doc/example/fixed_parameters.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fixed parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook we will show how to use fixed parameters. Therefore,\n",
    "we employ our Rosenbrock example. We define two problems, where for the\n",
    "first problem all parameters are optimized, and for the second we fix some\n",
    "of them to specified values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# install if not done yet\n",
    "# %pip install pypesto --quiet"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "\n",
    "import pypesto\n",
    "import pypesto.optimize as optimize\n",
    "import pypesto.visualize as visualize\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "objective = pypesto.Objective(\n",
    "    fun=sp.optimize.rosen,\n",
    "    grad=sp.optimize.rosen_der,\n",
    "    hess=sp.optimize.rosen_hess,\n",
    ")\n",
    "\n",
    "dim_full = 5\n",
    "lb = -2 * np.ones((dim_full, 1))\n",
    "ub = 2 * np.ones((dim_full, 1))\n",
    "\n",
    "problem1 = pypesto.Problem(objective=objective, lb=lb, ub=ub)\n",
    "\n",
    "x_fixed_indices = [1, 3]\n",
    "x_fixed_vals = [1, 1]\n",
    "problem2 = pypesto.Problem(\n",
    "    objective=objective,\n",
    "    lb=lb,\n",
    "    ub=ub,\n",
    "    x_fixed_indices=x_fixed_indices,\n",
    "    x_fixed_vals=x_fixed_vals,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "optimizer = optimize.ScipyOptimizer()\n",
    "n_starts = 10\n",
    "\n",
    "result1 = optimize.minimize(\n",
    "    problem=problem1, optimizer=optimizer, n_starts=n_starts, filename=None\n",
    ")\n",
    "result2 = optimize.minimize(\n",
    "    problem=problem2, optimizer=optimizer, n_starts=n_starts, filename=None\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7ff3da236a20>"
      ]
     },
     "execution_count": 4,
     "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"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1332x180 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1332x108 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1332x180 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "visualize.waterfall(result1, ax)\n",
    "visualize.waterfall(result2, ax)\n",
    "visualize.parameters(result1)\n",
    "visualize.parameters(result2)\n",
    "visualize.parameters(result2, parameter_indices=\"all\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>fval</th>\n",
       "      <th>x</th>\n",
       "      <th>grad</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.563931e-14</td>\n",
       "      <td>[0.9999999859217336, 0.9999999812160436, 0.999...</td>\n",
       "      <td>[-3.7771869883630873e-06, 3.2004378806360524e-...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.103854e-14</td>\n",
       "      <td>[1.0000000033181213, 1.00000001070042, 1.00000...</td>\n",
       "      <td>[-1.6190347383411735e-06, 5.768553691118231e-0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.430040e-13</td>\n",
       "      <td>[0.9999999979980921, 0.9999999872750013, 0.999...</td>\n",
       "      <td>[3.4844693764909735e-06, 4.6873211372756083e-0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.993261e-12</td>\n",
       "      <td>[1.0000000655628785, 1.0000002137366326, 1.000...</td>\n",
       "      <td>[-3.291322500031286e-05, 6.600823794056182e-07...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.028019e-11</td>\n",
       "      <td>[1.0000002263273202, 0.9999999457510741, 1.000...</td>\n",
       "      <td>[0.00020321414758544783, -0.000184783444508992...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.504857e-10</td>\n",
       "      <td>[1.0000008747306284, 1.000001813929941, 1.0000...</td>\n",
       "      <td>[-2.4037728901340504e-05, -1.168240814877157e-...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3.713657e-10</td>\n",
       "      <td>[1.0000011952242212, 1.000001771893066, 1.0000...</td>\n",
       "      <td>[0.00024981346612303615, 0.0001962351003382311...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>4.012393e-10</td>\n",
       "      <td>[0.9999986079063197, 0.9999988670990364, 0.999...</td>\n",
       "      <td>[-0.000663297051531534, 0.000537723456872972, ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>5.247717e-10</td>\n",
       "      <td>[1.000000368254703, 1.0000009022274876, 0.9999...</td>\n",
       "      <td>[-6.555069341760695e-05, 0.0009407121705420637...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>3.930839e+00</td>\n",
       "      <td>[-0.9620510415103535, 0.9357394330313418, 0.88...</td>\n",
       "      <td>[-1.109923131625834e-06, 5.109232684041842e-06...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           fval                                                  x  \\\n",
       "0  2.563931e-14  [0.9999999859217336, 0.9999999812160436, 0.999...   \n",
       "1  4.103854e-14  [1.0000000033181213, 1.00000001070042, 1.00000...   \n",
       "2  2.430040e-13  [0.9999999979980921, 0.9999999872750013, 0.999...   \n",
       "3  2.993261e-12  [1.0000000655628785, 1.0000002137366326, 1.000...   \n",
       "4  3.028019e-11  [1.0000002263273202, 0.9999999457510741, 1.000...   \n",
       "5  1.504857e-10  [1.0000008747306284, 1.000001813929941, 1.0000...   \n",
