542 lines
3.6 MiB
Plaintext
542 lines
3.6 MiB
Plaintext
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" script.type = \"text\/javascript\";\n",
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"})];\n",
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" var e = document.getElementById(\"kotlin_out_0\");\n",
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" modifiers.forEach(function (gen) {\n",
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" var script = document.createElement(\"script\");\n",
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" gen(script)\n",
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" script.addEventListener(\"load\", function() {\n",
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" window[\"call_plotly\"] = function(f) {f();};\n",
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" window.kotlinQueues[\"plotly\"].forEach(function(f) {f();});\n",
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" window.kotlinQueues[\"plotly\"] = [];\n",
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" }, false);\n",
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" script.addEventListener(\"error\", function() {\n",
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" window[\"call_plotly\"] = function(f) {};\n",
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" window.kotlinQueues[\"plotly\"] = [];\n",
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" var div = document.createElement(\"div\");\n",
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" div.style.color = 'darkred';\n",
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" }, false);\n",
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" \n",
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" e.appendChild(script);\n",
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" });\n",
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" })();\n",
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" <\/script>"
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]
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},
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"metadata":{
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"output_type":"display_data"
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{
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"data":{
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"text\/html":[
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" <div id=\"kotlin_out_1\"\/>\n",
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" <script type=\"text\/javascript\">\n",
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" }\n",
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" window.kotlinQueues[\"plotlyConnect\"] = resQueue;\n",
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" window[\"call_plotlyConnect\"] = function(f) {\n",
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" resQueue.push(f);\n",
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" }\n",
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" }\n",
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" (function (){\n",
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" var modifiers = [(function(script) {\n",
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" script.textContent = \"\/**\\r\\n * Use existing plotly or load it from the CDN if it is not available\\r\\n * @param action\\r\\n *\/\\r\\nfunction withPlotly(action) {\\r\\n if (typeof Plotly !== \\\"undefined\\\") {\\r\\n action(Plotly);\\r\\n } else if (typeof window.promiseOfPlotly !== \\\"undefined\\\") {\\r\\n window.promiseOfPlotly.then(plotly => action(plotly));\\r\\n } else {\\r\\n console.warn(\\\"Plotly not defined. Loading the script from CDN\\\")\\r\\n window.promiseOfPlotly = new Promise((accept, reject) => {\\r\\n let plotlyLoaderScript = document.createElement(\\\"script\\\");\\r\\n plotlyLoaderScript.src = \\\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/plotly.js\/1.54.6\/plotly.min.js\\\";\\r\\n plotlyLoaderScript.type = 'text\/javascript';\\r\\n plotlyLoaderScript.onload = () => {\\r\\n accept(Plotly);\\r\\n }\\r\\n plotlyLoaderScript.onerror = (error) => {\\r\\n console.error(error);\\r\\n reject(error)\\r\\n }\\r\\n document.head.appendChild(plotlyLoaderScript);\\r\\n });\\r\\n }\\r\\n}\\r\\n\\r\\n\/**\\r\\n * Request and parse json from given address\\r\\n * @param url {URL}\\r\\n * @param callback\\r\\n * @return Promise<Json>\\r\\n *\/\\r\\nfunction getJSON(url, callback) {\\r\\n\\r\\n function handleErrors(response) {\\r\\n if (!response.ok) {\\r\\n throw Error(response.statusText);\\r\\n }\\r\\n return response;\\r\\n }\\r\\n\\r\\n try {\\r\\n fetch(url, {\\r\\n method: 'GET',\\r\\n headers: {\\r\\n Accept: 'application\/json',\\r\\n }\\r\\n })\\r\\n .then(handleErrors)\\r\\n .then(response => response.json())\\r\\n .then(json => callback(json))\\r\\n .catch(error => console.log(error));\\r\\n } catch (e) {\\r\\n alert(\\\"Fetch of plot data failed with error: \\\" + e)\\r\\n }\\r\\n}\\r\\n\\r\\n\/**\\r\\n * Safe call for Plotly.newPlot\\r\\n * @param id\\r\\n * @param data\\r\\n * @param layout\\r\\n * @param config\\r\\n *\/\\r\\nfunction makePlot(id, data, layout, config) {\\r\\n withPlotly(plotly => plotly.newPlot(id, data, layout, config))\\r\\n}\\r\\n\\r\\n\/**\\r\\n * Create a plot taking data from given url\\r\\n * @param id {string} element id for plot\\r\\n * @param from {URL} json server url\\r\\n * @param config {object} plotly configuration\\r\\n * @return {JSON}\\r\\n *\/\\r\\nfunction