2b:null 2c:["$","title",null,{"children":"RPS Matrix to Isoclines | Jasmine Otto | Observable"}] 31:Tbc5,plt = { let svg = DOM.svg(370, 320) // d3.select(svg).selectAll('g').remove() // refresh let plt = d3.select(svg).append('g') .attr('transform', 'translate(15,20)'), axes = plt.append('g') // put background layer beneath figures // isoclines plt.selectAll('path') .data(clines).enter() .append('path') .attr('d', d => d) .attr('stroke', 'black') // payoff indicator plt.selectAll('circle') // draw trace .data(d3.range(400)).enter() .append('circle') .attr('cx', i => pts[i][0]).attr('cy', i => pts[i][1]) .attr('r', 5) // payoff indicator plt.selectAll('rect') .data(d3.range(12).map(idx => { let i = 100*Math.floor(idx/3) return [i, idx%3, w(trace[i])[idx%3]] })).enter() .append('rect') .attr('x', ([i,j,w]) => pts[i][0] + 15 + [0,20,10][j] - 2.5*w) .attr('y', ([i,j,w]) => pts[i][1] - [0,0,15][j] - 2.5*w) .attr('width', ([i,j,w]) => 5*w) .attr('height', ([i,j,w]) => 5*w) .attr('stroke', 'white') plt.selectAll('text') .data(d3.range(4).map(i=>100*i)).enter() .append('text') .attr('x', i => pts[i][0] + 15) .attr('y', i => pts[i][1] + 15) .text(i => 't = ' + i) // w(trace[i]).map(u => parseFloat(u).toFixed(2)).join(',')) // print payoffs .attr('font-size', '8pt') // background for (let i=0; i<3; ++i){ for (let j=0; j <=5; ++j){ axes.append('path') .attr('d', ter.rule(j*20, i)) // % along, axis .attr('stroke', 'lightgray') } } /* let notches = ['orange', 'yellow', 'lightblue'].map((u,i) => { let v = [0,0,0]; v[i] = 1 return {color: u, pt: ter.point(v), dx: [5,-5,0][i], dy: [-3,-3,6][i]} }) axes.selectAll('circle') // corner annotations .data(notches).enter() .append('circle') .attr('cx', d => d.pt[0] + d.dx).attr('cy', d => d.pt[1] + d.dy) .attr('r', 3).style('fill', d => d.color) */ // interact /* plt.append('text') .attr('id', 'hover') .attr('x', 15).attr('y', 15) // FIXME: put attractiveness of strategy in that strategy's corner. plt.append('circle') .attr('id', 'hover-mark') .attr('r', 3) */ let update = () => { let e, res = undefined try { e = d3.mouse(svg) // FIXME: brittle offset for foreground transform e[0] -= 15; e[1] -= 20 res = ter.getValues(e) } catch(err) { res = mutable strategy } // use cache if necessary. if (res.every(u => u <= 1 && u >= 0)) { // clamp to all pops positive if (strategy != res) // update if necessary. mutable strategy = res // trigger updated trace. // plt.select('#hover') // .text(w(res).map(u => parseFloat(u).toFixed(2))) // print payoffs /* if (e) // unless initializing from cache plt.select('#hover-mark') .attr('cx', e[0]).attr('cy', e[1]) */ } } d3.select(svg).on('mousemove', update) update() return svg }32:T7aa,// adapted from // https://github.com/tomgp/d3-ternary/blob/master/ternary.js ternaryPlot = function(){ var ternary = {}; var height = Math.sqrt( 1*1 - (1/2)*(1/2)); var path; function rescale(range){ if(!range.length) range = [0, 1]; ternary.scale = d3.scaleLinear().domain([0, 1]).range(range); } function line(){ path = d3.line() .x(function(d) { return d[0]; }) .y(function(d) { return d[1]; }) } rescale([0, 400]); line(); ternary.range = function(range){ rescale(range); return ternary; }; //map teranry coordinate [a, b, c] to an [x, y] position ternary.point = function(coords){ var pos = [0,0]; var sum = d3.sum(coords); if(sum !== 0) { var normalized = coords.map( function(d){ return d/sum; } ); pos[0] = ternary.scale ( normalized[1] + normalized[2] / 2 ); pos[1] = ternary.scale ( height * normalized[0] + height * normalized[1] ); } return pos; }; //create an SVG path from a set of points ternary.line = function(coordsList, accessor, interpolator){ //path generator wrapper if(interpolator) line(interpolator) if(!accessor) accessor = function(d){ return d; } var positions = coordsList.map( function(d){ return ternary.point( accessor(d) ); }); return path(positions); }; ternary.rule = function(value, axis){ var ends = []; if(axis == 0){ ends = [ [value, 0, 100-value], [value, 100-value, 0] ]; }else if(axis == 1){ ends = [ [0, value, 100-value], [100-value, value, 0] ]; }else if(axis == 2){ ends = [ [0, 100-value, value], [100-value, 0, value] ]; } return ternary.line(ends); } // this inverse of point i.e. take an x,y positon and get the ternary coordinate ternary.getValues = function(pos){ // seems plausible now. pos = pos.map(ternary.scale.invert); var c = 1 - pos[1]*2/Math.sqrt(3); // cache altitude? var b = pos[0] - c/2; var a = 1 - b - c; return [a, b, c]; }; return ternary; }33:[] 2f:{"id":"e1ecfde5e5932e23","slug":"rps-matrix-to-isoclines","title":"RPS Matrix to Isoclines","thumbnail":"dcf3468d910891a61f7618ba1662c34d11b83f11bd4227fb520f508374755082","access_level":"public","create_time":"$D2018-10-07T19:21:59.328Z","update_time":"$D2019-01-06T02:24:20.580Z","view_time":null,"first_public_time":"$D2018-10-10T22:46:42.731Z","fork":false,"stars":1,"starred":false,"owner":{"type":"team","id":"43e035ce64fad801","login":"jazztap","name":"Jasmine Otto","avatar_url":"https://avatars-next.observableusercontent.com/1d847b962089e3524d821a011682b5ec09925cb269ab3f15456fb6e38e574bcc","tier":"starter_2024"},"version":830,"publish_version":830,"role":null,"authored":false,"authors":[{"type":"individual","id":"91a3f7bf83a60ddd","login":"jazztap","name":"Jasmine Otto","avatar_url":"https://avatars-next.observableusercontent.com/1d847b962089e3524d821a011682b5ec09925cb269ab3f15456fb6e38e574bcc","tier":null}],"members":[{"type":"individual","id":"91a3f7bf83a60ddd","login":"jazztap","name":"Jasmine Otto","avatar_url":"https://avatars-next.observableusercontent.com/1d847b962089e3524d821a011682b5ec09925cb269ab3f15456fb6e38e574bcc","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":0,"collection":{"id":"120791805dc1392c","slug":"lizard-browser","title":"lizard browser","owner":{"id":"43e035ce64fad801","login":"jazztap","name":"Jasmine Otto"}},"type":"notebook","body":{"title":"RPS Matrix to Isoclines","cells":[{"id":729,"value":"md`## RPS Matrix to Isoclines`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":53,"value":"ter = ternaryPlot().range([0,300]) // todo: interpret getValues([mouseX, mouseY])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":190,"value":"function times(A,B) { // matrix product (with no typechecking)\n let C = []\n for (let i = 0; i < A.length; ++i) {\n C.push([])\n for (let j = 0; j < B[0].length; ++j) {\n C[i].push(0)\n for (let k = 0; k < B.length; ++k)\n C[i][j] += A[i][k] * B[k][j]\n }\n }\n return C\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":246,"value":"function matWeight(A,B) { // hadamard (entrywise) product\n let C = []\n for (let i = 0; i < A.length; ++i) {\n C.push([])\n for (let j = 0; j < B[0].length; ++j) {\n C[i].push(A[i][j] * B[i][j])\n }\n }\n return C\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":186,"value":"W = [[1.0, .62, 2.23],\n [2.55, 1.0, 0.65],\n [0.91, 2.19, 1.0]]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":193,"value":"U = {\n return matWeight(W, [[b,a,a],[a,b,a],[a,a,b]])\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":257,"value":"function w(s) {\n // average payout of each strategy, with population 's'.