        <td> 0.5e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 3 </th>\n",
       "        <td> x3 </td>\n",
       "        <td> 2.54e3 </td>\n",
       "        <td> 0.19e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th> x0 </th>\n",
       "        <th> x1 </th>\n",
       "        <th> x2 </th>\n",
       "        <th> x3 </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x0 </th>\n",
       "        <td> 7.86e+03 </td>\n",
       "        <td style=\"background-color:rgb(250,241,241);color:black\"> 1.98e+03 <strong>(0.060)</strong> </td>\n",
       "        <td style=\"background-color:rgb(205,205,250);color:black\"> -1.41e+04 <strong>(-0.345)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,219,219);color:black\"> 3.41e+03 <strong>(0.207)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x1 </th>\n",
       "        <td style=\"background-color:rgb(250,241,241);color:black\"> 1.98e+03 <strong>(0.060)</strong> </td>\n",
       "        <td> 1.4e+05 </td>\n",
       "        <td style=\"background-color:rgb(173,173,250);color:black\"> -1.02e+05 <strong>(-0.590)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,197,197);color:black\"> 2.48e+04 <strong>(0.356)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x2 </th>\n",
       "        <td style=\"background-color:rgb(205,205,250);color:black\"> -1.41e+04 <strong>(-0.345)</strong> </td>\n",
       "        <td style=\"background-color:rgb(173,173,250);color:black\"> -1.02e+05 <strong>(-0.590)</strong> </td>\n",
       "        <td> 2.13e+05 </td>\n",
       "        <td style=\"background-color:rgb(156,156,250);color:black\"> -6.22e+04 <strong>(-0.722)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x3 </th>\n",
       "        <td style=\"background-color:rgb(250,219,219);color:black\"> 3.41e+03 <strong>(0.207)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,197,197);color:black\"> 2.48e+04 <strong>(0.356)</strong> </td>\n",
       "        <td style=\"background-color:rgb(156,156,250);color:black\"> -6.22e+04 <strong>(-0.722)</strong> </td>\n",
       "        <td> 3.47e+04 </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌──────────────────────────────────┬──────────────────────────────────────┐\n",
       "│ FCN = 65.9                       │              Nfcn = 126              │\n",
       "│ EDM = 1.1e-06 (Goal: 0.0002)     │                                      │\n",
       "├───────────────┬──────────────────┼──────────────────────────────────────┤\n",
       "│ Valid Minimum │ Valid Parameters │        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 │ x0   │  4.95e3   │  0.09e3   │            │            │    0    │         │       │\n",
       "│ 1 │ x1   │  23.0e3   │   0.4e3   │            │            │    0    │         │       │\n",
       "│ 2 │ x2   │   2.2e3   │   0.5e3   │            │            │    0    │         │       │\n",
       "│ 3 │ x3   │  2.54e3   │  0.19e3   │            │            │    0    │         │       │\n",
       "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌────┬─────────────────────────────────────────┐\n",
       "│    │        x0        x1        x2        x3 │\n",
       "├────┼─────────────────────────────────────────┤\n",
       "│ x0 │  7.86e+03  1.98e+03 -1.41e+04  3.41e+03 │\n",
       "│ x1 │  1.98e+03   1.4e+05 -1.02e+05  2.48e+04 │\n",
       "│ x2 │ -1.41e+04 -1.02e+05  2.13e+05 -6.22e+04 │\n",
       "│ x3 │  3.41e+03  2.48e+04 -6.22e+04  3.47e+04 │\n",
       "└────┴─────────────────────────────────────────┘"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m2 = Minuit(ExtendedBinnedNLL(n, xe, model2), (500, 2e4, 2e3, 3e3))\n",
    "m2.limits = (0, None)\n",
    "m2.migrad()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x13215b280>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_hist(xe, n)\n",
