PIMC.ipynb

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    "# Sesion III. Monte Carlo de Integrales de Trayectoria\n",
    "\n",
    "\n",
    "## 3.1 Mecánica Estadística Cuántica- Matrices de Densidad\n",
    "\n",
    "En el ensamble canónico con la distribución de Boltzmann la probabilidad de estar en un autoestado de energía es $E_i$ de un sistema cuántico es:\n",
    "\n",
    "$$p_i=\\frac{\\exp(-\\beta E_i)}{Z}\\;\\:\\: \\beta=\\frac{1}{k_{\\beta T}}$$\n",
    "\n",
    "Con \n",
    "\n",
    "$$Z=\\sum_{i} \\exp(-\\beta E_i)$$ \n",
    "\n",
    "Luego el promedio termico de un operador es $\\hat{O}$ es dado por:\n",
    "\n",
    "$$\\langle \\hat{O}\\rangle =\\frac{1}{Z}\\sum_{i}\\langle \\phi_i | \\hat{O} |\\phi_i\\rangle \\exp(-\\beta E_i)$$\n",
    "\n",
    "\n",
    "Lo cual puede ser escrito como: \n",
    "\n",
    "$$\\langle \\hat{O}\\rangle = \\frac{1}{Z} Tr \\left( \\hat{O}\\exp\\left(-\\beta\\hat{H}\\right)\\right)$$\n",
    "\n",
    "\n",
    "Donde el operador matriz densidad es: \n",
    "\n",
    "$$ \\exp\\left(-\\beta\\hat{H}\\right) $$\n",
    "\n",
    "Colocando este operador en representacion de una base de posición:\n",
    "\n",
    "$$\\begin{align}\n",
    "\\rho(R,R';\\beta) &= \\langle R | \\exp\\left(-\\beta\\hat{H}\\right) R' \\rangle\\\\\n",
    "&=\\sum_{i} \\phi_i^{*}(R)\\phi_i^(R') \\exp\\left(-\\beta E_{i}\\right)\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Esta es conocida como la __matriz densidad__, esta matriz es definida positiva y puede ser interpretada como una distribución de probabilidad. Los observables en la base de posición son descritos como:\n",
    "\n",
    "$$\n",
    "\\langle \\hat{O}\\rangle =\\frac{1}{Z}\\int dR dR'  \\rho(R,R';\\beta) \\langle R' | \\hat{O} |R\\rangle \n",
    "$$\n",
    "\n",
    "La función de partición puede ser escrita en la base de posición como:\n",
    "\n",
    "$$\n",
    "Z = \\int dR \\rho(R,R;\\beta)\n",
    "$$\n",
    "\n",
    "Es extremadamente complicado calcular la función de partición de sistemas de partículas clásicos y cuánticos. En el caso cuántico gran parte de la dificultad esta en el cálculo de los autovalores y autovectores  del sistema. Sin embargo usando la representación del sistema en la base de posición nos conduce a una serie de ecuaciones que nos permite usar Monte Carlo para solucionar las integrales.  \n",
    "\n",
    "\n",
    "Adicionalmente la propiedad de completez:\n",
    "\n",
    "$$\n",
    "I= dR\" \\int |R\"\\rangle\\langle R\" |\n",
    "$$\n",
    "\n",
    "Para un operador densidad definido como:\n",
    "\n",
    "$$\\exp(-(\\beta_1 +\\beta_2)\\hat{H})$$\n",
    "\n",
    "La matriz densidad cumple de forma exacta la siguiente propiedad: \n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\rho(R,R';\\beta_1 +\\beta_2) &= \\int dR\" \\langle R | \\exp\\left(-\\beta_1\\hat{H}\\right) R\" \\rangle \\langle R\" | \\exp\\left(-\\beta_2\\hat{H}\\right) R' \\rangle\\\\\n",
    "& \\int dR\" \\rho(R,R\";\\beta_1) \\rho(R\",R';\\beta_2)\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Esta propiedad es conocida como convolución es una condición importante del método de Monte Carlo de Integrales de Trayectoria. Si usamos un producto de operadores de matriz densidad tal que:\n",
    "\n",
    "$$\\exp\\left(-\\beta \\hat{H}\\right)= \\left(\\exp\\left(-\\tau \\hat{H}\\right)\\right)^M$$\n",
    "\n",
    "Donde \n",
    "\n",
    "$$\\tau=\\frac{\\beta}{M}$$\n",
    "\n",