       "6  3.713657e-10  [1.0000011952242212, 1.000001771893066, 1.0000...   \n",
       "7  4.012393e-10  [0.9999986079063197, 0.9999988670990364, 0.999...   \n",
       "8  5.247717e-10  [1.000000368254703, 1.0000009022274876, 0.9999...   \n",
       "9  3.930839e+00  [-0.9620510415103535, 0.9357394330313418, 0.88...   \n",
       "\n",
       "                                                grad  \n",
       "0  [-3.7771869883630873e-06, 3.2004378806360524e-...  \n",
       "1  [-1.6190347383411735e-06, 5.768553691118231e-0...  \n",
       "2  [3.4844693764909735e-06, 4.6873211372756083e-0...  \n",
       "3  [-3.291322500031286e-05, 6.600823794056182e-07...  \n",
       "4  [0.00020321414758544783, -0.000184783444508992...  \n",
       "5  [-2.4037728901340504e-05, -1.168240814877157e-...  \n",
       "6  [0.00024981346612303615, 0.0001962351003382311...  \n",
       "7  [-0.000663297051531534, 0.000537723456872972, ...  \n",
       "8  [-6.555069341760695e-05, 0.0009407121705420637...  \n",
       "9  [-1.109923131625834e-06, 5.109232684041842e-06...  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result1.optimize_result.as_dataframe([\"fval\", \"x\", \"grad\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>fval</th>\n",
       "      <th>x</th>\n",
       "      <th>grad</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4.679771e-17</td>\n",
       "      <td>[0.9999999998641961, 1.0, 1.0000000002266116, ...</td>\n",
       "      <td>[-1.0891474676223493e-07, nan, 2.2706484163692...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.825331e-16</td>\n",
       "      <td>[0.9999999995848748, 1.0, 0.9999999991941183, ...</td>\n",
       "      <td>[-3.329303753527845e-07, nan, -8.0749345757971...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.394704e-14</td>\n",
       "      <td>[1.0000000026325193, 1.0, 0.9999999987812758, ...</td>\n",
       "      <td>[2.1112804950914665e-06, nan, -1.2211616799204...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3.989975e+00</td>\n",
       "      <td>[-0.9949747468838975, 1.0, 0.9999999999585671,...</td>\n",
       "      <td>[-4.2116658605095836e-08, nan, -4.151572285811...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.989975e+00</td>\n",
       "      <td>[-0.9949747461383964, 1.0, 0.9999999963588824,...</td>\n",
       "      <td>[5.468066182068299e-07, nan, -3.64839985427999...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>3.989975e+00</td>\n",
       "      <td>[-0.9949747436177196, 1.0, 0.9999999894437084,...</td>\n",
       "      <td>[2.5380648831507813e-06, nan, -1.0577404068293...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3.989975e+00</td>\n",
       "      <td>[-0.9949747458936441, 1.0, 0.99999997533737, 1...</td>\n",
       "      <td>[7.40153570877311e-07, nan, -2.471195460075688...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>3.989975e+00</td>\n",
       "      <td>[-0.9949747793023977, 1.0, 1.000000023888003, ...</td>\n",
       "      <td>[-2.5651750697797127e-05, nan, 2.3935779637870...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>3.989975e+00</td>\n",
       "      <td>[-0.9949748033666262, 1.0, 1.0000000080319777,...</td>\n",
       "      <td>[-4.466176453288284e-05, nan, 8.0480417566767e...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>3.989975e+00</td>\n",
       "      <td>[-0.994974648260114, 1.0, 0.9999999725753793, ...</td>\n",
       "      <td>[7.78676721049365e-05, nan, -2.747946901432181...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           fval                                                  x  \\\n",
       "0  4.679771e-17  [0.9999999998641961, 1.0, 1.0000000002266116, ...   \n",
       "1  4.825331e-16  [0.9999999995848748, 1.0, 0.9999999991941183, ...   \n",
       "2  1.394704e-14  [1.0000000026325193, 1.0, 0.9999999987812758, ...   \n",
       "3  3.989975e+00  [-0.9949747468838975, 1.0, 0.9999999999585671,...   \n",
       "4  3.989975e+00  [-0.9949747461383964, 1.0, 0.9999999963588824,...   \n",
       "5  3.989975e+00  [-0.9949747436177196, 1.0, 0.9999999894437084,...   \n",
       "6  3.989975e+00  [-0.9949747458936441, 1.0, 0.99999997533737, 1...   \n",
       "7  3.989975e+00  [-0.9949747793023977, 1.0, 1.000000023888003, ...   \n",
       "8  3.989975e+00  [-0.9949748033666262, 1.0, 1.0000000080319777,...   \n",
       "9  3.989975e+00  [-0.994974648260114, 1.0, 0.9999999725753793, ...   \n",
       "\n",
       "                                                grad  \n",
       "0  [-1.0891474676223493e-07, nan, 2.2706484163692...  \n",
       "1  [-3.329303753527845e-07, nan, -8.0749345757971...  \n",
       "2  [2.1112804950914665e-06, nan, -1.2211616799204...  \n",
       "3  [-4.2116658605095836e-08, nan, -4.151572285811...  \n",
       "4  [5.468066182068299e-07, nan, -3.64839985427999...  \n",
       "5  [2.5380648831507813e-06, nan, -1.0577404068293...  \n",
       "6  [7.40153570877311e-07, nan, -2.471195460075688...  \n",
       "7  [-2.5651750697797127e-05, nan, 2.3935779637870...  \n",
       "8  [-4.466176453288284e-05, nan, 8.0480417566767e...  \n",
       "9  [7.78676721049365e-05, nan, -2.747946901432181...  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result2.optimize_result.as_dataframe([\"fval\", \"x\", \"grad\"])"
   ]
  }
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