ajam8.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c7e2e0d8",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f53949b",
   "metadata": {},
   "source": [
    "# Q1: Metropolis-Hastings\n",
    "\n",
    "For the spatial part of Hydrogen atom, we can guess a wave function $\\Psi_{T,\\alpha} \\propto e^{-\\alpha r}$. So, $E_{Local}$ is equal to\n",
    "\n",
    "$$ E_L = \\frac{\\hat{H}\\,\\Psi_{T,\\alpha}}{\\Psi_{T,\\alpha}} = -\\frac{1}{2}\\left(\\alpha^2 - 2\\frac{\\alpha}{r} \\right) - \\frac{1}{r}\\,. $$\n",
    "\n",
    "Now we need to calculate the best-fit value for $\\alpha$. Note that there are 3 more complications here compared to the question from the last problem set.\n",
    "\n",
    "1. $r$ here is not Cartesian but is the spatial part of spherical coordinates.\n",
    "\n",
    "2. $E_L$ at $\\alpha = 1$ becomes independent of $r$ (Spoiler: this is infact the correct answer).\n",
    "\n",
    "3. For $\\alpha \\ne 1$ there's a singularity at $r = 1$ in which the potential diverges."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6aedd08f",
   "metadata": {},
   "source": [
    "## (a)\n",
    "\n",
    "Like before, write a function to preform a Metropolis-Hastings algorithm to find a distribution for $r$ at a defined $\\alpha$ this time using a non-symmetric $Q(x^\\prime; x)$ as discussed in the lecture.\n",
    "\n",
    "P.S. Use two different functions for $Q$ at your choise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "06763320",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your code here"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "522d5a0a",
   "metadata": {},
   "source": [
    "## (b)\n",
    "\n",
    "Plot histograms for $r$ with different sizes for each choise of $Q$ and compare them to each other and the analytical function. Which choise of $Q$ is better? Do you think there's a mathematical reason behind this?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "cf128b3e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your code here"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44f3ab54",
   "metadata": {},
   "source": [
    "## (c)\n",
    "\n",
    "As before, plot $\\langle E_L \\rangle$ and $\\sigma^2 = \\langle E_L^2 \\rangle - \\langle E_L \\rangle^2$ for different values of $\\alpha$ and show that indeed $\\alpha = 1$ is the best-fit value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a8a832d1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your code here"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76c17429",
   "metadata": {},
   "source": [
    "# Q2: FFT (warm up)\n",
    "\n",
    "## (a)\n",
    "Using `'scipy.fft'`, calculate and the fourier modes of $x(t) = 2\\sin(t) + \\sin(10t)$. Plot the absolute values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "b6f6c3e3",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.fft import fft, fftshift, fftfreq,ifft\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "id": "84a5ef9d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'fft[x(t)]')"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 1000\n",
    "ti = 0    #s\n",
    "tf = 20   #s\n",
    "t=np.linspace(0,20,1000)\n",
    "x=2*np.sin(t)+np.sin(10*t)\n",
    "A = np.abs(fft(x))[:n // 2]\n",
    "Fourier = fftfreq(1000, 20/1000)[:n // 2]\n",
    "plt.figure(figsize = (10, 8))\n",
    "plt.plot(Fourier, A, 'ro')\n",
    "plt.xlabel('f[Hz]')\n",
    "plt.ylabel('fft[x(t)]')\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "31b287f9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "/* global mpl */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function () {\n",
       "    if (typeof WebSocket !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof MozWebSocket !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert(\n",
       "            'Your browser does not have WebSocket support. ' +\n",
       "                'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "                'Firefox 4 and 5 are also supported but you ' +\n",
       "                'have to enable WebSockets in about:config.'\n",
       "        );\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = this.ws.binaryType !== undefined;\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById('mpl-warnings');\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent =\n",
       "                'This browser does not support binary websocket messages. ' +\n",
       "                'Performance may be slow.';\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = document.createElement('div');\n",
       "    this.root.setAttribute('style', 'display: inline-block');\n",
       "    this._root_extra_style(this.root);\n",
       "\n",
       "    parent_element.appendChild(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen = function () {\n",
       "        fig.send_message('supports_binary', { value: fig.supports_binary });\n",
       "        fig.send_message('send_image_mode', {});\n",
       "        if (fig.ratio !== 1) {\n",
       "            fig.send_message('set_device_pixel_ratio', {\n",
       "                device_pixel_ratio: fig.ratio,\n",
       "            });\n",
       "        }\n",
       "        fig.send_message('refresh', {});\n",
       "    };\n",
       "\n",
       "    this.imageObj.onload = function () {\n",
       "        if (fig.image_mode === 'full') {\n",
       "            // Full images could contain transparency (where diff images\n",
       "            // almost always do), so we need to clear the canvas so that\n",
       "            // there is no ghosting.\n",
       "            fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "        }\n",
       "        fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "    };\n",
       "\n",
       "    this.imageObj.onunload = function () {\n",
       "        fig.ws.close();\n",
       "    };\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_header = function () {\n",
       "    var titlebar = document.createElement('div');\n",
       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
       "    var titletext = document.createElement('div');\n",
       "    titletext.classList = 'ui-dialog-title';\n",
       "    titletext.setAttribute(\n",
       "        'style',\n",
       "        'width: 100%; text-align: center; padding: 3px;'\n",
       "    );\n",
