07_Romberg.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "ae811d4d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.9899924966004454"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "#def f(x):\n",
    "#    return -x**2 + 4\n",
    "#\n",
    "#def F(x):\n",
    "#    return -x**3 / 3 + 4*x\n",
    "#\n",
    "#a = -2\n",
    "#b = 2\n",
    "def f(x):\n",
    "    return np.sin(x)\n",
    "\n",
    "def F(x):\n",
    "    return -np.cos(x)\n",
    "\n",
    "a = 0\n",
    "b = 3\n",
    "K = 6\n",
    "\n",
    "def exact_integral():\n",
    "    return F(b) - F(a)\n",
    "    \n",
    "exact_integral()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "4a6dea6e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.21168001 1.60208249 1.89582521 1.96661743 1.98415902 1.98853477]\n",
      "[1.77831248e+00 3.87910011e-01 9.41672859e-02 2.33750650e-02\n",
      " 5.83347505e-03 1.45772758e-03]\n"
     ]
    }
   ],
   "source": [
    "def trapezoidal_sum(f, N):\n",
    "    h = (b - a) / N\n",
    "    result = h * 0.5 * (f(a) + f(b))\n",
    "    for i in range(1, N):\n",
    "        result += h * f(a + i * h)\n",
    "    return result\n",
    "\n",
    "result_trap = np.zeros(K)\n",
    "errors_trap = np.zeros(K)\n",
    "\n",
    "for N in range(K):\n",
    "    result_trap[N] = trapezoidal_sum(f, 2**N)\n",
    "    errors_trap[N] = np.abs(result_trap[N] - exact_integral())\n",
    "print(result_trap)\n",
    "print(errors_trap)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "f5fa3082",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.60208249 1.99373945 1.98997986 1.98999251 1.9899925  1.9899925 ]\n",
      "[3.87910011e-01 3.74695563e-03 1.26322543e-05 1.11207259e-08\n",
      " 2.46869192e-12 4.44089210e-16]\n"
     ]
    }
   ],
   "source": [
    "def romberg(f, N, p=False):\n",
    "    Q = np.zeros((N, N))\n",
    "    for i in range(N):\n",
    "        Q[i, 0] = trapezoidal_sum(f, 2**(i+1))\n",
    "        \n",
    "    for k in range(1, N):\n",
    "        for i in range(k, N):\n",
    "            h_i = (b-a) / 2**i\n",
    "            h_ik = (b-a) / 2**(i-k)\n",
    "            Q[i, k] = Q[i, k-1] + (Q[i, k-1] - Q[i-1, k-1]) / ((h_ik**2) / (h_i**2) - 1)\n",
    "    if p:\n",
    "        print(Q)\n",
    "    return Q[N-1, N-1]\n",
    "    \n",
    "result_romb = np.zeros(K)\n",
    "errors_romb = np.zeros(K)\n",
    "\n",
    "for N in range(K):\n",
    "    result_romb[N] = romberg(f, N+1)\n",
    "    errors_romb[N] = np.abs(result_romb[N] - exact_integral())\n",
    "print(result_romb)\n",
    "print(errors_romb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "9cd7fb43",
   "metadata": {},
   "outputs": [
    {
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       "\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",
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       "        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",
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       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
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       "        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",
       "    var cursor = msg['cursor'];\n",
       "    switch (cursor) {\n",
       "        case 0:\n",
       "            cursor = 'pointer';\n",
       "            break;\n",
       "        case 1:\n",
       "            cursor = 'default';\n",
       "            break;\n",
       "        case 2:\n",
       "            cursor = 'crosshair';\n",
       "            break;\n",
       "        case 3:\n",
       "            cursor = 'move';\n",
       "            break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = 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 http://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",
       " * http://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, CTRL fixes aspect\", \"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",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager) {\n",
       "        manager = IPython.keyboard_manager;\n",
       "    }\n",
       "\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": {
      "text/html": [
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1.989992496600445"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib notebook\n",
    "import scipy.interpolate as sp_int\n",
    "def visualize(f, N):\n",
    "    h = np.zeros(N)\n",
    "    Q = np.zeros(N)\n",
    "    for i in range(N):\n",
    "        h[i] = (b-a) / 2**i\n",
    "        Q[i] = trapezoidal_sum(f, 2**(i+1))\n",
    "    plt.scatter(h**2, Q)\n",
    "    x = np.linspace(0, h[0]**2, 101)\n",
    "    y = sp_int.barycentric_interpolate(h**2, Q, x)\n",
    "    plt.plot(x, y)\n",
    "    return y[0]\n",
    "\n",
    "        \n",
    "visualize(f, K)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}