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maxnoe/cauchy_normal_ani.ipynb

Created May 19, 2021 10:05
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Cauchy and Normal Distribution Sample Mean and Std Dev Animation
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cauchy_normal_ani.ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": 14,
"id": "1cae90ed",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<style>.container { width:90% !important; }</style>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"from matplotlib.animation import FuncAnimation\n",
"import numpy as np\n",
"from numpy.random import default_rng, Generator\n",
"from scipy.stats import norm, cauchy\n",
"from tqdm.notebook import tqdm\n",
"\n",
"from IPython.core.display import display, HTML\n",
"display(HTML(\"<style>.container { width:90% !important; }</style>\"))\n",
"\n",
"%matplotlib notebook"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "532c2f36",
"metadata": {},
"outputs": [],
"source": [
"class OnlineStats:\n",
" '''\n",
" Calculate and update sample mean / std in an online fashion\n",
" \n",
" See https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Welford's_online_algorithm\n",
" '''\n",
" \n",
" def __init__(self):\n",
" self.count = 0\n",
" self._mean = 0\n",
" self._m2 = 0\n",
" \n",
" def update(self, val):\n",
" self.count += 1\n",
" \n",
" delta = val - self._mean\n",
" self._mean += delta / self.count\n",
" delta2 = val - self._mean\n",
" self._m2 += delta * delta2\n",
" \n",
" @property\n",
" def mean(self):\n",
" return self._mean if self.count > 0 else np.nan\n",
" \n",
" @property\n",
" def std(self):\n",
" if self.count <= 2:\n",
" return np.nan\n",
" return np.sqrt(self._m2 / (self.count - 1))"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "third-wells",
"metadata": {},
"outputs": [],
"source": [
"rng = default_rng(42)\n",
"\n",
"\n",
"dists = {'normal': {}, 'cauchy': {}}\n",
"\n",
"dists['normal']['dist'] = norm(0, 1)\n",
"dists['cauchy']['dist'] = cauchy()\n",
"\n",
"for dist in dists.values():\n",
" dist['sample_means'] = []\n",
" dist['sample_stds'] = []\n",
" dist['counts'] = []\n",
" dist['stats'] = OnlineStats()\n",
" \n",
" \n",
"n_per_step = 50"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "0793af32",
"metadata": {},
"outputs": [],
"source": [
"bins = np.linspace(-5, 5, 52)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "sharing-alcohol",
"metadata": {
"scrolled": false
},
"outputs": [
{
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" this.context.backingStorePixelRatio ||\n",
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"};\n",
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"};\n",
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"};\n",
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"};\n",
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"};\n",
"\n",
"// A function to construct a web socket function for onmessage handling.\n",
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" * Chrome. But how to set the MIME type? It doesn't seem\n",
" * to be part of the websocket stream */\n",
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" );\n",
" }\n",
"\n",
" fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
" img\n",
" );\n",
" fig.updated_canvas_event();\n",
" fig.waiting = false;\n",
" return;\n",
" } else if (\n",
" typeof evt.data === 'string' &&\n",
" evt.data.slice(0, 21) === 'data:image/png;base64'\n",
" ) {\n",
" fig.imageObj.src = evt.data;\n",
" fig.updated_canvas_event();\n",
" fig.waiting = false;\n",
" return;\n",
" }\n",
"\n",
" var msg = JSON.parse(evt.data);\n",
" var msg_type = msg['type'];\n",
"\n",
" // Call the \"handle_{type}\" callback, which takes\n",
" // the figure and JSON message as its only arguments.\n",
" try {\n",
" var callback = fig['handle_' + msg_type];\n",
" } catch (e) {\n",
" console.log(\n",
