VMC.ipynb

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    "\n",
    "# Sesión II. Monte Carlo Variacional \n",
    "\n",
    ">*<div style=\"text-align: justify\">\"The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation.\"<br></div>*\n",
    "Paul A. M. Dirac<br>\n",
    "__Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, Vol. 123, No. 792 (6 April 1929)__\n",
    "\n",
    "\n",
    "\n",
    "## 2.1 La ecuación de Schrödinger\n",
    "\n",
    "La ecuación que determina la evolución de un sistema cuántico es la ecuación de Schrödinger, esta describe la evolución de la función de onda de un sistema de partículas. Donde el Hamiltoniano pasa de ser una función real a un operador en el espacio de Hilbert determinado por el mismo $\\hat{H}=\\hat{T}+\\hat{V}$ \n",
    "\n",
    "$$ i\\hbar {\\frac {d}{dt}}\\vert \\Psi (t)\\rangle ={\\hat {H}}\\vert \\Psi (t)\\rangle $$\n",
    "\n",
    "La ecuación de Schrödinger determina la dependencia temporal de forma explicita en representación en el espacio real:  \n",
    "\n",
    "$$ i\\hbar {\\frac {\\partial }{\\partial t}}\\Psi (\\mathbf {r} ,t)=\\left[{-\\frac {\\hbar ^{2}}{2m}}\\nabla ^{2}+V(\\mathbf {r} ,t)\\right]\\Psi (\\mathbf {r} ,t)$$\n",
    "\n",
    "Observamos que el operador energía cinética es $$\\hat{T}=-\\frac{\\hbar ^{2}}{2m}\\nabla ^{2}$$ para efectos de este curso estamos interesados en el caso estacionario de la ecuación de Schrödinger \n",
    "\n",
    "$$\\Psi (\\mathbf {r} ,t)=\\Phi(t)\\psi(\\mathbf {r})$$\n",
    "\n",
    "Considerando adicionalmente $V(r)$ un potencial independiente del tiempo, tenemos:\n",
    "\n",
    "$$ i\\hbar {\\frac {\\partial }{\\partial t}}\\Phi(t)\\psi(\\mathbf {r})=\\left[{-\\frac {\\hbar ^{2}}{2m}}\\nabla^{2}+V(\\mathbf {r})\\right]\\Phi(t)\\psi(\\mathbf {r})$$\n",
    "\n",
    "Usando el Ansatz $\\Phi(t)=\\exp\\left(-\\frac{iEt}{\\hbar}\\right)$ la ecuación es simplificada: \n",
    "\n",
    "$$ E \\psi(\\mathbf {r})=\\left[{-\\frac {\\hbar ^{2}}{2m}}\\nabla^{2}+V(\\mathbf {r})\\right]\\psi(\\mathbf {r})$$\n",
    "\n",
    "\n",
    "## 2.2 El Principio Variacional \n",
    "\n",
    "Supongan tenemos la ecuación de Scrhodinger indpendiente del tiempo, para una dada función de onda $\\psi$\n",
    "\n",
    "$$H\\psi =E\\psi$$\n",
    "\n",
    "Con H un hamiltoniano de un sistema de muchos cuerpos bastante complejo, si $\\psi$ es normalizada el __Principio Variacional__ nos dice que el valor esperado de energía de la función de onda $\\psi$  es menor que la energía del estado base $E_{0}$\n",
    "\n",
    "$$ E_{0}\\leq \\langle \\psi | H | \\psi \\rangle  $$\n",
    "\n",
    "Esto quiere decir que si hacemos una variación de $\\psi$ el valor esperado de H puede ser minimizado para obtener una aproximación razonable al estado Base. Para probar el principio variacional partamos del hecho que debe existir un conjunto de autovectores y autovalores para H:\n",
    "\n",
    "$$H|\\psi_n\\rangle =E_n|\\psi_n\\rangle$$\n",
    "\n",
    "Por definición estos autovectores son ortonormales \n",
    "\n",
    "$$\\langle \\psi_n|\\psi_m \\rangle=\\delta_{mn}$$\n",
    "\n",
    "Sus autovalores estan ordenados: \n",
    "\n",
    "$$E_{0}<E_{1}<E_{2}<\\cdots<E_{n-1}<E_{n}$$\n",
    "\n",
    "De tal forma que este conjunto de autovectores forman una base para representar cualquier función de onda $\\psi$, como una combinación lineal de estos:\n",
    "\n",
    "$$|\\psi\\rangle=\\sum_{n} C_{n}|\\psi_{n}\\rangle$$\n",
    "\n",
    "Ya que $\\psi$ es normalizada, los coeficientes cumplen la condición:\n",
    "\n",
    "$$\\sum_{n}|C_{n}|^{2}=1$$\n",
    "\n",
    "Ahora calculemos el valor esperado de $\\psi$ en terminos de  esta expansión: \n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\langle \\psi | H | \\psi \\rangle & =  \\sum_{m} C^{*}_{m}\\langle \\psi_m | H \\sum_{n} C_{n}|\\psi_n\\rangle\\\\\n",
    "& =  \\sum_{m,n} C^{*}_{m} C_{n}|\\langle \\psi_m |H|\\psi_n\\rangle\\\\\n",
    "& =  \\sum_{m,n} C^{*}_{m} C_{n}| E_{n}\\langle psi_m |\\psi_n\\rangle \\\\\n",
    "& =  \\sum_{m,n} C^{*}_{m} C_{n}| E_{n}\\delta_{mn} \\\\\n",
    "& =  \\sum_{n} |C_{n}|^{2} | E_{n}\\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Esta expresión puede ser reordenada:\n",
    "\n",
    "\n",
    "$$\n",
    "\\langle \\psi | H | \\psi \\rangle  = |C_{0}|^{2} | E_{0}+ \\sum_{n>0} |C_{n}|^{2}  E_{n} \n",
    "$$\n",
    "\n",
    "Adicionalmente la condición de normalización de $\\psi$ sobre los coeficientes:\n",
    "\n",
    "$$|C_{0}|^{2}= 1-\\sum_{n>0}|C_{n}|^{2}$$\n",
    "\n",
    "Reemplazando esto en la expresión anterior:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\langle \\psi | H | \\psi \\rangle  &= \\left( 1-\\sum_{n>0}|C_{n}|^{2}\\right)| E_{0}+ \\sum_{n>0} |C_{n}|^{2} E_{n}\\\\\n",
    "&= E_{0}+ \\sum_{n>0} |C_{n}|^{2} (E_{n}-E_{0})\\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Esta expersión definida positivamente ya que $$(E_{n}-E_{0})>0\\; \\forall n>0 $$ de esta manera, obetenemos el __Principio Variacional__\n",
    "\n",
    "\n",
    "$$\\langle \\psi | H | \\psi \\rangle\\geq E_{0}$$\n",
    "\n",
    "Luego siempre podemos encontrar una función $\\psi$ que minimizada sera un limite superior al estado base. El exito del metodo Variacional dependera de la parametrización de la función de onda y de su minimizacion. Este principio constituye un pilar importante de la mayoria de metodos de Monte Carlo cuántco, tambien lo es para otros metodos variacionales como Densidad funciónal y otros metodos de quimica cuántca.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "## 2.3 Conectando el principio Variacional con Monte Carlo\n",
    "\n",
    "La evaluación de un observable cuántco a temperatura cero, dada una función de onda $|\\psi\\rangle$ que define el estado del sistema: \n",
    "\n",
    "$$\\langle \\hat{O} \\rangle = \\langle \\psi | \\hat{O} | \\psi\\rangle$$\n",
    "\n",
    "Usando la condición de normalización \n",
    "\n",
    "$$\\langle \\hat{O} \\rangle = \\frac{\\langle \\psi | \\hat{O} | \\psi\\rangle}{\\langle \\psi | \\psi\\rangle}$$\n",
    "\n",
    "Supongamos usamos una base de estados en el espacio de Hilbert que es completa y ortornormal tal que: \n",
    "\n",
    "$$\\sum_{N}|x\\rangle\\langle x|=\\mathbb{1}\\$$\n",
    "\n",
    "Usando esta relación de completes en el denominador y numerador de la expresión del observable:\n",
    "\n",
    "$$\n",
    "\\langle \\hat{O} \\rangle = \\frac{\\sum_{N}\\langle \\psi |x\\rangle\\langle x| \\hat{O}\\psi\\rangle}{\\sum_{N} \\langle \\psi |x\\rangle\\langle x| \\psi\\rangle}\n",
    "$$\n",
    "\n",
    "Si multiplicamos por $1=\\frac{\\langle x| \\psi\\rangle}{\\langle x| \\psi\\rangle}$:\n",
    "\n",
    "$$\\begin{align}\n",
    "\\langle \\hat{O} \\rangle &= \\frac{\\sum_{N}|\\langle x| \\psi\\rangle|^2 \\frac{\\langle x| \\hat{O} |\\psi\\rangle}{\\langle x| \\psi\\rangle}}{\\sum_{N} \\langle \\psi |x\\rangle\\langle x| \\psi\\rangle}\\\\\n",
