{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "UoSyknoTpm_q"
   },
   "source": [
    "# First order defferential equation\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 381
    },
    "id": "tLtUTjfcpm_5",
    "outputId": "6949dfae-b6a1-4511-ea93-f9e3a1a6b8e2"
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"640\"\n",
       "            height=\"360\"\n",
       "            src=\"https://www.youtube.com/embed/p_di4Zn4wz4\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "            \n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x1b04c16b130>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo('p_di4Zn4wz4',width=640,height=360)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "OdND5N8ipm_8"
   },
   "source": [
    "## <center>Analytical solution of a first order differential equation</center>\n",
    "<img src=\"https://github.com/chenziao/Computational-Neuroscience-Tutorials/blob/master/Getting%20Started%20with%20Math/analytical_solution.png?raw=1\" style=\"text-align:center\">  \n",
    "## <center>Numerical solution of a first order defferential equation</center>\n",
    "<img src=\"https://github.com/chenziao/Computational-Neuroscience-Tutorials/blob/master/Getting%20Started%20with%20Math/numerical_solution.png?raw=1\" style=\"text-align:center\">  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "MwS9OKcqpm_9"
   },
   "source": [
    "### Set up the first order differential equation and convert it into standard form assuming input u(t) is a constant.\n",
    "\n",
    "a1,a2 and a3 are coefficients of the first order differential equation:  $ a_{1}\\dot{y}\\left(t\\right) + a_{2}y(\\left(t\\right) = a_{3}u\\left(t\\right); \\ \\ y\\left(0\\right)=y_{0}, \\quad where\\: u\\left(t\\right) = 1 $.  \n",
    "Convert into standard form:  $ \\tau \\dot{y}\\left(t\\right) + y\\left(t\\right) = Ku\\left(t\\right); \\ \\ y\\left(0\\right)=y_{0} $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "JJSqR2A3pm_-"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "# coefficients of the first order differential equation: a1*y'(t) + a2*y(t) = a3*u(t),  where u(t) = 1\n",
    "a1,a2,a3 = 1,3,-30 # example of y'+3y=-30\n",
    "y0 = -60 # y(tstart) initial y at t=tstart\n",
    "\n",
    "# convert into standard form: tau*y'(t) + y(t) = K*u(t)\n",
    "tau = a1/a2\n",
    "K = a3/a2\n",
    "\n",
    "# computational parameters\n",
    "dt = 0.01  # time step size\n",
    "tstart = 0 # initial time\n",
    "tstop = 2  # stop time\n",
    "\n",
    "# initialize\n",
    "t = np.arange(tstart,tstop,dt)\n",
    "y = np.empty(t.shape)\n",
    "y[0] = Y = y0\n",
    "\n",
    "# iteratively solve\n",
    "for i in range(1,t.size):\n",
    "    Y += (K-Y)/tau*dt\n",
    "    y[i] = Y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "JK9DY9nnpm__"
   },
   "source": [
    "### Plot analytical solution and numerical solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 542
    },
    "id": "nt_seFutpm__",
    "outputId": "f2956856-e3cf-48a3-bdc3-7066002cc939"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_analy = K-(K-y0)*np.exp(-(t-tstart)/tau) # analytical solution\n",
    "\n",
    "y_tau = y0+(K-y0)*(1-np.exp(-1))  # y(tstart+tau) system reaches the 63.2% of the change in value from initial value in one time constant.\n",
    "\n",
    "plt.figure(figsize=(8,6))\n",
    "plt.plot(t,y,'b.',markersize=3)\n",
    "plt.plot(t,y_analy,'r')\n",
    "plt.plot(tstart+tau,y_tau,'go',markerfacecolor='none',markersize=8)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('y')\n",