" \"No handler for the '\" + msg_type + \"' message type: \",\n",
" msg\n",
" );\n",
" return;\n",
" }\n",
"\n",
" if (callback) {\n",
" try {\n",
" // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
" callback(fig, msg);\n",
" } catch (e) {\n",
" console.log(\n",
" \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
" e,\n",
" e.stack,\n",
" msg\n",
" );\n",
" }\n",
" }\n",
" };\n",
"};\n",
"\n",
"// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
"mpl.findpos = function (e) {\n",
" //this section is from http://www.quirksmode.org/js/events_properties.html\n",
" var targ;\n",
" if (!e) {\n",
" e = window.event;\n",
" }\n",
" if (e.target) {\n",
" targ = e.target;\n",
" } else if (e.srcElement) {\n",
" targ = e.srcElement;\n",
" }\n",
" if (targ.nodeType === 3) {\n",
" // defeat Safari bug\n",
" targ = targ.parentNode;\n",
" }\n",
"\n",
" // pageX,Y are the mouse positions relative to the document\n",
" var boundingRect = targ.getBoundingClientRect();\n",
" var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
" var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
"\n",
" return { x: x, y: y };\n",
"};\n",
"\n",
"/*\n",
" * return a copy of an object with only non-object keys\n",
" * we need this to avoid circular references\n",
" * http://stackoverflow.com/a/24161582/3208463\n",
" */\n",
"function simpleKeys(original) {\n",
" return Object.keys(original).reduce(function (obj, key) {\n",
" if (typeof original[key] !== 'object') {\n",
" obj[key] = original[key];\n",
" }\n",
" return obj;\n",
" }, {});\n",
"}\n",
"\n",
"mpl.figure.prototype.mouse_event = function (event, name) {\n",
" var canvas_pos = mpl.findpos(event);\n",
"\n",
" if (name === 'button_press') {\n",
" this.canvas.focus();\n",
" this.canvas_div.focus();\n",
" }\n",
"\n",
" var x = canvas_pos.x * this.ratio;\n",
" var y = canvas_pos.y * this.ratio;\n",
"\n",
" this.send_message(name, {\n",
" x: x,\n",
" y: y,\n",
" button: event.button,\n",
" step: event.step,\n",
" guiEvent: simpleKeys(event),\n",
" });\n",
"\n",
" /* This prevents the web browser from automatically changing to\n",
" * the text insertion cursor when the button is pressed. We want\n",
" * to control all of the cursor setting manually through the\n",
" * 'cursor' event from matplotlib */\n",
" event.preventDefault();\n",
" return false;\n",
"};\n",
"\n",
"mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
" // Handle any extra behaviour associated with a key event\n",
"};\n",
"\n",
"mpl.figure.prototype.key_event = function (event, name) {\n",
" // Prevent repeat events\n",
" if (name === 'key_press') {\n",
" if (event.key === this._key) {\n",
" return;\n",
" } else {\n",
" this._key = event.key;\n",
" }\n",
" }\n",
" if (name === 'key_release') {\n",
" this._key = null;\n",
" }\n",
"\n",
" var value = '';\n",
" if (event.ctrlKey && event.key !== 'Control') {\n",
" value += 'ctrl+';\n",
" }\n",
" else if (event.altKey && event.key !== 'Alt') {\n",
" value += 'alt+';\n",
" }\n",
" else if (event.shiftKey && event.key !== 'Shift') {\n",
" value += 'shift+';\n",
" }\n",
"\n",
" value += 'k' + event.key;\n",
"\n",
" this._key_event_extra(event, name);\n",
"\n",
" this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
" return false;\n",
"};\n",
"\n",
"mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
" if (name === 'download') {\n",
" this.handle_save(this, null);\n",
" } else {\n",
" this.send_message('toolbar_button', { name: name });\n",
" }\n",
"};\n",
"\n",
"mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
" this.message.textContent = tooltip;\n",
"};\n",
"\n",
"///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
"// prettier-ignore\n",
"var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n",
"mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
"\n",
"mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
"\n",
"mpl.default_extension = \"png\";/* global mpl */\n",
"\n",