createPlotFrom(id, from, config = {}) {\\r\\n getJSON(from, json => withPlotly(plotly => {\\r\\n plotly.newPlot(id, json.data, json.layout, config)\\r\\n }));\\r\\n}\\r\\n\\r\\n\/**\\r\\n * Update a plot taking data from given url\\r\\n * @param id {string} element id for plot\\r\\n * @param from {URL} json server url\\r\\n * @return {JSON}\\r\\n *\/\\r\\nfunction updatePlotFrom(id, from) {\\r\\n getJSON(from, json => withPlotly(plotly => plotly.react(id, json.data, json.layout)));\\r\\n}\\r\\n\\r\\n\/**\\r\\n * Start pull updates with regular requests from client side\\r\\n * @param id {string}\\r\\n * @param from\\r\\n * @param millis\\r\\n *\/\\r\\nfunction startPull(id, from, millis) {\\r\\n let action = function () {\\r\\n updatePlotFrom(id, from)\\r\\n };\\r\\n window.setInterval(action, millis)\\r\\n}\\r\\n\\r\\n\/**\\r\\n * Start push updates via websocket\\r\\n * @param id {string} element id for plot\\r\\n * @param ws {URL} a websocket address\\r\\n *\/\\r\\nfunction startPush(id, ws) {\\r\\n let socket = new WebSocket(ws);\\r\\n\\r\\n socket.onopen = function () {\\r\\n console.log(\\\"[Plotly.kt] A connection for plot with id = \\\" + id + \\\" with server established on \\\" + ws);\\r\\n };\\r\\n\\r\\n socket.onclose = function (event) {\\r\\n if (event.wasClean) {\\r\\n console.log(\\\"The connection with server is closed\\\");\\r\\n } else {\\r\\n co
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" script.type = \"text\/javascript\";\n",
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"})];\n",
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" var e = document.getElementById(\"kotlin_out_1\");\n",
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" modifiers.forEach(function (gen) {\n",
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" var script = document.createElement(\"script\");\n",
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" gen(script)\n",
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" script.addEventListener(\"load\", function() {\n",
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" window[\"call_plotlyConnect\"] = function(f) {f();};\n",
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" window.kotlinQueues[\"plotlyConnect\"].forEach(function(f) {f();});\n",
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" window.kotlinQueues[\"plotlyConnect\"] = [];\n",
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" }, false);\n",
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" script.addEventListener(\"error\", function() {\n",
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" window[\"call_plotlyConnect\"] = function(f) {};\n",
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" window.kotlinQueues[\"plotlyConnect\"] = [];\n",
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" var div = document.createElement(\"div\");\n",
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" div.style.color = 'darkred';\n",
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" div.textContent = 'Error loading resource plotlyConnect';\n",
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" document.getElementById(\"kotlin_out_1\").appendChild(div);\n",
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" }, false);\n",
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" \n",
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" e.appendChild(script);\n",
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" });\n",
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" })();\n",
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" <\/script>"
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]
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},
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"metadata":{
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},
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"output_type":"display_data"
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}
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],
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"metadata":{
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"datalore":{
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"node_id":"oUCrttLL2OmTMU5sqF0WoG",
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"type":"CODE",
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"hide_input_from_viewers":true,
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"hide_output_from_viewers":true
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}
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}
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},
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{
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"cell_type":"code",
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"source":[
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"Plotly.jupyter.notebook()"
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],
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"execution_count":2,
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"outputs":[
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{
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"data":{
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"text\/html":[
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"<div style=\"color: blue;\">Plotly notebook integration switch into the legacy mode.<\/div>\n"
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]
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},
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"metadata":{
