doc/example/prior_definition.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Prior definition\n",
    "\n",
    "In this notebook we demonstrate how to include prior knowledge into a parameter inference problem, in particular how to define (log-)priors for parameters. If you want to maximize your posterior distribution, you need to define\n",
    "\n",
    "* A (negative log-)likelihood\n",
    "* A (log-)prior\n",
    "\n",
    "The posterior is then built as an `AggregatedObjective`. If you import a problem via `PEtab` and the priors are contained in the parameter table, the definition of priors is done automatically.\n",
    "\n",
    "**CAUTION**: The user needs to specify the **negative** _log-likelihood_, while the _log-prior_ is internally mulitplied by -1."
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext",
    "tags": []
   },
   "source": [
    "In this notebook:\n",
    "* :class:`pypesto.objective.AggregatedObjective <pypesto.objective.AggregatedObjective>`\n",
    "* :func:`pypesto.objective.get_parameter_prior_dict <pypesto.objective.get_parameter_prior_dict>`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# install if not done yet\n",
    "# %pip install pypesto --quiet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "\n",
    "import pypesto"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Rosenbrock Banana\n",
    "\n",
    "We will use the Rosenbrock Banana\n",
    "\n",
    "\\begin{align}\n",
    "f(x, \\theta) = \\sum_{i=1}^{N} \\underbrace{100 \\cdot(x_{i}-x_{i-1}^2)^2}_{\\text{\"negative log-likelihood\"}} + \\underbrace{(x_{i-1}-1)^2}_{\\text{\"Gaussian log-prior\"}}\n",
    "\\end{align}\n",
    "\n",
    "as an example. Here we interpret the first term as the _negative log-likelihood_ and the second term as Gaussian _log-prior_ with mean $1$ and standard deviation $1/\\sqrt{2}$. \n",
    "\n",
    "Note that the second term is only equivalent to the negative log-distribution of a Gaussian up to a constant."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the negative log-likelihood"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_x = 5\n",
    "\n",
    "\n",
    "def rosenbrock_part_1(x):\n",
    "    \"\"\"\n",
    "    Calculate obj. fct + gradient of the \"likelihood\" part.\n",