       "    titlebar.appendChild(titletext);\n",
       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = (this.canvas_div = document.createElement('div'));\n",
       "    canvas_div.setAttribute(\n",
       "        'style',\n",
       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
       "            'overflow: hidden;' +\n",
       "            'position: relative;' +\n",
       "            'resize: both;'\n",
       "    );\n",
       "\n",
       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
       "    // Apply a ponyfill if ResizeObserver is not implemented by browser.\n",
       "    if (this.ResizeObserver === undefined) {\n",
       "        if (window.ResizeObserver !== undefined) {\n",
       "            this.ResizeObserver = window.ResizeObserver;\n",
       "        } else {\n",
       "            var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n",
       "            this.ResizeObserver = obs.ResizeObserver;\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    this.resizeObserverInstance.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'dblclick',\n",
       "        on_mouse_event_closure('dblclick')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus() {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', { width: x_pixels, height: y_pixels });\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_message = function (type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function () {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    fig.rubberband_canvas.style.cursor = msg['cursor'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\n",
       "                /* FIXME: We get \"Resource interpreted as Image but\n",
       "                 * transferred with MIME type text/plain:\" errors on\n",
       "                 * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "                 * to be part of the websocket stream */\n",
       "                img.type = 'image/png';\n",
       "            }\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "// from https://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function (e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e) {\n",
       "        e = window.event;\n",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
       "\n",
       "    return { x: x, y: y };\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * https://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    var canvas_pos = mpl.findpos(event);\n",
       "\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(data);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "\n",
    "..."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05dec31c",
   "metadata": {},
   "source": [
    "What's the prominent frequency? Does it make sense? If not, what's wrong with the code?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "id": "a33fff66",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Answer here"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "567fd6a9",
   "metadata": {},
   "source": [
    "## (b)\n",
    "\n",
    "Calculate and plot Fourier transform of sawtooth function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "89a9320a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.signal import sawtooth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "880d6f3c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1ee98479b20>]"
      ]
     },
     "execution_count": 131,
     "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": [
    "t = np.linspace(0, 20, 50)\n",
    "y= sawtooth(2 * np.pi * 5 * t)\n",
    "plt.plot(t,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "id": "3378c2c3",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Reza Ajam\\anaconda3\\lib\\site-packages\\numpy\\core\\_asarray.py:102: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return array(a, dtype, copy=False, order=order)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'fft[x(t)]')"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ra= (fft(x))[:1000 // 2]\n",
    "fourier = fftfreq(1000, 20/1000)[:1000 // 2]\n",
    "plt.figure(figsize = (10, 8))\n",
    "plt.plot(fourier, ra, 'ro')\n",
    "plt.xlabel('f[Hz]')\n",
    "plt.ylabel('fft[x(t)]')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4fbb7db1",
   "metadata": {},
   "source": [
    "# Q3: Sunspot data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be22bf6d",
   "metadata": {},
   "source": [
    "The attached file `Sunspots.csv` contains monthly solar activity data over a 272 year period. First read the data in a pandas Dataframe and tell pandas to interpret the second column as `datetime`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "42c142e4",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "9c5b2072",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       Num        Date  Monthly\n",
      "0        0  1749-01-31     96.7\n",
      "1        1  1749-02-28    104.3\n",
      "2        2  1749-03-31    116.7\n",
      "3        3  1749-04-30     92.8\n",
      "4        4  1749-05-31    141.7\n",
      "...    ...         ...      ...\n",
      "3260  3260  2020-09-30      0.6\n",
      "3261  3261  2020-10-31     14.4\n",
      "3262  3262  2020-11-30     34.0\n",
      "3263  3263  2020-12-31     21.8\n",
      "3264  3264  2021-01-31     10.4\n",
      "\n",
      "[3265 rows x 3 columns]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Date'>"
      ]
     },
     "execution_count": 66,
     "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": [
    "df=pd.read_csv('Sunspots.csv')\n",
    "print(df)\n",
    "df.plot(x='Date', y='Monthly')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b98fe304",
   "metadata": {},
   "source": [
    "## (a)\n",
    "\n",
    "Do an appropriate Fourier analysis to determine the main cylce of solar activity. What's the period?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "1f184955",
