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November 15, 2020 10:49
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1D Hubbard chain binding energy vs U
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "code", | |
| "execution_count": 5, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "import numpy as np" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Two-body energy eigenstate, $E$, satisfies\n", | |
| "\n", | |
| "$$\n", | |
| "\\frac{1}{U} = \\frac{1}{L} \\sum_k \\frac{1}{2\\epsilon_k - E}\n", | |
| "$$\n", | |
| "\n", | |
| "where the sum over $k$ runs over the 1st Brillouin zone and $\\epsilon_k = 2(1 - \\cos{k})$ is the single-particle dispersion for a single Hubbard chain. Here we set $t=1$ to fix the energy scale and shift the bottom of the single-particle band so that $\\epsilon_{k=0} = 0$ for convenience.\n", | |
| "\n", | |
| "Note that the *binding* energy, $E^{b}$, is counted from the bottom of the band, so that \n", | |
| "\n", | |
| "$$\n", | |
| "\\mathrm{binding\\ energy} = -E\n", | |
| "$$\n", | |
| "\n", | |
| "For a single chain, the binding energy is (see, e.g. Orso et al, arXiv:1010.3105, just below Eq. (8)).\n", | |
| "\n", | |
| "$$\n", | |
| "E^b = \\sqrt{U^2 + 16} - 4\n", | |
| "$$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 47, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "def U1(E, L):\n", | |
| " \"\"\" R.h.s. of the two-body energy equation.\n", | |
| " \"\"\"\n", | |
| " k = 2*np.pi * np.arange(-L//2, L//2) / L\n", | |
| " ene = 2*(1 - np.cos(k))\n", | |
| " denom = 2*ene - E\n", | |
| " return np.sum( 1./denom ) / L" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 58, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "array([0.9 , 1.72952205, 2.30336981, 2.78438463, 3.21451435,\n", | |
| " 3.61198375, 3.98657373, 4.34420683, 4.68876479, 5.02293907,\n", | |
| " 5.34867628, 5.66743138, 5.98032091, 6.28822053, 6.59182949,\n", | |
| " 6.89171489, 7.18834275, 7.48210052, 7.77331361, 8.06225775])" | |
| ] | |
| }, | |
| "execution_count": 58, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "# binding energies\n", | |
| "Es = np.linspace(0.1, 5, 20)\n", | |
| "\n", | |
| "UU = np.asarray([1./U1(-e, 100) for e in Es])\n", | |
| "UU" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 64, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "def Eb(U):\n", | |
| " return np.sqrt(UU**2 + 16) - 4" | |
| ] | |
| }, | |
| { | |
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| "execution_count": 66, | |
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| " // Updates the figure title.\n", | |
| " fig.header.textContent = msg['label'];\n", | |
| "};\n", | |
| "\n", | |
| "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n", | |
| " var cursor = msg['cursor'];\n", | |
| " switch (cursor) {\n", | |
| " case 0:\n", | |
| " cursor = 'pointer';\n", | |
| " break;\n", | |
| " case 1:\n", | |
| " cursor = 'default';\n", | |
| " break;\n", | |
| " case 2:\n", | |
| " cursor = 'crosshair';\n", | |
| " break;\n", | |
| " case 3:\n", | |
| " cursor = 'move';\n", | |
| " break;\n", | |
| " }\n", | |
| " fig.rubberband_canvas.style.cursor = cursor;\n", | |
| "};\n", | |
| "\n", | |
| "mpl.figure.prototype.handle_message = function (fig, msg) {\n", | |
| " fig.message.textContent = msg['message'];\n", | |
| "};\n", | |
| "\n", | |
| "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n", | |
| " // Request the server to send over a new figure.\n", | |
| " fig.send_draw_message();\n", | |
| "};\n", | |
| "\n", | |
| "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n", | |
| " fig.image_mode = msg['mode'];\n", | |
| "};\n", | |
| "\n", | |
| "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n", | |
| " for (var key in msg) {\n", | |
| " if (!(key in fig.buttons)) {\n", | |
| " continue;\n", | |
| " }\n", | |
| " fig.buttons[key].disabled = !msg[key];\n", | |
| " fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n", | |
| " }\n", | |
| "};\n", | |
| "\n", | |
| "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n", | |
| " if (msg['mode'] === 'PAN') {\n", | |
| " fig.buttons['Pan'].classList.add('active');\n", | |
| " fig.buttons['Zoom'].classList.remove('active');\n", | |
| " } else if (msg['mode'] === 'ZOOM') {\n", | |
| " fig.buttons['Pan'].classList.remove('active');\n", | |
| " fig.buttons['Zoom'].classList.add('active');\n", | |
| " } else {\n", | |
| " fig.buttons['Pan'].classList.remove('active');\n", | |
| " fig.buttons['Zoom'].classList.remove('active');\n", | |
| " }\n", | |
| "};\n", | |
| "\n", | |
| "mpl.figure.prototype.updated_canvas_event = function () {\n", | |
| " // Called whenever the canvas gets updated.\n", | |
| " this.send_message('ack', {});\n", | |
| "};\n", | |
| "\n", | |
| "// A function to construct a web socket function for onmessage handling.\n", | |
| "// Called in the figure constructor.\n", | |
| "mpl.figure.prototype._make_on_message_function = function (fig) {\n", | |
| " return function socket_on_message(evt) {\n", | |
| " if (evt.data instanceof Blob) {\n", | |
| " /* 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", | |
| "\n", | |
| " fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n", | |
| " evt.data\n", | |
| " );\n", | |
| " fig.updated_canvas_event();\n", | |
| " fig.waiting = false;\n", | |
| " return;\n", | |
| " } else if (\n", | |
| " typeof evt.data === 'string' &&\n", | |
| " evt.data.slice(0, 21) === 'data:image/png;base64'\n", | |
| " ) {\n", | |
| " fig.imageObj.src = evt.data;\n", | |
| " fig.updated_canvas_event();\n", | |
| " fig.waiting = false;\n", | |
| " return;\n", | |
| " }\n", | |
| "\n", | |
| " var msg = JSON.parse(evt.data);\n", | |
| " var msg_type = msg['type'];\n", | |
| "\n", | |
| " // Call the \"handle_{type}\" callback, which takes\n", | |
| " // the figure and JSON message as its only arguments.\n", | |
| " try {\n", | |
| " var callback = fig['handle_' + msg_type];\n", | |
| " } catch (e) {\n", | |
| " console.log(\n", | |
| " \"No handler for the '\" + msg_type + \"' message type: \",\n", | |
| " msg\n", | |
| " );\n", | |
| " return;\n", | |
| " }\n", | |
| "\n", | |
| " if (callback) {\n", | |
| " try {\n", | |
| " // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n", | |
| " callback(fig, msg);\n", | |
| " } catch (e) {\n", | |
| " console.log(\n", | |
| " \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n", | |
| " e,\n", | |
| " e.stack,\n", | |