    "    \"\"\"\n",
    "    obj = sum(100.0 * (x[1:] - x[:-1] ** 2.0) ** 2.0)\n",
    "\n",
    "    grad = np.zeros_like(x)\n",
    "    grad[:-1] += -400 * (x[1:] - x[:-1] ** 2.0) * x[:-1]\n",
    "    grad[1:] += 200 * (x[1:] - x[:-1] ** 2.0)\n",
    "\n",
    "    return (obj, grad)\n",
    "\n",
    "\n",
    "neg_log_likelihood = pypesto.Objective(fun=rosenbrock_part_1, grad=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the log-prior\n",
    "\n",
    "A prior on an individual parameter is defined in a `prior_dict`, which contains the following key-value pairs:\n",
    "\n",
    "* `index`: Index of the parameter\n",
    "* `density_fun`: (Log-)posterior. (Scalar function!)\n",
    "* `density_dx`: d/dx (Log-)posterior (optional)\n",
    "* `density_ddx`: d^2/dx^2 (Log-)posterior (optional)\n",
    "\n",
    "A `prior_dict` can be either obtained by `get_parameter_prior_dict` for several common priors, or defined by the user."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pypesto.objective.priors import get_parameter_prior_dict\n",
    "\n",
    "# create a list of prior dicts...\n",
    "prior_list = []\n",
    "mean = 1\n",
    "std_dev = 1 / np.sqrt(2)\n",
    "\n",
    "for i in range(n_x - 1):\n",
    "    prior_list.append(get_parameter_prior_dict(i, \"normal\", [mean, std_dev]))\n",
    "\n",
    "# create the prior\n",
    "neg_log_prior = pypesto.objective.NegLogParameterPriors(prior_list)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the negative log-posterior and the problem\n",
    "\n",
    "The negative log-posterior is defined as an `AggregatedObjective`. Since optimization/visualization is not the main focus of this notebook, the reader is referred to other examples for a more in-depth presentation of these."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "neg_log_posterior = pypesto.objective.AggregatedObjective(\n",
    "    [neg_log_likelihood, neg_log_prior]\n",
    ")\n",
    "\n",
    "lb = -5 * np.ones((n_x, 1))\n",
    "ub = 5 * np.ones((n_x, 1))\n",
    "\n",
    "problem = pypesto.Problem(\n",
    "    objective=neg_log_posterior,\n",
    "    lb=lb,\n",