    "plot_hist(xe, np.diff(model2(xe, m2.values)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 52.27 </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"No. of function evaluations in last call and total number\"> Nfcn = 336 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 7.46e-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 style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Parameters </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> x0 </td>\n",
       "        <td> 5.03e3 </td>\n",
       "        <td> 0.09e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 1 </th>\n",
       "        <td> x1 </td>\n",
       "        <td> 24.5e3 </td>\n",
       "        <td> 0.6e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 2 </th>\n",
       "        <td> x2 </td>\n",
       "        <td> 5.8e3 </td>\n",
       "        <td> 0.9e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 3 </th>\n",
       "        <td> x3 </td>\n",
       "        <td> 4.3e3 </td>\n",
       "        <td> 0.6e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 4 </th>\n",
       "        <td> x4 </td>\n",
       "        <td> 2.07e3 </td>\n",
       "        <td> 0.21e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th> x0 </th>\n",
       "        <th> x1 </th>\n",
       "        <th> x2 </th>\n",
       "        <th> x3 </th>\n",
       "        <th> x4 </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x0 </th>\n",
       "        <td> 8.3e+03 </td>\n",
       "        <td style=\"background-color:rgb(250,219,219);color:black\"> 1.06e+04 <strong>(0.207)</strong> </td>\n",
       "        <td style=\"background-color:rgb(209,209,250);color:black\"> -2.7e+04 <strong>(-0.316)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,242,242);color:black\"> 2.81e+03 <strong>(0.051)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 558 <strong>(0.029)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x1 </th>\n",
       "        <td style=\"background-color:rgb(250,219,219);color:black\"> 1.06e+04 <strong>(0.207)</strong> </td>\n",
       "        <td> 3.16e+05 </td>\n",
       "        <td style=\"background-color:rgb(152,152,250);color:black\"> -3.97e+05 <strong>(-0.752)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,178,178);color:black\"> 1.63e+05 <strong>(0.480)</strong> </td>\n",
       "        <td style=\"background-color:rgb(221,221,250);color:black\"> -2.66e+04 <strong>(-0.223)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x2 </th>\n",
       "        <td style=\"background-color:rgb(209,209,250);color:black\"> -2.7e+04 <strong>(-0.316)</strong> </td>\n",
       "        <td style=\"background-color:rgb(152,152,250);color:black\"> -3.97e+05 <strong>(-0.752)</strong> </td>\n",
       "        <td> 8.82e+05 </td>\n",
       "        <td style=\"background-color:rgb(151,151,250);color:black\"> -4.33e+05 <strong>(-0.761)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,190,190);color:black\"> 7.95e+04 <strong>(0.400)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x3 </th>\n",
       "        <td style=\"background-color:rgb(250,242,242);color:black\"> 2.81e+03 <strong>(0.051)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,178,178);color:black\"> 1.63e+05 <strong>(0.480)</strong> </td>\n",
       "        <td style=\"background-color:rgb(151,151,250);color:black\"> -4.33e+05 <strong>(-0.761)</strong> </td>\n",
       "        <td> 3.68e+05 </td>\n",
       "        <td style=\"background-color:rgb(157,157,250);color:black\"> -9.17e+04 <strong>(-0.714)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x4 </th>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 558 <strong>(0.029)</strong> </td>\n",
       "        <td style=\"background-color:rgb(221,221,250);color:black\"> -2.66e+04 <strong>(-0.223)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,190,190);color:black\"> 7.95e+04 <strong>(0.400)</strong> </td>\n",
       "        <td style=\"background-color:rgb(157,157,250);color:black\"> -9.17e+04 <strong>(-0.714)</strong> </td>\n",
       "        <td> 4.48e+04 </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌──────────────────────────────────┬──────────────────────────────────────┐\n",