"var comm_websocket_adapter = function (comm) {\n",
" // Create a \"websocket\"-like object which calls the given IPython comm\n",
" // object with the appropriate methods. Currently this is a non binary\n",
" // socket, so there is still some room for performance tuning.\n",
" var ws = {};\n",
"\n",
" ws.binaryType = comm.kernel.ws.binaryType;\n",
" ws.readyState = comm.kernel.ws.readyState;\n",
" function updateReadyState(_event) {\n",
" if (comm.kernel.ws) {\n",
" ws.readyState = comm.kernel.ws.readyState;\n",
" } else {\n",
" ws.readyState = 3; // Closed state.\n",
" }\n",
" }\n",
" comm.kernel.ws.addEventListener('open', updateReadyState);\n",
" comm.kernel.ws.addEventListener('close', updateReadyState);\n",
" comm.kernel.ws.addEventListener('error', updateReadyState);\n",
"\n",
" ws.close = function () {\n",
" comm.close();\n",
" };\n",
" ws.send = function (m) {\n",
" //console.log('sending', m);\n",
" comm.send(m);\n",
" };\n",
" // Register the callback with on_msg.\n",
" comm.on_msg(function (msg) {\n",
" //console.log('receiving', msg['content']['data'], msg);\n",
" var data = msg['content']['data'];\n",
" if (data['blob'] !== undefined) {\n",
" data = {\n",
" data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
" };\n",
" }\n",
" // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
" ws.onmessage(data);\n",
" });\n",
" return ws;\n",
"};\n",
"\n",
"mpl.mpl_figure_comm = function (comm, msg) {\n",
" // This is the function which gets called when the mpl process\n",
" // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
"\n",
" var id = msg.content.data.id;\n",
" // Get hold of the div created by the display call when the Comm\n",
" // socket was opened in Python.\n",
" var element = document.getElementById(id);\n",
" var ws_proxy = comm_websocket_adapter(comm);\n",
"\n",
" function ondownload(figure, _format) {\n",
" window.open(figure.canvas.toDataURL());\n",
" }\n",
"\n",
" var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
"\n",
" // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
" // web socket which is closed, not our websocket->open comm proxy.\n",
" ws_proxy.onopen();\n",
"\n",
" fig.parent_element = element;\n",
" fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
" if (!fig.cell_info) {\n",
" console.error('Failed to find cell for figure', id, fig);\n",
" return;\n",
" }\n",
" fig.cell_info[0].output_area.element.on(\n",
" 'cleared',\n",
" { fig: fig },\n",
" fig._remove_fig_handler\n",
" );\n",
"};\n",
"\n",
"mpl.figure.prototype.handle_close = function (fig, msg) {\n",
" var width = fig.canvas.width / fig.ratio;\n",
" fig.cell_info[0].output_area.element.off(\n",
" 'cleared',\n",
" fig._remove_fig_handler\n",
" );\n",
" fig.resizeObserverInstance.unobserve(fig.canvas_div);\n",
"\n",
" // Update the output cell to use the data from the current canvas.\n",
" fig.push_to_output();\n",
" var dataURL = fig.canvas.toDataURL();\n",
" // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
" // the notebook keyboard shortcuts fail.\n",
" IPython.keyboard_manager.enable();\n",
" fig.parent_element.innerHTML =\n",
" '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
" fig.close_ws(fig, msg);\n",
"};\n",
"\n",
"mpl.figure.prototype.close_ws = function (fig, msg) {\n",
" fig.send_message('closing', msg);\n",
" // fig.ws.close()\n",
"};\n",
"\n",
"mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
" // Turn the data on the canvas into data in the output cell.\n",
" var width = this.canvas.width / this.ratio;\n",
" var dataURL = this.canvas.toDataURL();\n",
" this.cell_info[1]['text/html'] =\n",
" '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
"};\n",
"\n",
"mpl.figure.prototype.updated_canvas_event = function () {\n",
" // Tell IPython that the notebook contents must change.\n",
" IPython.notebook.set_dirty(true);\n",
" this.send_message('ack', {});\n",
" var fig = this;\n",
" // Wait a second, then push the new image to the DOM so\n",