    "Luego la matriz densidad puede ser escrita como un producto de M matrices densidad a temperatura $\\tau$:\n",
    "\n",
    "$$\n",
    "\\rho(R_0,R_M;\\beta)= \\int dR_1 dR_2\\cdots dR_{M-1} \\rho(R_0,R_1;\\tau) \\rho(R_1,R_2;\\tau) \\cdots \\rho(R_{M-1},R_{M};\\tau)\n",
    "$$\n",
    "\n",
    "Esta representación de la matriz densidad es conocida como la Integrales de Feynnman. La integración es realizda sobre las configuraciones intermedias $R_1,R_2\\cdots R_{M-1}$, dejando los extremos fijos $R_{0},R_{M}$. \n",
    "\n",
    "La acción de la integral es definida como:\n",
    "\n",
    "$$\n",
    "S_{path}(R_{0},R_{1},\\cdots R_{M}) =-\\ln [\\rho(R_0,R_1;\\tau) \\rho(R_1,R_2;\\tau) \\cdots \\rho(R_{M-1},R_{M};\\tau)]\n",
    "$$\n",
    "\n",
    "Luego:\n",
    "\n",
    "$$\n",
    "\\rho(R_0,R_M;\\beta)=\\int dR_1 dR_2\\cdots dR_{M-1} \\exp\\left(-S_{path}(R_{0},R_{1},\\cdots R_{M}) \\right)\n",
    "$$\n",
    "\n",
    "Si M es finito tenemos un camino discreto sobre el cual se calculo la integral en el límite  $M\\to\\infty$ el camino es conituno. Es importante notar que esta expresión es __exacta__ no se ha introducido ninguna aproximación.\n",
    "\n",
    "\n",
    "## Acción Primitiva\n",
    "\n",
    "La evaluación de la matriz densidad requiere una aproximación del operador densidad, ya que no podemos aplicar este de manera directa, porque implicaria la solución de la ecuación de Schrödinger. Asi una aproximación para la apliación del operador densidad consiste en hacer una expansión de Trotter en terminos separados del operador $\\hat{T}$,$\\hat{V}$:\n",
    "\n",
    "$$\n",
    "\\exp(-\\tau\\hat{H})=\\exp(-\\tau\\hat{T})\\exp(-\\tau\\hat{V})\\exp\\left(-\\frac{\\tau^2}{2}[\\hat{T},\\hat{V}]\\right)+O(\\tau^3)\n",
    "$$\n",
    "\n",
    "Para $\\tau<<1$, tenemos: \n",
    "\n",
    "$$\n",
    "\\exp(-\\tau\\hat{H})\\sim \\exp(-\\tau\\hat{T})\\exp(-\\tau\\hat{V})\n",
    "$$\n",
    "\n",
    "Para un sistema de N partículas en 3 dimensiones tenemos que: \n",
    "\n",
    "$$\n",
    "\\rho(R_{0},R_{M},\\tau)=\\int dR_1 dR_2\\cdots dR_{M-1} (4\\pi\\lambda\\tau)^{-\\frac{3N}{2}} \\exp\\left(-\\sum_{m=1}^{N}\\left[ \\frac{(R_{m-1}-R_{m})^2}{4\\lambda\\tau}+\\frac{\\tau}{2}(V(R_{m-1}+V(R_{m}))\\right]\\right)\n",
    "$$\n",
    "\n",
    "Con \n",
    "\n",
    "$$\n",
    "\\lambda=\\frac{\\hbar^2}{2m}\n",
    "$$\n",
    "De esto podemos inferir la definición de la acción cinética o de partícula libre y la acción potencial:\n",
    "\n",
    "\n",
    "$$\n",
    "K_{path}(R_{0},R_{M},\\tau)= \\frac{3N}{2}\\ln(4\\pi\\lambda\\tau)+\\sum_{m=1}^{N}\\left[ \\frac{(R_{m-1}-R_{m})^2}{4\\lambda\\tau}\\right]\n",
    "$$\n",
    "\n",
    "$$\n",
    "V_{path}(R_{0},R_{M},\\tau) = \\frac{\\tau}{2} \\sum_{m=1}^{N}(V(R_{m-1}+V(R_{m}))\n",
    "$$\n",
    "\n",
    "Recordando que los observables son tomados como:\n",
    "\n",
    "$$\n",
    "\\langle R | \\hat{O} R \\rangle = \\frac{1}{Z}\\int dR dR'  \\exp\\left(-S_{path}(R, R_{'}) \\right) \\langle R' | \\hat{O} |R\\rangle \n",
    "$$\n",
    "\n",
    "Luego se puede inferir que los caminos que definen los observable son cerrados $R_{M}=R_{0}$.\n",
    "\n",
    "\n",
    "Definidas estas cantidades ya podemos delinear como se puede construir un algotimo Metropolis, para muestrear la integral basado en la probabilidad: \n",
    "\n",
    "\n"
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    "#Cargue desde el inicio las bibliotecas necesarias para no llamarlas de nuevo a lo largo del cuaderno jupyter. \n",