       "│ FCN = 52.27                      │              Nfcn = 336              │\n",
       "│ EDM = 7.46e-05 (Goal: 0.0002)    │                                      │\n",
       "├───────────────┬──────────────────┼──────────────────────────────────────┤\n",
       "│ Valid Minimum │ Valid Parameters │        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 │ x0   │  5.03e3   │  0.09e3   │            │            │    0    │         │       │\n",
       "│ 1 │ x1   │  24.5e3   │   0.6e3   │            │            │    0    │         │       │\n",
       "│ 2 │ x2   │   5.8e3   │   0.9e3   │            │            │    0    │         │       │\n",
       "│ 3 │ x3   │   4.3e3   │   0.6e3   │            │            │    0    │         │       │\n",
       "│ 4 │ x4   │  2.07e3   │  0.21e3   │            │            │    0    │         │       │\n",
       "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌────┬───────────────────────────────────────────────────┐\n",
       "│    │        x0        x1        x2        x3        x4 │\n",
       "├────┼───────────────────────────────────────────────────┤\n",
       "│ x0 │   8.3e+03  1.06e+04  -2.7e+04  2.81e+03       558 │\n",
       "│ x1 │  1.06e+04  3.16e+05 -3.97e+05  1.63e+05 -2.66e+04 │\n",
       "│ x2 │  -2.7e+04 -3.97e+05  8.82e+05 -4.33e+05  7.95e+04 │\n",
       "│ x3 │  2.81e+03  1.63e+05 -4.33e+05  3.68e+05 -9.17e+04 │\n",
       "│ x4 │       558 -2.66e+04  7.95e+04 -9.17e+04  4.48e+04 │\n",
       "└────┴───────────────────────────────────────────────────┘"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m3 = Minuit(ExtendedBinnedNLL(n, xe, model2), (500, 1000, 1000, 1000, 1000))\n",
    "m3.limits = (0, None)\n",
    "m3.migrad()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1321b15e0>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_hist(xe, n)\n",
    "plot_hist(xe, np.diff(model2(xe, m3.values)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 49.14 </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"No. of function evaluations in last call and total number\"> Nfcn = 456 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 7.25e-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 style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Parameters </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> x0 </td>\n",
       "        <td> 4.97e3 </td>\n",
       "        <td> 0.10e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 1 </th>\n",
       "        <td> x1 </td>\n",
       "        <td> 25.2e3 </td>\n",
       "        <td> 0.7e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 2 </th>\n",
       "        <td> x2 </td>\n",
       "        <td> 8.0e3 </td>\n",
       "        <td> 1.5e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 3 </th>\n",
       "        <td> x3 </td>\n",
       "        <td> 8.6e3 </td>\n",
       "        <td> 2.0e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 4 </th>\n",
       "        <td> x4 </td>\n",
       "        <td> 2.1e3 </td>\n",
       "        <td> 1.0e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 5 </th>\n",
       "        <td> x5 </td>\n",
       "        <td> 2.38e3 </td>\n",
       "        <td> 0.29e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th> x0 </th>\n",
       "        <th> x1 </th>\n",
       "        <th> x2 </th>\n",
       "        <th> x3 </th>\n",
       "        <th> x4 </th>\n",
       "        <th> x5 </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x0 </th>\n",
       "        <td> 9.6e+03 </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -4.21e+03 <strong>(-0.061)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,216,216);color:black\"> 3.4e+04 <strong>(0.224)</strong> </td>\n",
       "        <td style=\"background-color:rgb(194,194,250);color:black\"> -8.4e+04 <strong>(-0.428)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,196,196);color:black\"> 3.7e+04 <strong>(0.359)</strong> </td>\n",
