2d:null 2e:["$","title",null,{"children":"Random Numbers and Dimensionality | quantlib.js | Observable"}] 33:T7c3,{ var mt = new ql.MersenneTwisterUniformRng().init1(42); var margin = { top: 20, right: 20, bottom: 30, left: 40 }, width = 500 - margin.left - margin.right, height = 500 - margin.top - margin.bottom; // DOM.svg() is a Observables specific convenience method which creates an SVG DOM element. const svg = d3 .select( DOM.svg( width + margin.left + margin.right, height + margin.top + margin.bottom ) ) .attr("transform", "translate(" + margin.left + "," + margin.top + ")") .style("overflow", "visible"); //Set up scales that we can use to draw the axes var x = d3 .scaleLinear() .domain([0.0, 1.0]) .range([0, width]); var y = d3 .scaleLinear() .domain([0.0, 1.0]) .range([height, 0]); //Setting up the axes var xAxis = d3 .axisBottom() .scale(x) .ticks(5); var yAxis = d3 .axisLeft() .scale(y) .ticks(5); //Add the axis to our svg element // x-axis svg .append("g") .attr("class", "x axis label") .attr("transform", "translate(" + 0 + "," + height + ")") .call(xAxis) .append("text") .text("x") .attr("x", width) .attr("y", -6) .attr("fill", "currentColor") .style("text-anchor", "end"); // y-axis svg .append("g") .attr("class", "y axis label") .call(yAxis) .append("text") .text("y") .attr("transform", "rotate(-90)") .attr("x", 6) .attr("y", 6) .attr("fill", "currentColor") .style("text-anchor", "end"); var dataset = []; for (var i = 0; i < 2048; i++) { dataset.push([mt.next().value, mt.next().value]); } svg .selectAll("circle") .data(dataset) .enter() .append("circle") .attr("cx", function(d) { return x(d[0]); }) .attr("cy", function(d) { return y(d[1]); }) .attr("r", 3); // Once we append the vis elments to it, we return the DOM element for Observable to display above. return svg.node(); }34:T7dd,{ var margin = { top: 20, right: 20, bottom: 30, left: 40 }, width = 500 - margin.left - margin.right, height = 500 - margin.top - margin.bottom; // DOM.svg() is a Observables specific convenience method which creates an SVG DOM element. const svg = d3 .select( DOM.svg( width + margin.left + margin.right, height + margin.top + margin.bottom ) ) .attr("transform", "translate(" + margin.left + "," + margin.top + ")") .style("overflow", "visible"); //Set up scales that we can use to draw the axes var x = d3 .scaleLinear() .domain([0.0, 1.0]) .range([0, width]); var y = d3 .scaleLinear() .domain([0.0, 1.0]) .range([height, 0]); //Setting up the axes var xAxis = d3 .axisBottom() .scale(x) .ticks(5); var yAxis = d3 .axisLeft() .scale(y) .ticks(5); //Add the axis to our svg element // x-axis svg .append("g") .attr("class", "x axis label") .attr("transform", "translate(" + 0 + "," + height + ")") .call(xAxis) .append("text") .text("x") .attr("x", width) .attr("y", -6) .attr("fill", "currentColor") .style("text-anchor", "end"); // y-axis svg .append("g") .attr("class", "y axis label") .call(yAxis) .append("text") .text("y") .attr("transform", "rotate(-90)") .attr("x", 6) .attr("y", 6) .attr("fill", "currentColor") .style("text-anchor", "end"); // sobol data set var rng = new ql.SobolRsg().init(1); var dataset = []; for (var i = 0; i < 2048; i++) { dataset.push([rng.nextSequence().value[0], rng.nextSequence().value[0]]); } svg .selectAll("circle") .data(dataset) .enter() .append("circle") .attr("cx", function(d) { return x(d[0]); }) .attr("cy", function(d) { return y(d[1]); }) .attr("r", 3); // Once we append the vis elments to it, we return the DOM element for Observable to display above. return svg.node(); }35:T7f7,{ var margin = { top: 20, right: 20, bottom: 30, left: 40 }, width = 500 - margin.left - margin.right, height = 500 - margin.top - margin.bottom; // DOM.svg() is a Observables specific convenience method which creates an SVG DOM element. const svg = d3 .select( DOM.svg( width + margin.left + margin.right, height + margin.top + margin.bottom ) ) .attr("transform", "translate(" + margin.left + "," + margin.top + ")") .style("overflow", "visible"); //Set