    "& =\\frac{\\sum_{N}|\\psi(x)|^2  O_{L}(x)}{\\sum_{N} |\\psi(x)|^2}\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Con el estimador del operador local: \n",
    "\n",
    "$$O_{L}(x)=\\frac{\\langle x| \\hat{O} |\\psi\\rangle}{\\langle x| \\psi\\rangle}$$\n",
    "\n",
    "Para hacer la conexión con Monte Carlo el observable debe ser la forma que es el promedio del observable por la probabilidad, podemos identificar:  \n",
    "\n",
    "$$P(x)=\\frac{\\psi(x)|^2}{\\sum_{N} |\\psi(x)|^2}$$\n",
    "\n",
    "Esta puede ser interpretada como probabilidad ya que es siempre positiva para todo x, además es fácil de observar que:\n",
    "\n",
    "$$\\sum_{N}P(x)=1$$\n",
    "\n",
    "\n",
    "El observable local es la función sobre la cual se calcula el valor esperado con probabilidad $P(x)$, reemplazando el observable por el hamiltoniano H: \n",
    "\n",
    "$$E_{L}(x)=\\frac{\\langle x| \\hat{H} |\\psi\\rangle}{\\langle x| \\psi\\rangle}$$\n",
    "\n",
    "Luego es posible definir un algoritmo que genere diferentes configuraciones ${|x_{n}\\rangle}$, una cadena de Markov usando el algoritmo de Metropolis, que muestrea $P(x)$. Asi el valor esperado del observable puede ser aproximado como el promedio del observable local sobre diferentes configuraciones: \n",
    "\n",
    "$$\n",
    "\\langle \\hat{O} \\rangle =\\frac{1}{N}\\sum_{n=1}^{N} O_{L}(x_{n})\n",
    "$$\n",
    "\n",
    "\n",
    "Para la energía total del sistema $E(\\psi(\\mathbf(x))$ o $E_{VMC}$\n",
    "\n",
    "\n",
    "$$\n",
    "E = \\frac{1}{N}\\sum_{n=1}^{N} E_{L}(x_{n})\n",
    "$$\n",
    "\n",
    "## 2.3 Principio de Varianza Cero\n",
    "\n",
    "La varianza de $\\hat{H}$ de manera analoga es es definida como:  \n",
    "\n",
    "$$\\begin{align}\n",
    "\\sigma_{E}^2 &=\\frac{\\langle \\psi | (\\hat{H}-\\langle H \\rangle)^2 |\\psi \\rangle }{\\langle \\psi|\\psi\\rangle }\\\\\n",
    "&=\\frac{\\langle \\psi | (\\hat{H}-E)^2 |\\psi \\rangle }{\\langle \\psi|\\psi\\rangle }\\\\\n",
    "&=  \\left(\\frac{\\langle \\psi | \\hat{H}^2|\\psi \\rangle }{\\langle \\psi|\\psi\\rangle}-E^2\\right)    \n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Para obtener un buen estimado de la energía la varianza debe ser minimizada, el primer termino de la varianza es\n",
    "un promedio del valor cuadrado de la energía local:\n",
    "\n",
    "$$  \n",
    "\\frac{\\langle \\psi | \\hat{H}^2|\\psi \\rangle }{\\langle \\psi|\\psi\\rangle}=\\frac{\\sum_{N} |\\psi(\\mathbf{x})|^2 |E_{L}(\\mathbf(x))|^2}{\\sum_{N}|\\psi(\\mathbf(x))|^2}\n",
    "$$\n",
    "\n",
    "\n",
    "En el caso especial en que la función de onda variacional $\\psi(\\mathbf(x)$ es un autestado de $H$ tenemos\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "E_{L}(x)&=\\frac{\\langle x| \\hat{H} |\\psi\\rangle}{\\langle x| \\psi\\rangle}\\\\\n",
    "&=E_{n}\\frac{\\langle x|\\psi\\rangle}{\\langle x| \\psi\\rangle}\\\\\n",
    "&=E_{n} \n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "La energía local $E_{L}(x)=E_{n}=Constante$, es decir independiente de la configuración $\\mathbf{x}$, es facil observar que:  \n",
    "\n",
    "$$\n",
    "\\sigma_{E}^2 = 0\n",
    "$$\n",
    "\n",
    "En general nuestro objetivo es minimizar la varianza de la energía local $E_{L}(x)$ tal que nuestra función de onda variacional se acerca al estado base con gran presicion.\n",
    "\n",
    "Usualmente $\\psi(\\mathbf(x))=\\psi(\\mathbf(x),\\{\\alpha_i\\})$, donde $\\left\\{\\alpha_1,\\alpha_2,\\cdots\\alpha_n\\right\\}$ son un conjunto de parametros ajustables. De tal manera que son escogidos para minimizar la varianza, acercando la función de prueba al estado base lo mejor posible.  \n",
    "\n",
    "\n",
    "\n",
    "## 2.3.1 Algoritmo Metropolis\n",
    "\n",
    "El algoritmo Monte Carlo seria el siguiente is $\\mathbf{X}$ es una configuración del sistema descrito por el hamiltoniano H, \n",
    "\n",
    "1. Generar una configuración  $\\mathbf{X'}\\rightarrow\\mathbf{\\zeta}+\\mathbf{X}$\n",
    "2. Calcular la razón del criterio de aceptación \n",
    "\n",
    "$$p_{accept}(\\mathbf{X'}|\\mathbf{X})= Min\\left\\{1,\\frac{T(\\mathbf{X}|\\mathbf{X'})\\frac{|\\psi(\\mathbf{X'})|^2}{\\sum_{N} |\\psi(\\mathbf{X''})|^2}}{T(\\mathbf{X'}|\\mathbf{X})\\frac{|\\psi(\\mathbf{X})|^2}{\\sum_{N} |\\psi(\\mathbf{X''})|^2}}\\right\\}$$\n",
    "Simplificando \n",
    "\n",
    "$$p_{accept}(\\mathbf{X'}|\\mathbf{X})= Min\\left\\{1,\\frac{T(\\mathbf{X}|\\mathbf{X'})|\\psi(\\mathbf{X'})|^2}{T(\\mathbf{X'}|\\mathbf{X})|\\psi(\\mathbf{X})|^2}\\right\\}$$\n",
    "\n",
    "3. Aceptar o rechazar el movimiento propuesto \n",
    "\n",
    "4. Calcular la energía local $E_{L}$ sumarla para estimar $E$\n",
    "\n",
    "Luego se repiten los pasos, sucesivamente generando la candena de markov de estados que muestrean $P(\\mathbf{X})$ y satisfacen el principio variacional. \n",
    "\n",
    "La idea es que Monte Carlo nos da la mejor energía variacional para una función de onda $\\psi(x,\\left\\{\\mathbf{\\alpha}\\right\\})$, con  ${\\mathbf{\\alpha}\\right\\}$ un conjunto de parametros de los cuales depende la función de onda. La ida es optener los parametros optimos para que la energia Variacional sea lo más cercana posible a la energía del estado base.  \n",
    "\n",
    "\n",
    "## 2.3.2 Monte Carlo Variacional: El Oscilador Armonico 1d\n",
    "\n",
    "El Oscilador armonico esta dado por el siguiente hamiltoniano en una dimensión:\n",
    "\n",
    "$$\n",
    "-\\frac{\\hbar}{2m} \\frac{d^2}{dx^2}+\\frac{1}{2}\\omega x^2\n",
    "$$\n",
    "\n",
    "\n",
    "Supongamos no conocemos la solución exacta a este problema queremos usar la función de onda de la siguiente forma:\n",
    "\n",
    "$$\n",
    "\\psi_{T}(x,\\alpha)= \\exp(-\\alpha x^2)\n",
    "$$\n",
    "\n",
    "Usando unidades normalizadas $m=\\hbar=\\omega=1$, antes de escribir nuestro algoritmo en python lo primero que debemos hacer es encontrar la función de la energía local data nuestra función de onda de prueba:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "E_{L}(x)&=\\frac{ \\hat{H}\\psi_{T}(x) }{ \\psi_{T}(x)}\\\\\n",
    "&=\\frac{1}{\\exp(-\\alpha x^2)}\\left(-\\frac{1}{2}\\frac{d^2}{dx^2}+x^2\\right)\\exp(-\\alpha x^2)\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "La segunda derivada de $\\psi_{T}$:\n",
    "\n",
    "$$\n",
    "\\frac{d^2}{dx^2} \\exp(-\\alpha x^2) =-2\\alpha \\exp(-\\alpha x^2)+4\\alpha^2 x^2 \\exp(-\\alpha x^2)\n",
    "$$\n",
    "\n",
    "Luego\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "E_{L}(x)&=\\frac{1}{\\exp(-\\alpha x^2)}\\left(-\\frac{1}{2}\\frac{d^2}{dx^2} \\exp(-\\alpha x^2)+\\frac{1}{2}x^2\\right)\\\\\n",
    "&=\\alpha -2\\alpha^2 x^2 +\\frac{1}{2}x^2\\\\\n",
    "&=\\alpha+(\\frac{1}{2}-2\\alpha^2) x^2\n",
    "\\end{align}\n",
    "$$"