" // that it is saved nicely (might be nice to debounce this).\n",
" setTimeout(function () {\n",
" fig.push_to_output();\n",
" }, 1000);\n",
"};\n",
"\n",
"mpl.figure.prototype._init_toolbar = function () {\n",
" var fig = this;\n",
"\n",
" var toolbar = document.createElement('div');\n",
" toolbar.classList = 'btn-toolbar';\n",
" this.root.appendChild(toolbar);\n",
"\n",
" function on_click_closure(name) {\n",
" return function (_event) {\n",
" return fig.toolbar_button_onclick(name);\n",
" };\n",
" }\n",
"\n",
" function on_mouseover_closure(tooltip) {\n",
" return function (event) {\n",
" if (!event.currentTarget.disabled) {\n",
" return fig.toolbar_button_onmouseover(tooltip);\n",
" }\n",
" };\n",
" }\n",
"\n",
" fig.buttons = {};\n",
" var buttonGroup = document.createElement('div');\n",
" buttonGroup.classList = 'btn-group';\n",
" var button;\n",
" for (var toolbar_ind in mpl.toolbar_items) {\n",
" var name = mpl.toolbar_items[toolbar_ind][0];\n",
" var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
" var image = mpl.toolbar_items[toolbar_ind][2];\n",
" var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
"\n",
" if (!name) {\n",
" /* Instead of a spacer, we start a new button group. */\n",
" if (buttonGroup.hasChildNodes()) {\n",
" toolbar.appendChild(buttonGroup);\n",
" }\n",
" buttonGroup = document.createElement('div');\n",
" buttonGroup.classList = 'btn-group';\n",
" continue;\n",
" }\n",
"\n",
" button = fig.buttons[name] = document.createElement('button');\n",
" button.classList = 'btn btn-default';\n",
" button.href = '#';\n",
" button.title = name;\n",
" button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
" button.addEventListener('click', on_click_closure(method_name));\n",
" button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
" buttonGroup.appendChild(button);\n",
" }\n",
"\n",
" if (buttonGroup.hasChildNodes()) {\n",
" toolbar.appendChild(buttonGroup);\n",
" }\n",
"\n",
" // Add the status bar.\n",
" var status_bar = document.createElement('span');\n",
" status_bar.classList = 'mpl-message pull-right';\n",
" toolbar.appendChild(status_bar);\n",
" this.message = status_bar;\n",
"\n",
" // Add the close button to the window.\n",
" var buttongrp = document.createElement('div');\n",
" buttongrp.classList = 'btn-group inline pull-right';\n",
" button = document.createElement('button');\n",
" button.classList = 'btn btn-mini btn-primary';\n",
" button.href = '#';\n",
" button.title = 'Stop Interaction';\n",
" button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
" button.addEventListener('click', function (_evt) {\n",
" fig.handle_close(fig, {});\n",
" });\n",
" button.addEventListener(\n",
" 'mouseover',\n",
" on_mouseover_closure('Stop Interaction')\n",
" );\n",
" buttongrp.appendChild(button);\n",
" var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
" titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
"};\n",
"\n",
"mpl.figure.prototype._remove_fig_handler = function (event) {\n",
" var fig = event.data.fig;\n",
" if (event.target !== this) {\n",
" // Ignore bubbled events from children.\n",
" return;\n",
" }\n",
" fig.close_ws(fig, {});\n",
"};\n",
"\n",
"mpl.figure.prototype._root_extra_style = function (el) {\n",
" el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
"};\n",
"\n",
"mpl.figure.prototype._canvas_extra_style = function (el) {\n",
" // this is important to make the div 'focusable\n",
" el.setAttribute('tabindex', 0);\n",
" // reach out to IPython and tell the keyboard manager to turn it's self\n",
" // off when our div gets focus\n",
"\n",
" // location in version 3\n",
" if (IPython.notebook.keyboard_manager) {\n",
" IPython.notebook.keyboard_manager.register_events(el);\n",
" } else {\n",
" // location in version 2\n",
" IPython.keyboard_manager.register_events(el);\n",
" }\n",
"};\n",
"\n",
"mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