       "        <td style=\"background-color:rgb(222,222,250);color:black\"> -5.97e+03 <strong>(-0.213)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x1 </th>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -4.21e+03 <strong>(-0.061)</strong> </td>\n",
       "        <td> 4.94e+05 </td>\n",
       "        <td style=\"background-color:rgb(153,153,250);color:black\"> -8.14e+05 <strong>(-0.748)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,175,175);color:black\"> 7e+05 <strong>(0.497)</strong> </td>\n",
       "        <td style=\"background-color:rgb(201,201,250);color:black\"> -2.8e+05 <strong>(-0.378)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,215,215);color:black\"> 4.65e+04 <strong>(0.231)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x2 </th>\n",
       "        <td style=\"background-color:rgb(250,216,216);color:black\"> 3.4e+04 <strong>(0.224)</strong> </td>\n",
       "        <td style=\"background-color:rgb(153,153,250);color:black\"> -8.14e+05 <strong>(-0.748)</strong> </td>\n",
       "        <td> 2.39e+06 </td>\n",
       "        <td style=\"background-color:rgb(138,138,250);color:black\"> -2.67e+06 <strong>(-0.863)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,143,143);color:black\"> 1.17e+06 <strong>(0.717)</strong> </td>\n",
       "        <td style=\"background-color:rgb(191,191,250);color:black\"> -2.02e+05 <strong>(-0.457)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x3 </th>\n",
       "        <td style=\"background-color:rgb(194,194,250);color:black\"> -8.4e+04 <strong>(-0.428)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,175,175);color:black\"> 7e+05 <strong>(0.497)</strong> </td>\n",
       "        <td style=\"background-color:rgb(138,138,250);color:black\"> -2.67e+06 <strong>(-0.863)</strong> </td>\n",
       "        <td> 4.01e+06 </td>\n",
       "        <td style=\"background-color:rgb(131,131,250);color:black\"> -1.93e+06 <strong>(-0.916)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,157,157);color:black\"> 3.54e+05 <strong>(0.618)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x4 </th>\n",
       "        <td style=\"background-color:rgb(250,196,196);color:black\"> 3.7e+04 <strong>(0.359)</strong> </td>\n",
       "        <td style=\"background-color:rgb(201,201,250);color:black\"> -2.8e+05 <strong>(-0.378)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,143,143);color:black\"> 1.17e+06 <strong>(0.717)</strong> </td>\n",
       "        <td style=\"background-color:rgb(131,131,250);color:black\"> -1.93e+06 <strong>(-0.916)</strong> </td>\n",
       "        <td> 1.11e+06 </td>\n",
       "        <td style=\"background-color:rgb(147,147,250);color:black\"> -2.39e+05 <strong>(-0.793)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> x5 </th>\n",
       "        <td style=\"background-color:rgb(222,222,250);color:black\"> -5.97e+03 <strong>(-0.213)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,215,215);color:black\"> 4.65e+04 <strong>(0.231)</strong> </td>\n",
       "        <td style=\"background-color:rgb(191,191,250);color:black\"> -2.02e+05 <strong>(-0.457)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,157,157);color:black\"> 3.54e+05 <strong>(0.618)</strong> </td>\n",
       "        <td style=\"background-color:rgb(147,147,250);color:black\"> -2.39e+05 <strong>(-0.793)</strong> </td>\n",
       "        <td> 8.19e+04 </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌──────────────────────────────────┬──────────────────────────────────────┐\n",
       "│ FCN = 49.14                      │              Nfcn = 456              │\n",
       "│ EDM = 7.25e-05 (Goal: 0.0002)    │                                      │\n",
       "├───────────────┬──────────────────┼──────────────────────────────────────┤\n",
       "│ Valid Minimum │ Valid Parameters │        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 │ x0   │  4.97e3   │  0.10e3   │            │            │    0    │         │       │\n",
       "│ 1 │ x1   │  25.2e3   │   0.7e3   │            │            │    0    │         │       │\n",