\n return U.map(u => u.reduce((sum, v,j) => sum + v*s[j], 0))\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":261,"value":"function iso(i,j) {\n // find all s such that W_i.s == W_j.s\n // i.e. (W_i - W_j).s == 0\n \n function broadcast(f, u,v) {\n // f an elementwise operation.\n let n = u.length < v.length ? u.length : v.length\n return d3.range(n).map(i => f(u[i], v[i]))\n }\n let c = broadcast((u,v) => u-v, U[i], U[j])\n \n // suppose s[0] = 0, s[1] = 1. repeat.\n return [[0, 1, -c[1]/c[2]],\n [-c[2]/c[0], 0, 1],\n [1, -c[0]/c[1], 0]]\n // expect 3 samples along the 1d locus.\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":708,"value":"md`female tradeoff: preference for rarity (*a*) vs integrity of genotype (*b*)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":488,"value":"viewof a = slider({min: .5, max: 4.5, value: 1})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":623,"value":"viewof b = slider({min: .5, max: 4.5, value: 1})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":492,"value":"tex`\\left[ {\\begin{matrix} ${U.map(u => u.map(v => v.toFixed(2)).join(' & ')).join(' \\\\\\\\ ')} \\end{matrix}} \\right]`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":76,"value":"$31","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":347,"value":"data = [iso(0,1), iso(1,2), iso(2,0)] // [[1,1,0], [1,0,1]]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":8,"value":"clines = data.map((d,i) =>\n ter.line(d.filter(p => p.every(c => c > -0.1))) // 2 of 3 candidates lie in the triangle's extent.\n ) // [d[i], d[(i+1)%3]] // brittle, works while limit cycle exists","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":591,"value":"pts = trace.map(s => ter.point(T(s))) // [ter.point(data[0][0])]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":524,"value":"mutable strategy = [1,0,0]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":556,"value":"I = [[1,0,0],[0,1,0],[0,0,1]]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":549,"value":"function linWeight(coeffs, mats) {\n function scale(k, A) {\n return A.map(row => row.map(u => k*u))\n }\n let ret = []\n for (let i = 0; i < mats[0].length; ++i) {\n ret.push([])\n for (let j = 0; j < mats[0][0].length; ++j) {\n ret[i].push(0)\n for (let k = 0; k < coeffs.length; ++k)\n ret[i][j] += coeffs[k] * mats[k][i][j]\n }\n }\n return ret\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":580,"value":"function normalize(s) { // s a *column* vector\n let sum = s.reduce((sum, u) => sum+u[0], 0)\n return s.map(u => [u/sum])\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":633,"value":"function T(s) {\n return s.map(row => row[0])\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":538,"value":"trace = {\n let s = strategy.map(u => [u]), // as column vector\n game = U, // linWeight([.1, .9], [U, I]), // control step size\n trace = [s]\n \n let T = 20, dt = .05\n for (let t = 1; t < T/dt; ++t) {\n let r = times(game, s)\n s = s.map((x,i) => [(1 + r[i]*dt)*x] )\n \n s = normalize(s) // FIXME: clamp dynamics to appropriate radius.\n trace.push(s)\n }\n return trace\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":447,"value":"style = html``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":4,"value":"d3 = require('d3@5')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":486,"value":"import {slider} from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":23,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W33","stdlib":"1","titling":"auto"}} 30:"$2f:body"