| " msg\n", | |
| " );\n", | |
| " }\n", | |
| " }\n", | |
| " };\n", | |
| "};\n", | |
| "\n", | |
| "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n", | |
| "mpl.findpos = function (e) {\n", | |
| " //this section is from http://www.quirksmode.org/js/events_properties.html\n", | |
| " var targ;\n", | |
| " if (!e) {\n", | |
| " e = window.event;\n", | |
| " }\n", | |
| " if (e.target) {\n", | |
| " targ = e.target;\n", | |
| " } else if (e.srcElement) {\n", | |
| " targ = e.srcElement;\n", | |
| " }\n", | |
| " if (targ.nodeType === 3) {\n", | |
| " // defeat Safari bug\n", | |
| " targ = targ.parentNode;\n", | |
| " }\n", | |
| "\n", | |
| " // pageX,Y are the mouse positions relative to the document\n", | |
| " var boundingRect = targ.getBoundingClientRect();\n", | |
| " var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n", | |
| " var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n", | |
| "\n", | |
| " return { x: x, y: y };\n", | |
| "};\n", | |
| "\n", | |
| "/*\n", | |
| " * return a copy of an object with only non-object keys\n", | |
| " * we need this to avoid circular references\n", | |
| " * http://stackoverflow.com/a/24161582/3208463\n", | |
| " */\n", | |
| "function simpleKeys(original) {\n", | |
| " return Object.keys(original).reduce(function (obj, key) {\n", | |
| " if (typeof original[key] !== 'object') {\n", | |
| " obj[key] = original[key];\n", | |
| " }\n", | |
| " return obj;\n", | |
| " }, {});\n", | |
| "}\n", | |
| "\n", | |
| "mpl.figure.prototype.mouse_event = function (event, name) {\n", | |
| " var canvas_pos = mpl.findpos(event);\n", | |
| "\n", | |
| " if (name === 'button_press') {\n", | |
| " this.canvas.focus();\n", | |
| " this.canvas_div.focus();\n", | |
| " }\n", | |
| "\n", | |
| " var x = canvas_pos.x * mpl.ratio;\n", | |
| " var y = canvas_pos.y * mpl.ratio;\n", | |
| "\n", | |
| " this.send_message(name, {\n", | |
| " x: x,\n", | |
| " y: y,\n", | |
| " button: event.button,\n", | |
| " step: event.step,\n", | |
| " guiEvent: simpleKeys(event),\n", | |
| " });\n", | |
| "\n", | |
| " /* This prevents the web browser from automatically changing to\n", | |
| " * the text insertion cursor when the button is pressed. We want\n", | |
| " * to control all of the cursor setting manually through the\n", | |
| " * 'cursor' event from matplotlib */\n", | |
| " event.preventDefault();\n", | |
| " return false;\n", | |
| "};\n", | |
| "\n", | |
| "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n", | |
| " // Handle any extra behaviour associated with a key event\n", | |
| "};\n", | |
| "\n", | |
| "mpl.figure.prototype.key_event = function (event, name) {\n", | |
| " // Prevent repeat events\n", | |
| " if (name === 'key_press') {\n", | |
| " if (event.which === this._key) {\n", | |
| " return;\n", | |
| " } else {\n", | |
| " this._key = event.which;\n", | |
| " }\n", | |
| " }\n", | |
| " if (name === 'key_release') {\n", | |
| " this._key = null;\n", | |
| " }\n", | |
| "\n", | |
| " var value = '';\n", | |
| " if (event.ctrlKey && event.which !== 17) {\n", | |
| " value += 'ctrl+';\n", | |
| " }\n", | |
| " if (event.altKey && event.which !== 18) {\n", | |
| " value += 'alt+';\n", | |
| " }\n", | |
| " if (event.shiftKey && event.which !== 16) {\n", | |
| " value += 'shift+';\n", | |
| " }\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, 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\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n", | |
| "\n", | |
| "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n", | |
| "\n", | |
| "mpl.default_extension = \"png\";/* global mpl */\n", | |
| "\n", | |
| "var comm_websocket_adapter = function (comm) {\n", | |
| " // Create a \"websocket\"-like object which calls the given IPython comm\n", | |
| " // object with the appropriate methods. Currently this is a non binary\n", | |
| " // socket, so there is still some room for performance tuning.\n", | |
| " var ws = {};\n", | |
| "\n", | |
| " ws.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 overridden (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 = document.getElementById(id);\n", | |
| " var ws_proxy = comm_websocket_adapter(comm);\n", | |
| "\n", | |
| " function ondownload(figure, _format) {\n", | |
| " window.open(figure.canvas.toDataURL());\n", | |
| " }\n", | |
| "\n", | |
| " var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n", | |
| "\n", | |
| " // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n", | |
| " // web socket which is closed, not our websocket->open comm proxy.\n", | |
| " ws_proxy.onopen();\n", | |
| "\n", | |
| " fig.parent_element = element;\n", | |
| " fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n", | |
| " if (!fig.cell_info) {\n", | |
| " console.error('Failed to find cell for figure', id, fig);\n", | |
| " return;\n", | |
| " }\n", | |
| "};\n", | |
| "\n", | |
| "mpl.figure.prototype.handle_close = function (fig, msg) {\n", | |
| " var width = fig.canvas.width / mpl.ratio;\n", | |
| " fig.root.removeEventListener('remove', this._remove_fig_handler);\n", | |
| "\n", | |
| " // Update the output cell to use the data from the current canvas.\n", | |
| " fig.push_to_output();\n", | |
| " var dataURL = fig.canvas.toDataURL();\n", | |
| " // Re-enable the keyboard manager in IPython - without this line, in FF,\n", | |
| " // the notebook keyboard shortcuts fail.\n", | |
| " IPython.keyboard_manager.enable();\n", | |
| " fig.parent_element.innerHTML =\n", | |
| " '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n", | |
| " fig.close_ws(fig, msg);\n", | |
| "};\n", | |
| "\n", | |
| "mpl.figure.prototype.close_ws = function (fig, msg) {\n", | |
| " fig.send_message('closing', msg);\n", | |
| " // fig.ws.close()\n", | |
| "};\n", | |
| "\n", | |
| "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n", | |
| " // Turn the data on the canvas into data in the output cell.\n", | |
| " var width = this.canvas.width / mpl.ratio;\n", | |
| " var dataURL = this.canvas.toDataURL();\n", | |
| " this.cell_info[1]['text/html'] =\n", | |
| " '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n", | |
| "};\n", | |
| "\n", | |
| "mpl.figure.prototype.updated_canvas_event = function () {\n", | |
| " // Tell IPython that the notebook contents must change.\n", | |
| " IPython.notebook.set_dirty(true);\n", | |
| " this.send_message('ack', {});\n", | |
| " var fig = this;\n", | |
| " // Wait a second, then push the new image to the DOM so\n", | |
