Hysteron Widget Vertical Version.ipynb

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    "# To use the notebook, please click Cell  → Run All"
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       "code_show=true; \n",
       "function code_toggle() {\n",
       " if (code_show){\n",
       " $('div.input').hide();\n",
       " } else {\n",
       " $('div.input').show();\n",
       " }\n",
       " code_show = !code_show\n",
       "} \n",
       "$( document ).ready(code_toggle);\n",
       "</script>\n",
       "<form action=\"javascript:code_toggle()\"><input type=\"submit\" value=\"View/Hide Code\"></form>"
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      "text/plain": [
       "<IPython.core.display.HTML object>"
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     "execution_count": 83,
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     "output_type": "execute_result"
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   "source": [
    "from IPython.display import HTML\n",
    "HTML('''<script>\n",
    "code_show=true; \n",
    "function code_toggle() {\n",
    " if (code_show){\n",
    " $('div.input').hide();\n",
    " } else {\n",
    " $('div.input').show();\n",
    " }\n",
    " code_show = !code_show\n",
    "} \n",
    "$( document ).ready(code_toggle);\n",
    "</script>\n",
    "<form action=\"javascript:code_toggle()\"><input type=\"submit\" value=\"View/Hide Code\"></form>''')"
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   "cell_type": "code",
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      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
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       "model_id": "cb34c2b23ba446b3b674b28d3fd1a726",
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       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(Button(description='Reset / Start', icon='trash', style=ButtonStyle(button_color='yellow', font…"
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     },
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     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib widget\n",
    "# %matplotlib notebook\n",
    "import ipywidgets as widgets\n",
    "from ipywidgets import Layout\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.colors as colors\n",
    "import numpy as np\n",
    "from matplotlib.gridspec import GridSpec\n",
    "import random\n",
    "from palettable.colorbrewer.sequential import Greys_9\n",
    "\n",
    "\n",
    "\n",
    "class app(object):\n",
    "    def __init__(self):\n",
    "        self.hys_per_side = 101\n",
    "        self.beta_values = np.around(np.linspace(0, 1, self.hys_per_side),2) # beta values\n",
    "        self.alpha_values = np.around(np.linspace(1,0, self.hys_per_side),2) # alpha values\n",
    "        self.beta_grid, self.alpha_grid = np.meshgrid(self.beta_values, self.alpha_values)\n",
    "        self.preisach_triangle = np.where(self.alpha_grid>self.beta_grid, 0, np.nan)\n",
    "        \n",
    "        \n",
    "        self.out = widgets.Output()\n",
    "        self.input_u = widgets.FloatSlider(\n",
    "                            value=0, \n",
    "                            min=0, max=1, step=0.01,\n",
    "                            description='input $u$',\n",
    "                            continuous_update=True,\n",
    "                            layout=Layout(width='50%')\n",
    "                       )\n",
    "        self.input_u.observe(self.update_app, 'value')\n",
    "        self.reset_button = widgets.Button(\n",
    "                                description='Reset / Start',\n",
    "                                icon=\"trash\",\n",
    "                                style={'font_weight': 'bold', 'button_color': 'yellow'}\n",
    "                            )\n",
    "        self.reset_button.on_click(self.on_button_clicked)# if you click it will activate the function\n",
    "        self.on_button_clicked(1) # We force a click to reset all the plots\n",
