2c:null 2d:["$","title",null,{"children":"Right Stochastic Matrix | Chuncheng | Observable"}] 32:T432,{ const flatten = flatMat(powerMat(mat, order)); const plt1 = Plot.plot({ color: { scheme: "Blues", nice: true, legend: true }, aspectRatio: 1.0, width: 500, marks: [ Plot.cell(flatten, { x: "i", y: (d) => d.j - mat.length + order, fill: "x" }), Plot.text(flatten, { x: "i", y: (d) => d.j - mat.length + order, text: "x", fill: "white", fontSize: "large" }) ] }); const plt2 = Plot.plot({ grid: true, color: { scheme: "Blues", nice: true, legend: true, domain: [0, 2 / 7] }, x: { nice: true }, y: { nice: true }, marks: [ Plot.ruleX([order - 1], { stroke: "gray" }), Plot.line(ground.res, { x: "i", y: "p", stroke: "gray" }), Plot.dot(ground.res, { x: "i", y: "p", tip: true, fill: "p" }), Plot.line(simulation.res, { x: "i", y: "p", z: "j", stroke: (d) => d3.schemeCategory10[d.j % 10] }) ] }); return htl.html`

${plt1} ${plt2}

`; }33:[] 30:{"id":"a2b78d7f92ab5f91","slug":"right-stochastic-matrix","title":"Right Stochastic Matrix","thumbnail":"7d910d24e48edc8c5bbbf55cb7dab566e2e1da1226075b4a24a123402f066b1f","access_level":"public","create_time":"$D2023-10-08T03:38:04.946Z","update_time":"$D2023-10-08T08:21:07.963Z","view_time":null,"first_public_time":"$D2023-10-08T03:38:04.946Z","has_unpublished_edits":null,"fork":{"id":"becbc8cde7e1f8cc","slug":"matrix-production","title":"Matrix production","owner":{"id":"bcd65cef1cb4d2ed","login":"listenzcc","name":"Chuncheng"}},"stars":0,"starred":false,"owner":{"type":"team","id":"bcd65cef1cb4d2ed","login":"listenzcc","name":"Chuncheng","avatar_url":"https://avatars-next.observableusercontent.com/bb3c68e77a708a587ffc2d663bb83421f20d67991dbe6c1623c6e5d2fb73d15e","tier":"starter_2024"},"version":324,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"16328058352682a8","login":"listenzcc","name":"Chuncheng","avatar_url":"https://avatars-next.observableusercontent.com/bb3c68e77a708a587ffc2d663bb83421f20d67991dbe6c1623c6e5d2fb73d15e","tier":null}],"members":[{"type":"individual","id":"16328058352682a8","login":"listenzcc","name":"Chuncheng","avatar_url":"https://avatars-next.observableusercontent.com/bb3c68e77a708a587ffc2d663bb83421f20d67991dbe6c1623c6e5d2fb73d15e","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":{"id":"3aa143c61490363d","slug":"math","title":"Math","owner":{"id":"bcd65cef1cb4d2ed","login":"listenzcc","name":"Chuncheng"}},"type":"notebook","body":{"titling":"auto","title":"Right Stochastic Matrix","cells":[{"id":0,"value":"# Right Stochastic Matrix","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":173,"value":"viewof order = Inputs.range([1, 30], { label: \"Order\", step: 1, value: 1 })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":256,"value":"viewof shuffle = Inputs.button(\"Shuffle\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":7,"value":"$32","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":221,"value":"","pinned":true,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":181,"value":"powerMat = (mat, n) => {\n var res = new ML.Matrix(mat),\n m = new ML.Matrix(mat);\n\n for (let i = 1; i < n; ++i) {\n res = res.mmul(m);\n }\n\n return res.data;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":144,"value":"flatMat = (mat) => {\n const arr = [];\n\n mat.map((vec, j) =>\n vec.map((x, i) => {\n arr.push({ i, j, x });\n })\n );\n\n return arr;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":113,"value":"simulation = {\n shuffle;\n\n const m = new ML.Matrix(mat),\n res = [],\n n = 7,\n rnd = d3.randomNormal(),\n rndVec = () => [...new Array(n)].map(rnd);\n\n var v = new ML.Matrix([...new Array(m.rows)].map(rndVec));\n\n for (let i = 0; i < 30; ++i) {\n v = m.mmul(v);\n for (let j = 0; j < n; ++j) {\n res.push({ i: i, j, p: v.data[m.rows - 1][j] });\n }\n }\n\n return { v, res };\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":80,"value":"ground = {\n const m = new ML.Matrix(mat),\n res = [];\n\n var v = new ML.Matrix([[0], [0], [0], [0], [0], [1]]);\n\n for (let i = 0; i < 30; ++i) {\n v = m.mmul(v);\n\n res.push({ i: i, p: v.data[m.rows - 1][0] });\n }\n\n return { v, res };\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":238,"value":"ev = new ML.EigenvalueDecomposition(m)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":40,"value":"m = new ML.Matrix(mat)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"mat1 = [\n [0, 1, 0, 0, 0, 0],\n [0, 0, 1, 0, 0, 0],\n [0, 0, 0, 1, 0, 0],\n [0, 0, 0, 0, 1, 0],\n [0, 0, 0, 0, 0, 1],\n [1 / 6, 1 / 6, 1 / 6, 1 / 6, 1 / 6, 1 / 6]\n]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":318,"value":"mat = {\n shuffle;\n return rndRightStochasticMatrix();\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":311,"value":"rndRightStochasticMatrix = (rows = 6, cols = 6) => {\n const rnd = d3.randomUniform();\n\n function rndRow() {\n const row = [...new Array(cols)].map(rnd),\n sum = d3.sum(row);\n\n return row.map((d) => d / sum);\n }\n\n return [...new Array(rows)].map(rndRow);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":34,"value":"ML = require(\"https://cdn.jsdelivr.net/npm/ml-matrix@6.10.5/matrix.umd.min.js\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":136,"value":"d3 = require(\"d3\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":296,"value":"

https://en.wikipedia.org/wiki/Stochastic_matrix

\n","pinned":true,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"}],"files":"$W33","stdlib":"1"}} 31:"$30:body"