    "plt.legend(['numerical solution','analytical solution','( \\u03C4, y(\\u03C4) )'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "gmIOxofxpnAC"
   },
   "source": [
    "### Interactive tool for getting the solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "tEEFwURUpnAD"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "import ipywidgets as widgets\n",
    "from ipywidgets import HBox,VBox,Label,Layout\n",
    "from IPython.display import display, Math\n",
    "\n",
    "def solveODE(a1,a2,a3,y0,tau,K,tstart,tstop,dt):\n",
    "    t = np.arange(tstart,tstop,dt)\n",
    "    y = np.empty(t.shape)\n",
    "    y[0] = Y = y0\n",
    "\n",
    "    for i in range(1,t.size):\n",
    "        Y += (K-Y)/tau*dt\n",
    "        y[i] = Y\n",
    "\n",
    "    y_analy = K-(K-y0)*np.exp(-(t-tstart)/tau) # analytical solution\n",
    "\n",
    "    y_tau = y0+(K-y0)*(1-np.exp(-1))  # y(tau) system reaches the 63.2% of the change in value from initial value in one time constant.\n",
    "\n",
    "    plt.figure(figsize=(10,6))\n",
    "    plt.plot(t,y,'b.',markersize=3)\n",
    "    plt.plot(t,y_analy,'r')\n",
    "    plt.plot(tstart+tau,y_tau,'go',markerfacecolor='none',markersize=8)\n",
    "    plt.grid()\n",
    "    plt.xlim(tstart,tstop)\n",
    "    plt.xlabel('t')\n",
    "    plt.ylabel('y')\n",
    "    plt.legend(['numerical solution','analytical solution','( \\u03C4, y(\\u03C4) )'])\n",
    "    plt.show()\n",
    "\n",
    "    print('Time constant: \\u03C4= %.2f' % tau)"
   ]
  },
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    {
     "data": {
      "text/latex": [
       "$\\displaystyle $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
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      "text/plain": [
       "HBox(children=(FloatText(value=0.0, description='Start time', layout=Layout(width='20%')), BoundedFloatText(va…"
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     },
     "metadata": {},
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     "data": {
      "text/latex": [
       "$\\displaystyle \\quad\\quad \\text{Differential equation:} \\quad a_{1}\\dot{y}\\left(t\\right) + a_{2}y\\left(t\\right) = a_{3}; \\quad y\\left(0\\right)=y_{0} $"
      ],
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       "<IPython.core.display.Math object>"
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      "text/plain": [
       "HBox(children=(HBox(children=(Label(value='a₁', layout=Layout(width='12%')), BoundedFloatText(value=1.0, layou…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
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     "data": {
      "text/latex": [
       "$\\displaystyle \\quad\\quad \\text{Standard form:} \\quad \\tau\\dot{y}\\left(t\\right) + y\\left(t\\right) = K; \\quad y\\left(0\\right)=y_{0}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
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       "HBox(children=(HBox(children=(Label(value='Initial value y₀', layout=Layout(width='20%')), FloatText(value=-60…"
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      "text/plain": [
       "Output()"
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   "source": [
    "# default settings\n",
    "a1,a2,a3 = 1,3,-30\n",
    "y0 = -60\n",
    "tau = a1/a2\n",
    "K = a3/a2\n",
    "tstart,tstop,dt = 0.0,2.0,0.01\n",
    "duration = tstop-tstart\n",
    "\n",
    "L_s = Layout(width='12%')\n",
    "L_m = Layout(width='20%')\n",
    "L_l = Layout(width='35%')\n",
    "L_ctr = Layout(justify_content='center')\n",