    "    ub=ub,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Optimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|█████████████████████████████████████████████████████████████████| 10/10 [00:00<00:00, 41.26it/s]\n"
     ]
    }
   ],
   "source": [
    "import pypesto.optimize as optimize\n",
    "\n",
    "result = optimize.minimize(problem=problem, n_starts=10, filename=None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Some basic visualizations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABDcAAADFCAYAAABAWBnWAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8/fFQqAAAACXBIWXMAAAsTAAALEwEAmpwYAAAeUklEQVR4nO3de5RkZX3u8e8zowQUUAPE0A2ZMSGKqJHk9KBiVKJ4vyUrRpJwkeScGDUqqNGI0UMLSLxfokHNCQZxUEGNBlQioodRwAuDGYminijOOM4YHbxEBEWE3/mjdo/dzcx0Nfbu3bX7+1mrlrveemvvp8parH5/877vTlUhSZIkSZI0qlZ0HUCSJEmSJOkXYXFDkiRJkiSNNIsbkiRJkiRppFnckCRJkiRJI83ihiRJkiRJGmkWNyRJkiRJ0kizuCFJ0jKQ5EFJvtJ1jh1JckSSb3adQ5IkjS6LG5IkLWFJNib5cZIfTXu8aYj3VZKDpp5X1Ser6h4tZTwryWltnHuUWbSRJGnx3K7rAJIkaU6Pr6qLuw4x6pLcrqp+1nWOYY1aXkmSuuTMDUmSRlSSg5KsS/LfSa5Ncm7T/ommy+ebmR5HzZ5F0MwIeX6Sq5Jcn+TMJHdNcmGS65JcnOQu0/q/J8l/Ndf6RJJ7Ne1PBY4GXtBc64KmfSzJ+5JsS/L1JM+edq49mtke309yNbBmjs9ZSZ6d5Jrmc74qyYrmtd9I8vEk321eOyfJnWd9zr9JchVwfZLbJXlhkq81n/PqJH8wrf/xSS5L8rokP2iueXjTvjnJd5I8ZVr/X0ry6iTfSPLtJG9pPt8dgQuBsWkzbsaSrJh2/e8mOS/JLzfnWt181v+Z5BvAx5PsnmRt0/cHSa5Ictd5/VAkSVoGLG5IkjS6TgUuAu4CHAC8EaCqHty8ft+q2rOqzt3J+/8QeDhwd+DxDAbjLwL2Y/A3wrOn9b0Q+E3gV4DPAec01/rH5viVzbUe3xQeLgA+D4wDDwNOTPLI5lwnA7/RPB4JPIW5/QEwAfwO8ETgz5v2AH8HjAH3BA4EJme990+AxwJ3bmZCfA14EHAn4KXA2iT7T+t/P+AqYB/gncC7GRRgDgKOAd6UZM+m78ub7+/Q5vVx4H9X1fXAo4GtzfeyZ1VtBZ4F/D7wkCbz94F/mJX3Ic1nmfpu7tR8rn2ApwE/HuL7kiRpWbG4IUnS0veB5l/tpx5/0bTfBKwCxqrqJ1V16TzP+8aq+nZVbQE+CXymqv69qn4CvB/47amOVfW2qrquqm5kUDy4b5I77eS8a4D9quqUqvppVV0D/B/gj5vXnwy8rKq+V1Wbgb8fIusrmv7fAF7PoGBBVX21qj5aVTdW1TbgtQyKA9P9fVVtrqofN+95T1VtrapbmsLPfwKHTev/9ar656q6GTiXQWHhlOYaFwE/BQ5KEuCpwHOabNcBp0/7nDvyNOBvq+qb077LJyWZvlR4sqqub/LexKCocVBV3VxVV1bVD4f4viRJWlbcc0OSpKXv93ey58YLGMze+GyS7wOvqaq3zeO83552/OMdPN8TIMlK4GXAHzGY1XFL02df4L93cN5VDJZj/GBa20oGBRQYzFjYPO21TUNknd1/rMl2V+ANDGZi7MXgH26+v4v3kuQ44LnA6qZpz+azTJn9PVBVO/pu9gPuAFw5qHMMTs/gs+7MKuD9SW6Z1nYzMH2pyfS872BQXHl3s9xmLYPiyE27uIYkScuOMzckSRpRVfVfVfUXVTUG/CVwxvQ7pCygP2WwFORIBkskVjftUyP6mtV/M4PZD3ee9tirqh7TvP4tBgP2Kb82RIbZ/bc2x6c3179PVe3NYNlIZr13e74kqxjMInkmsE9V3Rn4wg7eM4xrGRQ67jXtc96pqqaWrMz+XmDw3Tx61nezezN75lZ5q+qmqnppVR0CHA48DjjuNmSVJKnXLG5IkjSikvxRkgOap99nMCiemhHwbeDXF+hSewE3At9lMFPh9Fmvz77WZ4Hrmo0890iyMsm9k0xtHHoecFKSuzT5nzVEhuc3/Q8ETmCwXGQq24+A/04yDjx/jvPckcH3tA0gyZ8B9x7i+rdSVbcwKJS8LsmvNOcbn7a3yLeBfWYt33kL8LKmyEKS/ZI8cWfXSPJ7Se7TzJ75IYNlKrfsrL8kScuVxQ1Jkpa+C6bdceNHSd7ftK8BPpPkR8D5wAnN/hYw2Mvh7c0eHU/+Ba9/NoOlIFuAq4FPz3r9TOCQ5lofaPaqeByDTTa/zmCGwz8xmPUBg008NzWvXcRg6cVc/hW4EtgAfKi55tS5fofB8pgPAf+yq5NU1dXAa4BPMSg+3Ae4bIjr78zfAF8FPp3kh8DFwD2aa30ZeBdwTfPdjDFYQnM+cFGS6xh8l/fbxfl/FXgvg8LGl4B1DPd9SZK0rKRqRzMmJUmSloYkBfxmVX216yySJGlpcuaGJEmSJEkaaRY3JEmSJEnSSHNZiiRJkiRJGmnO3JAkSZIkSSPN4oYkSZIkSRppt+s6wFz23XffWr16ddcxJEmSJElSx6688sprq2q/2e1LvrixevVq1q9f33UMSZIkSZLUsSSbdtS+6MtSkjwlyX82j6cs9vUlSZIkSVK/LGpxI8kvAycD9wMOA05OcpfFzLCYJicnu44gSZI0f+PjkPz8MT7edSJJ0gLq41i1tVvBJlkDnMmgiLES+CzwbuCAqvrLps9bgUuq6l07O8/ExESN6rKUJHirXUmSNFLGx2Hr1lu3j43Bli2Ln0eStOBGeaya5Mqqmpjd3tqeG1V1RZLzgdOAPYC1wE3A5mndvgn4TwGSJElLxY4KG7tqlyRpCWh7WcopwMOBCeCVw74pyVOTrE+yftu2ba2Fa8Pk5CRJSAKw/biP034kSZIkSaOh72PV1palACTZH7gUuBFYAzwBOGI5LEs54ogjWLdu3chO9ZEkSctU80fvDvl3jSSNvFEfq+5sWUrbMzfeCrwEOAd4BfAR4BFJ7tJsJPqIpk2SJElLwdjY/NolSVoCWttzI8lxwE1V9c4kK4HLgUOBU4Ermm6nVNX32srQtVWrVnUdQZIkaX62bLn1pqJuJipJvdLHsWqbG4qeDZzdHN/M4PavU97W1nWXktWrV3cdQZIkaf62bIEVKwbLUNauhaOP7jqRJGkB9XGs2lpxY7l78pOf3HUESZIkSZJm6OtY1eJGS57xjGd0HUGSJEmSpBn6OlZte0PRZeuGG27ghhtu6DqGJEmSJEnb9XWs6syNljzmMY8B4JJLLuk2iCRJkiRJjb6OVZ25IUmSJEmSRprFDUmSJEmSNNIsbkiSJEmSpJFmcUOSJEmSJI00NxRtyfHHH991BEmSJEmSZujrWNXiRkv6+oORJEmSJI2uvo5VXZbSkmuvvZZrr7226xiSJEmSJG3X17GqMzda8qQnPQno372DJUmSJEmjq69jVWduSJIkSZKkkWZxQ5IkSZIkjTSLG5IkSZIkaaRZ3JAkSZIkSSPNDUVb8vSnP73rCJIkSZIkzdDXsarFjZYcddRRXUeQJEmSJGmGvo5VXZbSks2bN7N58+auY0iSJEmStF1fx6rO3GjJscceC/Tv3sGSJEmSpNHV17GqMzckSZIkSdJIs7ghSZIkSZJG2qIWN5L8W5IfJPngYl5XkiRJkiT112LP3HgVcOwiX7MzGzdu7DqCJEnS/I2PQ9Xg+JhjBs8lSb3Rx7FqK8WNJGuSXJVk9yR3TPLFJPeuqo8B17VxzaXmec97Hps2beo6hiRJ0vyMj8PWrTPbtm61wCFJPdHXsWord0upqiuSnA+cBuwBrK2qL7RxraXq8Y9/fNcRJEmS5m92YWOudknSSOnrWLXNZSmnAA8HJoBXzueNSZ6aZH2S9du2bWslXFsmJydJQhKA7ceTk5PdBpMkSZIkLVt9H6umptZTLvSJk/2BS4EbgTVVdX3TfgTw11X1uGHOMzExUevXr28lY5uOOOII1q1bR1vfryRJUiuaP3p3yL9rJGnkjfpYNcmVVTUxu73NmRtvBV4CnAO8osXrSJIkaaGMjc2vXZKkJaCtDUWPA26qqncCLwfWJHlokk8C7wEeluSbSR7ZxvWXilWrVnUdQZIkaX62bLl1IWNsbNAuSeqFPo5V29pQ9Gzg7Ob4ZuB+zUsfb+N6S9Xq1au7jiBJkjR/W7bAihWDZShr18LRR3edSJK0gPo4Vm1zWYokSZIkSVLrWpm5IXjxi1/cdQRJkiRJkmbo61h1zuJGkpXA2VXlfMR5OPLII7uOIEmSJEnSDH0dq865LKXZM2NVkt0WIU9vbNiwgQ0bNnQdQ5IkSZKk7fo6Vh12Wco1wGVJzgeun2qsqte2kqoHTjzxRAAuueSSTnNIkiRJkjSlr2PVYYsbX2seK4C92osjSZIkSZI0P0MVN6rqpQBJ7lBVN7QbSZIkSZIkaXhD3Qo2yQOSXA18uXl+3yRntJpMkiRJkiRpCEMVN4DXA48EvgtQVZ8HHtxSJkmSJEmSpKENu+cGVbU5yfSmmxc+Tn+cfvrpXUeQJEmSJGmGvo5Vhy1ubE5yOFBJbg+cAHypvVij7/DDD+86giRJkiRJM/R1rDrsspSnAX8FjANbgEOBZ7SUqRcuv/xyLr/88q5jSJIkSZK0XV/HqsPO3LhHVR09vSHJA4HLFj5SP7zoRS8C+nfvYEmSJEnS6OrrWHXYmRtvHLJNkiRJkiRpUe1y5kaSBwCHA/slee60l/YGVrYZTJIkSZIkaRhzLUvZDdiz6bfXtPYfAk9qK5QkSZIkSdKwdlncqKp1wLokZ1XVpiR3qKobFimbJEmSJEnSnIbdUHQsyYUMZnH8WpL7An9ZVd4xZSde//rXdx1BkiRJkqQZ+jpWHba48XrgkcD5AFX1+SQPbitUHxx66KFdR5AkSZIkaYa+jlWHvVsKVbV5VtPNC5ylVy6++GIuvvjirmNIkiRJkrRdX8eqw87c2JzkcKCS3B44AfhSe7FG32mnnQbAkUce2XESSZIkSZIG+jpWHXbmxtOAvwLGgS3Aoc1zSZIkSZKkTg01c6OqrgWO/kUulORQ4M3A3gyWtLysqs79Rc4pSZIkSZI0VHEjyd2AZwGrp7+nqp4wj2vdABxXVf+ZZAy4MslHquoH8zjHSNm4cWPXESRJkuZvfByqBsfHHAMveAFs2dJtJknSgunjWHXYPTc+AJwJXADcMlfnJGua/ocBK4HPAkdV1RcAqmprku8A+wE/mHfqEbFp06auI0iSJM3P+Dhs3TqzbevWQbsFDknqhT6OVVNTVflddUo+U1X3m9eJk9OA3YE9gG9W1d9Ne+0w4O3Avapql8WSiYmJWr9+/XwuvSR85Stf4eCDD2aY71eSJGnJSHb+mn/XSNLIG/WxapIrq2pidvuwG4q+IcnJSR6Q5HemHnO85xTg4cAE8MppQfYH3gH82c4KG0memmR9kvXbtm0bMuLSMDk5SRIOPvhgAJKQhMnJyW6DSZIkSZKWrb6PVYedufF3wLHA1/j5spSqqofu4j37A5cCNwJrqur6JHsDlwCnV9V7hwk4qjM3LrjgAp7whCeMbDVMkiQtU87ckKReG/Wx6s5mbgy758YfAb9eVT+dxzXfCrwEuBvwiiTPBd4PnD1sYWOUveY1r+k6giRJ0vyNjd16z42pdknSyOvrWHXY4sYXgDsD3xmmc5LjgJuq6p1JVgKXA38MPBjYJ8nxTdfjq2rDfAKPklWrVnUdQZIkaX62bLn1pqJjY24mKkk90sex6rDFjTsDX05yBYNlJsDObwVbVWcDZzfHNwNTm5GefZuTjqDVq1d3HUGSJGn+tmyBFSsGy1DWroWjj+46kSRpAfVxrDpscePkVlNIkiRJkiTdRkMVN6pqXdtBJEmSJEmSbouhihtJ7g+8EbgnsBuwEri+qvZuMdtIe8c73tF1BEmSJEmSZujrWHXYZSlvYrAh6HuACeA44O5theqDAw88sOsIkiRJkiTN0Nex6ophO1bVV4GVVXVzVf0z8Kj2Yo2+c889l3PPPbfrGJIkSZIkbdfXseqwMzduSLIbsCHJK4FvMY/CyHL05je/GYCjjjqq4ySSJEmSJA30daw6bIHi2KbvM4HrgQOBP2wrlCRJkiRJ0rDmnLmRZCVwelUdDfwEeGnrqSRJkiRJkoY058yNqroZWNUsS5EkSZIkSVpSht1z4xrgsiTnM1iWAkBVvbaVVJIkSZIkSUMatrjxteaxAtirvTj98d73vrfrCJIkSZIkzdDXsepQxY2qcp+Nedp33327jiBJkiRJ0gx9HasOVdxIsh/wAuBewO5T7VX10JZyjbyzzjoLgOOPP77THJIkSZIkTenrWHXYW8GeA3wZuBuDu6VsBK5oKVMvnHXWWdt/NJIkSZIkLQV9HasOW9zYp