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},
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"output_type":"display_data"
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}
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],
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"metadata":{
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"datalore":{
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"node_id":"pqfKI18qbEcbcjxf22n1hF",
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"type":"CODE",
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"hide_input_from_viewers":true,
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"hide_output_from_viewers":true
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}
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}
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},
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{
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"cell_type":"markdown",
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"source":[
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"# Центральная предельная теорема\n",
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"\n",
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"[Центральная предельная теорема](https:\/\/ru.wikipedia.org\/wiki\/%D0%A6%D0%B5%D0%BD%D1%82%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D0%BF%D1%80%D0%B5%D0%B4%D0%B5%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D1%82%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%D0%B0) в вльной формулировке гласит, что сумма случайных величин, имеющих распределение с конечным средним и дисперсией, распределена по нормальному распределению со средним, равным сумме средних компонент и дисперсией, равно сумме дисперсий.\n",
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"\n",
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"На доказательство этой теоремы в общем виде обычно уходит львиная доля семестра в курсе теории вероятности. В данной задаче мы попробуем проверить эту теорему на практике.\n",
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"\n",
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"Для этого мы возьмем некоторое распределение и посчитаем численно распределение суммы.\n",
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"\n",
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"Для решения задачи нам потребуется:\n",
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"\n",
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"* Определить функцию плотности вероятности распределения\n",
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"* Создать функцию для расчета распределения суммы двух случайных величин. Распределение суммы случайных величин вычисляется как свертка распределений (см. ниже).\n",
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"* Последовательно посчитатать распределение суммы нескольких величин `a + a + a + a = (((a + a) + a) +a)`\n",
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"* Сравнить результат с нормальным распределением.\n",
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"\n",
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"Для решения задачи может понадобится представление функции в виде набора точек при помощи процедуры [линейной интерпояции](https:\/\/ru.wikipedia.org\/wiki\/%D0%9B%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D0%B0%D1%8F_%D0%B8%D0%BD%D1%82%D0%B5%D1%80%D0%BF%D0%BE%D0%BB%D1%8F%D1%86%D0%B8%D1%8F).\n",
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"\n",
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"## Свертка\n",
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"\n",
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"[Сверткой](https:\/\/ru.wikipedia.org\/wiki\/%D0%A1%D0%B2%D1%91%D1%80%D1%82%D0%BA%D0%B0_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B8%D0%B9_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7)) \n",
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"двух функций называется следующее интегральное преобразование:\n",
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"$$\n",
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" h(x) = f(x) \\otimes g(x) = \\int {f(x-y) g(y) dy }\n",
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"$$\n",
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"Интегрирование ведется по всей области определения функций. Очевидно, что переменные под интегрированием можно менять местами. Для вычисления интеграла можно использовать [метод прямоугольников](https:\/\/ru.wikipedia.org\/wiki\/%D0%9C%D0%B5%D1%82%D0%BE%D0%B4_%D0%BF%D1%80%D1%8F%D0%BC%D0%BE%D1%83%D0%B3%D0%BE%D0%BB%D1%8C%D0%BD%D0%B8%D0%BA%D0%BE%D0%B2) или [метод трапеций](https:\/\/ru.wikipedia.org\/wiki\/%D0%9C%D0%B5%D1%82%D0%BE%D0%B4_%D1%82%D1%80%D0%B0%D0%BF%D0%B5%D1%86%D0%B8%D0%B9)."
|
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|
],
|
|||
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|
"attachments":{
|
|||
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|
|||
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|
},
|
|||
|
|
"metadata":{
|
|||
|
|
"datalore":{
|
|||
|
|
"node_id":"Qt6aQ5KMLEic2fkkr4qlVt",
|
|||
|
|
"type":"MD",
|
|||
|
|
"hide_input_from_viewers":true,
|
|||
|
|
"hide_output_from_viewers":true
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type":"markdown",
|
|||
|
|
"source":[
|
|||
|
|
"\n",
|
|||
|
|
"## Интерполяция\n",
|
|||
|
|
"\n",
|
|||
|
|
"Для помощи в решении задачи можно использовать готовую реализацию линейной интерполяции."