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "'<' not supported between instances of 'list' and 'int'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32mC:\\Users\\REZAAJ~1\\AppData\\Local\\Temp/ipykernel_11016/1122315804.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      6\u001b[0m     \u001b[0mlis2\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mj\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      7\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlis\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mlis2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 8\u001b[1;33m \u001b[0mfft\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlis2\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mlis\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      9\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     10\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\scipy\\fft\\_backend.py\u001b[0m in \u001b[0;36m__ua_function__\u001b[1;34m(method, args, kwargs)\u001b[0m\n\u001b[0;32m     21\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mfn\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     22\u001b[0m             \u001b[1;32mreturn\u001b[0m \u001b[0mNotImplemented\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 23\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mfn\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     24\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     25\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\scipy\\fft\\_pocketfft\\basic.py\u001b[0m in \u001b[0;36mc2c\u001b[1;34m(forward, x, n, axis, norm, overwrite_x, workers, plan)\u001b[0m\n\u001b[0;32m     21\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     22\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mn\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 23\u001b[1;33m         \u001b[0mtmp\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcopied\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_fix_shape_1d\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtmp\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mn\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     24\u001b[0m         \u001b[0moverwrite_x\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0moverwrite_x\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0mcopied\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     25\u001b[0m     \u001b[1;32melif\u001b[0m \u001b[0mtmp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0maxis\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m<\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\scipy\\fft\\_pocketfft\\helper.py\u001b[0m in \u001b[0;36m_fix_shape_1d\u001b[1;34m(x, n, axis)\u001b[0m\n\u001b[0;32m    138\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    139\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0m_fix_shape_1d\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mn\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 140\u001b[1;33m     \u001b[1;32mif\u001b[0m \u001b[0mn\u001b[0m \u001b[1;33m<\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    141\u001b[0m         raise ValueError(\n\u001b[0;32m    142\u001b[0m             \"invalid number of data points ({0}) specified\".format(n))\n",
      "\u001b[1;31mTypeError\u001b[0m: '<' not supported between instances of 'list' and 'int'"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error in callback <function flush_figures at 0x000001EE859CD9D0> (for post_execute):\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\matplotlib_inline\\backend_inline.py\u001b[0m in \u001b[0;36mflush_figures\u001b[1;34m()\u001b[0m\n\u001b[0;32m    119\u001b[0m         \u001b[1;31m# ignore the tracking, just draw and close all figures\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    120\u001b[0m         \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 121\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mshow\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;32mTrue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    122\u001b[0m         \u001b[1;32mexcept\u001b[0m \u001b[0mException\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    123\u001b[0m             \u001b[1;31m# safely show traceback if in IPython, else raise\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\matplotlib_inline\\backend_inline.py\u001b[0m in \u001b[0;36mshow\u001b[1;34m(close, block)\u001b[0m\n\u001b[0;32m     39\u001b[0m     \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     40\u001b[0m         \u001b[1;32mfor\u001b[0m \u001b[0mfigure_manager\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mGcf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_all_fig_managers\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 41\u001b[1;33m             display(\n\u001b[0m\u001b[0;32m     42\u001b[0m                 \u001b[0mfigure_manager\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcanvas\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     43\u001b[0m                 \u001b[0mmetadata\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0m_fetch_figure_metadata\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfigure_manager\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcanvas\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\IPython\\core\\display.py\u001b[0m in \u001b[0;36mdisplay\u001b[1;34m(include, exclude, metadata, transient, display_id, *objs, **kwargs)\u001b[0m\n\u001b[0;32m    318\u001b[0m             \u001b[0mpublish_display_data\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mobj\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmetadata\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mmetadata\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    319\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 320\u001b[1;33m             \u001b[0mformat_dict\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmd_dict\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mformat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mobj\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0minclude\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0minclude\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mexclude\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mexclude\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    321\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mformat_dict\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    322\u001b[0m                 \u001b[1;31m# nothing to display (e.g. _ipython_display_ took over)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\IPython\\core\\formatters.py\u001b[0m in \u001b[0;36mformat\u001b[1;34m(self, obj, include, exclude)\u001b[0m\n\u001b[0;32m    178\u001b[0m             \u001b[0mmd\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    179\u001b[0m             \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 180\u001b[1;33m                 \u001b[0mdata\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mformatter\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mobj\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    181\u001b[0m             \u001b[1;32mexcept\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    182\u001b[0m                 \u001b[1;31m# FIXME: log the exception\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\decorator.py\u001b[0m in \u001b[0;36mfun\u001b[1;34m(*args, **kw)\u001b[0m\n\u001b[0;32m    230\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mkwsyntax\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    231\u001b[0m                 \u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkw\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfix\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkw\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msig\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 232\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mcaller\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mextras\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkw\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    233\u001b[0m     \u001b[0mfun\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__name__\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__name__\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    234\u001b[0m     \u001b[0mfun\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__doc__\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__doc__\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\IPython\\core\\formatters.py\u001b[0m in \u001b[0;36mcatch_format_error\u001b[1;34m(method, self, *args, **kwargs)\u001b[0m\n\u001b[0;32m    222\u001b[0m     \u001b[1;34m\"\"\"show traceback on failed format call\"\"\"\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    223\u001b[0m     \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 224\u001b[1;33m         \u001b[0mr\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmethod\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    225\u001b[0m     \u001b[1;32mexcept\u001b[0m \u001b[0mNotImplementedError\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    226\u001b[0m         \u001b[1;31m# don't warn on NotImplementedErrors\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\IPython\\core\\formatters.py\u001b[0m in \u001b[0;36m__call__\u001b[1;34m(self, obj)\u001b[0m\n\u001b[0;32m    339\u001b[0m                 \u001b[1;32mpass\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    340\u001b[0m             \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 341\u001b[1;33m                 \u001b[1;32mreturn\u001b[0m \u001b[0mprinter\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mobj\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    342\u001b[0m             \u001b[1;31m# Finally look for special method names\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    343\u001b[0m             \u001b[0mmethod\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mget_real_method\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mobj\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mprint_method\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\IPython\\core\\pylabtools.py\u001b[0m in \u001b[0;36mprint_figure\u001b[1;34m(fig, fmt, bbox_inches, base64, **kwargs)\u001b[0m\n\u001b[0;32m    149\u001b[0m         \u001b[0mFigureCanvasBase\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfig\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    150\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 151\u001b[1;33m     \u001b[0mfig\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcanvas\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mprint_figure\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mbytes_io\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkw\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    152\u001b[0m     \u001b[0mdata\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mbytes_io\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mgetvalue\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    153\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mfmt\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34m'svg'\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\matplotlib\\backend_bases.py\u001b[0m in \u001b[0;36mprint_figure\u001b[1;34m(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)\u001b[0m\n\u001b[0;32m   2228\u001b[0m                        else suppress())\n\u001b[0;32m   2229\u001b[0m                 \u001b[1;32mwith\u001b[0m \u001b[0mctx\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 2230\u001b[1;33m                     \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdraw\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrenderer\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   2231\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2232\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mbbox_inches\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\matplotlib\\artist.py\u001b[0m in \u001b[0;36mdraw_wrapper\u001b[1;34m(artist, renderer, *args, **kwargs)\u001b[0m\n\u001b[0;32m     72\u001b[0m     \u001b[1;33m@\u001b[0m\u001b[0mwraps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdraw\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     73\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0mdraw_wrapper\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0martist\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrenderer\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 74\u001b[1;33m         \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdraw\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0martist\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrenderer\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     75\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mrenderer\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_rasterizing\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     76\u001b[0m             \u001b[0mrenderer\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstop_rasterizing\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\matplotlib\\artist.py\u001b[0m