" var manager = IPython.notebook.keyboard_manager;\n",
" if (!manager) {\n",
" manager = IPython.keyboard_manager;\n",
" }\n",
"\n",
" // Check for shift+enter\n",
" if (event.shiftKey && event.which === 13) {\n",
" this.canvas_div.blur();\n",
" // select the cell after this one\n",
" var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
" IPython.notebook.select(index + 1);\n",
" }\n",
"};\n",
"\n",
"mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
" fig.ondownload(fig, null);\n",
"};\n",
"\n",
"mpl.find_output_cell = function (html_output) {\n",
" // Return the cell and output element which can be found *uniquely* in the notebook.\n",
" // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
" // IPython event is triggered only after the cells have been serialised, which for\n",
" // our purposes (turning an active figure into a static one), is too late.\n",
" var cells = IPython.notebook.get_cells();\n",
" var ncells = cells.length;\n",
" for (var i = 0; i < ncells; i++) {\n",
" var cell = cells[i];\n",
" if (cell.cell_type === 'code') {\n",
" for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
" var data = cell.output_area.outputs[j];\n",
" if (data.data) {\n",
" // IPython >= 3 moved mimebundle to data attribute of output\n",
" data = data.data;\n",
" }\n",
" if (data['text/html'] === html_output) {\n",
" return [cell, data, j];\n",
" }\n",
" }\n",
" }\n",
" }\n",
"};\n",
"\n",
"// Register the function which deals with the matplotlib target/channel.\n",
"// The kernel may be null if the page has been refreshed.\n",
"if (IPython.notebook.kernel !== null) {\n",
" IPython.notebook.kernel.comm_manager.register_target(\n",
" 'matplotlib',\n",
" mpl.mpl_figure_comm\n",
" );\n",
"}\n"
],
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"data": {
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"source": [
"fig, axs = plt.subplots(2, 3, constrained_layout=True, figsize=(12.8, 7.2), dpi=100)\n",
"\n",
"dists['normal']['axs'] = axs[0]\n",
"dists['cauchy']['axs'] = axs[1]\n",
"\n",
"dists['normal']['axs'][0].set_ylabel('Standard Normal')\n",
"dists['cauchy']['axs'][0].set_ylabel('Standard Cauchy')\n",
"\n",
"dists['normal']['axs'][0].set_title('Samples')\n",
"dists['normal']['axs'][1].set_title('Sample Mean Evolution')\n",
"dists['normal']['axs'][2].set_title('Sample Std. Dev. Evolution')\n",
"\n",
"\n",
"for dist in dists.values():\n",
" dist['hist'], _, dist['plot'] = dist['axs'][0].hist([], bins=bins)\n",
" dist['mean_line'], = dist['axs'][1].plot([], [])\n",
" dist['std_line'], = dist['axs'][2].plot([], [])\n",
"\n",
"def update_hist(hist, new_counts, ax):\n",
" for count, bar in zip(new_counts, hist.patches):\n",
" bar.set_height(count) \n",
" ax.set_ylim(0, new_counts.max() * 1.05)\n",
"\n",
"\n",
"def update(frame, bar):\n",
" bar.update(1)\n",
" \n",
" for dist in dists.values():\n",
" sample = dist['dist'].rvs(n_per_step, rng)\n",
" \n",
" dist['hist'] += np.histogram(sample, bins=bins)[0]\n",
" update_hist(dist['plot'], dist['hist'], dist['axs'][0])\n",
"\n",
" for val in sample:\n",
" dist['stats'].update(val)\n",
" \n",
" dist['counts'].append(dist['stats'].count)\n",
" dist['sample_means'].append(dist['stats'].mean)\n",
" dist['sample_stds'].append(dist['stats'].std)\n",
" \n",
" dist['mean_line'].set_data(dist['counts'], dist['sample_means'])\n",
" dist['std_line'].set_data(dist['counts'], dist['sample_stds'])\n",
" \n",
" for i in [1, 2]:\n",
" dist['axs'][i].set_xlim(0, 1.1 * dist['counts'][-1])\n",
" \n",
" dist['axs'][1].set_ylim(np.min(dist['sample_means']), np.max(dist['sample_means']))\n",
" dist['axs'][2].set_ylim(np.min(dist['sample_stds']), np.max(dist['sample_stds']))\n",
" \n",
"frames = 1000\n",
"bar = tqdm(total=frames + 1)\n",
"ani = FuncAnimation(fig=fig, func=update, fargs=(bar,), frames=frames, interval=50, repeat=False)\n",
"ani.save('cauchy.mp4')"
]
}
],
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