demo.ipynb

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   "source": [
    "# SYNDy Demonstration"
   ]
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  {
   "cell_type": "markdown",
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    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "## Plotting Stuff"
   ]
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    "%matplotlib inline\n",
    "%config InlineBackend.figure_formats=['svg']\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams[\"figure.figsize\"] = (14, 4)\n",
    "gr ,  re,  bl,  yl,  bk = '#32AF4B', '#AF324B', '#323BAF', '#AFAF4B', '#000000'\n",
    "lgr, lre, lbl, lyl, lbk = '#ccffcc', '#ffcccc', '#ccccff', '#AFAFBB', '#333333'"
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   "source": [
    "## SIR Example\n",
    "\n",
    "$SIR$ is a simple model given by:\n",
    "\n",
    "\\begin{align}\n",
    "\\dot{S} &= -\\beta SI           \\\\\n",
    "\\dot{I} &= \\beta IS - \\gamma I \\\\\n",
    "\\dot{R} &= \\gamma I\n",
    "\\end{align}\n",
    "\n",
    "In what follows, we just run some random $SIR$ model and use the produced data to test SINDy."
   ]
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   "execution_count": 2,
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     "metadata": {},
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    }
   ],
   "source": [
    "from SIR import *\n",
    "sir = SIR(tstart=0.00, tend=5, dt=.001, beta=4, gamma=1, N=1)\n",
    "sir.Initialize(S0=0.8, I0=0.2, R0=0);\n",
    "sir.Simulate();\n",
    "sir.PlotSIR(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prepare data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of course in any real life situation, data is going to be noisy. So here we add noise to both data and its derivative. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import random as rn\n",
    "eps    = 0.05\n",
    "noise  = eps*np.random.randn(3,sir._Time.shape[0])\n",
    "dnoise = eps*np.random.randn(3,sir._Time.shape[0])\n",
    "\n",
    "data  = np.transpose(np.insert(np.array([sir._SS , sir._II , sir._RR]) + noise,0,sir._Time,axis=0))\n",
    "ddata = np.transpose(np.insert(np.array([sir._dSS, sir._dII, sir._dRR])+dnoise,0,sir._Time,axis=0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SINDy at work"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initiated a class for Sparse Identification from Numerical Dynamics\n",
      "**** Derivative Set ****\n",
      "**** Candidate functions library has been created ****\n",
      "**** Performing regression. Please wait... ****\n",
      "Iteration in progress:  1, 2, 3, 4, 5, 6, 7, 8, 9, 10, \n",
      "**** Identification is complete. We now use it to simulate the system. ****\n"
     ]
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d021110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from SINDy import *\n",
    "sin = SINDy(data=data,polyorder=2,usesine=False,cutoff=0.025)\n",
    "sin.SetDerivative(ddata)\n",
    "sin.RunSINDy(simulate=True)\n",
    "sin.SINDyPlot(statesymbols=[\"Susceptible\",\"Infected\",\"Recovered\"],\n",
    "              datacolors=[lbl,lre,lgr],\n",
    "              simcolors =[ bl, re, gr])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dS/dt =  0.782 R  +  0.480 S^2  +  0.449 S R  +  0.486 I^2  +  0.564 I R \n",
      "dI/dt =  0.084 +  0.504 S  +  0.038 I  +  1.485 I S  +  0.645 R^2 \n",
      "dR/dt =  0.329 +  0.477 I  +  0.302 S R  +  0.092 I^2 \n"
     ]
    }
   ],
   "source": [
    "sin.StringModelView(StateVariables=[\"S\",\"I\",\"R\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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