| " // that it is saved nicely (might be nice to debounce this).\n", | |
| " setTimeout(function () {\n", | |
| " fig.push_to_output();\n", | |
| " }, 1000);\n", | |
| "};\n", | |
| "\n", | |
| "mpl.figure.prototype._init_toolbar = function () {\n", | |
| " var fig = this;\n", | |
| "\n", | |
| " var toolbar = document.createElement('div');\n", | |
| " toolbar.classList = 'btn-toolbar';\n", | |
| " this.root.appendChild(toolbar);\n", | |
| "\n", | |
| " function on_click_closure(name) {\n", | |
| " return function (_event) {\n", | |
| " return fig.toolbar_button_onclick(name);\n", | |
| " };\n", | |
| " }\n", | |
| "\n", | |
| " function on_mouseover_closure(tooltip) {\n", | |
| " return function (event) {\n", | |
| " if (!event.currentTarget.disabled) {\n", | |
| " return fig.toolbar_button_onmouseover(tooltip);\n", | |
| " }\n", | |
| " };\n", | |
| " }\n", | |
| "\n", | |
| " fig.buttons = {};\n", | |
| " var buttonGroup = document.createElement('div');\n", | |
| " buttonGroup.classList = 'btn-group';\n", | |
| " var button;\n", | |
| " for (var toolbar_ind in mpl.toolbar_items) {\n", | |
| " var name = mpl.toolbar_items[toolbar_ind][0];\n", | |
| " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", | |
| " var image = mpl.toolbar_items[toolbar_ind][2];\n", | |
| " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", | |
| "\n", | |
| " if (!name) {\n", | |
| " /* Instead of a spacer, we start a new button group. */\n", | |
| " if (buttonGroup.hasChildNodes()) {\n", | |
| " toolbar.appendChild(buttonGroup);\n", | |
| " }\n", | |
| " buttonGroup = document.createElement('div');\n", | |
| " buttonGroup.classList = 'btn-group';\n", | |
| " continue;\n", | |
| " }\n", | |
| "\n", | |
| " button = fig.buttons[name] = document.createElement('button');\n", | |
| " button.classList = 'btn btn-default';\n", | |
| " button.href = '#';\n", | |
| " button.title = name;\n", | |
| " button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n", | |
| " button.addEventListener('click', on_click_closure(method_name));\n", | |
| " button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n", | |
| " buttonGroup.appendChild(button);\n", | |
| " }\n", | |
| "\n", | |
| " if (buttonGroup.hasChildNodes()) {\n", | |
| " toolbar.appendChild(buttonGroup);\n", | |
| " }\n", | |
| "\n", | |
| " // Add the status bar.\n", | |
| " var status_bar = document.createElement('span');\n", | |
| " status_bar.classList = 'mpl-message pull-right';\n", | |
| " toolbar.appendChild(status_bar);\n", | |
| " this.message = status_bar;\n", | |
| "\n", | |
| " // Add the close button to the window.\n", | |
| " var buttongrp = document.createElement('div');\n", | |
| " buttongrp.classList = 'btn-group inline pull-right';\n", | |
| " button = document.createElement('button');\n", | |
| " button.classList = 'btn btn-mini btn-primary';\n", | |
| " button.href = '#';\n", | |
| " button.title = 'Stop Interaction';\n", | |
| " button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n", | |
| " button.addEventListener('click', function (_evt) {\n", | |
| " fig.handle_close(fig, {});\n", | |
| " });\n", | |
| " button.addEventListener(\n", | |
| " 'mouseover',\n", | |
| " on_mouseover_closure('Stop Interaction')\n", | |
| " );\n", | |
| " buttongrp.appendChild(button);\n", | |
| " var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n", | |
| " titlebar.insertBefore(buttongrp, titlebar.firstChild);\n", | |
| "};\n", | |
| "\n", | |
| "mpl.figure.prototype._remove_fig_handler = function () {\n", | |
| " this.close_ws(this, {});\n", | |
| "};\n", | |
| "\n", | |
| "mpl.figure.prototype._root_extra_style = function (el) {\n", | |
| " el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n", | |
| " el.addEventListener('remove', this._remove_fig_handler);\n", | |
| "};\n", | |
| "\n", | |
| "mpl.figure.prototype._canvas_extra_style = function (el) {\n", | |
| " // this is important to make the div 'focusable\n", | |
| " el.setAttribute('tabindex', 0);\n", | |
| " // reach out to IPython and tell the keyboard manager to turn it's self\n", | |
| " // off when our div gets focus\n", | |
| "\n", | |
| " // location in version 3\n", | |
| " if (IPython.notebook.keyboard_manager) {\n", | |
| " IPython.notebook.keyboard_manager.register_events(el);\n", | |
| " } else {\n", | |
| " // location in version 2\n", | |
| " IPython.keyboard_manager.register_events(el);\n", | |
| " }\n", | |
| "};\n", | |
| "\n", | |
| "mpl.figure.prototype._key_event_extra = function (event, _name) {\n", | |
| " var manager = IPython.notebook.keyboard_manager;\n", | |
| " if (!manager) {\n", | |
| " manager = IPython.keyboard_manager;\n", | |
| " }\n", | |
| "\n", | |
| " // Check for shift+enter\n", | |
| " if (event.shiftKey && event.which === 13) {\n", | |
| " this.canvas_div.blur();\n", | |
| " // select the cell after this one\n", | |
| " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n", | |
| " IPython.notebook.select(index + 1);\n", | |
| " }\n", | |
| "};\n", | |
| "\n", | |
| "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", | |
| " fig.ondownload(fig, null);\n", | |
| "};\n", | |
| "\n", | |
| "mpl.find_output_cell = function (html_output) {\n", | |
| " // Return the cell and output element which can be found *uniquely* in the notebook.\n", | |
| " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", | |
| " // IPython event is triggered only after the cells have been serialised, which for\n", | |
| " // our purposes (turning an active figure into a static one), is too late.\n", | |
| " var cells = IPython.notebook.get_cells();\n", | |
| " var ncells = cells.length;\n", | |
| " for (var i = 0; i < ncells; i++) {\n", | |
| " var cell = cells[i];\n", | |
| " if (cell.cell_type === 'code') {\n", | |
| " for (var j = 0; j < cell.output_area.outputs.length; j++) {\n", | |
| " var data = cell.output_area.outputs[j];\n", | |
| " if (data.data) {\n", | |
| " // IPython >= 3 moved mimebundle to data attribute of output\n", | |
| " data = data.data;\n", | |
| " }\n", | |
| " if (data['text/html'] === html_output) {\n", | |
| " return [cell, data, j];\n", | |
| " }\n", | |
| " }\n", | |
| " }\n", | |
| " }\n", | |
| "};\n", | |
| "\n", | |
| "// Register the function which deals with the matplotlib target/channel.\n", | |
| "// The kernel may be null if the page has been refreshed.\n", | |
| "if (IPython.notebook.kernel !== null) {\n", | |
| " IPython.notebook.kernel.comm_manager.register_target(\n", | |