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       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width);\n",
       "        canvas.attr('height', height);\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\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 nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\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",
       "\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",
       "\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]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'];\n",
       "    var y0 = fig.canvas.height - msg['y0'];\n",
       "    var x1 = msg['x1'];\n",
       "    var y1 = fig.canvas.height - msg['y1'];\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, 0, fig.canvas.width, fig.canvas.height);\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",
       "    {\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.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",
       "            /* 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",
       "            evt.data.type = \"image/png\";\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",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\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(\"No handler for the '\" + msg_type + \"' message type: \", msg);\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(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\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",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\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",
       "    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",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x;\n",
       "    var y = canvas_pos.y;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\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",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             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",
       "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\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";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.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",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['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 = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\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.get(0);\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",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    fig.root.unbind('remove')\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).html('<img src=\"' + dataURL + '\">');\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 dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\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 () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('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",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\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",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\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('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Energia Variacional Calculada 0.566239662967\n"
     ]
    }
   ],
   "source": [
    "#defina una funcion para E local\n",
    "def E_loc(x, alpha):\n",
    "    return alpha + x**2 * (0.5 - 2.0 * alpha**2);\n",
    "\n",
    "#defina una funcion para la probabilidad de transicion\n",
    "def dP(x_old, x_new, alpha):\n",
    "    return np.exp(-2*alpha*(x_new**2-x_old**2));\n",
    "\n",
    "#inicialize las variables del algorithm\n",
    "delta = 1.0;\n",
    "npasos=60000; \n",
    "alfa = 0.3; \n",
    "#vectores de numeros aleatorios\n",
    "dx=delta*(np.random.uniform(-0.5,0.5,npasos));\n",
    "#print dx\n",
    "eta=np.random.uniform(0,1,npasos);\n",
    "naccept=0;\n",
    "#condicion inial\n",
    "x=0.1;\n",
    "E=np.zeros(npasos);\n",
    "EC=np.zeros(npasos);\n",
    "Eit=0.0;\n",
    "for i in range(0, npasos):\n",
    "    #mueva la particula a una nueva posicion\n",
    "    xnew=x+dx[i];\n",
    "     #Rechaza o acepta el movimiento\n",
    "    if (eta[i]<=dP(x,xnew,alfa)):\n",
    "        x=xnew;\n",
    "        naccept+=1;\n",
    "    E[i]=E_loc(x,alfa);    \n",
    "    Eit+=E[i];\n",
    "    EC[i]=Eit*(1.0/(i+1));\n",
    "\n",
    "Ev=(1.0*Eit)/npasos;        \n",
    "#dibuje el vector de energia local        \n",
    "plt.figure()\n",
    "plt.plot(EC, linestyle='solid', marker='o', markerfacecolor='r', markeredgecolor='r', markersize=1)\n",
    "plt.xlabel(\"n pasos\")\n",
    "plt.ylabel(\"$E_{v}(npasos)$\")\n",
    "print \"Energia Variacional Calculada\", Ev    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "   * Que pasa con la energía variacional con el número de pasos $E_{V}$?\n",
    "   \n",
    "   * Debo considerar todos los valores de E en la simulación?\n",
    "   \n",
    "   * como calculo el error de $E_{v}$?\n",
    "   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.4 Calculando el error en Monte Carlo cuando los datos estan correlacionados?\n",
    "\n",
    "El error estadar de variables estocasticas independientes esta definido como: \n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\sigma_{E}& =\\sqrt{\\frac{\\sigma^2}{n}}\\\\\n",
    "& =\\sqrt{\\frac{\\langle E^2 \\rangle -\\langle E\\rangle^2}{n}}\\\\\n",
    "& =\\sqrt{\\frac{1}{n}\\left({\\overline{E^2} -\\overline{E}^2}\\right)}\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Dado que en en Monte Carlo la cadena de Markov generada dependen de la posición anterior vemos que hay una correlación es decir para un $t$ y $t'$ arbitratios: $x_{t}$ y $x_{t'}$ no son independientes $\\langle x_{t} x_{t'}\\rangle \\neq 0$. Sin embargo existe un número de pasos \"n_{c}\" para los cuales $x_{t}$ y $x_{t'}$ son independientes $\\langle x_{t} x_{t'}\\rangle = 0$. Es deseable que dado $T(x_{t'} | x_{t})$ el tiempo de correlación se a corto de tal manera que los estados generados son independientes y muestrea con mas facilidad el espacio de configuración que define la distribución de equilibrio. \n",
    "\n",
    "Luego para calcular el error correctamente es deseable tener una representación de nuestra información de forma que no hay correlación en esa representation de nuestros para poder aplicar la definición de error para variables independientes. Una simple técnica como __análisis de bloque__ hacer el promedio sobre bloques de datos de la simulación por ejemplo si $E_{i}=E_{x_{i}}\\; , \\left\\{E_{1},E_{2},\\cdots, E_{npasos}\\right\\}$, podemos agrupar la información en promedios de bloques continuos de datos de tamaño  $t_{b}$ es decir los nuevos datos seria:\n",
    "\n",
    "$$E({b_{i}})=\\overline{E}_{b_{i}}=\\frac{1}{t_b}\\sum_{i\\in t_b}E_{i}\\;,\\;\\;\\left\\{\\overline{E}_{1},\\overline{E}_{2},\\cdots, \\overline{E}_{NB}\\right\\}  $$\n",
