{
 "cells": [
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   "cell_type": "markdown",
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   "source": [
    "# Ipywidgets\n",
    "\n",
    "If you publish widgets in a TeachBook they might (depending on your implementation) require an active python kernel for the output to be interactive. Using the [thebe-integration](../examples/live_code.md), this is possible. Note: You can circumvent the use of a kernel by using packages which don't need such a kernel, for example the [non-kernel-based widgets using Plotly](./plotly.ipynb).\n",
    "\n",
    "## `matplotlib` widgets\n",
    "When you'd like to use `ipywidgets` in combinations with a `matplotlib` figure, import the following packages:\n",
    "\n",
    "```python\n",
    "import ipywidgets as widgets\n",
    "import micropip\n",
    "await micropip.install(\"ipympl\")\n",
    "```\n",
    "\n",
    "Activate the correct output format:\n",
    "\n",
    "```python\n",
    "%matplotlib widget\n",
    "```\n",
    "\n",
    "Write the code which generates your plot in a function:\n",
    "\n",
    "```python\n",
    "fig = plt.figure()  # Define the figure once\n",
    "ax = fig.add_subplot(1,1,1)       # Define the axis once\n",
    "\n",
    "def update_plot(input_variables_from_widget):\n",
    "    ax.clear()   # Clear the existing plot\n",
    "    ax.plot(x,y) # Plot your actual data\n",
    "    plt.draw()   # Update the plot whenever this function is executed\n",
    "```\n",
    "\n",
    "Initiate the widget:\n",
    "\n",
    "```python\n",
    "input_slider = widgets.FloatSlider(value=0, min=0, max=10, step=1, description='Input variable:') # Defines a widget, more options than just FloatSlider\n",
    "widgets.interact(update_plot, input_variable_from_widget = input_slider);\n",
    "```\n",
    "\n",
    "Finally, When using `%matplotlib widget`, there's the following toolbar:\n",
    "\n",
    "![](./figures/toolbar.png)\n",
    "\n",
    "Which only shows up when you hoover above. If you want to disable the toolbar you can use:\n",
    "```python\n",
    "fig = plt.gcf()\n",
    "fig.canvas.toolbar_visible = False\n",
    "```\n",
    "\n",
    "If you want it to be visible even if you don't hoover above it, use:\n",
    "\n",
    "```python\n",
    "fig = plt.gcf()\n",
    "fig.canvas.toolbar_visible = True\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Please note:\n",
    "- You might want to hide the output before the thebe has been activated.\n",
    "- You can hide the code by adding a custom-made tag: `thebe-remove-input-init`.\n",
    "- You can automatically start the thebe functionality when you add `auto-execute-page` to a cell. \n",
    "\n",
    "## Example\n",
    "The code below shows an example of the strain energy in a structure and work done by a force for different trial functions. Because of the actual python code, the plot 'refreshes' upon updating a widgets. This can be avoided by updating the current figure instead of plotting a new figure. Remember, first press {fa}`rocket` --> {guilabel}`Live Code` and then wait until all cells are executed:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "thebe-remove-input-init",
     "auto-execute-page"
    ]
   },
   "outputs": [],
   "source": [
    "import sympy as sp\n",
    "F = 10\n",
    "EI = 20e3\n",
    "L = 3\n",
    "\n",
    "# Polynomial trial function\n",
    "x, C1, C2, C3, C4, F, u0= sp.symbols('x, C1, C2, C3, C4, F, u0')\n",
    "w = C1*x**3+C2*x**2+C3*x + C4\n",
    "eq1 = sp.Eq(w.subs(x,0),0)\n",
    "eq2 = sp.Eq(w.diff(x).subs(x,0),0)\n",
    "eq3 = sp.Eq((-w.diff(x,2)*EI).subs(x,L),0)\n",
    "eq4 = sp.Eq(w.subs(x,L),u0)\n",
    "sol = sp.solve((eq1, eq2,eq3,eq4),(C1,C2,C3,C4))\n",
    "w_sol = sp.nsimplify(w.subs(sol))\n",
    "w_numpy_polynomial = sp.lambdify((u0,x),w_sol)\n",
    "\n",
    "M_sol_polynomial = sp.nsimplify(EI * w_sol.diff(x,2))\n",
    "\n",
    "Ev_polynomial = sp.integrate(sp.nsimplify(M_sol_polynomial**2/(EI*2)),(x,0,3))\n",
    "\n",
    "Ev_numpy_polynomial = sp.lambdify(u0,Ev_polynomial)\n",
    "\n",
    "V_polynomial = Ev_polynomial - 10 * u0\n",