       "│ 2 │ x2   │   8.0e3   │   1.5e3   │            │            │    0    │         │       │\n",
       "│ 3 │ x3   │   8.6e3   │   2.0e3   │            │            │    0    │         │       │\n",
       "│ 4 │ x4   │   2.1e3   │   1.0e3   │            │            │    0    │         │       │\n",
       "│ 5 │ x5   │  2.38e3   │  0.29e3   │            │            │    0    │         │       │\n",
       "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌────┬─────────────────────────────────────────────────────────────┐\n",
       "│    │        x0        x1        x2        x3        x4        x5 │\n",
       "├────┼─────────────────────────────────────────────────────────────┤\n",
       "│ x0 │   9.6e+03 -4.21e+03   3.4e+04  -8.4e+04   3.7e+04 -5.97e+03 │\n",
       "│ x1 │ -4.21e+03  4.94e+05 -8.14e+05     7e+05  -2.8e+05  4.65e+04 │\n",
       "│ x2 │   3.4e+04 -8.14e+05  2.39e+06 -2.67e+06  1.17e+06 -2.02e+05 │\n",
       "│ x3 │  -8.4e+04     7e+05 -2.67e+06  4.01e+06 -1.93e+06  3.54e+05 │\n",
       "│ x4 │   3.7e+04  -2.8e+05  1.17e+06 -1.93e+06  1.11e+06 -2.39e+05 │\n",
       "│ x5 │ -5.97e+03  4.65e+04 -2.02e+05  3.54e+05 -2.39e+05  8.19e+04 │\n",
       "└────┴─────────────────────────────────────────────────────────────┘"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m4 = Minuit(ExtendedBinnedNLL(n, xe, model2), (500, 1000, 1000, 1000, 1000, 1000))\n",
    "m4.limits = (0, None)\n",
    "m4.migrad()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x132b2c490>]"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_hist(xe, n)\n",
    "plot_hist(xe, np.diff(model2(xe, m4.values)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x132c0bf70>"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sig1, fcn1, _ = m1.mnprofile(\"a\")\n",
    "sig2, fcn2, _ = m2.mnprofile(\"x0\")\n",
    "sig3, fcn3, _ = m3.mnprofile(\"x0\")\n",
    "sig4, fcn4, _ = m4.mnprofile(\"x0\")\n",
    "plt.plot(sig1, fcn1, label=\"model1\")\n",
    "plt.plot(sig2, fcn2, label=\"model2(2)\")\n",
    "plt.plot(sig3, fcn3, label=\"model2(3)\")\n",
    "plt.plot(sig4, fcn4, label=\"model2(4)\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "sig, fcn1, ok = m1.mnprofile(\"a\", size=50, bound=(4500, 5500))\n",
    "assert np.all(ok)\n",
    "_, fcn2, ok = m2.mnprofile(\"x0\", size=50, bound=(4500, 5500))\n",
    "assert np.all(ok)\n",
    "_, fcn3, ok = m3.mnprofile(\"x0\", size=50, bound=(4500, 5500))\n",
    "assert np.all(ok)\n",
    "_, fcn4, ok = m4.mnprofile(\"x0\", size=50, bound=(4500, 5500))\n",
    "assert np.all(ok)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "def akaike(npar, n):\n",
    "    return 2 * npar / (1 - (npar + 1) / n)\n",
    "\n",
    "def simple(npar, n):\n",
    "    return npar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "fcn_min = np.inf\n",
    "for fcn, npar in ((fcn1, m1.nfit), (fcn2, m2.nfit), (fcn3, m3.nfit), (fcn4, m4.nfit)):\n",
    "    fcn_min = np.minimum(fcn_min, fcn + akaike(npar, len(n)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1331c2a00>"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sig, fcn1-offset, label=\"model1\")\n",
    "plt.plot(sig, fcn2-offset, label=\"model2(2)\")\n",
    "plt.plot(sig, fcn3-offset, label=\"model2(3)\")\n",
    "plt.plot(sig, fcn4-offset, label=\"model2(4)\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 20.0)"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "offset = np.min(fcn_min)\n",
    "\n",
    "plt.plot(sig, fcn1-offset+simple(m1.nfit, len(n)), label=\"model1\")\n",
    "plt.plot(sig, fcn2-offset+simple(m2.nfit, len(n)), label=\"model2(2)\")\n",
    "plt.plot(sig, fcn3-offset+simple(m3.nfit, len(n)), label=\"model2(3)\")\n",
    "plt.plot(sig, fcn4-offset+simple(m4.nfit, len(n)), label=\"model2(4)\")\n",
    "plt.plot(sig, fcn_min-offset, color=\"k\", label=\"min\")\n",
    "plt.legend()\n",
    "plt.ylim(0, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.8.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}