    "\n",
    "\n",
    "Con $NB$ el número de bloques dado \n",
    "\n",
    "$$NB=n_{pasos}\\bmod t_b$$\n",
    "\n",
    "luego nuestros nuevos datos empezaran a verse como variables independientes. Básicamente lo que ocurre es que se hace el análisis para encontrar el tamaño en que el promedio de los bloques de datos estan distribuidos sin correlación.  \n",
    "\n",
    "Ahora queda una pregunta mas, como cálculo $t_{b}$ el tamaño del bloque adecuado. Para esto lo mas simple es observar el cambio del cálculo del error con el número de bloque y luego escogemos el valor donde \n",
    "\n",
    "$$\\frac{\\partial \\sigma_{E}(t_b)}{\\partial t_b}=0$$.  \n",
    "\n",
    "Para ilustrar como funcióna esto tomemos los datos del cálculo de la energía del oscilador armonico unidimensional a continuación, para hacerlo de manera simple y sistematica se agrupan de datos de dos en dos, el tamannho minimo de bloque es $tb_{min}=2^{0}=1$ y el tamaño maximo $tb_{max}=2^{\\lfloor\\log_{2}(n_{pasos})\\rfloor}$, siendo consistentes se debe usar el mismo número de datos para esto elegimos los ultimos $tb_{max}$ valores para descartar los valores inciales de equilibración. Defina una funciónpara el error estandar que dependa del tamaño de bloque en terminos de una potencia de dos, cambie el tamaño de bloque y defina el error\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "60000 27232 15 (32768,)\n"
     ]
    },
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\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('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",
       "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 = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(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",
       "            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",
       "        this.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 = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width);\n",
       "        canvas.attr('height', height);\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\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 nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\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",
       "\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",
       "\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]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'];\n",
       "    var y0 = fig.canvas.height - msg['y0'];\n",
       "    var x1 = msg['x1'];\n",
       "    var y1 = fig.canvas.height - msg['y1'];\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, 0, fig.canvas.width, fig.canvas.height);\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",
       "    {\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.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",
       "            /* 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",
       "            evt.data.type = \"image/png\";\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",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\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(\"No handler for the '\" + msg_type + \"' message type: \", msg);\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(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\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",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\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",
       "    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",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x;\n",
       "    var y = canvas_pos.y;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\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",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             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",
       "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\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";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.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",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['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 = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\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.get(0);\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",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    fig.root.unbind('remove')\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).html('<img src=\"' + dataURL + '\">');\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 dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\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 () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('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",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\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",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\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('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f1393379050>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Analisis de bloque\n",
    "#potencia maxima de 2 \n",
    "maxpow2=int(np.floor(np.log2(npasos)));\n",
    "index0=int(npasos-(2**maxpow2));\n",
    "#descarta el numero de pasos inicial\n",
    "e=E[index0:];\n",
    "\n",
    "print npasos, index0, maxpow2, e.shape\n",
    "\n",
    "def blockerror(data):\n",
    "    maxp2=int(np.floor(np.log2(data.shape[0])));\n",
    "    i0=int(data.shape[0]-(2**maxp2));\n",
    "    data=data[i0:].tolist();\n",
    "    errores=[];  \n",
    "    bloques=[];  \n",
    "    for i in range(maxp2):\n",
    "        new_data = [];\n",
    "        media = 0.0;\n",
    "        media2 = 0.0;\n",
    "        N = len(data);\n",
    "        while data != []:\n",
    "            x = data.pop()\n",
    "            y = data.pop()\n",
    "            media += x + y\n",
    "            media2 += x ** 2 + y ** 2\n",
    "            new_data.append((x + y) / 2.0 )\n",
    "        errores.append(np.sqrt(media2 / N - (media / N) ** 2) / np.sqrt(N))\n",
    "        bloques.append(i)\n",
    "        data = new_data[:];\n",
    "    \n",
    "    return errores, bloques\n",
    "    \n",
    "    \n",
    "aerror, blocks =blockerror(e);    \n",
    "\n",
    "#print len(aerror),len(blocks)\n",
    "\n",
    "#print aerror\n",
    "#print blocks\n",
    "plt.figure()\n",
    "plt.plot(blocks, aerror, 'ro-')\n",
    "plt.xlabel('t_b')\n",
    "plt.ylabel('Error')\n",
    "plt.title('Bunching: naive error vs iteration number')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "El error es  0.0106045229613 tamanho del bloque 256\n"
     ]
    },
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\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('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",