in \u001b[0;36mdraw_wrapper\u001b[1;34m(artist, renderer, *args, **kwargs)\u001b[0m\n\u001b[0;32m     49\u001b[0m                 \u001b[0mrenderer\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstart_filter\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     50\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 51\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mdraw\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0martist\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrenderer\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     52\u001b[0m         \u001b[1;32mfinally\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     53\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0martist\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_agg_filter\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\matplotlib\\figure.py\u001b[0m in \u001b[0;36mdraw\u001b[1;34m(self, renderer)\u001b[0m\n\u001b[0;32m   2788\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2789\u001b[0m             \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpatch\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdraw\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrenderer\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 2790\u001b[1;33m             mimage._draw_list_compositing_images(\n\u001b[0m\u001b[0;32m   2791\u001b[0m                 renderer, self, artists, self.suppressComposite)\n\u001b[0;32m   2792\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\matplotlib\\image.py\u001b[0m in \u001b[0;36m_draw_list_compositing_images\u001b[1;34m(renderer, parent, artists, suppress_composite)\u001b[0m\n\u001b[0;32m    130\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mnot_composite\u001b[0m \u001b[1;32mor\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mhas_images\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    131\u001b[0m         \u001b[1;32mfor\u001b[0m \u001b[0ma\u001b[0m \u001b[1;32min\u001b[0m \u001b[0martists\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 132\u001b[1;33m             \u001b[0ma\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdraw\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrenderer\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    133\u001b[0m     \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    134\u001b[0m         \u001b[1;31m# Composite any adjacent images together\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\matplotlib\\artist.py\u001b[0m in \u001b[0;36mdraw_wrapper\u001b[1;34m(artist, renderer, *args, **kwargs)\u001b[0m\n\u001b[0;32m     49\u001b[0m                 \u001b[0mrenderer\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstart_filter\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     50\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 51\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mdraw\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0martist\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrenderer\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     52\u001b[0m         \u001b[1;32mfinally\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     53\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0martist\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_agg_filter\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\matplotlib\\_api\\deprecation.py\u001b[0m in \u001b[0;36mwrapper\u001b[1;34m(*inner_args, **inner_kwargs)\u001b[0m\n\u001b[0;32m    429\u001b[0m                          \u001b[1;32melse\u001b[0m \u001b[0mdeprecation_addendum\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    430\u001b[0m                 **kwargs)\n\u001b[1;32m--> 431\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0minner_args\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0minner_kwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    432\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    433\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0mwrapper\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\matplotlib\\axes\\_base.py\u001b[0m in \u001b[0;36mdraw\u001b[1;34m(self, renderer, inframe)\u001b[0m\n\u001b[0;32m   2919\u001b[0m             \u001b[0mrenderer\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstop_rasterizing\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2920\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 2921\u001b[1;33m         \u001b[0mmimage\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_draw_list_compositing_images\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrenderer\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0martists\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   2922\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2923\u001b[0m         \u001b[0mrenderer\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mclose_group\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'axes'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\matplotlib\\image.py\u001b[0m in \u001b[0;36m_draw_list_compositing_images\u001b[1;34m(renderer, parent, artists, suppress_composite)\u001b[0m\n\u001b[0;32m    130\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mnot_composite\u001b[0m \u001b[1;32mor\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mhas_images\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    131\u001b[0m         \u001b[1;32mfor\u001b[0m \u001b[0ma\u001b[0m \u001b[1;32min\u001b[0m \u001b[0martists\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 132\u001b[1;33m             \u001b[0ma\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdraw\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrenderer\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    133\u001b[0m     \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    134\u001b[0m         \u001b[1;31m# Composite any adjacent images together\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\matplotlib\\artist.py\u001b[0m in \u001b[0;36mdraw_wrapper\u001b[1;34m(artist, renderer, *args, **kwargs)\u001b[0m\n\u001b[0;32m     49\u001b[0m                 \u001b[0mrenderer\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstart_filter\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     50\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 