| " 'matplotlib',\n", | |
| " mpl.mpl_figure_comm\n", | |
| " );\n", | |
| "}\n" | |
| ], | |
| "text/plain": [ | |
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| "output_type": "display_data" | |
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5JNPPD1FDhstswUM1R8RsBXGZsZvu+22KlW3UUZbFGLPidV3bGsRiJlLe2YykuxtxNOec7TXxFVfBNIQA2iLh+yZ08oLVGwLGFsVbyPLdRnAaNk21gA25P6o7V5viJZr65eGLAKp716PlrHLd1Z92uJzCERLAAMYLSnOiyuByBdk5E0gVriNOkRMkE392fNMtZmbhhgh2+rFRhFt+tSe57IRIVsV2pBtYOpLClYfM26HHHKINwJmozmWVG3608otKCiodxWwmQCrp5Vl28CYCVm7dq23tY09c2Y/N6Td0V5vW9dsTJtsmjWy8XF9b8uoLjhrty3EsA2Pb7/9dm9vvshhW3jY1iZ2bds2yEa1jIs9u/aXv/ylyrnVrxuZurXFELaq1kYEbQ8+G220/fns/yOLQ2za154prG1fQtOPrTi3V8FZP9sKb3sWsbajLgMY2QbGRpLsehkZGd6qd3tmr7ZtYBpiAM3o2Ah0ZJsce/bSGNlo7LamgKNl62IAo9VSbcapIVqurS+Mra3+tQUbtg2M9ZuN+NoKbVtcVXkbmPru9WgZYwDjmk4orA4CGECkkZAEIl+QlStnSdj26LKpNvsv8to31y9T2xbGzIQ98G8moqEbQdeXFCJtsBFAmz60JG/TsLaowEazzIBYEq7vMANshthGzezZJxttsNFQ2+cu8oaKaKaAIyNL0VxvWwbQPmtom2ykzUbybATP2lB91e22GJhZsb3yrN9tQYr1VeSw615//fXes382NWzXt2cMTSdmuOs77DlBGw2zhSA22mg6MzNoz8uZIYwc1le2YMCms82cVT5s6tdGDM082mikbSptq5wbYgDtXFvYYtqovhF05Y2y6+rnbbXTjJzp3KapbQTWVo3bs7T2/OORRx5Z5whgtGxdDGC0WqrtXrfYaLVcFx/Tk4302uirGUHbYshGdG1Fd+WNoOu716Nl7PqdVZ+e+RwC0RDAAEZDiXMg0EQEbHsTM4Q2NZwqx7baZCOsNjpm08eV92dMlrbbc4g2umgjixxNTyAV74+mp0YJEIiOAAYwOk6cBQFnAtU3iTXTZyN4Nm1ke7wl49HQNm3r1W7J0H577s+2oKnttXXJUP9ErmNDtZTIbaFuEEgGAhjAZOgl6pgSBGzLGdvOxJ4hs0Us9hou2w7Fpvzs+bNkPKJtky3YsOct7fk4W/Vrzy5yQKAygWi1BDUIQCA2BDCAseHIVSBQLwFbrWh7yNmzb7aliI0i2V52tlVJsh7RtsmMr73FxVay2vNP1VcyJ2v7qXfsCESrpdiVyJUg4G8CGEB/9z+thwAEIAABCEDAhwQwgD7sdJoMAQhAAAIQgIC/CWAA/d3/tB4CEIAABCAAAR8SwAD6sNNpMgQgAAEIQAAC/iaAAXTof9ts1jZ/tffJRjYldrgcoRCAAAQgAAEIxIGAvSJy/fr13r6kaWlpcSgx8YrAADr0yTfffOO90YEDAhCAAAQgAIHkI/D1119XeatQ8rWg8TXGADaenYqKirz3RJqAKr9E3uGShEIAAhCAAAQg0MQE7JV/NoBjr+/Lyclp4tIS8/IYQId+MQGZcMwIYgAdQBIKAQhAAAIQiCMB8reEAXQQHAJygEcoBCAAAQhAoJkIkL8xgE7SQ0BO+AiGAAQgAAEINAsB8jcG0El4CMgJH8EQgAAEIACBZiFA/sYAOgkPATnhIxgCEIAABCDQLATI3xhAJ+EhICd8BEMAAhCAAASahQD5GwPoJDwE5ISPYAhAAAIQgECzECB/YwCdhIeAnPARDAEIQAACEGgWAuRvDKCT8BCQEz6CIQABCEAAAs1CgPyNAXQSHgJywkcwBCAAAQhAoFYC5cGQ3vl8rX5YX6xObbN1cPf2Sk8LxIwW+dvnBnDs2LEaN25cFUHttdde+uijj6ISGQKKChMnQQACEIAABKImMGdZocbNXq7CouKKmNycbI0Z3FODeuVGfZ1tnUj+xgDqySef1Kuvvlqhk4yMDO2www5RCQwBRYWJkyAAAQhAAAJRETDzN3LqYoWqnR0Z+5s8vE9MTCD5GwOomTNnqqCgICphVj8JATUKG0EQgAAEIACBGgRs2rf/hHlVRv4qn2QmsHNOthaMHuA8HUz+xgBq4sSJysnJUXZ2tvr166fx48erW7dutd6aW7Zskf0XOUxAXbt2VVFRkdq1a8ftDAEIQAACEIBAIwksXLlGQ6csqojuoh+1SjYjV/XZv+kj+qpfjw6NLCUchgH0uQF88cUXtWHDBtlzf4WFhd7zgKtWrdKyZcvUtm3bGuKq7ZlBOwkD6HQfEgwBCEAAAhDQrIJVGjUjPCOXF1ihR7Ju1ePlR+rmsmFVTOCk/DwNyeviRAwD6HMDWF0969at0y677KI77rhD5513Xg1xMQLodL8RDAEIQAACEKiTQGQE8MDAR3owa6LaBjbr3eCeGl5yrbYoqyKOEcDYiCgQCoWqP2sZmysn6VUOOuggHX300d5UcH0Hf0HUR4jPIQABCEAAAtERsGcAfzv+Pv2j5Dq1DmzRW+U99bvSK7VJ2d4FeAYwOo7RnoUBrETKpoPt+T+b6r300kvrZYgBrBcRJ0AAAhCAAASiJvDyki+U/eRw7/zfl16uYrWoMH/2A6uAo0ZZ74m+NoBXXnmlBg8e7E37fvvttxozZoy3Inj58uXq2LFjvfAwgPUi4gQIQAACEIBAgwi8XPCZbn7hY335c7Aijn0AG4QwqpN9bQDz8/M1f/58rVmzxjN8/fv3180336wePXpEBQ8DGBUmToIABCAAAQjUTeDD2dKq96RfjZEC4RW/vAmk6QXjawPoihcD6EqQeAhAAAIQ8DWBZU9JT42QQuXSqQ9IvU6JCw7yN6uAnYSGgJzwEQwBCEAAAn4msGSGNHOkFApKvfOlE/8hpaXHhQj5GwPoJDQE5ISPYAhAAAIQ8CuBxY9Iz9piy5B0wFnS4ElxM3+GnPyNAXS69RCQEz6CIQABCEDAjwTemSK9cGW45QeeJx17u5SWFlcS5G8MoJPgEJATPoIhAAEIQMBvBFZ/Kt19cHjat++F0jG3VCz8iCcK8jcG0ElvCMgJH8EQgAAEIOBHAosfldaurLLqN94YyN8YQCfNISAnfARDAAIQgIAfCNgLx0o2SC3aJkxryd8YQCcxIiAnfARDAAIQgECKEaixf9+u2yv9tZukD5+Tzn1ealP/SxbigYT8jQF00hkCcsJHMAQgAAEIpBCBOcsKNW72chUWFf+vVSHd0vpxnVn+bPjfJ06W8s5MiBaTvzGATkJEQE74CIYABCAAgRQhYOZv5NTFtqmLdwQU1JiMR3Ruxsvev5fnXa+eJ16VMK0lf2MAncSIgJzwEQwBCEAAAilAwKZ9+0+YVzHyZ+bv5oz7dWbGvxUMBXR92W/17zbHacHoAUpPC7/qrbkP8jcG0EmDCMgJH8EQgAAEIJACBBauXKOhUxZ5LUlTULdl/lOnps9XeSigP5aer6eCh3ufTR/RV/16dEiIFpO/MYBOQkRATvgIhgAEIACBFCAwq2CVRs0o8FrSXj/rmawb1CWwWpeXXqhng4dUtHBSfp6G5HVJiBaTvzGATkJEQE74CIYABCAAgRQgUHkE0JrTRT9q77SvNDf4iyqtYwQwsTo7EArZBj0cjSGAAWwMNWIgAAEIQCCVCJRv2aRRt/9Tz6/fo2IRSOX22VN/nXOyeQYwwTodA+jQIRhAB3iEQgACEIBA8hMo2ShNz1fwizc1csulejl4UBUTGFnyMXl4Hw3qlZsw7SV/MwXsJEYE5ISPYAhAAAIQSGYCxT9Lj50mfb1Iymqrt/tN1h8Wtaq0D6CUm5OtMYN7JpT5M+Tkbwyg062HgJzwEQwBCEAAAslKYNNaaeop0reLpewcafjT0s4HqsabQLq3T5itXyqjJn9jAJ1uPQTkhI9gCEAAAhBIRgIbV0uPnCh9v1Rq2V46e6aUu39StYT8jQF0EiwCcsJHMAQgAAEIJBuBzeukB46RfvxIat1JOudZqdM+ydYKpoDtbS2sAm68bjGAjWdHJAQgAAEIJCEB2zjk+culT16Szn5W2mH3JGwEzwBap2EAHaSLAXSARygEIAABCCQngWBQ2vij1HbH5Kw/i0C8fsMAOsgXA+gAj1AIQAACEEgOAqtXSAvvlI69XUrPTI4611NL8jcG0EnICMgJH8EQgAAEIJDoBL5fLj0yRNr4g3ToKGngjYle46jqR/7GAEYllLpOQkBO+AiGAAQgAIFEJlC4JLzad/Naacf9wqt9W++QyDWOum7kbwxg1GKp7UQE5ISPYAhAAAIQSBACNfbvy/xM6Y+dIm0pknbqIw1/SmrVPkFq614N8jcG0ElFCMgJH8EQgAAEIJAABOYsK9S42csr3uBxcOBDPdhiolqrWOraVxr2hJTdLgFqGrsqkL8xgE5qQkBO+AiGAAQgAIFmJmDmb+TUxRXv722pYs1v8Qd1DPyst8p7auMpj2pgXnJu9bIttORvDKDTrYeAnPARDAEIQAACzUjApn37T5hX5d29Vp1+aR/o7PSXdVnpRdo+p50WjB6QkK9zc0FH/sYAuuiHncSd6BEMAQhAAALNSWDhyjUaOmWRV4VWKtYmZddanekj+qpfjw7NWdWYl40BxAA6iQoBOeEjGAIQgAAEmpHArIJVGjWjQCelvaFrM6fpzJLr9Glo5xo1mpSfpyF5XZqxprEvmvyNAXRSFQJywkcwBCAAAQg0IwEbAZz9wM26KeMBpQVCurfsOI0vG1ajRowANmMnNWHRvAnEAS4G0AEeoRCAAAQg0KwEgm/dpbSXr/Pq8FDZ/2lc2dkKKa2iTgFJnXOyeQawWXup6QrHADqwxQA6wCMUAhCAAASah0AoJM2/Xfr3TV75k8sG67ayfIVkli98RH6aPLyPBvXKbZ56NmGp5G+mgJ3khYCc8BEMAQhAAALxJmDmb+44acFfwyUfdb3mtB+mcc99WGU1cG5OtsYM7pmS5s+aTf7GADrdegjICR/BEIAABCAQbwJlW8Lv9v1qofR/N0uHXOzVoMabQLq3T7mtXyqjJn9jAJ1uPQTkhI9gCEAAAhBoDgLFP0sr50r7ntQcpSdEmeRvDKCTEBGQEz6CIQABCEAgHgTKS6WPX5B6DolHaUlRBvkbA+gkVATkhI9gCEAAAhBoagI25fvEb6SPn5cG/lk69NKmLjEprk/+xgA6CRUBOeEjGAIQgAAEmpJAySbp8WHSynlSegvp9EekvQY1ZYlJc23yNwbQSawIyAkfwRCAAAQg0FQEtqyXpp0hffmmlNlKGjpd2u3Ipiot6a5L/sYAOokWATnhIxgCEIAABJqCwOafpKmnSKvek1q0k4Y9IXXr2xQlJe01yd8YQCfxIiAnfARDAAIQgIADgVq3bgmWSvcNkL5bKrXcXjrrGWmnAxxKSc1Q8jcG0EnZCMgJH8EQgAAEINBIAnOWFWrc7OW1b968YWZ4o+ezZko79mxkCakdRv7GADopHAE54SMYAhCAAAQaQcDM38ipixWqFlvl9W09ssMjgBy1EiB/YwCdbg0E5ISPYAhAAAIQaCABm/btP2FelZG/7oFCXZvxmK4ovUDr1Uadc7K1YPSAlH6TRwOx1Tid/I0BdNIQAnLCRzAEIAABCDSQwMKVazR0yqKKqD0DX+uxrFvUMVCkp8r764rSC73Ppo/oq349OjTw6v45nfyNAXRSOwJywkcwBCAAAQg0kMCsglUaNaPAi+odWKmHsyZo+8AGfRDcRWeVXKO1aud9Nik/T0PyujTw6v45nfyNAXRSOwJywkcwBCAAAQg0kEBkBPDgwIe6P+t2tQ1s1uLg7jq35I/6WW0qrsYI4LbBkr8xgA289aqejoCc8BEMAQhAAAINJGDPAF45/naNL5mg7ECp3izfVyNKr9AmZXtXsoUgPANYP1TyNwawfpVs4wwE5ISPYAhAAAIQaCiBshJt+msftdr4teaWH6ALS0dpi7IqzJ/9MHl4Hw3qldvQK/vqfPI3BjxYKLQAACAASURBVNBJ8AjICR/BEIAABCDQGAKrP9VXL/xFZ35zkr75uaziCrk52RozuCfmLwqm5G8MYBQyqfsUBOSEj2AIQAACEIiWwE9fStvvUuXsWt8EkhbZDTDaC/vzPPI3BtBJ+QjICR/BEIAABCAQDYE37pBeGy8NnSHt/qtoIjinHgLkbwyg002CgJzwEQwBCEAAAtsiEApJc2+UFtwRPuuo66UjroJZDAiQvzGATjJCQE74CIYABCAAgboIBIPSnNHSO/8MnzHwRunQUfCKEQHyNwbQSUoIyAkfwRCAAAQgUBuB8jLp2UukJdPCG7scf4d04G9hFUMC5G8MoJOcEJATPoIhAAEIQKA6gbIS6anzpA+flQLp0omTpf3PgFOMCZC/MYAVkrr11lt1zTXXaNSoUfrb3/4WldQQUFSYOAkCEIAABKIlYFO/M0dKHzwtnfqAtM/gaCM5rwEEyN8YQE8u7777rk4//XS1a9dORx11FAawATcRp0IAAhCAQIwJ2BTw90ulnQ6I8YW5XIQABhADqA0bNqhPnz76xz/+oZtuukl5eXkYQL4jIAABCECgyQjU2L9vRyn93XulI0ZLaelNVi4X3koAA4gB1DnnnKP27dvrr3/9q4488kgMIN8QEIAABCDQZATmLCvUuNnLVVhU7JXRUT9pRssJ6hH6Sup3sXTMzU1WNhfGAFbWQCAUso2G/HnMmDFDN998szcFnJ2dXa8B3LJli+y/ykPIXbt2VVFRkTd9zAEBCEAAAhCoi4CZv5FTFyuSdLvoR03NukXd077X96Ht9MkxU3XYIYcBMA4EGAH08Qjg119/rQMPPFCvvPKKevfu7cmtvhHAsWPHaty4cTWkiQGMw91KERCAAASSmIBN+/afMK9i5K97oNAzf10Ca/R1sKOGlV6r0na7aMHoAUrndW5N3tMYQB8bwJkzZ+qkk05SevrW5y3Ky8sVCASUlpbmjfRV/szUyAhgk9+TFAABCEAgJQksXLlGQ6cs8tq2d+ArPZo1Xh0DRVoR3EnDSq7V92rvfTZ9RF/169EhJRkkUqMwgD42gOvXr9eXX35ZRY+/+c1vtPfee2v06NHq1atXvVpFQPUi4gQIQAACEJA0q2CVRs0oUAuVaH6LP2jHwDp9ENxFZ5dcrTXKqWA0KT9PQ/K6wKyJCZC/fWwAa9NWfVPA1WMQUBPfoVweAhCAQIoQqDwCOCBtsUakv6DzSy/Tz2pdpYWMAManw8nfGMAqSsMAxufGoxQIQAACfiNQvmWj+t+xSN8VFf9vEYgtBQlUYLCfOudk8wxgnISBAcQAOkkNATnhIxgCEICAPwgUTJPm3aTXD3lQ585c7bW58vYbERs4eXgfDeqV6w8mzdxK8jcG0EmCCMgJH8EQgAAEUp/AonukOaPD7ex/ueZ0/n2VfQDt17k52RozuCfmL45qIH9jAJ3khoCc8BEMAQhAIHUJ2Ba7r98mvXZLuI19L5L+7yYpLU013gTSvT1bv8RZCeRvDKCT5BCQEz6CIQABCKQmATN/L10nLbo73L6jrpMOv0oKbH3mLzUbnjytIn9jAJ3UioCc8BEMAQhAIPUIBMul2ZdK708Nt23QBKnvBanXziRvEfkbA+gkYQTkhI9gCEAAAqlHYMsG6eHjpcIl0pB/SHlDU6+NKdAi8jcG0EnGCMgJH8EQgAAEUpPAxjXSt4ulPQamZvtSoFXkbwygk4wRkBM+giEAAQikBoHN66RPX5Z6n54a7fFBK8jfGEAnmSMgJ3wEQwACEEh+Aht+kB49Wfp+qTT479Ivzkn+NvmgBeRvDKCTzBGQEz6CIQABCCQ3gXVfS48MkdaulFp3ks56Rupc/3vkk7vRqVF78jcG0EnJCMgJH8EQgAAEkoZAjb372q5R+tSTpJ+/kXK6SWfPlDr0SJr2+L2i5G8MoNM9gICc8BEMAQhAICkIzFlWWOXtHfsGvtCjLW5Ve/0s7bCndNZMKadLUrSFSoYJkL8xgE73AgJywkcwBCAAgYQnYOZv5NTFFe/u3UFFmtfiCrULbNLS4K76Ycg0/eoX+yZ8O6hgVQLkbwyg0z2BgJzwEQwBCEAgoQnYtG//CfNUWFRcpZ4Xpc/U4en/1YiSK9U6p70WjB7Aq9wSuidrVo78jQF0kiwCcsJHMAQgAIGEJrBw5RoNnbLIq2Oaggoq7X/1DSlT5SpVhvfv6SP6ql+PDgndFirHCGB1DQRCIXtpIUdjCGAAG0ONGAhAAALJQWBWwSqNmlGgM9Pn6pT0+Tqr5BptUnaNyk/Kz9OQPJ4BTI5eDdeS/M0IoJNeEZATPoIhAAEIJDSBhStW640Hr9UfMx/36nlD6Tl6pPyYGnVmBDChu7HWypG/MYBOqkVATvgIhgAEIJC4BEIhBV+6XmmL7vLqeGfZifpL2WmSAhV1tp8652TzDGDi9mKdNSN/YwCdZIuAnPARDAEIQCAxCZSXSbMvlQoe8+r359LheqD82IqVwPa7iA2cPLyPBvXKTcx2UCsM4DY0wDOADjcIBtABHqEQgAAEEpFAabH05G+lj5+XAunSkLs0J+OoKvsAWrVzc7I1ZnBPzF8i9mEUdSJ/MwIYhUzqPgUBOeEjGAIQgEDiEfjpS+m+o6XiIum0B6W9j/PqWONNIN3bs/VL4vVe1DUif2MAoxZLbSciICd8BEMAAhBITALfLZU2r5O6H5aY9aNWzgTI3xhAJxEhICd8BEMAAhBIDALrvpbWrpR2OzIx6kMtmpwA+RsD6CQyBOSEj2AIQAACzU/gx0+kR0+UNq2Vzp4ldftl89eJGjQ5AfI3BtBJZAjICR/BEIAABJqXwKrF0mOnSpvWSDvsKZ31jJSzc/PWidLjQoD8jQF0EhoCcsJHMAQgAIHmI/D5fGn6UKlkg7TTAdKwp6TWvM6t+TokviWTvzGATopDQE74CIYABCDQPAQ+fC681Uv5FmnXw6Sh06UWbZunLpTaLATI3xhAJ+EhICd8BEMAAhCIP4EvF0oPHSuFgtLex0un3C9l1ny/b/wrRonxJED+xgA66Q0BOeEjGAIQgECTEqh1775QufTEOVL2dtLgSVJ6RpPWgYsnJgHyNwbQSZkIyAkfwRCAAASajMCcZYWV3t4RUppC2jGnVfjtHXt3kNIzpcDW9/o2WUW4cEISIH9jAJ2EiYCc8BEMAQhAoEkImPkbOXWx9+7eNAX154wHlakyjS77vfcWX97f2yTYk+qi5G8MoJNgEZATPoIhAAEIxJyATfv2nzBPhUXFylKp7sicrOPTFykYCujUkjF6P7SnOudka8HoAbzKLeb0k+eC5G8MoJNaEZATPoIhAAEIxJzAwpVrNHTKIrXWZt2T+Vcdlr5MJaF0/aH0Ir0Q7FtR3vQRfdWvB9u+xLwDkuSC5G8MoJNUEZATPoIhAAEIxJzArIJVGjdjvh7Muk37p32mjaEWuqD0Mr0R7F2lrEn5eRqS1yXm5XPB5CBA/sYAOikVATnhIxgCEIBAzAksXrJEOU+doR5phVobaqPflPxRS0K71yiHEcCYo0+qC5K/MYBOgkVATvgIhgAEIBBzAuUrXlNw6in6IbSdziq5Wp+FdqpShq375RnAmGNPuguSvzGATqJFQE74CIYABCDQJATee/kxXTQvqO/V3lsJHDkim76wCrhJsCfVRcnfGEAnwSIgJ3wEQwACEIgNgU9eltp3l3bYo+J6VfcBDP86Nyc7vA9gr9zYlMtVkpYA+RsD6CReBOSEj2AIQAAC7gQKpkmzLpbadZFGzJXadKq4Zq1vAklj82d36Ml/BfI3BtBJxQjICR/BEIAABNwIvDlJeuWG8DX2HyqdcGf4DR8cEKiHAPkbA+h0kyAgJ3wEQwACEGgcgVBIeuVP0lt3huMPuUQ6+kYpLa1x1yPKdwTI3xhAJ9EjICd8BEMAAhBoOIHyUunZS6Ul08KxA2+UDh3V8OsQ4WsC5G8MoNMNgICc8BEMAQhAoOEE5t4ovfEXKZAenvI9YFjDr0GE7wmQvzGATjcBAnLCRzAEIACBhhPYtFaaerJ0xGhpr183PJ4ICEgif2MAnW4EBOSEj2AIQAAC0RHYskFq0WbrucEgz/tFR46z6iBA/sYAOt0cCMgJH8EQgAAEqhCodduWtSukR0+WDr1UOngExCAQEwLkbwygk5AQkBM+giEAAQhUEKht4+YBbb/WPYFblVXyk9RhD+mCBVJmNtQg4EyA/I0BdBIRAnLCRzAEIAABj4CZv5FTF1d5bVv/tKW6N/MOtQ5sUdH2+yrnvFlSm44Qg0BMCJC/MYBOQkJATvgIhgAEICCb9u0/YZ4Ki4oraByftlB3ZP5DWYFyLSjvpTEtr9HLVx+ndN7igWJiRID8jQF0khICcsJHMAQgAAEtXLlGQ6csqiBxdvpLGpvxiNICIc0u76srSkeqRJmaPqKv+vXoADEIxIQA+RsD6CQkBOSEj2AIQAACmlWwSqNmFFSQ+H36bF2bOV0Plw3UuLJzFFT47R6T8vM0JK8LxCAQEwLkbwygk5AQkBM+giEAAQjUGAGUQjosbaneCO4nKVBBiBFAxBJLAuRvDKCTnhCQEz6CIQABCKi8eIOemHi+bt54otarVQ0iZgE752RrwegBPAOIXmJGgPyNAXQSEwJywkcwBCDgdwIbV0uPnSZ9u1ivlvfRiNIrq6wEjoz/TR7eR4N65fqdFu2PIQHyNwbQSU4IyAkfwRCAgJ8JrP1cmnqKtHal1LK9Fvb9hy5/K6vKauDcnGyNGdwT8+dnnTRR28nfGEAnaSEgJ3wEQwACfiVQuESaeqq08Qcpp5t01tPSDnt4W8K88/la/bC+WJ3aZuvg7u2Z9vWrRpq43eRvDKCTxBCQEz6CIQABPxJY+W/p8bOkkvXSjvtJw56Q2jG960cpNGebyd8YQCf9ISAnfARDAAJ+I1BWIt11oLTuS2nXw6T8x6TsHL9RoL0JQID8jQF0kiECcsJHMAQg4EcC338gvX2PdOztUkYLPxKgzQlAgPztcwM4efJk2X9ffPGFJ8d9991XN9xwg379619HJU8EFBUmToIABPxMIBiUfvhA6mz7+nFAIDEIkL99bgBnz56t9PR07bHHHgqFQnr44Yc1ceJEvf/++54ZrO9AQPUR4nMIQMDXBGzKd9aF0vJnpbOekXY91Nc4aHziECB/+9wA1ibF9u3beybwvPPOq1epCKheRJwAAQj4lcCW9dLjw6XPXpPSMqQT75F6n+ZXGrQ7wQiQvzGAFZIsLy/XE088oXPOOccbAezZs2e9ckVA9SLiBAhAwI8ENvwgPXaqZNu9ZLaWznhE2v1oP5KgzQlKgPyNAdTSpUvVr18/FRcXq02bNpo2bZqOPfbYWiW7ZcsW2X+RwwTUtWtXFRUVqV27dgkqc6oFAQhAoOkI1Ni7r91PSp92ivTTF1KrHcLbvHTp03QV4MoQaAQBDCAGUCUlJfrqq688E/fkk0/qvvvu0+uvv17rCODYsWM1bty4GlLDADbi7iMEAhBIegJzlhVq3OzlFW/v2Dnwg55tcYPa62dp+12l4U9LHXokfTtpQOoRwABiAGuo+uijj1aPHj1077331viMEcDU+xKgRRCAQOMImPkbOXVxtXf3BnVn5l3qFvheq094VAMOZOVv4+gS1dQEMIAYwBoaGzBggLp166aHHnqoXv0hoHoRcQIEIJCCBGzat/+EeZXe2xuSFPBamqVSZalMbXO214LRA3iVWwr2fyo0ifztcwN4zTXXeHv+meFbv3699/zfhAkT9NJLL2ngwIH1ahwB1YuIEyAAgRQksHDlGg2dskhSSBemz9Kead/ostILFVJaldZOH9FX/Xp0SEECNCnZCZC/fW4AbauXuXPnqrCwUDk5Oerdu7dGjx4dlfkz8SOgZP8KoP4QgEBjCMwqWKXLZ7ynGzMe0rCMud4lfltypeYFqy72mJSfpyF5XRpTBDEQaFIC5G+fG0BXdSEgV4LEQwACyUjg7Y++1vrHztLR6e8rGApoXNnZerj8mBpNYQQwGXvXH3Umf2MAnZSOgJzwEQwBCCQjgQ0/KDTtDAW+XaziUKZGlV6sl4IHVWmJPQ3YOSebZwCTsX99UmfyNwbQSeoIyAkfwRCAQLIRWL1Ceiy8x19J1nbKX/8HvR/as9pK4HCjJg/vo0G9cpOthdTXJwTI3xhAJ6kjICd8BEMAAslG4Is3pUdPlNrtJA17SnO+a11lH0BrTm5OtsYM7on5S7a+9Vl9yd8YQCfJIyAnfARDAALJSODTV6Xc3lKbTl7ta7wJpHt7tn5Jxn71WZ3J3xhAJ8kjICd8BEMAAslA4N37pG6HSDvW/370ZGgOdYSAESB/YwCd7gQE5ISPYAhAIJEJBIPSqzdIb90ptesijXxTarl9IteYukEgagLkbwxg1GKp7UQE5ISPYAhAIFEJlBZLM0dKHzwdruGvxkj9L5MC4bd9cEAg2QmQvzGAThpGQE74CIYABBKRwOafpBnDpC/flNIypSF3S/ufkYg1pU4QaDQB8jcGsNHisUAE5ISPYAhAINEIrPtKmnqqtPpjqUU76YxHpd2OTLRaUh8IOBMgf2MAnUSEgJzwEQwBCCQagSfPk5Y9KbXdSRr+pLTjvolWQ+oDgZgQIH9jAJ2EhICc8BEMAQgkGoHiIum5y6SBf5ZyeIdvonUP9YkdAfI3BtBJTQjICR/BEIBAMxCosW9f1udK73pgM9SEIiHQfATI3xhAJ/UhICd8BEMAAnEmMGdZYaU3d4Q0Kv1pXZb5lD7sfbX2OfmaONeG4iDQfATI3xhAJ/UhICd8BEMAAnEkYOZv5NTF3nt7M1SmmzMe0BkZr3k1uLtsiHrkT+D1bXHsD4pqXgLkbwygkwIRkBM+giEAgTgRsGnf/hPmqbCoWK21WXdn/l1Hpi9ReSigG8p+o2nlR6tzTrYWjB7Aa9zi1CcU07wEyN8YQCcFIiAnfARDAAJxIrBw5RoNnbJIO2qtHsiaqH3TvtSmUAtdUnqx5gZ/UVGL6SP6ql+PDnGqFcVAoPkIkL8xgE7qQ0BO+AiGAATiRGBWwSqNnvG2Xm1xlXYOrNaPoXb6XcmVWhLavUoNJuXnaUgeq3/j1C0U04wEyN8YQCf5ISAnfARDAAJxIhAZATw3fY6Gpc/Vb0r/qG9CHWuUzghgnDqEYpqdAPkbA+gkQgTkhI9gCEAgHgS2bFB5ZmvvGcDviorVQltk/1v5sDf88gxgPDqDMhKFAPk7iQ3gJ598ookTJ2rNmjXq3bu3LrnkEnXoEN9nVxBQotzK1AMCEKhBIBiUXvmT9Okr0nkva87Kzd4qYDtsJXDkMPNnx+ThfVgFjIx8Q4D8ncQGsFevXho1apTy8vK0ePFi3X///br11ls1YMCAuAkYAcUNNQVBAAINIVCySXp6hPTRc+Gok++Tep+mqvsAhj/KzcnWmME9MX8N4cu5SU+A/J3EBvDAAw/Uf/7znwoR/vDDDxo4cKCWLFkSN2EioLihpiAIQCBaAht+kKbnS6vek9KzpBMnS/udWhFd400g3duz9Uu0bDkvZQiQv5PQAF566aXeqN+HH36oXXbZRRdffLEnyPLycpkpfP/99+MmUAQUN9QUBAEIREPgh4+kaadJ676SWm4v5U+TdjkkmkjOgYCvCJC/k9AAvvDCC/rvf/9b8d/mzZu1zz77aOXKlTr++OO95wLjdSCgeJGmHAhAoF4CX78jTT1V2lIktd9NOvMJaYeq27zUew1OgIBPCJC/k8AAnnvuufrHP/6hVq1a1SrLkpISLV++vMIQ3n777XGTLwKKG2oKggAE6iOw/jvpvqOldl3CI3+t47sorr7q8TkEEokA+TsJDGB6eroKCwvVqVMnTzsjR47U+PHjtd1221VoqaysTBkZGXHXFgKKO3IKhAAEKhMIhaRAZB2vpLWfS21zpcxsOEEAAtsgQP5OAgOYlpam7777rsIAtmvXTgUFBdptt928rv3+++/VvXt3bdq0Ke5iR0BxR06BEIBAhEDZFmnWxdIeA6Xep8MFAhBoAAHydxIawLZt23orfSsbwNzcXAVtz6s4HwgozsApDgIQCBPYtFaaMUz66i0ps7X0h6VM+aINCDSAAPk7RQzgTjvt5K0CjveBgOJNnPIg4C8CtW7Z8tNn0mOnSWtXSi3aSac/IvU4yl9gaC0EHAmQv5PEAN5xxx06/PDDtd9++6l9+/Y1RgAxgI53AuEQgEDCEaht0+Zj2n6uOwMTlVWyTsrpKg17Quq0T8LVnQpBINEJYACTwAAeccQR3jN/69evV2ZmpmzBx5lnnqlDDz3U2w+wY8eO2nPPPRkBTPS7jfpBAAJREzDzZ69tq/zKtuPTFuovmfeoRaBURdv3Us5vn5ba7hj1NTkRAhDYSgADmAQGMNJdn376qd577z3vtW+R/9atW6fA/1bAMQXMrQ0BCKQCAZv27T9hngqLiqs058qMx3Vxxiy9XP4LjW95hV69+lje4JEKHU4bmoUABjCJDGBtCvn888+918HZ2z9uueWWuIsIAcUdOQVCIOUJLFy5RkOnLKrRzoCCOjHtTc0KHqqg0jR9RF/168FefykvCBrYJATI30luAJtEFQ24KAJqACxOhQAEoiIwq2CVRs0o0HZar1EZT+vWsqHaoqwasZPy8zQkr0tU1+QkCECgKgHyNwbQ6Z5AQE74CIYABGohYCOA19/3lO7PvF27pn2vGWVH6uqy39c4kxFA5AOBxhMgf2MAG68eSQjICR/BEIBALQTKV/xbm6aeqbbapK+DHXVe6ZX6JNS14kx770fnnGwtGD2AZwBREAQaSYD8jQFspHTCYQjICR/BEIBAdQLv3i+9cJUUKte7wT01suQyrVZOFfNn/5g8vI8G9cqFHwQg0EgC5G8MYCOlgwF0AkcwBCBQlUB5mfTyddLb94R/3ztfL/W4VmNfWFFlNXBuTrbGDO6J+UM/EHAkgAHEADpJCAE54SMYAhCIEChaJd17mLRpjTTgT9JhV0iBgGp9E0iaTQJzQAACLgTI3xhAF/0wBexEj2AIQKAKgS/fkjb+KPUcAhgIQKCJCWAAMYBOEkNATvgIhoC/CXy5UCrZKO1xtL850HoINAMB8jcG0El2CMgJH8EQ8C+BgunS7Eul9BbSiLlSx738y4KWQ6AZCJC/MYBOskNATvgIhoD/CASD0rw/SwvuCLd9n8HSSfdKWa39x4IWQ6AZCZC/MYBO8kNATvgIhoC/CNh07zPnSx/ODrfbFnocdb2UluYvDrQWAglAgPyNAXSSIQJywkcwBPxD4Odvpen5UuESKT1LOuFOaf98/7SflkIgwQiQvzGATpJEQE74CIaAfwi8OlZa8FepVQcpf5rUra9/2k5LIZCABMjfGEAnWSIgJ3wEQyClCGxzz77yUunF0dKhl0rb75pS7aYxEEhGAuRvDKCTbhGQEz6CIZAyBOYsK9S42csrvbUjpHPavKNDThihY3pvfY9vyjSYhkAgyQmQvzGAThJGQE74CIZAShAw8zdy6mKF/teaFirR+Mz7dHL6Aj1SNlCd8u/k1W0p0dM0IpUIkL8xgE56RkBO+AiGQNITsGnf/hPmVYz8dVCR7s36qw5M+0RloTSNKTtX89ocrwWjByidV7glfX/TgNQhQP7GADqpGQE54SMYAklPYOHKNRo6ZZHXjn0CX2pK1l+0c2C1ikKtdGHpKL0Z3M/7bPqIvurXo0PSt5cGQCBVCJC/MYBOWkZATvgIhkDSE5hVsEqjZhTo12lv6y+Z96hVYIs+D+6o80qv0mehnSraNyk/T0PyuiR9e2kABFKFAPkbA+ikZQTkhI9gCCQ9ARsBvHDKy5rf4jK1DWzW/PL9dHHpJfpZbaq0jRHApO9qGpBiBMjfGEAnSSMgJ3wEQyDpCUSeAdxv/QIdlPaRbi0bqnKlV7QrIKlzTjbPACZ9T9OAVCNA/sYAOmkaATnhIxgCyUtg7WfSxjVS14MUWQVsjYmsBLafzfzZMXl4H1YBJ29PU/MUJUD+xgA6SRsBOeEjGALJSWDlv6UnzpXSMqTf/1varptnAqvuAyjl5mRrzOCemL/k7GVqneIEyN8YQCeJIyAnfARDILkIhELS2/dIL10nhcqlLgdKZ0yV2uV67djmm0CSq6XUFgIpT4D8jQF0EjkCcsJHMASSh0DZFum5y6WCqeE673+mdPxfpczs5GkDNYUABCoIkL99bgDHjx+vp59+Wh999JFatmypQw45RBMmTNBee+0V1W2CgKLCxEkQSG4C67+THh8uffOuFEiT/u9mqe9IKRB5yi+5m0ftIeBHAuRvnxvAQYMGKT8/XwcddJDKysp07bXXatmyZVq+fLlat25d7z2BgOpFxAkQSH4CL1wlvfNPKTtHOvVBafdfJX+baAEEfE6A/O1zA1hd/z/++KM6deqk119/XYcffni9twcCqhcRJ0Ag+QmUbJKevUQ66lqpQ4/kbw8tgAAERP7GAFa5DVasWKE99thDS5cuVa9evWrcIlu2bJH9FzlMQF27dlVRUZHatWvHLQUBCKQCgWC59N9/Sb3PkNLSUqFFtAECEKhGAAOIAayQRDAY1AknnKB169ZpwYIFtd4sY8eO1bhx42p8hgHkuwUCKUJg80/Sk+dJK+dKR14rHTk6RRpGMyAAgcoEMIAYwAo9jBw5Ui+++KJn/nbeeeda7xRGAPkCgUAKE/jxE2l6vrR2pZTRUjrxH1Kvk1O4wTQNAv4lgAHEAHrqv/jiizVr1izNnz9f3bt3j/qOQEBRo+JECCQMgVr361vxivTUedKWn6WcrlL+NCm3d8LUmYpAAAKxJUD+9rkBDIVCuuSSS/TMM8/otdde857/a8iBgBpCi3Mh0PwEar6xI6SrWr+oC8sfU8Be5NbtEOn0R6Q2HZu/stQAAhBoMgLkb58bwAsvvFDTpk3zRv8q7/2X3ZETRQAAIABJREFUk5Pj7QtY34GA6iPE5xBIHAKRd/ZWfl/vboFv9WLW1WoRKNNXu52hbmfeJWVkJU6lqQkEINAkBMjfPjeAgTo2cn3wwQd17rnn1is6BFQvIk6AQEIQsGnf/hPmqbCouEZ9Tk1/Xdkq0dw2g7Vg9AClp7HBc0J0GpWAQBMSIH/73AC6agsBuRIkHgLxIbBw5RoNnbLIK6xf2gf6OdRaH4R2rVH49BF91a9Hh/hUilIgAIFmI0D+xgA6iQ8BOeEjGAJxIzCrYJVGzXhfI9Kf19UZ0/VtaAcNLrlJ69S2Sh0m5edpSF6XuNWLgiAAgeYhQP7GADopDwE54SMYAnEj8PZHX+rHx0bo+PS3vTKfKDtc15f9VltU9Xk/RgDj1iUUBIFmJUD+xgA6CRABOeEjGALxIbD6U4VmDFNg9ccqCaVrXNk5eqzc3ue79Vk/+6lzTjbPAManRygFAs1OgPyNAXQSIQJywkcwBJqewIezpWdGSiXrVdxyRw1dd6EKQnvYhi8VR8QGTh7eR4N65TZ9nSgBAhBodgLkbwygkwgRkBM+giHQtARCIWna6dKnL0u79JdOe1BzvijXuNnLq6wGzs3J1pjBPTF/TdsbXB0CCUWA/I0BdBIkAnLCRzAEmp7AprXSu/dL/S+T0jO88mp9EwhbvzR9X1ACBBKIAPkbA+gkRwTkhI9gCMSewKrFkk37/uoGqY59PmNfKFeEAASSjQD5GwPopFkE5ISPYAjElsDiR6Tnr5TKt0gn3Svtnx/b63M1CEAgZQiQvzGATmJGQE74CIZAbAiUbZFeuEpa/HD4ensdJ500WcrOic31uQoEIJByBMjfGEAnUSMgJ3wEQ8CdQNE30uNnSd8uDm/rMuB6qf/lUlqa+7W5AgQgkLIEyN8YQCdxIyAnfARDwI3A5/OlJ86VNq2RWm4vnXKftPvRbtckGgIQ8AUB8jcG0EnoCMgJH8EQcCOwYq409RSp837SGVOl7Xdxux7REICAbwiQvzGATmJHQE74CIbANgnUul2L7dpceXXvx3Ok3Y6QMltCEwIQgEDUBMjfGMCoxVLbiQjICR/BEKiTwJxlhTU2bO7bdrUmt31A2w97QOrQA3oQgAAEGk2A/I0BbLR4LBABOeEjGAK1EjDzN3Lq4iqvaxuU9o5uz7xHbQLF+rHz4ep4wWzoQQACEGg0AfI3BrDR4sEAOqEjGAK1ErBp3/4T5lW8qi1d5boq41+6ICNs+BaW99SfW16p2VefrHTe3oGKIACBRhLAAGIAGymdcBgCcsJHMARqEFi4co2GTlnk/X4HFelvmXepf/oH3r//WXacJpTlq1zpmj6ir/r16ABBCEAAAo0iQP7GADZKOJEgBOSEj2AI1CAwq2CVRs0o0G6BbzUj6yZ1CqzTxlALjS79vZ4L9qs4f1J+nobkdYEgBCAAgUYRIH9jABslHAygEzaCIVAngcgIYKbK9ETWOLVSsS4sHaUVoZ2rxDACiIggAAEXAhhADKCLfpgCdqJHMASqEdi4WuVZ7dT/9jf0XVGxdtBP2qCW2qzsihNtF5jOOdlaMHoAzwAiIAhAoNEEMIAYwEaLxwIRkBM+giGwlcDnb0hPnSftP1Rzci/wVgHbEarEyMyfHZOH99GgXrnQgwAEINBoAuRvDGCjxYMBdEJHMATCBILl0ht3SK/dIoWCUqee0oh5mvPxuhr7AObmZGvM4J6YP7QDAQg4E8AAYgCdRISAnPAR7HcCG36Qnh4hffZamETecOnY26Ss1t4/a30TCFu/+F01tB8CMSFA/sYAOgkJATnhI9jPBCJTvhu+lzJbScfdIeUN9TMR2g4BCMSRAPkbA+gkNwTkhI9gvxLYvE76237Slp+ljntLpz0sddrbrzRoNwQg0AwEyN8YQCfZISAnfAT7mcB//xWe+j12YsWUr59x0HYIQCC+BMjfGEAnxSEgJ3wE+4nA5/OltExpl62bOfup+bQVAhBILALkbwygkyIRkBM+gv1AwFvl+xfptfFS607SBQukNh390HLaCAEIJDAB8jcG0EmeCMgJH8GpTqD6Kt8Dhku/tinfVqnectoHAQgkOAHyNwbQSaIIyAkfwalMwKZ8n/qdxCrfVO5l2gaBpCVA/sYAOokXATnhIzjJCdS6T5+9u+ON