    "import numpy as np\n",
    "#%matplotlib inline\n",
    "%matplotlib notebook\n",
    "import matplotlib.pyplot as plt"
   ]
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       "}\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 0x7f97bf3a2ed0>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def rho_free(x, xp, beta):\n",
    "    return (np.exp(-(x - xp) ** 2 / (2.0 * beta)) /\n",
    "            np.sqrt(2.0 * np.pi * beta))\n",
    "\n",
    "def rho_harmonic_trotter(grid, beta):\n",
    "    return np.array([[rho_free(x, xp, beta) * \\\n",
    "                         np.exp(-0.5 * beta * 0.5 * (x ** 2 + xp ** 2)) \\\n",
    "                         for x in grid] for xp in grid])\n",
    "\n",
    "x_max = 5.0\n",
    "nx = 100\n",
    "dx = 2.0 * x_max / (nx - 1)\n",
    "x = [i * dx for i in range(-(nx - 1) / 2, nx / 2 + 1)]\n",
    "x=np.asarray(x);\n",
    "beta_tmp = 2.0 ** (-5)\n",
    "beta     = 2.0 ** (3)\n",
    "rho = rho_harmonic_trotter(x, beta_tmp)\n",
    "\n",
    "plt.figure()\n",
    "plt.imshow(rho, extent=[-x_max, x_max, -x_max, x_max], origin='lower')\n",
    "#plt.colorbar()\n",
    "plt.title('$\\beta = 2^{%i}$' % beta)\n",
    "plt.xlabel('$x$', fontsize=18)\n",
    "plt.ylabel('$x\\'$', fontsize=18)\n",
    "#plt.savefig('plot-harmonic-rho.png')\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cuadrados de Matrices \n",
    "\n",
    "Hay una propiedad fundamental que nos permite ir de altas temperaturas a bajas temperaturas, usando la propuedad de convolucion de la matriz densidad esto es:\n",
    "\n",
    "$$\n",
    "\\rho(R,R';(\\beta_{1}+\\beta_{2})) = \\int dR\" \\rho(R,R\";\\beta_{1})\\rho(R\",R';\\beta_{2}) \n",
    "$$\n",
    "\n",
    "Si $\\beta_1 =\\beta_2 =\\beta$, entonces $\\beta_{1}+\\beta_{2}=\\beta$\n",
    "\n",
    "Luego es fácil de observar que, de manera aproximada o para $\\beta$ pequeño se puede reemplzar la integral por una sumatoria enconces tenemos que:\n",
    "\n",
    "$$\n",
    "\\sum_{l} \\rho_{kl} \\rho_{lm} = (\\rho^2)_{km} \n",
    "$$\n",
    "\n",
    "Luego si se multiplica sucesivamente una matriz se esta bajando una temperatura a la mitad cada vez ue se hace esta operación. De esta manera podemos optener la matriz densidad a bajas temperaturas desde temperatuaras más altas. \n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f97bef21910>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Matrix squaring\n",
    "\n",
    "import math \n",
    "\n",
    "beta_tmp = 2.0 ** (-8)                   # initial value of beta (power of 2)\n",
    "beta     = 2.0 ** 2                      # actual value of beta (power of 2)\n",
    "rho = rho_harmonic_trotter(x, beta_tmp)  # density matrix at initial beta\n",
    "while beta_tmp < beta:\n",
    "    rho = np.dot(rho, rho)\n",
    "    rho *= dx\n",
    "    beta_tmp *= 2.0\n",
    "\n",
    "# graphics output\n",
    "plt.figure()\n",
    "plt.imshow(rho, extent=[-x_max, x_max, -x_max, x_max], origin='lower')\n",
    "plt.colorbar()\n",
    "plt.title('$\\\\beta = 2^{%i}$' % math.log(beta, 2))\n",
    "plt.xlabel('$x$', fontsize=18)\n",
    "plt.ylabel('$x\\'$', fontsize=18)\n",