       "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 = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(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",
       "            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",
       "        this.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 = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width);\n",
       "        canvas.attr('height', height);\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\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 nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\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",
       "\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",
       "\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]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'];\n",
       "    var y0 = fig.canvas.height - msg['y0'];\n",
       "    var x1 = msg['x1'];\n",
       "    var y1 = fig.canvas.height - msg['y1'];\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, 0, fig.canvas.width, fig.canvas.height);\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",
       "    {\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.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",
       "            /* 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",
       "            evt.data.type = \"image/png\";\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",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\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(\"No handler for the '\" + msg_type + \"' message type: \", msg);\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(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\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",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\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",
       "    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",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x;\n",
       "    var y = canvas_pos.y;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\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",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             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",
       "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\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";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.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",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['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 = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\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.get(0);\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",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    fig.root.unbind('remove')\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).html('<img src=\"' + dataURL + '\">');\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 dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\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 () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('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",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\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",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\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('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f13932c6e50>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#calcular la derivada usando diferencias centradas\n",
    "derror=[];\n",
    "for i in range(1,len(aerror)-1):\n",
    "    derror.append((aerror[i+1]-aerror[i-1])*0.5);\n",
    "    \n",
    "#print derror\n",
    "derror=np.asarray(np.abs(derror));\n",
    "#print np.amin(derror), np.argmin(derror), derror[np.argmin(derror)]\n",
    "\n",
    "#index error block\n",
    "ie=int(np.argmin(derror))+1;\n",
    "\n",
    "print \"El error es \", aerror[ie], \"tamanho del bloque\", 2**ie \n",
    "\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(blocks[1:len(aerror)-1], derror, 'go-')\n",
    "plt.xlabel('t_b')\n",
    "plt.ylabel('dError')\n",
    "plt.title('Bunching: naive error vs Block Size')\n",
    "\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ejercicio\n",
    "\n",
    "0. La media es independiente del tamaño de bloque? \n",
    "\n",
    "1. Escriba una nueva función blockerror, para que de el error real, no solo el vector de errores.  \n",
    "\n",
    "2. Escriba una Función Metropolis, cuyo unico parametro sea alfa que retorne la energia del oscilador armonico y su error calculado con la función del punto 1.\n",
    "\n",
    "3. Calcule la energia para diferentes valores de alfas entre 0 y 1, que puede observar cerca de cual valor de alfa esta el mínimo. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0.57090239208489335, 0.010068607253531439)\n"
     ]
    }
   ],
   "source": [
    "#1. Defina la Funcion blockerror\n",
    "\n",
    "def blockerror(data): \n",
    "    maxp2=int(np.floor(np.log2(data.shape[0])));\n",
    "    i0=int(data.shape[0]-(2**maxp2));\n",
    "    data=data[i0:].tolist();\n",
    "    errores=[];  \n",
    "    bloques=[];  \n",
    "    for i in range(maxp2):\n",
    "        new_data = [];\n",
    "        media = 0.0;\n",
    "        media2 = 0.0;\n",
    "        N = abs(len(data));\n",
    "        while data != []:\n",
    "            x = data.pop()\n",
    "            y = data.pop()\n",
    "            media += x + y\n",
    "            media2 += x ** 2 + y ** 2\n",
    "            new_data.append((x + y) / 2.0 )\n",
    "        errores.append(np.sqrt(media2 / N - (media / N) ** 2) / np.sqrt(N))\n",
    "        bloques.append(i)\n",
    "        data = new_data[:];\n",
    "    \n",
    "    derror=[];\n",
    "    for i in range(1,len(errores)-1):\n",
    "        derror.append((errores[i+1]-errores[i-1])*0.5);  \n",
    "     #print derror\n",
    "    derror=np.asarray(np.abs(derror));\n",
    "    ie=int(np.argmin(derror))+1;\n",
    "        \n",
    "    return aerror[ie];\n",
    "\n",
    "\n",
    "#1. Defina la Funcion Metropolis\n",
    "\n",
    "def Metropolis(alfa):\n",
    "    #inicialize las variables del algorithm\n",
    "    delta = 1.0;\n",
    "    npasos=50000; \n",
    "    #vectores de numeros aleatorios\n",
    "    dx=delta*(np.random.uniform(-0.5,0.5,npasos));\n",
    "    #print dx\n",
    "    eta=np.random.uniform(0,1,npasos);\n",
    "    E=np.zeros(npasos);\n",
    "    naccept=0;\n",
    "    #condicion inial\n",
    "    x=0.5;\n",
    "    Ev=0.0;\n",
    "    for i in range(0, npasos):\n",
    "        #mueva la particula a una nueva posicion\n",
    "        xnew=x+dx[i];\n",
    "        #Rechaza o acepta el movimiento\n",