28NTvraxc8d9pNMfljruleStpfoQgEAqESB/YwCd9IyAnPARnMQE5iwrrP1NHcfvo0EfXSd98LTElG8S9zBVh0BqEyB/YwCdFI6AnPARnKQEzPzZu3orv6fX3tobUPhtvf88Y08NzFwq9To5SVtItSEAgVQnQP7GADppHAE54SM4CQnYtG//CfNUWFTs1T5NQV2cPlN7pX2li0pHeSawc062FoweoHRe25aEPUyVIeAPAuRvDKCT0hGQEz6Ck5DAwpVrNHTKIq/muVqjv2RO1iHpy71/Dy+5RguC+3k/Tx/RV/16dEjCFlJlCEDADwTI3xhAJ50jICd8BCchgVkFqzRqRoGOS1ukWzLvU05gkzaFWuj60t/o6eDhFS2alJ+nIXldkrCFVBkCEPADAfI3BtBJ5wjICR/BSUjgnQ+/0NfTLtYp6W94tS8I7qY/lF6kL0K5VVrDCGASdi5VhoCPCJC/MYBOckdATvgITkICoYdPUODz11UeCuju8iH6e9nJKlNGRUtsGQjPACZhx1JlCPiMAPkbA+gkeQTkhI/gZCTw1SJtfHyEzl17rv4T2rvKSuDwGmBp8vA+GtSr6ohgMjaVOkMAAqlLgPyNAXRSNwJywkdwMhBYs1L6/gOp5wlba1tepjkf/lj7PoCDe2L+kqFfqSMEfE6A/I0BdLoFEJATPoITmUAoJC1+RJpzTfiNHufPlzruWaXGtb4JhK1fErlXqRsEIPA/AuRvDKDTzYCAnPARnKgENq6RZl8qffRcuIa7HiaddI+Us3Oi1ph6QQACEGgQAfI3BrBBgql+MgJywkdwIhJYMVeaeaG04TspLVMacL10yCVSWnoi1pY6QQACEGgUAfI3BrBRwokEISAnfAQnGoGXrpMW3hWu1Q57SadMkXL3T7RaUh8IQAACzgTI3xhAJxEhICd8BCcagX+Pl16/VTpohDTwRimrVaLVkPpAAAIQiAkB8jcG0ElICMgJH8HNTSAYlDavlVrvEK5JeZn09SJp1/7NXTPKhwAEINCkBMjfGEAngSEgJ3wENyeBnwulmRdItuBjxFwpo0Vz1oayIQABCMSVAPkbA+gkOATkhI/g5iKw/NnwKt/NP0kZLaWzZ0ndftlctaFcCEAAAnEnQP7GADqJDgE54SO4CQnUukdf6QZpztXS+1PDJdsCj5Pvq7G/XxNWi0tDAAIQSAgC5G8MoJMQEZATPoKbiMCcZYU13tJxdNsvNSlrslpv/EpSQOr/B+nIa6WMrCaqBZeFAAQgkLgEyN8YQCd1IiAnfAQ3AQEzfyOnLq7yjl4ppBlZN6lv2ofa3GontTx9Cgs9moA9l4QABJKHAPkbA+ikVgTkhI/gGBOwad/+E+apsKi4xpV3DvygS9Jn6r5W52nO1YOVzivbYkyfy0EAAslEgPyNAXTSKwJywkdwjAksXLlGQ6csUpqCOif9Je0Y+Em3lp1Zo5TpI/qqX48OMS6dy0EAAhBIHgLkbwygk1oRkBM+gmNMYFbBKv398ed1W+Y/9Yu0T72rH7flZn0Q6l6lpEn5eRqS1yXGpXM5CEAAAslDgPyNAXRSKwJywkdwLAmUl+qr2eO14/uT1CJQpvWhlrql7EzNKD9KIaVVKYkRwFiC51oQgEAyEiB/YwCddIuAnPARHCsChUukWRdJ3y31rjivPE/XlZ6nQlWd5g1I6pyTrQWjB/AMYKzYcx0IQCApCZC/MYBOwkVATvgIjgWB0mLpb/tJG3+QWm6vJb2u0Ylv2PRuoMpKYDN/dkwe3keDeuXGomSuAQEIQCBpCZC/fW4A58+fr4kTJ+q9995TYWGhnnnmGZ144olRCxoBRY2KE5uSwJIZ0scvSsdOlNp0Um37AObmZGvM4J6Yv6bsB64NAQgkDQHyt88N4Isvvqg333xTv/jFL3TyySdjAJPm1vVxRUs2SvNuknY5VNrn+DCIUEgKRMb4wr+q9U0gbP3iY+HQdAhAoDIBDKDPDWBlMQQCAQwg3w+JTeCz18Pv8P3pC6lNZ+nS96WsVoldZ2oHAQhAIAEJYAAxgBWyxAAm4B1KlcIEioukl/8kLX44/O92O0uD/ybtMRBCEIAABCDQCAIYQAxggwzgli1bZP9FDhNQ165dVVRUpHbt2jVCgoRAoB4CH8+RnrtMWv9t+MQDz5OOHitloze0AwEIQKCxBDCAGMAGGcCxY8dq3LhxNfSGAWzsLUjcNgkU/le697DwKe13k064k3f4IhkIQAACMSCAAcQANsgAMgIYg7uOSzSMwDMjpdYdpCOv5Xm/hpHjbAhAAAJ1EsAAYgAbZACrKwkB8e0SUwLrv5NeGSMdPUZqt1P40rWs8I1pmVwMAhCAgA8JkL99bgA3bNigFStWeNI/4IADdMcdd+ioo45S+/bt1a1bt3pvCQRULyJOqESgzq1ZzOQVTJNeuia84GPv46X8x2AHAQhAAAJNRID87XMD+Nprr3mGr/pxzjnn6KGHHqpXdgioXkSc8D8CdW3OPH5Ajo785BZp5dzwmbl50pC7pc69YAcBCEAAAk1EgPztcwPoqisE5ErQH/Fm/kZOXVzt1WxBnZX+qv6YMUNtAsVSegvpqGulfhdL6Rn+AEMrIQABCDQTAfI3BtBJegjICZ8vgm3at/+EeSosKq7S3nPT52hs5iPe7woC+2i/Cx9Vesc9fMGERkIAAhBobgLkbwygkwYRkBM+XwQvXLlGQ6csqtHWlirWU1njNKP8SD1aPlDTRhyifj06+IIJjYQABCDQ3ATI3xhAJw0iICd8vgieVbBKo2a8r1+lLdbJ6W/oktJLFVSa1/Y0BSt+npSfpyF5XXzBhEZCAAIQaG4C5G8MoJMGEZATPl8Ev7/4XRU9c4WOTF/itfeq0t/rifIja7R9+oi+jAD6QhE0EgIQSAQC5G8MoJMOEZATvtQOLv5Zmn+bQosmKxAsU0koXfeXH6u7yk7URrWsaHtAUuecbC0YPUDpafYvDghAAAIQaGoC5G8MoJPGEJATvtQMDgalJdOlV8dKG3/w2vhD7pE644vB+iKUW20lcBjB5OF9NKhXbmryoFUQgAAEEpAA+RsD6CRLBOSELzWDzQDeP1Ba9R+pw+7SoFulPQaqrn0AxwzuiflLTSXQKghAIIEJkL8xgE7yREBO+FIn2F7hltVGatEm3KZV70lfviUdfL6UkVXRzjrfBJI6JGgJBCAAgaQgQP7GADoJFQE54Uv+4LIS6e3J0uu3SQePkI4em/xtogUQgAAEfECA/I0BdJI5AnLCl9zBn7wszblaWrsy3I5uh0jnPi+lhbd44YAABCAAgcQlQP7GADqpEwE54UvO4NUrpJeukT59OVz/1p2kgeOk3vmYv+TsUWoNAQj4kAD5GwPoJHsE5IQv+YKXPik9c4EULJXSMqW+I6XDr5Ky2yVfW6gxBCAAAR8TIH9jAJ3kj4Cc8CVfcNE30l0HSbscGl7du8PuydcGagwBCEAAAiJ/YwCdbgME5IQv8YO/eU9a8Yp05NVb67r2c6l998SvOzWEAAQgAIE6CZC/MYBOtwcCcsKXuMHrv5fm3igVTA3X0RZ37No/cetLzSAAAQhAoEEEyN8YwAYJpvrJCMgJX7MF17kfn7etyz3hbV1K1ofrt//Q8PYubTs3W30pGAIQgAAEYkuA/I0BdFIUAnLC1yzBdb2R484DV+vAj26T1qwI12unA6RfT5S6HtQs9aRQCEAAAhBoOgLkbwygk7oQkBO+uAeb+Rs5dXGV9/FaJVqoRK+1uFy5gbVS647hEb/9z2Rbl7j3EAVCAAIQiA8B8jcG0ElpCMgJX1yDbdq3/4R5Kiwq9sptpWJtVpZCCm/cfHzaQh3S8gudccVdSm+1XVzrRmEQgAAEIBBfAuRvDKCT4hCQE764Bi9cuUZDpyxSSxVrWPpcnZ/xnCaU5evJ8iOq1GP6iL7q16NDXOtGYRCAAAQgEF8C5G8MoJPiEJATvrgGP//uJ1o28y/6Xcbz6hAIL/B4N7inTisZIylQUZdJ+XkaktclrnWjMAhAAAIQiC8B8jcG0ElxCMgJX3yCN6+T3r5XZW/drYySIq/ML4OddFf5iXqmvL/KlMEIYHx6glIgAAEIJAwB8jcG0EmMCMgJX3yCHx8ufTg7bPwCXTRpywmaFTxE5UqvUr6NAXbOydaC0QOUnrZ1RDA+laQUCEAAAhCIJwHyNwbQSW8IyAlf0wRv+FFKS5datQ9f/6tF0nOXSYdfqTmhX2rkY0u8X4cqlR6xe5OH99GgXrlNUy+uCgEIQAACCUOA/I0BdBIjAnLCF9vg9d9Jb/5d+s8D0kHnScfcvPX6oZAUCNu8uvYBHDO4J+Yvtj3C1SAAAQgkLAHyNwbQSZwIyAlfbIKLvpHenCS997BUviV8zV36S+c+V2H6qhdU55tAYlMjrgIBCEAAAglOgPyNAXSSKAJywucW/NOX0oI7pPcfk4Kl4Wt1/aV0+B+l3X9Vp/lzK5RoCEAAAhBIBQLkbwygk44RkBM+t+AXr5benhy+xq6HSYdfJXU/HOPnRpVoCEAAAr4gQP7GADoJHQE54WtY8I8fh/fr67hnOO7nb6XZo6T+l0m7HNKwa3E2BCAAAQj4mgD5GwPodAMgICd80QV//4E0f6L0wUxpj/+Thv0rujjOggAEIAABCNRBgPyNAXS6ORCQE75tBxcukV6/Tfroua3n7X28dOqDUkZWExbMpSEAAQhAINUJkL8xgE4aR0BO+GoP/rZAem289Mmc/30ekHoOCT/j17lXExTIJSEAAQhAwG8EyN8YQCfNIyAnfLUHvzNFeuFKKZAm9TpVOuwKqdPeTVAQl4QABCAAAb8SIH9jAJ20j4Ciw1fnvnu2QfMXC6TykvDWLXaUFkuv3CD98nypQ4/oCuAsCEAAAhCAQAMIkL8xgA2QS81TEVD9+Gp980a7Fvr7wT/poK/ul75aKHXYXbronfAr3DggAAEIQAACTUyA/I0BdJIYAto2PjN/I6curvTe3ZCOSivQpRnP6IC0FeHg9BZSn7Olo8dILdo69QfBEIAABCAAgWgIkL8xgNHopM5zEFDd+Gzat/+EeSosKvZOOijwkW7IfET7pX3h/XtzKEuzMv5Pp106Uek5Ozn1A8EQgAAEIACBhhAgf2MAG6KXGucioLrxLfr0O51//+sqUhvvpEPSlmla1i3aGGqhR8sH6r6y47RaOZo+oq/69ejg1A8EQwACEIAABBpCgPyNAWyIXjCA9dEqL5O+eEP64GmVLJ2lJzYfqOvKzvtfVEjD01/V8+W/1E9qV3GlSfl5GpLXpb4r8zkEIAABCEAgZgQwgBhAJzEhIEnBcunLtzzTp+XPSptWVzD9OLizjimZEH6FWx0HI4BOEiQYAhCAAAQaQYD8jQFshGy2hiAgSfcNlL55ZyuUlu2lfQarvOfJOuJfJVr1c2mlRSBbTzNL2DknWwtGD1B6Wt0G0amDCIYABCAAAQjUQoD8jQF0ujF8JSDbs++b/0gfzZaOun7r69hsz773HpL2Hiz1OknqfoSUnulxjawCtp9DlUhH7N7k4X00qFeuUx8QDAEIQAACEGgoAV/l7zrgBEIhy+wcjSGQ8gIyaXz7vvTBM9IHM6Wir8KYhj0p7TEw/HNxkZTRss7389a6D2BOtsYM7on5a4zoiIEABCAAAWcCKZ+/oyCEAYwCUl2npKyAilZJ794XNn4/fb61+VltpL1+LfW7SNrpgKjJ1fkmkKivwIkQgAAEIACB2BFI2fzdAEQYwAbAqn5qSgmodLOU2TLcxO8/kCYfEv45s5W05zHSvieHR/0i5zhwIxQCEIAABCDQnARSKn83EiQGsJHgLCzpBbT6U2nZ0+GRvs69pFPuC9Owqd8X/yh16yvtOUjKau1AiVAIQAACEIBAYhFI+vwdA5wYQAeISSmgtZ/9z/TNlL5furX1tnr3yk+l9AwHIoRCAAIQgAAEEp9AUubvGGPFADoATToBPTVCWvqvrS1Oy5B2O0rqdbK017FSy+0caBAKAQhAAAIQSA4CSZe/mwArBtABakILqOgbafksqc85Uovw69g0f6L07/FS98PDpm/v46VW7R0IEAoBCEAAAhBIPgIJnb/jhBMD6AA64QT0c2HY9NlbOb5+O9yyU+6X9js1/POmtVIoKLXewaHVhEIAAhCAAASSm0DC5e9mwIkBdIDeVAJq0LYpm9dJS58IL+SwV7JVbLkckLr1kw67fOuefQ5tJRQCEIAABCCQKgSaKn8nEx8MoENvNYWAoto4ORiU0tLCNf/pS2lS762t2Png8PRuzyFSu50cWkcoBCAAAQhAIDUJNEX+TjZSGECHHou1gCKvTqv+ahZ7dVo7bdDUQ3/Ufuvmhffiy39sa81nXSx13EvqeaK0XVeHFhEKAQhAAAIQSH0Csc7fyUgMA+jQa7EUkE379p8wT4VFxRU1aqtNGpj2Hx2X/rYOS/uvsgLl4c/