    "#plt.savefig('plot-harmonic-rho.png')\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos establecer el algorithmo Metropolis, primero debemos notar que como mencionado anteriormente para hacer cálculo de los observables estamos muestreando sobre integrales en caminos cerrados, esto es un path de la siguiente forma.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img 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\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f97bec5f7d0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta=3.0;\n",
    "nb= 10; #number of beads\n",
    "x=delta*np.random.uniform(-0.5,0.5,nb);\n",
    "y=delta*np.random.uniform(-0.5,0.5,nb);\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(x,y, 'bo-', markersize=10)\n",
    "plt.plot([x[0],x[-1]],[y[0],y[-1]], 'bo-', markersize=10)\n",
    "plt.xlim(-2,2)\n",
    "plt.ylim(-2,3)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.title(\"Closed Path\")\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Esto es un homomorfismo, en el que se mapea una partícula cuántica a un sistema clásico este path puede ser entendido como un anillo polimerico cuyos links o beads, estan unidos por interacciones armonicas o un resorte de constante elástica:\n",
    "\n",
    "$$\\frac{1}{(4\\lambda\\tau)}$$\n",
    "\n",
    "La interaccion entre dos párticulas es dada por el potencial, sin embargo cuando una párticula interactua con otra, es decir dos polimeros interactuando los beads de cada polimero interactuan solamente uno a uno con el bead del mismo indice esto es una conseguencia de la propiedad de convolución de la matrix densidad. \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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>"
      ]
     },
     "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 0x7f97bea2cfd0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta=3.0;\n",
    "nb= 10; #number of beads\n",
    "x=delta*np.random.uniform(-0.5,0.5,nb);\n",
    "y=delta*np.random.uniform(-0.5,0.5,nb);\n",
    "\n",
    "\n",
    "x2=3.0+delta*np.random.uniform(-0.5,0.5,nb);\n",
    "y2=3.0+delta*np.random.uniform(-0.5,0.5,nb);\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(x,y, 'bo-', markersize=10)\n",
    "plt.plot([x[0],x[-1]],[y[0],y[-1]], 'bo-', markersize=10)\n",
    "\n",
    "\n",
    "plt.plot(x2,y2, 'ro-', markersize=10)\n",
    "plt.plot([x2[0],x2[-1]],[y2[0],y2[-1]], 'ro-', markersize=10)\n",
    "\n",
    "\n",
    "for i in range(0,nb):\n",
    "    plt.plot([x[i],x2[i]],[y[i],y2[i]], 'y:', linewidth=3)\n",
    "\n",
    "plt.xlim(-2,6)\n",
    "plt.ylim(-2,6)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.title(\"Closed Path\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algoritmo Metropolis \n",
    "\n",
    "Una vez que tenemos una representación adecuada para muestrear la matrix densidad en este caso en el espacio real y además sabemos como estan definidos los observables en esta representación. El caso más basico en el que se muestrea una partícula a la vez y más especificamente un bead a la vez el esquema del algoritmo, usando la accipon primitiva:\n",
    "\n",
    "\n",
    "1. Escoja una partícula aleatoriamente. \n",
    "\n",
    "2. Escoga un bead aleatoeriamente para proponer un dezplazamiento. \n",
    "\n",
    "3. Proponga el nuevo desplazamiento del bead como:\n",
    "\n",
    "$$x' =x+\\eta \\sqrt{\\lambda\\tau}$$\n",
    "\n",
    "4. Calcule el cambio de la acción $\\Delta=S_{new}-S_{old}$\n",
    "\n",
    "5. Acepte o rechace el movimeinto segun el criterio de aceptación de Metropolis:\n",
    "\n",
    "$$A(R_{old},R_{new})=\\min\\left(1,\\exp\\left(-\\beta(S_{new}-S_{old})\\right)\\right)$$\n",