    "L_left = Layout(justify_content='flex-start')\n",
    "\n",
    "w_tstart = widgets.FloatText(value=tstart,description='Start time',layout=L_m)\n",
    "w_tstop = widgets.BoundedFloatText(value=tstop,min=tstart+10*dt,max=tstart+1e9,step=1,description='Stop time',layout=L_m)\n",
    "w_dt = widgets.FloatLogSlider(value=dt,base=10,min=-5,max=0,step=0.05,description='Time step',readout_format='.5f',layout=L_l)\n",
    "w_a1 = widgets.BoundedFloatText(value=a1,min=1e-9,max=1e9,layout=L_l)\n",
    "w_a2 = widgets.BoundedFloatText(value=a2,min=1e-9,max=1e9,layout=L_l)\n",
    "w_a3 = widgets.FloatText(value=a3,layout=L_l)\n",
    "w_y0 = widgets.FloatText(value=y0,layout=L_m)\n",
    "w_K = widgets.FloatText(value=K,layout=L_m)\n",
    "w_tau = widgets.FloatSlider(value=tau,min=dt,max=duration,step=dt,continuous_update=False,readout_format='.2f',layout=L_l)\n",
    "\n",
    "def update_tstop(*args):\n",
    "    w_tstop.value = w_tstart.value+duration\n",
    "    w_tstop.min = w_tstart.value+10*w_dt.value\n",
    "    w_tstop.max = w_tstart.value+1e9\n",
    "w_tstart.observe(update_tstop,'value')\n",
    "w_dt.observe(update_tstop,'value')\n",
    "\n",
    "def update_duration(*args):\n",
    "    global duration\n",
    "    duration = w_tstop.value-w_tstart.value\n",
    "w_tstop.observe(update_duration,'value')\n",
    "\n",
    "def update_tau(*args):\n",
    "    w_tau.min = w_dt.value\n",
    "    w_tau.max = max(duration,w_a1.value/w_a2.value)\n",
    "    w_tau.step = w_dt.value\n",
    "    w_tau.value = w_a1.value/w_a2.value\n",
    "    w_K.value = w_a3.value/w_a2.value\n",
    "w_a1.observe(update_tau,'value')\n",
    "w_a2.observe(update_tau,'value')\n",
    "w_a3.observe(update_tau,'value')\n",
    "w_tstop.observe(update_tau,'value')\n",
    "w_dt.observe(update_tau,'value')\n",
    "\n",
    "def update_a(*args):\n",
    "    w_a1.value = w_a2.value*w_tau.value\n",
    "    w_a3.value = w_a2.value*w_K.value\n",
    "w_tau.observe(update_a,'value')\n",
    "w_K.observe(update_a,'value')\n",
    "\n",
    "ui1 = HBox([w_tstart,w_tstop,w_dt],layout=L_left)\n",
    "expr1 = Math(r'$\\quad\\quad \\text{Differential equation:} \\quad a_{1}\\dot{y}\\left(t\\right) + a_{2}y\\left(t\\right) = a_{3}; \\quad y\\left(0\\right)=y_{0} $')\n",
    "ui2 = HBox([HBox([Label(value='a₁',layout=L_s),w_a1],layout=L_ctr),HBox([Label(value='a₂',layout=L_s),w_a2],layout=L_ctr),\n",
    "                 HBox([Label(value='a₃',layout=L_s),w_a3],layout=L_ctr)],layout=L_left)\n",
    "expr2 = Math(r'$\\quad\\quad \\text{Standard form:} \\quad \\tau\\dot{y}\\left(t\\right) + y\\left(t\\right) = K; \\quad y\\left(0\\right)=y_{0}$')\n",
    "ui3 = HBox([HBox([Label(value='Initial value y₀',layout=L_m),w_y0,Label(value='Final value K',layout=L_m),w_K],layout=L_ctr),\n",
    "                 Label(value='Time constant \\u03C4',layout=L_s),w_tau],layout=L_left)\n",
    "\n",
    "out = widgets.interactive_output(solveODE,{'tstart':w_tstart,'tstop':w_tstop,'dt':w_dt,\n",
    "                                              'a1':w_a1,'a2':w_a2,'a3':w_a3,'y0':w_y0,'K':w_K,'tau':w_tau})\n",
    "\n",
    "display(Math(r''),ui1,expr1,ui2,expr2,ui3,out)"
   ]
  },
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         "text/plain": "<Figure size 1000x600 with 1 Axes>"
        },
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       },
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        "text": [
         "Time constant: τ= 0.33\n"
        ]
       }
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