51\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mdraw\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0martist\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrenderer\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     52\u001b[0m         \u001b[1;32mfinally\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     53\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0martist\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_agg_filter\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\matplotlib\\axis.py\u001b[0m in \u001b[0;36mdraw\u001b[1;34m(self, renderer, *args, **kwargs)\u001b[0m\n\u001b[0;32m   1151\u001b[0m         \u001b[1;31m# the actual bbox\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1152\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1153\u001b[1;33m         \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_update_label_position\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrenderer\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1154\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1155\u001b[0m         \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlabel\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdraw\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrenderer\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\matplotlib\\axis.py\u001b[0m in \u001b[0;36m_update_label_position\u001b[1;34m(self, renderer)\u001b[0m\n\u001b[0;32m   2083\u001b[0m         \u001b[1;31m# get bounding boxes for this axis and any siblings\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2084\u001b[0m         \u001b[1;31m# that have been set by `fig.align_xlabels()`\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 2085\u001b[1;33m         \u001b[0mbboxes\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mbboxes2\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_get_tick_boxes_siblings\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrenderer\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mrenderer\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   2086\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2087\u001b[0m         \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlabel\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_position\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\matplotlib\\axis.py\u001b[0m in \u001b[0;36m_get_tick_boxes_siblings\u001b[1;34m(self, renderer)\u001b[0m\n\u001b[0;32m   1871\u001b[0m             \u001b[0maxis\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_get_axis_map\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0maxis_name\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1872\u001b[0m             \u001b[0mticks_to_draw\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0maxis\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_update_ticks\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1873\u001b[1;33m             \u001b[0mtlb\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtlb2\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0maxis\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_get_tick_bboxes\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mticks_to_draw\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrenderer\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1874\u001b[0m             \u001b[0mbboxes\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mextend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtlb\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1875\u001b[0m             \u001b[0mbboxes2\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mextend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtlb2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\matplotlib\\axis.py\u001b[0m in \u001b[0;36m_get_tick_bboxes\u001b[1;34m(self, ticks, renderer)\u001b[0m\n\u001b[0;32m   1066\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0m_get_tick_bboxes\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mticks\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrenderer\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1067\u001b[0m         \u001b[1;34m\"\"\"Return lists of bboxes for ticks' label1's and label2's.\"\"\"\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1068\u001b[1;33m         return ([tick.label1.get_window_extent(renderer)\n\u001b[0m\u001b[0;32m   1069\u001b[0m                  for tick in ticks if tick.label1.get_visible()],\n\u001b[0;32m   1070\u001b[0m                 [tick.label2.get_window_extent(renderer)\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\matplotlib\\axis.py\u001b[0m in \u001b[0;36m<listcomp>\u001b[1;34m(.0)\u001b[0m\n\u001b[0;32m   1066\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0m_get_tick_bboxes\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mticks\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrenderer\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1067\u001b[0m         \u001b[1;34m\"\"\"Return lists of bboxes for ticks' label1's and label2's.\"\"\"\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1068\u001b[1;33m         return ([tick.label1.get_window_extent(renderer)\n\u001b[0m\u001b[0;32m   1069\u001b[0m                  for tick in ticks if tick.label1.get_visible()],\n\u001b[0;32m   1070\u001b[0m                 [tick.label2.get_window_extent(renderer)\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\matplotlib\\text.py\u001b[0m in \u001b[0;36mget_window_extent\u001b[1;34m(self, renderer, dpi)\u001b[0m\n\u001b[0;32m    901\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    902\u001b[0m         \u001b[1;32mwith\u001b[0m \u001b[0mcbook\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_setattr_cm\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdpi\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mdpi\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 903\u001b[1;33m             \u001b[0mbbox\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0minfo\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdescent\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_get_layout\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_renderer\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    904\u001b[0m             \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_unitless_position\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    