2e:null 2f:["$","title",null,{"children":"Weighted Adjacency Matrix for Orbital | justjoolz | Observable"}] 34:[] 32:{"id":"0aaddd3dbf78848d","slug":"weighted-adjacency-matrix-for-orbital","title":"Weighted Adjacency Matrix for Orbital","thumbnail":"7f677d0596b5272ced12e18a9d20fc1697d6d8aeda71abba46dc0530ecad5828","access_level":"public","create_time":"$D2020-08-10T06:33:23.869Z","update_time":"$D2020-11-17T04:16:20.702Z","view_time":null,"first_public_time":"$D2020-08-10T15:44:32.456Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"c647648a9123c450","login":"justjoolz","name":"","avatar_url":"https://avatars-next.observableusercontent.com/1d93159d0079666441bf244a278db273fe1754351618a7a5d6f58d75171ffecd","tier":"starter_2024"},"version":536,"publish_version":536,"role":null,"authored":false,"authors":[{"type":"individual","id":"5a7de677c184511b","login":"justjoolz","name":"","avatar_url":"https://avatars-next.observableusercontent.com/1d93159d0079666441bf244a278db273fe1754351618a7a5d6f58d75171ffecd","tier":null}],"members":[{"type":"individual","id":"5a7de677c184511b","login":"justjoolz","name":"","avatar_url":"https://avatars-next.observableusercontent.com/1d93159d0079666441bf244a278db273fe1754351618a7a5d6f58d75171ffecd","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":1,"collection":null,"type":"notebook","body":{"title":"Weighted Adjacency Matrix for Orbital","cells":[{"id":0,"value":"md`# Weighted Adjacency Matrix for Orbital`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":484,"value":"md `Calculating token payout matrix in different ways... `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":3,"value":"function generateMatrix( n=12, start=1) { // this is most basic way of calculating \n var matrix = []\n //matrix.push(0) // to index by n not n-1\n for (let x=start; x (x+y) ) // bottom of fraction = sum of divisors\n let weightedRow = row.map( (z) => z/denominator ) \n // matrix.push(weightedRow)\n matrix.push( {payoutTokens: row, payoutAmounts: weightedRow} )\n }\n return matrix\n}(12,5)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":165,"value":"md `This is an array including the zero payments.... Rendered as a 2D triangular array making the payoutTokens Redundant as that is simply the index of the column+1`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":164,"value":"function generateMatrix( n=12) {\n var matrix = []\n //matrix.push(0) // to index by n not n-1\n for (let x=1; x (x+y) ) // bottom of fraction = sum of divisors\n let weightedRow = row.map( (z) => z/denominator ) \n // matrix.push(weightedRow)\n matrix.push( weightedRow )\n }\n \n // calculate sums for each token.... \n var sums = []\n for (let t=1; t x/n*100 ) // this is same as doing when pushing see above \n return {tokenReturnsPerEpoch: matrix, sums}\n}(10)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":172,"value":"md `As we are working with trianglular array we can flatted it to a single dimension and index by the triangular numbers`\n","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":175,"value":"function triangle( n ) { // returns the triangular number for n (total size of array)\n return (n*(n+1)/2)\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":188,"value":"function triangleIndex( n ) { // \n let end = triangle(n)\n return [ triangle(n-1), end-1 ]\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":228,"value":"// Function to calculate sum of all proper divisors \n// num --> given natural number \nfunction divSum( num) \n{ \n // Final result of summation of divisors \n var result = 0; \n \n // find all divisors which divides 'num' \n for (let i=1; i<=Math.sqrt(num+2); i++) \n { \n // if 'i' is divisor of 'num' \n if (num%i==0) \n { \n // if both divisors are same then add \n // it only once else add both \n if (i==(num/i)) \n result += i; \n else\n result += (i + num/i); \n } \n } \n return (result); \n}\n ","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":255,"value":"function sumOfFactors(n) \n{ \n // Traversing through all prime factors. \n let res = 1; \n for (let i = 2; i <= Math.sqrt(n); i++) \n { \n let curr_sum = 1; \n let curr_term = 1; \n while (n % i == 0) { \n \n n = n / i; \n \n curr_term *= i; \n curr_sum += curr_term; \n } \n \n res *= curr_sum; \n } \n \n // This condition is to handle \n // the case when n is a prime \n // number greater than 2. \n if (n >= 2) \n res *= (1 + n); \n \n return res; \n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":275,"value":"function generateFlattenedTriangleArrayOfWeights( n=12) { // this is flattened \n let array = []\n for (let x=1; x x != 0 )","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":325,"value":"function getWeights(n=12) { // gets weight for specific dimension (more efficient than above)\n let array = []\n for(let y=1; y< n+1; y++) {\n if (n%y == 0) // if divisible with no remainder \n array.push(y/ sumOfFactors(n) )\n else\n array.push(0)\n }\n return array\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":363,"value":"function tokenReturns( n=10 ) {\n // calculate token returns for specific token\n let tokenReturns = [];\n // get array of all weights \n let array = generateFlattenedTriangleArrayOfWeights(n)\n // find start and end position in array for token n\n\n \n for( let token=1; token