|
|||
|
|
],
|
|||
|
|
"attachments":{
|
|||
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|
|||
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|
},
|
|||
|
|
"metadata":{
|
|||
|
|
"datalore":{
|
|||
|
|
"node_id":"4NbaS7idD8SbiGNmBoJkSg",
|
|||
|
|
"type":"MD",
|
|||
|
|
"hide_input_from_viewers":true,
|
|||
|
|
"hide_output_from_viewers":true
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type":"code",
|
|||
|
|
"source":[
|
|||
|
|
"typealias Function = (Double) -> Double\n",
|
|||
|
|
"\n",
|
|||
|
|
"fun pointsFromRange(from: Double, to: Double, numPoints: Int = 100): List<Double>{\n",
|
|||
|
|
" require( to > from)\n",
|
|||
|
|
" require(numPoints > 2)\n",
|
|||
|
|
" val step = (to - from)\/(numPoints - 1)\n",
|
|||
|
|
" require(step>0)\n",
|
|||
|
|
" return List(numPoints){i -> from + step * i}\n",
|
|||
|
|
"}\n",
|
|||
|
|
"\n",
|
|||
|
|
"fun Function.interpolate(from: Double, to: Double, numPoints: Int = 100): Function{\n",
|
|||
|
|
" \/\/compute xs\n",
|
|||
|
|
" val xs = pointsFromRange(from, to, numPoints) \n",
|
|||
|
|
" \/\/compute function values\n",
|
|||
|
|
" val ys = xs.map{ invoke(it) }\n",
|
|||
|
|
" \n",
|
|||
|
|
" \/\/ return an anonimous function\n",
|
|||
|
|
" return { x ->\n",
|
|||
|
|
" \/\/ check interpolation region. Zerop outside the region\n",
|
|||
|
|
" if(x < xs.first() || x > xs.last()) 0.0\n",
|
|||
|
|
" \/\/ find section number\n",
|
|||
|
|
" val num: Int = xs.indexOfFirst { it > x }\n",
|
|||
|
|
" \/\/ num >=1\n",
|
|||
|
|
" if(num <= 0){\n",
|
|||
|
|
" 0.0\n",
|
|||
|
|
" } else{\n",
|
|||
|
|
" \/\/return the result as last expression\n",
|
|||
|
|
" ys[num - 1] + (ys[num] - ys[num - 1])\/(xs[num] - xs[num - 1])*(x - xs[num - 1])\n",
|
|||
|
|
" }\n",
|
|||
|
|
" }\n",
|
|||
|
|
"}"
|
|||
|
|
],
|
|||
|
|
"execution_count":3,
|
|||
|
|
"outputs":[
|
|||
|
|
|
|||
|
|
],
|
|||
|
|
"metadata":{
|
|||
|
|
"datalore":{
|
|||
|
|
"node_id":"a8NBDUb8ifDAPZYpU3OSzM",
|
|||
|
|
"type":"CODE",
|
|||
|
|
"hide_input_from_viewers":true,
|
|||
|
|
"hide_output_from_viewers":true
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type":"markdown",
|
|||
|
|
"source":[
|
|||
|
|
"# Решение"
|
|||
|
|
],
|
|||
|
|
"attachments":{
|
|||
|
|
|
|||
|
|
},
|
|||
|
|
"metadata":{
|
|||
|
|
"datalore":{
|
|||
|
|
"node_id":"hqV4unJLx6pKvlyMqRhdnP",
|
|||
|
|
"type":"MD",
|
|||
|
|
"hide_input_from_viewers":true,
|
|||
|
|
"hide_output_from_viewers":true
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type":"markdown",
|
|||
|
|
"source":[
|
|||
|
|
"### Проверка"
|
|||
|
|
],
|
|||
|
|
"attachments":{
|
|||
|
|
|
|||
|
|
},
|
|||
|
|
"metadata":{
|
|||
|
|
"datalore":{
|
|||
|
|
"node_id":"6jRPRbjVKunp5d7dhFCKU6",
|
|||
|
|
"type":"MD",
|
|||
|
|
"hide_input_from_viewers":true,
|
|||
|
|
"hide_output_from_viewers":true
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type":"code",
|
|||
|
|
"source":[
|
|||
|
|
"fun l2RelativeDiff(res: Function, order: Int, baseDispersion: Double): Double{\n",
|
|||
|
|
" val numPointForDiff = 100\n",
|
|||
|
|
" val dispersion = baseDispersion * order\n",
|
|||
|
|
" val sigma = sqrt(dispersion)\n",
|
|||
|
|
" val xs = ArrayList<Double>()\n",
|
|||
|
|
" for(i in 0 until numPointForDiff){\n",