    "    def draw_arrow(self,ax, start, end):\n",
    "        ax.annotate('', xy=end, xytext=start, xycoords='data', textcoords='data',\n",
    "                      arrowprops=dict(headwidth=4.0, headlength=4.0, width=0.2,\n",
    "                                      facecolor = \"black\", linewidth = 0.5),zorder=0)\n",
    "    def on_button_clicked(self, b): # its just the jupiter format for clicking\n",
    "        plt.clf()\n",
    "        self.fig = plt.figure(1, figsize=(10,5))\n",
    "        # self.fig.canvas.layout.width = '1000px'\n",
    "        HTML('''\n",
    "        <style>\n",
    "        div.jupyter-widgets.widget-label {display: none;}\n",
    "        </style>\n",
    "        ''')\n",
    "        gs1 = GridSpec(1, 3, width_ratios=[1,1,1],\n",
    "                             height_ratios=[1],\n",
    "                             left=0.03, right=0.95,\n",
    "                             bottom=0.60, top=0.9,\n",
    "                             wspace=0.6, hspace=0.2)\n",
    "        gs2 = GridSpec(1, 2, width_ratios=[1,1],\n",
    "                             height_ratios=[1],\n",
    "                             left=0.13, right=0.95,\n",
    "                             bottom=0.03, top=0.45,\n",
    "                             wspace=0.3, hspace=0.5)\n",
    "        self.ax1 = plt.subplot(gs1[0, 0])\n",
    "        self.ax2 = plt.subplot(gs1[0, 1])\n",
    "        self.ax3 = plt.subplot(gs1[0, 2])\n",
    "        self.ax4 = plt.subplot(gs2[0, 0])\n",
    "        self.ax5 = plt.subplot(gs2[0, 1])\n",
    "        # x is the same as the input u, but it's a static array, used for plotting\n",
    "        self.x = np.arange(0, 1, 0.005)\n",
    "        \n",
    "        # Setting all 3 hysterons\n",
    "        self.reset_AB() # randomly draw alpha and beta for the hysterons, then plot\n",
    "        self.plot_hysteron(self.ax1, self.A1, self.B1, 1)\n",
    "        self.plot_hysteron(self.ax2, self.A2, self.B2, 2)\n",
    "        self.plot_hysteron(self.ax3, self.A3, self.B3, 3)        \n",
    "        \n",
    "        # Hysteresis plot\n",
    "        self.ax4.axis([-0.05, 1.2, -0.3, 3.8])\n",
    "        self.draw_arrow(self.ax4, (-0.035, -0.2),(-0.035,3.4))\n",
    "        self.ax4.annotate('Output', xy=(-0.05,3.6))\n",
    "        self.draw_arrow(self.ax4, (-0.035, -0.2),(1.1, -0.2))\n",
    "        self.ax4.text(1.175, -0.25, \"$u$\", ha=\"right\")\n",
    "        self.ax4.spines['top'].set_visible(False)\n",
    "        self.ax4.spines['right'].set_visible(False)\n",
    "        self.ax4.spines['bottom'].set_visible(False)\n",
    "        self.ax4.spines['left'].set_visible(False)\n",
    "        self.ax4.set_xticks([])\n",
    "        self.ax4.set_yticks([])\n",
    "        self.ax4.tick_params(axis=u'both', which=u'both',length=0)\n",
    "\n",
    "        # Preisach triangle plot\n",
    "        self.ax5.axis([0.0, 1.2, -0.05, 1.1])\n",
    "        self.ax5.scatter([self.B1, self.B2, self.B3], [self.A1, self.A2, self.A3], color='tab:red', s=15,zorder=3)\n",
    "        self.ax5.annotate(\"1\", (self.B1 + 0.03, self.A1 - 0.015),color=\"tab:red\",zorder=3, size=10)\n",
    "        self.ax5.annotate(\"2\", (self.B2 + 0.03, self.A2 - 0.015),color=\"tab:red\",zorder=3, size=10)\n",
    "        self.ax5.annotate(\"3\", (self.B3 + 0.03, self.A3 - 0.015),color=\"tab:red\",zorder=3, size=10)\n",
    "        self.ax5.text(0.5,1.1,\"Limit Triangle\", ha=\"center\")                  \n",
    "        self.ax5.text(-0.1, 1.05, r\"$\\alpha$\")                                   \n",
    "        self.ax5.text(1.075, 0.99, r\"$u$\")          \n",
    "        self.ax5.text(1.125, -0.025, r\"$\\beta$\")\n",
    "        self.draw_arrow(self.ax5, (0,0),(1.1, 0))\n",
    "        self.draw_arrow(self.ax5, (0,0),(0, 1.09))\n",
    "        self.draw_arrow(self.ax5, (0,0),(1.05, 1.05))\n",
    "        self.ax5.spines['top'].set_visible(False)\n",