    "        if (eta[i]<=dP(x,xnew,alfa)):\n",
    "            x=xnew;\n",
    "            naccept+=1;\n",
    "        E[i]=E_loc(x,alfa)\n",
    "        Ev+=E[i];\n",
    "    Ev=(1.0*Ev)/npasos;    \n",
    "    err = blockerror(E);\n",
    "    \n",
    "    return Ev, err;\n",
    "\n",
    "print Metropolis(0.3)\n",
    "\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python2.7/dist-packages/ipykernel_launcher.py:20: RuntimeWarning: invalid value encountered in sqrt\n"
     ]
    },
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\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('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",
       "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 = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(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",
       "            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",
       "        this.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 = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width);\n",
       "        canvas.attr('height', height);\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\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 nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\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",
       "\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",
       "\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]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'];\n",
       "    var y0 = fig.canvas.height - msg['y0'];\n",
       "    var x1 = msg['x1'];\n",
       "    var y1 = fig.canvas.height - msg['y1'];\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, 0, fig.canvas.width, fig.canvas.height);\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",
       "    {\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.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",
       "            /* 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",
       "            evt.data.type = \"image/png\";\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",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\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(\"No handler for the '\" + msg_type + \"' message type: \", msg);\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(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\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",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\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",
       "    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",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x;\n",
       "    var y = canvas_pos.y;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\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",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             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",
       "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\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";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.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",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['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 = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\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.get(0);\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",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    fig.root.unbind('remove')\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).html('<img src=\"' + dataURL + '\">');\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 dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\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 () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('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",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\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",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\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('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "indice valor minimo 8 valor de alfa 0.5\n"
     ]
    }
   ],
   "source": [
    "#calcule la energia variacional para diferentes valores de alfa entre 0-1, usando la funcion metropolis \n",
    " \n",
    "\n",
    "\n",
    "\n",
    "#Haga una grafica de Ev vs alfa\n",
    "\n",
    "alfa=np.arange(0.1, 1.05, 0.05);\n",
    "\n",
    "data=np.zeros((2,alfa.shape[0]));\n",
    "\n",
    "for j in range(0,alfa.shape[0]):\n",
    "    data[:,j]=Metropolis(alfa[j]);\n",
    "\n",
    "#print data\n",
    "\n",
    "#print len(data), len(data[0])\n",
    "\n",
    "#print alfa.shape\n",
    "plt.figure()\n",
    "plt.plot(alfa,data[0,:], 'mo-')\n",
    "plt.xlabel(\"$\\alpha$\")\n",
    "plt.ylabel(\"$E_{v}$\")    \n",
    "    \n",
    "    \n",
    "iemin=int(np.argmin(data[0,:]));\n",
    "\n",
    "print \"indice valor minimo\", iemin, \"valor de alfa\", alfa[iemin]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La solución exacta a este problema es: \n",
    "\n",
    "$$\\psi _{n}(x)={\\frac {1}{\\sqrt {2^{n}\\,n!}}}\\cdot \\left({\\frac {m\\omega }{\\pi \\hbar }}\\right)^{1/4}\\cdot e^{-{\\frac {m\\omega x^{2}}{2\\hbar }}}\\cdot H_{n}\\left({\\sqrt {\\frac {m\\omega }{\\hbar }}}x\\right),\\qquad n=0,1,2,\\ldots$$\n",
    "\n",
    "Donde $H_{n}$ son polinomios de Hermite:\n",
    "\n",
    "$$ H_{n}(z)=(-1)^{n}~e^{z^{2}}{\\frac {d^{n}}{dz^{n}}}\\left(e^{-z^{2}}\\right)$$ \n",
    "\n",
    "Con los niveles de energía correspondientes:\n",
    "\n",
    "$$ E_{n}=\\hbar \\omega \\left(n+{1 \\over 2}\\right)=(2n+1){\\hbar \\over 2}\\omega $$\n",
    "\n",
    "Usando las unidades normalizadas: \n",
    "\n",
    "$$ E_{n}=\\left(n+{1 \\over 2}\\right)=\\left(n+\\frac{1}{2}\\right)$$\n",
    "\n",
    "\n",
    "Luego para $\\alpha=0.5$, $E_{v}=E_{0}=0.5$, valor de varianza cero.  \n",
    "\n",
    "__Pregunta: Existe otro valor de alfa para nuestra funcion de onda con varianza cero?__ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.5 El átomo de Helio\n",
    "\n",
    "Ahora nos vamos a concentrar en la tarea de hacer el calculo de Monte Carlo variacional del átomo de Helio, para esto utilizamos el hamiltoniano del átomo de Helio en la arpximación de Born-Oppenheinmer, es decir tratamos el nucleo del átomo en una posición fija y nos enfocamos en la interacción electronica.  Usando unidades atomicas:\n",
    "\n",
    "$$\\hbar\\; =\\; e\\; =\\; m\\; = 1 $$\n",
    "\n",
    "$$-\\frac{1}{2} (\\nabla_1^2 + \\nabla_2^2) - \\frac{2}{r_1} - \\frac{2}{r_2} + \\frac{1}{r_{12}}$$\n",
    "\n",