    "\n",
    "6. Actualice la posición del bead si fue aceptado. \n",
    "\n",
    "Repita estos pasos, un numero dado de iteraciones has que el calculo converga.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "xold [ 0.31699229  0.97325868 -0.6400509  -0.05926937  0.84709539  0.90870109\n",
      "  0.39831787 -0.27166972]\n",
      "xnew [ 0.04511405  0.21632346  0.25242115  0.76968498 -0.83637536 -0.15990713\n",
      " -0.79129098 -0.27166972]\n",
      "accepted steps 6690\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>"
      ]
     },
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     "output_type": "display_data"
    },
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\">"
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      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f97b5c47590>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#harmonic Oscillator\n",
    "\n",
    "beta = 8.0\n",
    "N = 8\n",
    "dtau = beta / N\n",
    "delta = 1.0\n",
    "n_steps = 10000;\n",
    "x = np.random.uniform(-1.0,1.0,N);\n",
    "xold=x;\n",
    "xdata=[];\n",
    "print 'xold', xold\n",
    "\n",
    "dx = np.random.uniform(-delta, delta,n_steps);\n",
    "dx.shape\n",
    "\n",
    "eta= np.random.uniform(0.0, 1.0,n_steps);\n",
    "\n",
    "accept=0;\n",
    "for step in range(n_steps):\n",
    "    k = np.random.randint(0, N - 1)\n",
    "    knext, kprev = (k + 1) % N, (k - 1) % N\n",
    "    #print step\n",
    "    x_new = x[k] +dx[step]; \n",
    "    old_weight  = (rho_free(x[knext], x[k], dtau) *\n",
    "                   rho_free(x[k], x[kprev], dtau) *\n",
    "                   np.exp(-0.5 * dtau * x[k] ** 2))\n",
    "    new_weight  = (rho_free(x[knext], x_new, dtau) *\n",
    "                   rho_free(x_new, x[kprev], dtau) *\n",
    "                   np.exp(-0.5 * dtau * x_new ** 2))\n",
    "    if eta[step] < (1.0*new_weight/old_weight):\n",
    "        accept+=1; \n",
    "        x[k] = x_new;\n",
    "        xdata.append(x[k]);\n",
    "        \n",
    "print \"xnew\", x\n",
    "print 'accepted steps', accept\n",
    "\n",
    "y=np.arange(0,N);\n",
    "\n",
    "\n",
    "xgrid = [i * 3.0/50 for i in range(-50, 50)]\n",
    "piT = [(math.sqrt(math.tanh(0.5*beta))/math.sqrt(math.pi))*math.exp(- (xi*xi)*math.tanh(beta/2)) for xi in xgrid]\n",
    "\n",
    "plt.figure()\n",
    "n, bins, patches = plt.hist(xdata, 500, normed=1, histtype='stepfilled', label='pi histrogram')\n",
    "plt.plot(xgrid, piT, 'r-', lw=1.5, label='pi theoretical')\n",
    "#plt.setp(patches, 'facecolor', 'g', 'alpha', 0.75)\n",
    "plt.title('Path histogram')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('Normalized Frequency')\n",
    "plt.legend()\n",
    "#plt.savefig('ho_histogram.png')\n",
    "#plt.show() \n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Levy Flight\n",
    "\n",
    "Existe una manera más eficiente de hacer los movimientos sobre el path que define la partícula, en facil de observar que mover un bead lejos de sus vecinos puede resultar en una rechazo del movimiento. Se puede usar una aproximación más general si tenemos un bead $x_j$, y fijamos los beads $x_k$ y $x_{k+m}$, tal que $k<j<k+m$. Que estan a una distancia en tiempo imaginario: $\\tau(j-k)$ y $\\tau(k+m-j)$ de j respectivamente. \n",
    "\n",
    "Uno puede descartar los terminos independientes de $j$ para la parte cinetica o de particula libre como:\n",
    "\n",