SMqU/fiZlt3OoPaEQgAAEIAABfxKIZf5OVoIYQIeei6WAFq5co6FTFlXU5vKMf+n89OfUIlBW8bsPg13Vus/p6tb/TGmH3R1qTigEIAABCEDAvwRimb+TlSIG0KHnYimgWQWrNGpGQUVtzkl/SeMyH9aK4E56LthXs8v7aWWoiybl52lIXheHWhMKAQhAAAIQ8DeBWObvZCWJAXTouVgKqPoIYI42qHNgrT4O2TN99hRg+Jg+oq/69ejgUGtCIQABCEAAAv4mEMv8nawkMYAOPRdLAUWeAfyuqLhiI5fKVTML2DknWwtGD1B62lZD6FB9QiEAAQhAAAK+JBDL/J2sAH1vAO+++25NnDhR3333nfbff3/deeedOvjgg6Pqz1gLKLIK2AqvvBI4YvcmD++jQb1yo6obJ0EAAhCAAAQgUDuBWOfvZOTsawP4+OOP6+yzz9Y999yjX/7yl/rb3/6mJ554Qh9//LE6depUb382hYCi2gew3ppxAgQgAAEIQAACdRFoivydbLR9bQDN9B100EG66667vH4LBoPq2rWrLrnkEl199dX19mVTCahBbwKpt5acAAEIQAACEIBAZQJNlb+TibJvDWDJ/7d3J7BZFG8cx3+CIMhRELSGHiKXBowBFE2RELxAEDmDyhE5VCICCoZDQaFERYEEUKOIkaAJMQqEI2AMItFyVCuoEI2iEBSL1SBGsIYIgvzzTNKGgv4pfbu77+58J2lIy7u7M5+ZfffZ2ZnZ48d18cUXa+XKlerXr195nQ0fPlyHDx/W2rVrz6rHY8eOyX7KkjUgCxiPHDmihg1Zky9ODZ+8IoAAAgj4K0AAKHkbAJaUlCgrK0uFhYXKy8srPwumTJmigoICFRUVnXVm5Ofna9asWWf9nQDQ3y8RSo4AAgggED8BAkACwPMKAOkBjN9JTo4RQAABBBA4U4AA0OMAsCqPgGlAfIkggAACCCAQfwECQI8DQGu+NgnElnyxpV8s2SSQ3NxcjRs3LtJJIPE/tSgBAggggAAC6StAAOh5AGjLwNikj8WLF7tA0JaBWb58uXbv3q3MzMxztlwa0DmJ+AACCCCAAAJpJ8D12/MA0FqkLQFTthB0+/bt9eKLL7qewcokGlBllPgMAggggAAC6SXA9ZsAMKUWSQNKiY+NEUAAAQQQiESA6zcBYEoNjwaUEh8bI4AAAgggEIkA128CwJQaHg0oJT42RgABBBBAIBIBrt8EgCk1PFsAulGjRiouLuZNIClJsjECCCCAAALhCZS9ycve/JWRkRHegdPoSN6+CaQ66uDAgQPuVXAkBBBAAAEEEIifgHXgZGdnxy/j1ZBjAsAUEG3dQHulXIMGDXTBBReksKfKb1p21+JjryNlz/Gyt5l6p959e9c6bT74Nn/q1CmVlpaqWbNmqlGjRuUvwgn6JAFgzCrT53ELlD1DPr53mnqn3n0MAO2xJOd7w5hdoeOVXQLAeNWXuBjypcjFMGYnbQrZ5XznfOd8T+EEYtP/K0AAGLMGwgWBCwIXhJidtClkl/Od853zPYUTiE0JAJPUBo4dO6bnnntOTzzxhC666KIkFe2cZaHs1Dtt/pynSWI+wPnO+e7b+R72yUsPYNjiHA8BBBBAAAEEEIhYgAAw4grg8AgggAACCCCAQNgCBIBhi3M8BBBAAAEEEEAgYgECwIgrgMMjgAACCCCAAAJhCxAAhi3O8RBAAAEEEEAAgYgFCAAjroDKHn7z5s2aN2+ePvvsM/38889avXq1+vXrV9nNY/s5m/G8atUq7d69W3Xr1lXnzp01Z84cXXXVVbEtU2UzvmjRItnPDz/84DZp166dZsyYoZ49e1Z2F4n53PPPP+9mvj/66KNauHBhYsr1bwXJz8/XrFmzKvyXtXc7B3xIP/30k6ZOnar33ntPR48eVatWrbR06VJdf/31iS5+8+bNtX///rPK+PDDD+vll19OdNlPnjwpa/fLli3TL7/84t7OMWLECD355JOhvWUr0cD/UTgCwJjUun0Zbtu2Tdddd50GDBjgTQB4xx136N5771WnTp104sQJTZs2TV999ZW+/vpr1atXLya1V7Vsrlu3TjVr1lTr1q1lry1688033U3AF1984YJBX9L27dt19913y9ZDu/nmm70IAFeuXKkPPvigvIovvPBCNW3aNPFV/vvvv6tDhw6unseMGaNLL71Ue/bsUcuWLd1PktOvv/4qC4TKkn3P3X777frwww/VrVu3JBdds2fP1vz58913nH237dixQyNHjtSzzz6rRx55JNFlj7JwBIBR6lfx2PbeYV96AM8ksi8pRPOwAAAI7ElEQVTJyy67TAUFBeratWsVBeO72SWXXOKCwPvvvz++hTiPnP/555/q2LGjXnnlFT3zzDNq3769FwHgmjVrtHPnzvOQSsZHH3/8cXeju2XLlmQUKIVSTJgwQevXr3cBcFjvmk8huylt2rt3b2VmZmrJkiXl+xk4cKB76mO9gqRgBAgAg3ENdK8+B4B79+51PWJffvmlrrnmmkCd02nn1jOwYsUKDR8+3PUAtm3bNp2yF1herLwW9C5YsMD1gvgSAFqQb++CrVOnjvLy8tzi77m5uYE5p8uOrV336NFDBw4ccDd5WVlZskegDz74YLpkMZR8HD9+3D0Gfeyxx9xTj6Qn6wF87bXX9P7776tNmzbatWuXunfv7noFhw4dmvTiR1Y+AsDI6Kt+YF8DwH/++Ud9+vTR4cOHtXXr1qoDxmhLC3QtAPjrr79Uv359vfXWW+rVq1eMSlD1rL799tvuEZA9ArZAyJcA0IZ7WM+njfuz8b42HtDGxdkjwQYNGlQdNAZbWj1bssBn0KBBru5t3Oerr77qbn58ScuXL9eQIUP0448/ukAw6cm+2y3QnTt3rhv2Yje8du7buF9ScAIEgMHZBrZnXwNAGxNkF0cL/rKzswPzTacdW0+AXQSOHDkiGxf2+uuvu56RpPcAFhcXu0H/Gzdu1LXXXuuqxJcA8Mz2Zzc8V1xxhesNSfqj/9q1a7t6LywsLGewMWAWCH788cfpdGoGmhfrBTULGwfsQ7KbvcmTJ7vhLTYG0IY/2CNwa/M+Bf5h1zUBYNji1XA8HwPAcePGae3atbLZ0FdeeWU1KMZzF7fddpsbDL948eJ4FqCSubYxcP3793e9AWXJegWs7deoUUP2ntjT/6+Su43tx2wSlNW9PQpOcrJA1yY+2I1OWbKZ8Db+03pBfUg2E7hFixZu9YO+ffv6UGTl5OTIxn+OHTu2vLxW5zb+z5fZ71FUNAFgFOopHtOnANBmv44fP95Nevnoo4/c+D+f0y233OLGgr3xxhuJZigtLT1rSQybFXj11Ve7JUJ8Gv9pj4Otzm2ZjKTPiLTHntb7e/okkIkTJ6qoqKhCr2CSG7/Vs93gmYPN/vYhNWnSxAX59pSnLNnNji3/89133/lAEEkZCQAjYT//g9pFwCZAWLJlEqxr3JZKsAHySR4cbgPAbdyb9f6dvvafDZC3GWJJTjb+xdb8s/q1gMgcbA3EDRs2uF4S35Ivj4AnTZqku+66yz32LSkp0cyZM90jMVv6yJZFSXKyR7221qeNe7Slfz799FM3AcQmCPgwGcDGwtkTjsGDB8vWvvQl2Zp/tuyRBb72CNgmuo0ePVqjRo1y33mkYAQIAINxrfa9Wu+XBXxnJhsfkeTeoP9a/sDuDO1LI8nJxntt2rTJTQSwgNfGwlnvl4/Bn9WzLwGgrXtpQx1+++03F/B16dLFDYhP+jp4ZeeyLX1iNz+2/IkFQzYhxJdZwDYL1sb/ffvtt242rC/JbnCfeuop96Tn4MGDbuKLBcG28L2NhSQFI0AAGIwre0UAAQQQQAABBNJWgAAwbauGjCGAAAIIIIAAAsEIEAAG48peEUAAAQQQQACBtBUgAEzbqiFjCCCAAAIIIIBAMAIEgMG4slcEEEAAAQQQQCBtBQgA07ZqyBgCCCCAAAIIIBCMAAFgMK7sFQEEEEAAAQQQSFsBAsC0rRoyhgACCCCAAAIIBCNAABiMK3tFAAEEEEAAAQTSVoAAMG2rhowhgAACCCCAAALBCBAABuPKXhFAIM0FTp06pcaNG+vpp5/W+PHjK+TW3kG9Y8cO9y7asjRy5EhlZWW5l9ZPnDhR+/fv16pVq9K8lGQPAQQQ+HcBAkBaBgIIeCmwd+9etW7dWoWFhcrLy6tgcOONN6pjx45atGiR+/vJkyd1+eWX691339UNN9ygm266SXfeeaemTZvmpR2FRgCB+AsQAMa/DikBAghUQeCdd97RsGHD9Mcff6hu3brle/j777/VsGFDvfTSS3rggQfc37ds2aJ77rlH33//verXr68TJ06Uf96CxU8++aQKOWATBBBAIDoBAsDo7DkyAghEKDBlyhRt2LBBu3btqpCLnTt3qkOHDvr888/dv5YmT57sAkXrEbRHwxb02ecyMzNVp04dNWrUKMKScGgEEEDg/AUIAM/fjC0QQCABArfeequaN2+uJUuWVCiN/T527FiVlpaqVq1a7v/atGmjBQsWuMe+a9ascT2Dhw4dSoACRUAAAV8FCAB9rXnKjYDnAjYBZPbs2RozZkwFCZsAsn37dvdj6ZtvvlGnTp1cwGe9fTNnztTWrVu1adMmzwUpPgIIxFmAADDOtUfeEUCgSgLFxcXKzc1VQUGBunbtWmEf1tvXs2dPvfDCC+7vc+bMcWP8Vq9e7X7v27evWrZsqfnz51fp2GyEAAIIpIMAAWA61AJ5QACBUAX27dvngjib1durV6/yY2/cuFHdu3fXtm3b1LlzZ/d3+3f06NEaMWKE+71FixbKz8/XfffdF2qeORgCCCBQnQIEgNWpyb4QQCAWArYGYNu2bVW7dm3Xk9e0aVMVFRVp+vTp6t27t5YuXerKcfDgQWVnZ6ukpMR9xpKNGxw6dKgbJ1ivXj1lZGTEosxkEgEEEDhdgACQ9oAAAl4KWC/gpEmTtHnzZtnSL61atdJDDz2kUaNGqWbNms7EJoRYMGhj/srSsmXLNHXqVBcU2vbz5s3z0o9CI4BAvAUIAONdf+QeAQQCFOjTp4+6dOkiWzKGhAACCCRJgAAwSbVJWRBAoFoF5s6dq8GDBysnJ6da98vOEEAAgagFCACjrgGOjwACCCCAAAIIhCxAABgyOIdDAAEEEEAAAQSiFiAAjLoGOD4CCCCAAAIIIBCyAAFgyOAcDgEEEEAAAQQQiFqAADDqGuD4CCCAAAIIIIBAyAIEgCGDczgEEEAAAQQQQCBqAQLAqGuA4yOAAAIIIIAAAiELEACGDM7hEEAAAQQQQACBqAUIAKOuAY6PAAIIIIAAAgiELEAAGDI4h0MAAQQQQAABBKIW+B+bGBPlHqfaagAAAABJRU5ErkJggg==\" width=\"640\">" | |
| ], | |
| "text/plain": [ | |
| "<IPython.core.display.HTML object>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "import matplotlib.pyplot as plt\n", | |
| "\n", | |
| "plt.plot(UU, Es, 'o')\n", | |
| "plt.plot(UU, Eb(UU), '--')\n", | |
| "\n", | |
| "plt.ylabel(r\"$E_b$\")\n", | |
| "plt.xlabel(r\"$U/t$\")\n", | |
| "plt.title(r\"Binding energy vs $U/t$ for a single chain\")\n", | |
| "\n", | |
| "plt.show()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [] | |
| } | |
| ], | |
| "metadata": { | |
| "kernelspec": { | |
| "display_name": "Python 3", | |
| "language": "python", | |
| "name": "python3" | |
| }, | |
| "language_info": { | |
| "codemirror_mode": { | |
| "name": "ipython", | |
| "version": 3 | |
| }, | |
| "file_extension": ".py", | |
| "mimetype": "text/x-python", | |
| "name": "python", | |
| "nbconvert_exporter": "python", | |
| "pygments_lexer": "ipython3", | |
| "version": "3.8.5" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 4 | |
| } |
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