905\u001b[0m             \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_transform\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtransform\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\matplotlib\\text.py\u001b[0m in \u001b[0;36m_get_layout\u001b[1;34m(self, renderer)\u001b[0m\n\u001b[0;32m    312\u001b[0m             \u001b[0mclean_line\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mismath\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_preprocess_math\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mline\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    313\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mclean_line\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 314\u001b[1;33m                 w, h, d = renderer.get_text_width_height_descent(\n\u001b[0m\u001b[0;32m    315\u001b[0m                     clean_line, self._fontproperties, ismath=ismath)\n\u001b[0;32m    316\u001b[0m             \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\matplotlib\\backends\\backend_agg.py\u001b[0m in \u001b[0;36mget_text_width_height_descent\u001b[1;34m(self, s, prop, ismath)\u001b[0m\n\u001b[0;32m    238\u001b[0m         \u001b[0mflags\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mget_hinting_flag\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    239\u001b[0m         \u001b[0mfont\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_get_agg_font\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mprop\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 240\u001b[1;33m         \u001b[0mfont\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mset_text\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ms\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0.0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mflags\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mflags\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    241\u001b[0m         \u001b[0mw\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mh\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfont\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_width_height\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m  \u001b[1;31m# width and height of unrotated string\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    242\u001b[0m         \u001b[0md\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfont\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_descent\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "\n",
    "\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 328,
   "id": "157ca964",
   "metadata": {},
   "outputs": [],
   "source": [
    "# The main period is: ..."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f86b4688",
   "metadata": {},
   "source": [
    "## (b)\n",
    "First do an inverse Fourier analysis to confirm that you get back the same data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 340,
   "id": "8337e039",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.fft import ifft"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a58f33f8",
   "metadata": {},
   "source": [
    "## (c)\n",
    "\n",
    "Remover the first ten biggest values of Fourier transformed series, do an inverse transform once more and plot the results."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c82dd951",
   "metadata": {},
   "source": [
    "Why does the plot look different? And what's the difference?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 394,
   "id": "aa3d2a38",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Explain here ..."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dabdc648",
   "metadata": {},
   "source": [
    "# Q4: Correlation function and power spectrum"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f1c72a3",
   "metadata": {},
   "source": [
    "Remember from last homework that we calculated autocorrelation function for a data that we made?\n",
    "\n",
    "Load the data saved as `2pcf.txt`, calculate the correlation function once more and then plot the power spectrum using that data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8ec4bc40",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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1H8Zd08mc0x+iJL9ZVT/r7r8XOLeq3jPmshaU5ELgv7oT7B8HqKoPjrmseSX5PeCXwOeAv62qg2Mu6UW6S4z8L32XGAEum8RLjAAk+SPgaeDGqvr9cddzKkk2Ahur6t4krwTuAd46if9tkwR4eVU9neQ04FvA+6rq7jGX9jw7/SE6EfidlwMTfUStqq9W1bPdw7vpfW9iIlXVw1U1yd/Ofv4SI1X1f8CJS4xMpKr6JvDUuOsYRFUdq6p7u/s/Bx6m9+3+iVM9T3cPT+tuE5UDhv6QJbkmyWHgL4G/H3c9S/DXwH+Mu4gpNt8lRiYymKZZkhngdcC3x1zKgpKsS3IIOA7sr6qJqtXQX6IkX0vywDy37QBV9eGq2gTcBFw53moXr7fb58PAs/RqHptBalW7krwCuA14/0mfqidKVT1XVVvpfXLelmSips8m7to7k66q/mTAXW8C9gFXr2I5i1qs3iR/BfwZcEGN+QTPEv7bTiIvMbKKuvnx24Cbqur2cdcziKr6SZKvAxcBE3PC3E5/iJJs6Xu4HfjuuGoZRPcHbf4O+POqembc9Uw5LzGySrqTo9cDD1fVJ8ddz6kkWX9iFVyS36B3Yn+icsDVO0OU5Dbgd+mtMnkceE9VTWy3l2QOeBnwo27o7kldbZTkbcC/AuuBnwCHquotYy3qJEkuAf6FFy4xcs14K1pYkpuB8+ld/vcJ4Oqqun6sRS0gyZuA/wbup/f/FsBVVbVvfFXNL8kfADfQ+zfwEuDWqvroeKt6MUNfkhri9I4kNcTQl6SGGPqS1BBDX5IaYuhLUkMMfUlqiKEvSQ35f7Vfw/aNwr9yAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "09b0705a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your answers here"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e535676a",
   "metadata": {},
   "source": [
    "# Q5: Real world example (Bonous question)\n",
    "\n",
    "The two point correlation function is like autocorrelation but for multi-dimensional data. Here instead of \"lags\" we use distances.\n",
    "\n",
    "The file `cmb_camb_N1024_PS12.npy` is part of the CMB temperature map, you can read it directly using `np.load` function.\n",
    "\n",
    "Calculate the two point correlation for the CMB map, plot it, and then calculate the power spectrum and plot it too.\n",
    "\n",
    "P.S. the provided data is 1024$\\times$1024, it needs too much computational power to calculate correlation for every point. You may use only a fraction of data points, if they are chosen randomly, the result would be the same. Also for the distances, you do not need to cover the whole length of the image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1609d819",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "07adc3ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your answers here"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}