6rOBG6qqnVV9eeAszYkSZIkSVLnht1Q9Kbmf7+V5LHAVuCX24kkSZIkSZI0vGGLG6cluRPwPOCNwN7Ac1pLJUmSJEmSNKRdFjeS7A48DTgIGAfOrKrfW4xgkiRJkiRJw5hr5sbbGSxJ+STwaOAQ4IS2Q/XBhz/84a4jSJIkSZI0Q1/HqnMVNw6pqvsAJDkT+Gz7kfrhDne4Q9cRJEmSJEmaoa9j1bnuljK1kShV9bOWs/TKGWecwRlnnNF1DEmSJEmStuvrWHWu4sZ9k/yweVwH/NbUcZIfLkbAUXXeeedx3nnndR1DkiRJkqTt+jpW3eWylKpauZAXS7IKeD+DosrtgTdW1VsW8hqSJEmSJGl5mWvmxkL7FvCAqjoUuB/wwiRji5xh0WzcuLHrCJIkSfM3Pg5Vg+Njjhk8lyT1Rh/Hqq0VN5KsSXJVkt2T3DHJF4G7V9WNTZdfavP6S8GmTZu6jiBJkjQ/4+OwdevMtq1bLXBIUo/0caw6191SbrOquiLJ+cBpwB7A2qr6QpIDgQ8BBwHPr6qtuzqPJEmSFtHswsZc7ZIkLQFtz5w4BXg4MAG8EqCqNlfVbzEobjwlyV1nvynJU5OsT7J+27ZtLUdcWJOTkyRh3bp1ACQhCZOTk90GkyRJkiQtW30fq6am1lO2cfJkf+BS4EZgTVVdP+v1twEfrqr37uwcExMTtX79+tYytikJbX6/kiRJCy7Z+Wv+XSNJvTDKY9UkV1bVxOz2tmduvBV4CXAO8IokByTZowl0F+B3ga+0nKETr371q7uOIEmSNH9jO9nrfWftkqSR0texamt7biQ5Dripqt6ZZCVwOXAv4FVJCgjw6qr6j7YydOmDH/wgq1at6jqGJEnS/GzZcutNRcfGBu2SpJHX17FqmxuKng2c3RzfzODWrwAfaeuaS83q1au7jiBJkjR/W7bAihWDZShr18LRR3edSJK0gPo4Vu31rVglSZIkSVL/WdyQJEmSJEkjrbVlKcvdHnvs0XUESZIkSZJm6OtY1eJGSy688MKuI0iSJEmSNENfx6ouS5EkSZIkSSPN4kZLTj31VE499dSuY0iSJEmStF1fx6oWN1rysY99jI997GNdx5AkSZIkabu+jlUtbkiSJEmSpJFmcUOSJEmSJI00ixuSJEmSJGmkeSvYluyzzz5dR5AkSZIkaYa+jlUtbrTkfe97X9cRJEmSJEmaoa9jVZelSJIkSZKkkWZxoyUnnXQSJ510UtcxJEmSJEnarq9jVZeltORTn/pU1xEkSZIkSZqhr2NVZ25IkiRJkqSRZnFDkiRJkiSNNIsbkiRJkiRppLnnRksOOOCAriNIkiRJkjRDX8eqFjdasnbt2q4jSJIkSZI0Q1/Hqi5LkSRJkiRJI83iRktOPPFETjzxxK5jSJIkSZK0XV/Hqp0sS0myN3A18IGqemYXGdq2YcOGriNIkiRJkjRDX8eqXc3cOBX4REfXXjQbN27sOoIkSdL8jY9D1eD4mGMGzyVJvdHHsWprxY0ka5JclWT3JHdM8sUk907yP4C7Ahe1de2lYtOmTV1HkCRJmp/xcdi6dWbb1q0WOCSpR/o4Vm1tWUpVXZHkfOA0YA9gLYOlKB8HjgGObOvakiRJuo1mFzbmapckaQloe1nKKcDDgQnglcAzgA9X1Td39aYkT02yPsn6bdu2tRxxYU1OTpKEdevWAZCEJExOTnYbTJIkSZK0bPV9rJqaWk/ZxsmT/YFLgRuBNcA/Ag8CbgH2BHYDzqiqF+7sHBMTE7V+/frWMrYpCW1+v5IkSQsu2flr/l0jSb0wymPVJFdW1cTs9rbvlvJW4CXA3YBXVNXR0wIdD0zsqrAhSZKkRTY2tuMlKGNji59FkqQhtbmh6HHATVX1TuDlwJokD23rekvRySef3HUESZKk+dmy5daFjLGxQbskqRf6OFZtdVnKQhjlZSmSJEmSJGnh7GxZStsbikqSJEmSJLVqyc/cSLIN6N9NeNWmfYFruw4hLRJ/71pO/L1rufC3ruXE37vma1VV7Te7cckXN6T5SrJ+R9OUpD7y967lxN+7lgt/61pO/L1robgsRZIkSZIkjTSLG5IkSZIkaaRZ3FAf/WPXAaRF5O9dy4m/dy0X/ta1nPh714Jwzw1JkiRJkjTSnLkhSZIkSZJGmsUN9VqS5yWpJPt2nUVqS5JXJflykquSvD/JnbvOJC2kJI9K8pUkX03ywq7zSG1JcmCS/5vk6iRfTHJC15mkNiVZmeTfk3yw