    "V_numpy_polynomial = sp.lambdify(u0,V_polynomial)\n",
    "\n",
    "#cosine trial function\n",
    "w_sol = u0*sp.sin(x/12*2*sp.pi-sp.pi/2)+u0\n",
    "w_numpy_sin = sp.lambdify((u0,x),w_sol)\n",
    "\n",
    "M_sol_sin = sp.nsimplify(EI * w_sol.diff(x,2))\n",
    "\n",
    "Ev_sin = sp.integrate(sp.nsimplify(M_sol_sin**2/(EI*2)),(x,0,3))\n",
    "\n",
    "Ev_numpy_sin = sp.lambdify(u0,Ev_sin)\n",
    "\n",
    "V_sin = Ev_sin - 10 * u0\n",
    "V_numpy_sin = sp.lambdify(u0,V_sin)\n",
    "\n",
    "#sin trial function\n",
    "w_sol = 2*u0*(sp.cosh(x/sp.pi))-2*u0\n",
    "w_numpy_cosh = sp.lambdify((u0,x),w_sol)\n",
    "\n",
    "M_sol_cosh = sp.nsimplify(EI * w_sol.diff(x,2))\n",
    "\n",
    "Ev_cosh = sp.integrate(sp.nsimplify(M_sol_cosh**2/(EI*2)),(x,0,3))\n",
    "\n",
    "Ev_numpy_cosh = sp.lambdify(u0,Ev_cosh)\n",
    "\n",
    "V_cosh = Ev_cosh - 10 * u0\n",
    "V_numpy_cosh = sp.lambdify(u0,V_cosh)\n",
    "\n",
    "import matplotlib.pylab as plt\n",
    "import numpy as np\n",
    "from ipywidgets import widgets, interact\n",
    "\n",
    "def func(u,trial_function):\n",
    "    fig, axs = plt.subplots(2, 2, figsize=(10, 6))\n",
    "\n",
    "    x = np.linspace(0,3,100)\n",
    "    if trial_function == 'Polynomial':\n",
    "        w_numpy = w_numpy_polynomial\n",
    "        Ev_numpy = Ev_numpy_polynomial\n",
    "        V_numpy = V_numpy_polynomial\n",
    "    elif trial_function == 'cos':\n",
    "        w_numpy = w_numpy_sin\n",
    "        Ev_numpy = Ev_numpy_sin\n",
    "        V_numpy = V_numpy_sin\n",
    "    elif trial_function == 'cosh':\n",
    "        w_numpy = w_numpy_cosh\n",
    "        Ev_numpy = Ev_numpy_cosh\n",
    "        V_numpy = V_numpy_cosh\n",
    "    axs[0,0].plot(x,w_numpy(u,x))\n",
    "    axs[0,0].set_xlim([-0.2,3.2])\n",
    "    axs[0,0].set_ylim([-0.003,0.01])\n",
    "    axs[0,0].invert_yaxis()\n",
    "    axs[0,0].annotate(text='', xy=(3,w_numpy(u,3)), xytext=(3,0), arrowprops=dict(arrowstyle='fancy'))\n",
    "    axs[0,0].text(3.1,w_numpy(u,3),'$u_0$')\n",
    "    axs[0,0].axis('off')\n",
    "    axs[0,1].axis('off')\n",
    "    axs[0,1].set_xlim([-0.2,3.2])\n",
    "    axs[0,1].set_ylim([-0.003,0.01])\n",
    "    axs[0,1].annotate(text='', xy=(1.5,w_numpy(u,3)), xytext=(1.5,w_numpy(u,3)-0.003), arrowprops=dict(arrowstyle='simple'))\n",
    "    axs[0,1].invert_yaxis()\n",
    "    x_axis= ['$E_v$','$A_F$','$E_v - A_F$']\n",
    "    y_axis = [Ev_numpy(u),w_numpy(u,3)*10,Ev_numpy(u)-w_numpy(u,3)*10]\n",
    "    axs[1,0].bar(x_axis,y_axis,color=('blue','green','orange'))\n",
    "    axs[1,0].set_ylim([-0.03,0.1])\n",
    "    axs[1,0].set_yticklabels([])\n",
    "    axs[1,0].set_yticks([])\n",
    "    \n",
    "    u_range=np.linspace(-0.0015,0.01,100)\n",
    "    axs[1,1].plot(u_range,Ev_numpy(u_range),label='$E_v$',color='blue')\n",
    "    axs[1,1].plot(u_range,w_numpy(u_range,3)*10,label='$F_A$',color='green')\n",
    "    axs[1,1].plot(u_range,V_numpy(u_range),label='$E_v - A_F$',color='orange')\n",
    "    axs[1,1].legend()\n",
    "    axs[1,1].plot(u,Ev_numpy(u),'o',color='blue')\n",
    "    axs[1,1].plot(u,w_numpy(u,3)*10,'o',color='green')\n",
    "    axs[1,1].plot(u,Ev_numpy(u)-w_numpy(u,3)*10,'o',color='orange')\n",
    "    axs[1,1].set_ylim([-0.03,0.1])\n",
    "    axs[1,1].set_xlim([-0.0015,0.01])\n",
    "    axs[1,1].set_xlabel('$u_0$')\n",
    "    axs[1,1].set_xticks([])\n",
    "    axs[1,1].set_xticklabels([])\n",
    "    axs[1,1].set_yticks([])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The graph will appear below in interactive mode:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "thebe-remove-input-init"
    ]
   },
   "outputs": [],
   "source": [
    "interact(func, u = widgets.FloatSlider(min=-0.001, max=0.01, value=0, step=0.0002, description=\"Displacement u_0\",readout_format='.4f',style= {'description_width': '180px'},layout = {'width': '400px'}),\n",
    "        trial_function = widgets.ToggleButtons(options=['Polynomial', 'cos', 'cosh']));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  }
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