    "\n",
    "$$\n",
    "\\rho_{free}(r_k,r_j,\\tau(j-k)) \\rho_{free}(r_j,r_{k+m},\\tau(k+m-j))=\\exp\\left( \\frac{|r_j-r_k|^2}{4\\lambda\\tau(j-k)}\\right)\\exp\\left( \\frac{|r_{k+m}-r_j|^2}{4\\lambda\\tau(k+m-j)}\\right) \n",
    "$$\n",
    "\n",
    "\n",
    "Si ignoramos por un momento los terminos independientes de $j$, es decir la contricuion de los extremos tenemos que: \n",
    "\n",
    "\n",
    "$$\n",
    "\\rho_{free}(r_k,r_j,\\tau(j-k)) \\rho_{free}(r_j,r_{k+m},\\tau(k+m-j))\\propto\\exp\\left( \\frac{|r_j-\\overline{r}|^2}{2\\sigma^2}\\right) \n",
    "$$\n",
    "\n",
    "Donde: \n",
    "\n",
    "$$\n",
    "\\overline{r}=\\frac{r_k(k+m-j)+r_{k+m}(j-k)}{m}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\sigma^2 = \\frac{2\\lambda}{\\frac{1}{(k+mj)\\tau}+\\frac{1}{(j-k)\\tau}}\n",
    "$$\n",
    "\n",
    "Luego vemos que esto es una distribución Gaussiana que puede ser muestreada directamente, generando un número con media $\\overline{r}$ y varianza $\\sigma^2$. Uno puede crear un segmento de path de una partícula libre sin rechazos, de la siguiente manera:\n",
    "\n",
    "1. Escoja aleatorimente dos extermos fijos k y k+m. \n",
    "\n",
    "2. Cresca el camino de $r_{k}$ a $r_{k+m-1}$ in orden ascendente de la muestra para $j=k+1,\\cdots k+m-1$:\n",
    "\n",
    "\n",
    "- Muestre r_{k+j} de una distribucion Gaussiana con media $\\overline{r}$ y varianza $\\sigma^2$.\n",
    "\n",
    "- Aumente j=j+1 fije nuevas posiciones para los extremos fijos r_{k+j-1}, r_{k+m}\n",
    "\n",
    "- Continue el loop hasta j=k+m-1\n",
    "\n",
    "3. Regrese al principio, \n",
    "\n",
    "\n",
    "Podemos observar que para la parte cinética o de partícula libre se crece el camino o path a partir de extermos fijos, creciendo un path completamente nuevo entre los extremos. \n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "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": [
      "[0.0, 0.4411431197130108]\n",
      "[0, 1]\n",
      "[0.0, 0.4411431197130108, 0.2702229824128156]\n",
      "[0, 1, 2]\n",
      "[0.0, 0.4411431197130108, 0.2702229824128156, 1.0764995482034814]\n",
      "[0, 1, 2, 3]\n"
     ]
    }
   ],
   "source": [
    "beta = 1.0\n",
    "N = 4\n",
    "dtau = beta / N\n",
    "nsteps = 1                      # number of paths to be generated\n",
    "xstart, xend = 0.0, 1.0          # initial and final points\n",
    "for step in range(nsteps):\n",
    "    x = [xstart]\n",
    "    Y = [0];\n",
    "    plt.figure()\n",
    "    for k in range(1, N):        # loop over internal slices\n",
    "        dtau_prime = (N - k) * dtau\n",
    "        x_mean = (dtau_prime * x[k - 1] + dtau * xend) / \\\n",
    "                 (dtau + dtau_prime)\n",
    "        sigma = math.sqrt(1.0 / (1.0 / dtau + 1.0 / dtau_prime))\n",
    "        xnew=np.random.normal(x_mean, sigma)\n",
    "        x.append(xnew)\n",
    "        Y.append(k)\n",
    "        print x\n",
    "        print Y\n",
    "        plt.plot(xstart,0, 'bo',markersize=10)\n",
    "        plt.plot(x,Y,'ro-',markersize=10)\n",
    "        \n",
    "        plt.plot(xend,N, 'bo',markersize=10)\n",
    "        plt.xlim(-2,2)\n",
    "        plt.ylim(-1, N+1)\n",
    "    x.append(xend)\n",
    "    #print x\n",
    "\n",
    "\n",
    "\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",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    " "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}