    "        self.ax5.spines['right'].set_visible(False)\n",
    "        self.ax5.spines['bottom'].set_visible(False)\n",
    "        self.ax5.spines['left'].set_visible(False)\n",
    "        self.ax5.set_xticks([])\n",
    "        self.ax5.set_yticks([])\n",
    "        self.ax5.set_aspect('equal', adjustable='box')\n",
    "        self.ax5.tick_params(axis=u'both', which=u'both',length=0)\n",
    "        self.ax5.fill_between(self.x, self.x, y2=1.0, color=\"gray\", alpha=0.2,zorder=1)\n",
    "        self.on_state = self.ax5.fill_between([0], [0], 0, color=\"black\",zorder=0)\n",
    "        \n",
    "        \n",
    "        self.input_u.value = 0.0\n",
    "        self.input_history = [0.0]\n",
    "        self.output_history = [0.0]\n",
    "        \n",
    "        self.reset_markers()\n",
    "        \n",
    "    def plot_hysteron(self, ax, A, B, hysteron_number):\n",
    "        ax.spines['top'].set_visible(False)\n",
    "        ax.spines['right'].set_visible(False)\n",
    "        ax.spines['bottom'].set_visible(False)\n",
    "        ax.spines['left'].set_visible(False)\n",
    "        ax.set_xticks([])\n",
    "        ax.set_yticks([])\n",
    "        self.draw_arrow(ax, (0,0),(1, 0))\n",
    "        self.draw_arrow(ax, (0,0),(0, 1.5))\n",
    "        ax.text(1.075, 0, \"$u$\", ha=\"right\")\n",
    "        ax.plot(np.where(self.x < A , self.x,np.nan), np.where(self.x < A , 0,np.nan), zorder=1,color=\"black\")\n",
    "        ax.plot(np.where(self.x > A , self.x,np.nan), np.where(self.x > A , 1,np.nan), zorder=1,color=\"black\")\n",
    "        ax.plot([A,A], [0,1], zorder=1,color=\"tab:orange\")\n",
    "        ax.plot(np.where(self.x < B , self.x,np.nan), np.where(self.x < B , 0,np.nan), zorder=1,color=\"black\")\n",
    "        ax.plot(np.where(self.x > B , self.x,np.nan), np.where(self.x > B , 1,np.nan), zorder=1,color=\"black\")\n",
    "        ax.plot([B,B], [0,1], zorder=1, color=\"tab:blue\")\n",
    "        ax.plot([A],[0.5],marker=\"^\", color=\"tab:orange\",zorder=0)\n",
    "        ax.plot([B],[0.5],marker=\"v\", color=\"tab:blue\",zorder=0)\n",
    "        ax.text(A, -0.25, r\"$\\alpha$\", horizontalalignment=\"center\")\n",
    "        ax.text(B, -0.25, r\"$\\beta$\", horizontalalignment=\"center\")\n",
    "        ax.axis([0, 1, -0.2, 1.5])\n",
    "        ax.text(0.5,1.3,\"hysteron {}\".format(hysteron_number), ha=\"center\")\n",
    "\n",
    "    def reset_AB(self):\n",
    "        \"\"\"\n",
    "        Resetting all Alphas and Betas\n",
    "        \"\"\"\n",
    "        A_vec = []\n",
    "        B_vec = []\n",
    "        for i in range(3):\n",
    "            beta  = np.random.randint(1, 9) # beta between 1 and 8\n",
    "            alpha = np.random.randint(beta+1, 10) # alpha between beta+1 and 9\n",
    "            A_vec.append(0.1*alpha)\n",
    "            B_vec.append(0.1*beta)\n",
    "        self.A1, self.A2, self.A3 = A_vec\n",
    "        self.B1, self.B2, self.B3 = B_vec\n",
    "\n",
    "    def reset_markers(self):\n",
    "        self.H1 = 0.0\n",
    "        self.H2 = 0.0\n",
    "        self.H3 = 0.0\n",
    "        self.marker1, = self.ax1.plot([0], self.H1, 'ro', zorder=2, clip_on=False)\n",
    "        self.marker2, = self.ax2.plot([0], self.H2, 'ro', zorder=2, clip_on=False)\n",
    "        self.marker3, = self.ax3.plot([0], self.H3, 'ro', zorder=2, clip_on=False)\n",
    "        self.marker_hysteresis, = self.ax4.plot([0], self.H3, 'ro', zorder=5, clip_on=False)\n",
    "        self.hysteresis_curve, = self.ax4.plot(self.input_history, self.output_history, color='green')\n",
    "    \n",
    "    def update_hysteron_value(self, u0, u1, alpha, beta, previous_state):\n",
    "        \"\"\"\n",
    "        This is the core of the algorithm\n",
    "        The value of the hysteron can only change if there is a threshold crossing.\n",
    "        If the input increased (u1-u0>0), the threshold is alpha, otherwise beta.\n",
    "        \n",