    "Los dos primeros terminos correponden a la energía cinetica, el sistema de de referencia esta centrado en el nucleo del átomo, luego el tercer y cuarto termino corresponen a la interación de coulmb con el nucle y el ultimo termino a la repulsiónentre los electrones.Ya que estamos interesados en la función de onda de los electrones, estas particulas al ser fermiones deben tener una función de onda antisimetrica. Para esto vamos a utilizar una función de onda antisimetrica: \n",
    "\n",
    "\n",
    "$$\\psi(r_{1},r_{2})=\\phi(r_1)\\phi(r_2) \\frac{1}{2}\\left(|\\uparrow\\downarrow\\rangle +|\\downarrow \\uparrow\\rangle\\right)$$\n",
    "\n",
    "\n",
    "Donde hemos dejado la parte antisimetrica en las variables de espin, $r_i$,$r_ij$ son las distancias entre cada electron y el nucleo, asi como la distancia entre los dos electrones respectivamente. La ocupación de spin para este ejemplo vamos a dejarla fija, para que capture la antisimetria de la función de onda. Los orbitales de la función de onda deben  ser una buna aproximación que refleje al fisica del sistema. Para esto usualmente se sigue las restriccciones impuestas por __\"Cusp Conditions\"__ o condiciones de Cuspide, es decir las condiciones para eleminar o tratar con las singularidades entre la interacción de Coulumb cuando el nucleo y un electron estan cerca, o los electrones estan cerca de tal modo que $|r|\\to 0$.\n",
    "\n",
    "Suponga que los electrones en el átomo de Helio estan separadados y el segundo electron a distancia $r_2$, esta alejado del nucle, sin embargo el primer electron esta cerca $|r_1|\\to 0$. La Función de energía local debe evadir esta divergencia, entonces debemos encontrar una función de onda que satisfaga esta condicion.  La energía local estaria dada por: \n",
    "\n",
    "$$E_{L}=\\frac{1}{\\psi_t}\\left(-\\frac{1}{2} \\nabla_1^2 - \\frac{2}{r_1}+E(r_{12},r_2)\\right)\\psi_t$$\n",
    "\n",
    "Donde los terminos dominantes estan dados por $r_1$ y la contribución de $E(r_{12},r_2)$ puede ser considerada despreciable, escribiendo la energía cinetica en coordenadas esfericas, con momento algular $l=04 para el electron 1:\n",
    "\n",
    "$$E_{L}=\\frac{1}{R_t(r_1)}\\left(-\\frac{1}{2}\\frac{d^2}{dr_{1}^{2}}-\\frac{1}{r_1}\\frac{d}{dr_1} - \\frac{2}{r_1}+E(r_{12},r_2)\\right)R_t(r_1)$$\n",
    "\n",
    "Luego la condición de cuspide me pide eliminar los terminos divergentes $\\frac{1}{r_1}$ esto es:\n",
    "\n",
    "$$\\lim_{r_1\\to 0} E_L(R_t(r1))= \\frac{1}{R_t(r_1)}\\left(-\\frac{1}{r_1}\\frac{d}{dr_1} - \\frac{2}{r_1}\\right)R_t(r_1)$$\n",
    "\n",
    "La segunda derivada no diverge entonces para mantener la energía local finita se debe cumplir:\n",
    "\n",
    "\n",
    "$$\\frac{1}{R_t(r_1)}\\frac{d R_t(r_1)}{dr_1} =-2$$\n",
    "\n",
    "En general es igual a Z la carga del nucle atomico, para Helio Z=2. esta ecuación implica que: \n",
    "\n",
    "$$R_T(r_1)\\propto\\exp(-Zr_1)$$\n",
    "\n",
    "\n",
    "De manera analoga usando el mismo razonamiento para el electron 2, cuando $r_2\\to 0$ y momento angular $l>1$\n",
    "\n",
    "$$\\frac{1}{R_t(r_2)}\\frac{d R_t(r_2)}{dr_2} =-\\frac{Z}{l+1}$$\n",
    "\n",
    "Luego\n",
    "\n",
    "$$R_T(r_2)\\propto\\exp\\left(-\\frac{Z}{l+1}r_2\\right)$$\n",
    "\n",
    "\n",
    "Otra restricción puede ser encontrada sobre la función de onda en el caso cuando los dos electrones estan muy cerca $r_{12}\\to 0$, la ecuación radial es similar a la que aparece entre un electron y el nucleo cuando se acercan, despreciando la contribución del centro de masa de los electrones de manera similar a las aproximaciones anteriores: \n",
    "\n",
    "\n",
    "$$\\lim_{r_{12}\\to 0} E_L(R_t(r_{12}))= \\frac{1}{R_t(r_{12})}\\left(2\\frac{d^2}{dr_{12}^{2}}+\\frac{4}{r_{12}}\\frac{d}{dr_{12}} - \\frac{2}{r_{12}}-\\frac{l(l+1)}{r_{12}^2}+E(r_{1},r_2)\\right)R_t(r_{12})$$\n",
    "\n",
    "Eliminando los terminos de la divergencia aparece la condicion:\n",
    "\n",
    "$$\n",
    "\\frac{d R_t(r_{12})}{dr_{12}}=-\\frac{1}{2(l+1)}R_t(r_{12})\n",
    "$$\n",
    "\n",
    "Luego considerando espines anti paralelos y l=0:\n",
    "\n",
    "$$\n",
    "R_T(r_{12})\\propto \\exp\\left(\\frac{r_{12}}{2}\\right)\n",
    "$$\n",
    "\n",
    "En general estas condiciones pueden ser escritas en una forma mas general, la función de onda de prueba tiene la forma:\n",
    "\n",
    "$$\n",
    "\\psi_{T}(R)=phi(r_{1})phi(r_{2})\\cdots \\phi(r_{N})\\prod_{i<j}f(r_{ij})\n",
    "$$\n",
    "\n",
    "\n",
    "Las condiciones de cuspide nos llevaron a encontrar la forma funcional basica que define la mayor parte de modelos de funciones de onda para solidos y moleculas. La parte de las funciones $\\phi(r_i)$ es considerada como la parte fermionica de la función de onda. Las funciones $f(r_{ij}) es la parte que adiciona correlación al sistema. \n",
    "\n",
    "Retomando el caso del átomo de Helio una función de onda que evade las condiciones de cuspide de los electrones con el nucleo seria:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\phi_1(r1) & =\\exp(-\\alpha r_1)\\\\\n",
    "\\phi_2(r2) & =\\exp(-\\alpha r_2)\\\\\n",
    "\\psi(r_1,r_2) & = \\phi_1(r_1) \\phi_2(r_2) = \\exp(-\\alpha (r_1+r_2))\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Donde $\\alpha$ podria ser interpretado como una carga variacional efectiva. Considerando esta función de onda, para escribir el algorithmo Metropolis debemos conocer la expresiónde la energía local, en este caso corresponde a: \n",
    "\n",
    "$$\n",
    "E_{L}(r_1,r_2)=-\\alpha^2+\\frac{\\alpha}{r_{1}}+\\frac{\\alpha}{r_2}-\\frac{2}{r_1}-\\frac{2}{r_2}+\\frac{1}{r_{12}}\n",
    "$$\n",
    "\n",
    "Luego podemos implementar el algoritmo usando las funciones que ya habiamos escrito para el oscilador armonico con pequenos cambios en la dimensionalidad del problema. En las unidades dadas el valor de refencia experimental de la energía del estado base del Helio es:\n",
    "\n",
    "$$2.9037\\;\\; Ha$$\n",
    "\n",
    "1. Escriba una función de energía local para esta función de onda de prueba. \n",
    "\n",
    "2. Escriba una función que calcule el radio de la probabilidad de la función de onda de prueba \n",
    "\n",
    "3. Escriba una función Metropolis para este sistema\n",
    "\n",
    "4. haga una variaciaon de parametros para encontrar el $\\alpha$ optimo y la energía variacional del mismo\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\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('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",
       "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 = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(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",
       "            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",
       "        this.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 = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width);\n",
       "        canvas.attr('height', height);\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\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 nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\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",