6ywafRY31FtJDgQeAXyj6yxSyz4K3Luqfgv4f8BJHeeRFkySlcA/AI8GDgH+JMkh3aaSWvMz4HlVdQhwf+Cv/L2r504AvtR1CPWDxQ312euAFwBuLKNeq6qLqupnzdNPAwd0mUdaYIcBX62qa6rqp8C7gSd2nElqRVV9q6o+1xxfx2DQN95tKqkdSQ4AHgv8U9dZ1A8WN9RLSZ4IbKmqz3edRVpkfw5c2HUIaQGNA5unPf8mDva0DCRZDfw28JmOo0hteT2Df4i8peMc6onbdR1Auq2SXAz86g5e+lvgRQyWpEi9sKvfe1X9a9PnbxlMaT5nMbNJkhZWkj2B9wEnVtUPu84jLbQkjwO+U1VXJjmi4zjqCYsbGllVdeSO2pPcB7gb8PkkMJii/7kkh1XVfy1iRGnB7Oz3PiXJ8cDjgIeV9/hWv2wBDpz2/ICmTeqlJLdnUNg4p6r+pes8UkseCDwhyWOA3YG9k6ytqmM6zqURFv8GVt8l2QhMVNW1XWeR2pDkUcBrgYdU1bau80gLKcntGGyU+zAGRY0rgD+tqi92GkxqQQb/KvN24HtVdWLHcaRF0czc+OuqelzHUTTi3HNDkkbfm4C9gI8m2ZDkLV0HkhZKs1nuM4GPMNhc8TwLG+qxBwLHAg9t/nu+ofmXbUnSHJy5IUmSJEmSRpozNyRJkiRJ0kizuCFJkiRJkkaaxQ1JkiRJkjTSLG5IkiRJkqSRZnFDkiRJkiSNNIsbkiSJJDc3t538QpL3JLnDEsh0RJLDF/maq5N8YTGvKUmSfnEWNyRJEsCPq+rQqro38FPgacO8KcntWsx0BDCv4kbLeSRJ0hJlcUOSJM32SeCgJI9P8pkk/57k4iR3BUgymeQdSS4D3tHMdvhkks81j8ObfkckWZfkX5Nck+TlSY5O8tkk/5HkN5p++yV5X5IrmscDk6xmUGB5TjOj5EE76rejPNM/SJJ3J3nstOdnJXnSzjLPeu/xSd407fkHkxzRHD8iyaea974nyZ4L+X+AJEmaH/91Q5IkbdfMfHg08G/ApcD9q6qS/C/gBcDzmq6HAL9bVT9ulrA8vKp+kuQ3gXcBE02/+wL3BL4HXAP8U1UdluQE4FnAicAbgNdV1aVJfg34SFXdM8lbgB9V1aubbO+c3a8594w8sz7SucCTgQ8l2Q14GPB0ILvIPNd3tC/wYuDIqro+yd8AzwVOGeb9kiRp4VnckCRJAHsk2dAcfxI4E7gHcG6S/YHdgK9P63/+tELC7YE3JTkUuBm4+7R+V1TVtwCSfA24qGn/D+D3muMjgUOSTL1n753MhNhVv/N3UNgAuBB4Q5JfAh4FfKIpyNxpF5nncn8GxZTLmiy7AZ+ax/slSdICs7ghSZKg2XNjekOSNwKvrarzm+UYk9Nevn7a8XOAbzOYpbEC+Mm0126cdnzLtOe38PO/Q1YwmCEy/X1MK2IwRL/rZ3cGaGZmXAI8EjgKePcQmaf8jJlLeHefuiTw0ar6kx1dU5IkLT733JAkSTtzJ2BLc/yUOfp9q6puAY4FVs7zOhcxWKICQDObAuA6YK8h+s3lXODPgAcxWG4zbOaNwKFJViQ5EDisaf808MAkBzU57phkPjM/JEnSArO4IUmSdmYSeE+SK4Frd9HvDOApST4PHMxOZlHswrOBiSRXJbman9+p5QLgD6Y2FN1Fv7lcBDwEuLiqfjqPzJcxWIpzNfD3wOcAqmobcDzwriRXMViScvB8PrAkSVpYqaquM0iSJEmSJN1mztyQJEmSJEkjzeKGJEmSJEkaaRY3JEmSJEnSSLO4IUmSJEmSRprFDUmSJEmSNNIsbkiSJEmSpJFmcUOSJEmSJI00ixuSJEmSJGmk/X+3xq30+HJqSQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1332x180 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pypesto.visualize as visualize\n",
    "\n",
    "visualize.waterfall(result, size=(15, 6))\n",
    "\n",
    "# parallel coordinates plot for best 5 fits\n",
    "visualize.parameters(result, start_indices=5);"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}