|
|||
|
|
" xs.add(-3*sigma + i.toDouble()\/(numPointForDiff-1)*6*sigma)\n",
|
|||
|
|
" }\n",
|
|||
|
|
"\n",
|
|||
|
|
" fun normal(x: Double): Double{\n",
|
|||
|
|
" return 1.0\/sqrt(2* PI*dispersion)*exp(-x.pow(2)\/2.0\/dispersion)\n",
|
|||
|
|
" }\n",
|
|||
|
|
"\n",
|
|||
|
|
" return xs.sumOf{ x-> \n",
|
|||
|
|
" (res(x)\/normal(x) - 1.0).pow(2)\n",
|
|||
|
|
" }\n",
|
|||
|
|
"}"
|
|||
|
|
],
|
|||
|
|
"execution_count":4,
|
|||
|
|
"outputs":[
|
|||
|
|
|
|||
|
|
],
|
|||
|
|
"metadata":{
|
|||
|
|
"datalore":{
|
|||
|
|
"node_id":"xlUgyZfYueDee0UowZZW1O",
|
|||
|
|
"type":"CODE",
|
|||
|
|
"hide_input_from_viewers":true,
|
|||
|
|
"hide_output_from_viewers":true
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type":"code",
|
|||
|
|
"source":[
|
|||
|
|
"\n",
|
|||
|
|
"fun integrate(f: Function, from: Double, to: Double, numPoints: Int = 100): Double{\n",
|
|||
|
|
" val xs = pointsFromRange(from, to, numPoints)\n",
|
|||
|
|
" return xs.sumOf { f(it) } * (to - from) \/ numPoints\n",
|
|||
|
|
"}\n",
|
|||
|
|
"\n",
|
|||
|
|
"fun convolve(f: Function, g: Function, from: Double, to: Double, numPoints: Int = 100): Function{\n",
|
|||
|
|
" val res: Function = { x ->\n",
|
|||
|
|
" val integrand: Function = { y -> f(x - y) * g(y)}\n",
|
|||
|
|
" integrate(integrand, from, to, numPoints)\n",
|
|||
|
|
" }\n",
|
|||
|
|
"\n",
|
|||
|
|
" \/\/We need interpolation here to limit complexity\n",
|
|||
|
|
" \/\/With interpolation it linear, without it is exponential\n",
|
|||
|
|
" return res.interpolate(from, to, numPoints)\n",
|
|||
|
|
"}"
|
|||
|
|
],
|
|||
|
|
"execution_count":5,
|
|||
|
|
"outputs":[
|
|||
|
|
|
|||
|
|
],
|
|||
|
|
"metadata":{
|
|||
|
|
"datalore":{
|
|||
|
|
"node_id":"MyDmwsnS5H82wfWbgopf8U",
|
|||
|
|
"type":"CODE",
|
|||
|
|
"hide_input_from_viewers":true,
|
|||
|
|
"hide_output_from_viewers":true
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type":"code",
|
|||
|
|
"source":[
|
|||
|
|
"val f: Function = {x -> if(x in (-1.0..1.0)) 0.5 else 0.0}\n",
|
|||
|
|
"\n",
|
|||
|
|
"val from = -5.0\n",
|
|||
|
|
"val to = 5.0\n",
|
|||
|
|
"\n",
|
|||
|
|
"val num = 300\n",
|
|||
|
|
"\n",
|
|||
|
|
"val first: Function = convolve(f, f, from, to, num)\n",
|
|||
|
|
"val second: Function = convolve(first, f, from, to, num)\n",
|
|||
|
|
"val third: Function = convolve(second, f, from, to, num)\n",
|
|||
|
|
"val fourth: Function = convolve(third, f, from, to, num)\n",
|
|||
|
|
"val fifth: Function = convolve(fourth, f, from, to, num)"
|
|||
|
|
],
|
|||
|
|
"execution_count":6,
|
|||
|
|
"outputs":[
|
|||
|
|
|
|||
|
|
],
|
|||
|
|
"metadata":{
|
|||
|
|
"datalore":{
|
|||
|
|
"node_id":"81kNX1pA9p6s28xxrLf9cr",
|
|||
|
|
"type":"CODE",
|
|||
|
|
"hide_input_from_viewers":true,
|
|||
|
|
"hide_output_from_viewers":true
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type":"code",
|
|||
|
|
"source":[
|
|||
|
|
"val xs = pointsFromRange(from, to, num)\n",
|
|||
|
|
"\n",
|
|||
|
|
"Plotly.plot { \n",
|
|||
|
|
"\n",
|
|||
|
|
" scatter { \n",
|
|||
|
|
" name = \"initial\"\n",
|
|||
|
|
" x.numbers = xs\n",
|
|||
|
|
" y.numbers = xs.map(f)\n",
|
|||
|
|
" }\n",
|
|||
|
|
"\n",
|
|||
|
|
" scatter { \n",
|
|||
|
|
" name = \"first\"\n",