       "\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",
       "\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]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'];\n",
       "    var y0 = fig.canvas.height - msg['y0'];\n",
       "    var x1 = msg['x1'];\n",
       "    var y1 = fig.canvas.height - msg['y1'];\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, 0, fig.canvas.width, fig.canvas.height);\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",
       "    {\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.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",
       "            /* 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",
       "            evt.data.type = \"image/png\";\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",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\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(\"No handler for the '\" + msg_type + \"' message type: \", msg);\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(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\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",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\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",
       "    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",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x;\n",
       "    var y = canvas_pos.y;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\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",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             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",
       "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\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";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.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",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['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 = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\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.get(0);\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",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    fig.root.unbind('remove')\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).html('<img src=\"' + dataURL + '\">');\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 dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\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 () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('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",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\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",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\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('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
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     "output_type": "display_data"
    },
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\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "indice valor minimo 16 valor de alfa 1.7 -2.85598734396\n",
      "finish\n"
     ]
    }
   ],
   "source": [
    "def E_locHev1(r_in,alpha):\n",
    "    #pasar un arreglo o matriz de numpy como copia de objeto, necesario cuando la funcion tiene mas de un argumento\n",
    "    r=r_in.copy();  \n",
    "    r1=np.linalg.norm(r[0,:]);\n",
    "    r2=np.linalg.norm(r[1,:]);\n",
    "    r12=np.linalg.norm(r[0,:]-r[1,:]);\n",
    "    Eloc=-(alpha**2)+(alpha/r1)+(alpha/r2)-(2.0/r1)-(2.0/r2)+(1.0/r12);\n",
    "    \n",
    "    return Eloc;\n",
    "\n",
    "\n",
    "def dPHev1(r_in,rnew_in,alpha):\n",
    "    r=r_in.copy();\n",
    "    rnew=rnew_in.copy();\n",
    "    r1=np.linalg.norm(r[0,:]);\n",
    "    r2=np.linalg.norm(r[1,:]);\n",
    "    rnew1=np.linalg.norm(rnew[0,:]);\n",
    "    rnew2=np.linalg.norm(rnew[1,:]);\n",
    "    dp=np.exp(-2.0*alpha*((rnew1+rnew2)-(r1+r2)));\n",
    "    \n",
    "    return dp;\n",
    "    \n",
    "    \n",
    "\n",
    "def MetropolisHev1(alfa):\n",
    "    #inicialize las variables del algorithm\n",
    "    delta = 1.0;\n",
    "    npasos=50000; \n",
    "    #vectores de numeros aleatorios\n",
    "    dr=delta*(np.random.uniform(-0.5,0.5,(npasos,2,3)));\n",
    "    #print dx\n",
    "    eta=np.random.uniform(0,1,npasos);\n",
    "    E=np.zeros(npasos);\n",
    "    naccept=0;\n",
    "    #condicion inial\n",
    "    r=np.zeros((2,3));          \n",
    "    r[0,1]=0.3;\n",
    "    r[1,1]=-0.3;          \n",
    "    Ev=0.0;\n",
    "    for i in range(0, npasos):\n",
    "        #mueva la particula a una nueva posicion\n",
    "        rnew=r+dr[i,:,:];\n",
    "        #Rechaza o acepta el movimiento\n",
    "        if (eta[i]<=dPHev1(r,rnew,alfa)):\n",
    "            r=rnew;\n",
    "            naccept+=1;\n",
    "            #print naccept\n",
    "        E[i]=E_locHev1(r,alfa)\n",
    "        Ev+=E[i];\n",
    "    Ev=(1.0*Ev)/npasos;    \n",
    "    err = blockerror(E);\n",
    "    \n",
    "    return Ev, err;\n",
    "\n",
    "\n",
    "alfas=np.arange(0.1,5.0,0.1);\n",
    "\n",
    "#print alfas.shape[0]\n",
    "dataHev1=np.zeros((alfas.shape[0],2));\n",
    "\n",
    "#print dataHev1.shape\n",
    "\n",
    "for i in range(0,alfas.shape[0]):\n",
    "    dataHev1[i,:]=MetropolisHev1(alfas[i]);\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(alfas,dataHev1[:,0],'r*-')\n",
    "\n",
    "iemin=int(np.argmin(dataHev1[:,0]));\n",
    "\n",
    "print \"indice valor minimo\", iemin, \"valor de alfa\", alfas[iemin], dataHev1[iemin,0]\n",
    "print \"finish\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Por último una función de onda que también satisfaga las condiciones de cuspide cuando los electrones se acercan:\n",
    "\n",
    "$$\\psi_T =\\exp\\left(-\\alpha(r_1+r_2)\\right)\\exp\\left(\\frac{r_{12}}{2}\\right)$$\n",
    "\n",
    "\n",
    "## Ejercicio Extra\n",
    "\n",
    "1. Calcule la Energía Local para esta última función de onda de prueba. \n",
    "\n",
    "2. Escriba un algoritmo Metropolis y haga una variación de parametros para encontrar el $\\alpha$ óptimo, que tan diferente es de la función de onda anterior. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Referencias\n",
    "\n",
    "1. Statistical Mechanics: Algorithms and Computations, W. Krauth, Oxford University Press, 2006\n",
    "2. Quantum Monte Carlo Approaches for Correlated Systems, Federico Becca, Sandro Sorella, Cambridge University Press, 2017\n",
    "3. Monte Carlo Methods, Malvin H. Kalos, Paula A. Whitlock, John Wiley & Sons, 2009\n",
    "4.  Computational Physics, Morten Hjorth Jensen, CreateSpace Independent Publishing Platform, 2015"
   ]
  }
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