    "        Case (a): input increased\n",
    "        If the input is to the right of alpha, then the histeron is surely on, no matter what was its previous state\n",
    "        Case (b): input decreased\n",
    "        If the input is to the left of beta, then the histeron is surely off, no matter what was its previous state\n",
    "        Is case we are neither to the right of alpha nor to the left of beta, then the hysteron remain as it was.\n",
    "        \"\"\"\n",
    "        if (u1 - u0) > 0:\n",
    "            threshold = alpha\n",
    "            if u1 >= threshold:\n",
    "                return 1.0\n",
    "        else:\n",
    "            threshold = beta\n",
    "            if u1 <= threshold:\n",
    "                return 0.0\n",
    "        return previous_state\n",
    "    def RegularPreisach(self, u):\n",
    "        alpha = self.alpha_grid\n",
    "        beta = self.beta_grid\n",
    "        preisach_triangle = self.preisach_triangle\n",
    "        # compare new input to previous input value and change hysteron values accordingly\n",
    "        \"\"\"This if u.new==0 is in order to cancel the last thin black patch in the left side\n",
    "         of the priesach trianle and make it a whole gray when u=0\"\"\"\n",
    "        if u.new==0:\n",
    "                preisach_triangle=np.where(self.alpha_grid>self.beta_grid, 0, np.nan)\n",
    "                preisach_triangle[-1][0]=1\n",
    "        elif u.new > u.old: # if input increases  \n",
    "            preisach_triangle = np.where(u.new>alpha, 1, preisach_triangle)\n",
    "        elif u.new < u.old: # if input increases\n",
    "            preisach_triangle = np.where(u.new<beta, 0, preisach_triangle)\n",
    "            \n",
    "\n",
    "        # values outside the presiach half-plane are set to nan\n",
    "        preisach_triangle = np.where(alpha>=beta, preisach_triangle, np.nan)\n",
    "        return preisach_triangle\n",
    "    def xy_on(self, triangle):\n",
    "        m = triangle \n",
    "        d = np.diff(m,axis=0)  # Calculate the difference between an element and the above\n",
    "        x = np.where(d==1)[1]  # Getting all the x-columns coordinate\n",
    "        y = self.hys_per_side-np.where(d==1)[0]-1  # Getting all the y-raws coordinate\n",
    "        x = np.append(x, x[-1]+1)  # adding missing point at...\n",
    "        y = np.append(y, y[-1])    # the end of the array\n",
    "        step_index = np.where(np.diff(y)!= 0)[0]\n",
    "        x = np.insert(x, step_index+1, x[step_index+1])\n",
    "        y = np.insert(y, step_index, y[step_index])\n",
    "        return [x/(self.hys_per_side-1), y/(self.hys_per_side-1)]\n",
    "    \n",
    "    def update_app(self, u):\n",
    "        self.preisach_triangle = self.RegularPreisach(u)\n",
    "        \n",
    "        #update hysterons\n",
    "        self.H1 = self.update_hysteron_value(u.old, u.new, self.A1, self.B1, self.H1)\n",
    "        self.H2 = self.update_hysteron_value(u.old, u.new, self.A2, self.B2, self.H2)\n",
    "        self.H3 = self.update_hysteron_value(u.old, u.new, self.A3, self.B3, self.H3)\n",
    "        self.marker1.set_data([u.new], [self.H1])\n",
    "        self.marker2.set_data([u.new], [self.H2])\n",
    "        self.marker3.set_data([u.new], [self.H3])\n",
    "        # update hysteresis graph\n",
    "        self.input_history.append(u.new)\n",
    "        self.output_history.append(self.H1 + self.H2 + self.H3)\n",
    "        self.hysteresis_curve.set_data(self.input_history, self.output_history)\n",
    "        self.marker_hysteresis.set_data([self.input_history[-1]], [self.output_history[-1]])\n",
    "        self.on_state.remove()\n",
    "        x_on, y_on = self.xy_on(self.preisach_triangle)\n",
    "        self.on_state = self.ax5.fill_between(x_on, x_on, y_on, color=\"black\")\n",
    "my_app = app()\n",
    "widgets.HBox([my_app.reset_button,my_app.input_u])\n",
    "\n"
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