|
|||
|
|
" x.numbers = xs\n",
|
|||
|
|
" y.numbers = xs.map(first)\n",
|
|||
|
|
" }\n",
|
|||
|
|
"\n",
|
|||
|
|
" scatter { \n",
|
|||
|
|
" name = \"second\"\n",
|
|||
|
|
" x.numbers = xs\n",
|
|||
|
|
" y.numbers = xs.map(second)\n",
|
|||
|
|
" }\n",
|
|||
|
|
"\n",
|
|||
|
|
" scatter { \n",
|
|||
|
|
" name = \"fifth\"\n",
|
|||
|
|
" x.numbers = xs\n",
|
|||
|
|
" y.numbers = xs.map(fifth)\n",
|
|||
|
|
" }\n",
|
|||
|
|
"\n",
|
|||
|
|
" val d = 6.0\/3.0\n",
|
|||
|
|
"\n",
|
|||
|
|
"\n",
|
|||
|
|
" scatter { \n",
|
|||
|
|
" name = \"normal\"\n",
|
|||
|
|
" x.numbers = xs\n",
|
|||
|
|
" y.numbers = xs.map{1.0\/sqrt(2*PI*d) * exp(- it.pow(2)\/d\/2) }\n",
|
|||
|
|
" }\n",
|
|||
|
|
" }"
|
|||
|
|
],
|
|||
|
|
"execution_count":7,
|
|||
|
|
"outputs":[
|
|||
|
|
{
|
|||
|
|
"data":{
|
|||
|
|
"text\/html":[
|
|||
|
|
"<html>\n",
|
|||
|
|
" <head>\n",
|
|||
|
|
" <meta charset=\"utf-8\">\n",
|
|||
|
|
" <title>Plotly.kt<\/title>\n",
|
|||
|
|
" <script type=\"text\/javascript\" src=\"https:\/\/cdn.plot.ly\/plotly-1.54.6.min.js\"><\/script>\n",
|
|||
|
|
" <\/head>\n",
|
|||
|
|
" <body>\n",
|
|||
|
|
" <div id=\"space.kscience.plotly.Plot@7acaf8c6\">\n",
|
|||
|
|
" <script>if(typeof Plotly !== \"undefined\"){\n",
|
|||
|
|
" Plotly.react(\n",
|
|||
|
|
" 'space.kscience.plotly.Plot@7acaf8c6',\n",
|
|||
|
|
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" {},\n",
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" {}\n",
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" ); \n",
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"} else {\n",
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" console.error(\"Plotly not loaded\")\n",
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"}<\/script>\n",
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" <\/div>\n",
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" <\/body>\n",
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"<\/html>\n"
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]
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},
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"metadata":{
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},
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}
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{
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],
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"execution_count":8,
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"outputs":[
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{
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"data":{
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"text\/plain":[
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"53.72510082115637"
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}
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],
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"metadata":{
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"display_name":"Kotlin",
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"version":3
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}
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}
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