a sample code of SALib

hello_salib.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from SALib.sample import saltelli\n",
    "from SALib.analyze import sobol\n",
    "from SALib.test_functions import Ishigami\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the model inputs\n",
    "problem = {\n",
    "    'num_vars': 3,\n",
    "    'names': ['x1', 'x2', 'x3'],\n",
    "    'bounds': [[-3.14159265359, 3.14159265359],\n",
    "               [-3.14159265359, 3.14159265359],\n",
    "               [-3.14159265359, 3.14159265359]]\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.76100994, -2.53413626,  0.11658254],\n",
       "       [ 1.11060209, -2.53413626,  0.11658254],\n",
       "       [-1.76100994, -1.38058271,  0.11658254],\n",
       "       ...,\n",
       "       [-0.44293695,  3.02692759,  1.72994683],\n",
       "       [-0.44293695,  0.70831563, -1.71153906],\n",
       "       [-0.44293695,  0.70831563,  1.72994683]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Generate samples\n",
    "param_values = saltelli.sample(problem, 10000)\n",
    "param_values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.29855261,  3.17651742,  5.76778927, ..., -0.72082547,\n",
       "        2.16617707,  2.15009772])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Run model (example)\n",
    "# f(x) = sin(x_1) + a sin^2(x_2) + b x_3^4 sin(x_1)\n",
    "Y = Ishigami.evaluate(param_values)\n",
    "Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'S1': array([ 0.31083647,  0.44241898, -0.00385449]),\n",
       " 'S1_conf': array([0.02116732, 0.01821357, 0.0148666 ]),\n",
       " 'ST': array([0.55862844, 0.44229062, 0.24334783]),\n",
       " 'ST_conf': array([0.03135821, 0.01448201, 0.00748677]),\n",
       " 'S2': array([[            nan,  1.43557004e-03,  2.48483365e-01],\n",
       "        [            nan,             nan, -8.46849668e-05],\n",
       "        [            nan,             nan,             nan]]),\n",
       " 'S2_conf': array([[       nan, 0.02567623, 0.03211867],\n",
       "        [       nan,        nan, 0.02109779],\n",
       "        [       nan,        nan,        nan]])}"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Perform analysis\n",
    "Si = sobol.analyze(problem, Y)\n",
    "Si"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<BarContainer object of 3 artists>"
      ]
     },
     "execution_count": 23,
     "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": [
    "x = np.arange( problem['num_vars'] )\n",
    "plt.xticks(x, problem['names'])\n",
    "plt.ylabel('Si')\n",
    "plt.bar(x, Si['S1'], yerr=Si['S1_conf'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<BarContainer object of 3 artists>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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h5r41yS2ZdnqS7yZ5UVXdXlXf74btAJ6d5KTev5l5oqc1e2jgB8vJgK/ajqLWmgGLqupugO7fyw+BGZ8mnu9rtnDUBcxnVbUtySTw58CzgX+qqm8d5tzPJ3kb8F5gJXBtVf1gaNjbgNuq6tGjWfd81teaJTkf2AicBbzrRHslOkqHWrMkK4BFwD2NufN6zbzFNGJJFgHbgEeA366qx7v2CeB9s92uSHIq8C1ga1W9bajv5cAkcHFVzfgfX09fX2vW9Z8NfAK4oKoe6aH8eWmWNTsd2AKsqaqtB5k7b9fMW0yj90LgFOC5TF+qNiU5f2BT7NKueQnwBPDrSZ41MHYJ8Hng3YZDL476mj2pqr4N/Ax4xdEve16bsWZJngd8AXj/k+Hgmj2VVxAj1l36bgKWAadX1VVd+wSzvBpNshD4GvCHwBpgZ1X9ZZJfBb4M/FlV/csx+BbmnR7WbBlwf7fheVY35lVVNR9+k+gxMbxmwNXAF4F/raqPzjJvfq9ZVfkY0QN4N3Bjd7wA+DrweuArwD7gYWAPcElj7jXAX3fHzwW+A5wN/Anwf8AdA49fG/X3eqI8elqzdzH9hoI7gNuAt4z6+zyRHgdZs3cDPx/6d3Kua/bUh1cQkqQm9yAkSU0GhCSpyYCQJDUZEJKkJgNCktRkQEiSmgwISVLT/wMV2OauQEEJNgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange( problem['num_vars'] )\n",
    "s2 = Si['S2']\n",
    "y = [ s2[0][1], s2[0][2], s2[1][2] ]\n",
    "e = Si['S2_conf']\n",
    "yerr = [ e[0][1], e[0][2], e[1][2] ]\n",
    "plt.xticks(x, ['x1-x2', 'x1-x3', 'x2-x3'])\n",
    "plt.ylabel('Sij')\n",
    "plt.bar(x, y, yerr=yerr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<BarContainer object of 3 artists>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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/3OecffEegSQ1zreGJKlxhkCSGmcIJKlxhkCSGmcIJKlxhkCSGmcIJKlx/wexLpmheMFRVwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange( problem['num_vars'] )\n",
    "plt.xticks(x, problem['names'])\n",
    "plt.ylabel('ST')\n",
    "plt.bar(x, Si['ST'], yerr=Si['ST_conf'])"
   ]
  },
  {
   "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": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}