up scales that we can use to draw the axes var x = d3 .scaleLinear() .domain([0.0, 1.0]) .range([0, width]); var y = d3 .scaleLinear() .domain([0.0, 1.0]) .range([height, 0]); //Setting up the axes var xAxis = d3 .axisBottom() .scale(x) .ticks(5); var yAxis = d3 .axisLeft() .scale(y) .ticks(5); //Add the axis to our svg element // x-axis svg .append("g") .attr("class", "x axis label") .attr("transform", "translate(" + 0 + "," + height + ")") .call(xAxis) .append("text") .text("x") .attr("x", width) .attr("y", -6) .attr("fill", "currentColor") .style("text-anchor", "end"); // y-axis svg .append("g") .attr("class", "y axis label") .call(yAxis) .append("text") .text("y") .attr("transform", "rotate(-90)") .attr("x", 6) .attr("y", 6) .attr("fill", "currentColor") .style("text-anchor", "end"); // sobol data set var rng = new ql.SobolRsg().init(2); var dataset = []; for (var i = 0; i < 2048; i++) { var seq = rng.nextSequence().value; dataset.push(JSON.parse(JSON.stringify([seq[0], seq[1]]))); } svg .selectAll("circle") .data(dataset) .enter() .append("circle") .attr("cx", function(d) { return x(d[0]); }) .attr("cy", function(d) { return y(d[1]); }) .attr("r", 3); // Once we append the vis elments to it, we return the DOM element for Observable to display above. return svg.node(); }36:T7f7,{ var margin = { top: 20, right: 20, bottom: 30, left: 40 }, width = 500 - margin.left - margin.right, height = 500 - margin.top - margin.bottom; // DOM.svg() is a Observables specific convenience method which creates an SVG DOM element. const svg = d3 .select( DOM.svg( width + margin.left + margin.right, height + margin.top + margin.bottom ) ) .attr("transform", "translate(" + margin.left + "," + margin.top + ")") .style("overflow", "visible"); //Set up scales that we can use to draw the axes var x = d3 .scaleLinear() .domain([0.0, 1.0]) .range([0, width]); var y = d3 .scaleLinear() .domain([0.0, 1.0]) .range([height, 0]); //Setting up the axes var xAxis = d3 .axisBottom() .scale(x) .ticks(5); var yAxis = d3 .axisLeft() .scale(y) .ticks(5); //Add the axis to our svg element // x-axis svg .append("g") .attr("class", "x axis label") .attr("transform", "translate(" + 0 + "," + height + ")") .call(xAxis) .append("text") .text("x") .attr("x", width) .attr("y", -6) .attr("fill", "currentColor") .style("text-anchor", "end"); // y-axis svg .append("g") .attr("class", "y axis label") .call(yAxis) .append("text") .text("y") .attr("transform", "rotate(-90)") .attr("x", 6) .attr("y", 6) .attr("fill", "currentColor") .style("text-anchor", "end"); // sobol data set var rng = new ql.SobolRsg().init(3); var dataset = []; for (var i = 0; i < 2048; i++) { var seq = rng.nextSequence().value; dataset.push(JSON.parse(JSON.stringify([seq[0], seq[1]]))); } svg .selectAll("circle") .data(dataset) .enter() .append("circle") .attr("cx", function(d) { return x(d[0]); }) .attr("cy", function(d) { return y(d[1]); }) .attr("r", 3); // Once we append the vis elments to it, we return the DOM element for Observable to display above. return svg.node(); }37:T7f7,{ var margin = { top: 20, right: 20, bottom: 30, left: 40 }, width = 500 - margin.left - margin.right, height = 500 - margin.top - margin.bottom; // DOM.svg() is a Observables specific convenience method which creates an SVG DOM element. const svg = d3 .select( DOM.svg( width + margin.left + margin.right, height + margin.top + margin.bottom ) ) .attr("transform", "translate(" + margin.left + "," + margin.top + ")") .style("overflow", "visible"); //Set up scales that we can use to draw the axes var x = d3 .scaleLinear() .domain([0.0, 1.0]) .range([0, width]); var y = d3 .scaleLinear() .domain([0.0, 1.0]) .range([height, 0]); //Setting up the axes var xAxis = d3 .axisBottom() .scale(x) .ticks(5); var yAxis = d3 .axisLeft() .scale(y) .ticks(5); //Add the axis to our svg element // x-axis svg .append("g") .attr("class", "x axis label") .attr("transform", "translate(" + 0 + "," + height + ")") .call(xAxis) .append("text") .text("x") .attr("x", width) .attr("y", -6) .attr("fill", "currentColor") .style("text-anchor", "end"); // y-axis svg .append("g") .attr("class", "y axis label") .call(yAxis) .append("text") .text("y") .attr("transform", "rotate(-90)") .attr("x", 6) .attr("y", 6) .attr("fill", "currentColor") .style("text-anchor", "end"); // sobol data set var rng = new ql.SobolRsg().init(3); var dataset = []; for (var i = 0; i < 2048; i++) { var seq = rng.nextSequence().value; dataset.push(JSON.parse(JSON.stringify([seq[0], seq[2]]))); } svg .selectAll("circle") .data(dataset) .enter() .append("circle") .attr("cx", function(d) { return x(d[0]); }) .attr("cy", function(d) { return y(d[1]); }) .attr("r", 3); // Once we append the vis elments to it, we return the DOM element for Observable to display above. return svg.node(); }38:T7f7,{ var margin = { top: 20, right: 20, bottom: 30, left: 40 }, width = 500 - margin.left - margin.right, height = 500 - margin.top - margin.bottom; // DOM.svg() is a Observables specific convenience method which creates an SVG DOM element. const svg = d3 .select( DOM.svg( width + margin.left + margin.right, height + margin.top + margin.bottom ) ) .attr("transform", "translate(" + margin.left + "," + margin.top + ")") .style("overflow", "visible"); //Set up scales that we can use to draw the axes var x = d3 .scaleLinear() .domain([0.0, 1.0]) .range([0, width]); var y = d3 .scaleLinear() .domain([0.0, 1.0]) .range([height, 0]); //Setting up the axes var xAxis = d3 .axisBottom() .scale(x) .ticks(5); var yAxis = d3 .axisLeft() .scale(y) .ticks(5); //Add the axis to our svg element // x-axis svg .append("g") .attr("class", "x axis label") .attr("transform", "translate(" + 0 + "," + height + ")") .call(xAxis) .append("text") .text("x") .attr("x", width) .attr("y", -6) .attr("fill", "currentColor") .style("text-anchor", "end"); // y-axis svg .append("g") .attr("class", "y axis label") .call(yAxis) .append("text") .text("y") .attr("transform", "rotate(-90)") .attr("x", 6) .attr("y", 6) .attr("fill", "currentColor") .style("text-anchor", "end"); // sobol data set var rng = new ql.SobolRsg().init(3); var dataset = []; for (var i = 0; i < 2048; i++) { var seq = rng.nextSequence().value; dataset.push(JSON.parse(JSON.stringify([seq[1], seq[2]]))); } svg .selectAll("circle") .data(dataset) .enter() .append("circle") .attr("cx", function(d) { return x(d[0]); }) .attr("cy", function(d) { return y(d[1]); }) .attr("r", 3); // Once we append the vis elments to it, we return the DOM element for Observable to display above. return svg.node(); }39:T801,{ var margin = { top: 20, right: 20, bottom: 30, left: 40 }, width = 500 - margin.left - margin.right, height = 500 - margin.top - margin.bottom; // DOM.svg() is a Observables specific convenience method which creates an SVG DOM element. const svg = d3 .select( DOM.svg( width + margin.left + margin.right, height + margin.top + margin.bottom ) ) .attr("transform", "translate(" + margin.left + "," + margin.top + ")") .style("overflow", "visible"); //Set up scales that we can use to draw the axes var x = d3 .scaleLinear() .domain([0.0, 1.0]) .range([0, width]); var y = d3 .scaleLinear() .domain([0.0, 1.0]) .range([height, 0]); //Setting up the axes var xAxis = d3 .axisBottom() .scale(x) .ticks(5); var yAxis = d3 .axisLeft() .scale(y) .ticks(5); //Add the axis to our svg element // x-axis svg .append("g") .attr("class", "x axis label") .attr("transform", "translate(" + 0 + "," + height + ")") .call(xAxis) .append("text") .text("x") .attr("x", width) .attr("y", -6) .attr("fill", "currentColor") .style("text-anchor", "end"); // y-axis svg .append("g") .attr("class", "y axis label") .call(yAxis) .append("text") .text("y") .attr("transform", "rotate(-90)") .attr("x", 6) .attr("y", 6) .attr("fill", "currentColor") .style("text-anchor", "end"); // sobol data set var rng = new ql.SobolRsg().init(5000, 242656); var dataset = []; for (var i = 0; i < 512; i++) { var seq = rng.nextSequence().value; dataset.push(JSON.parse(JSON.stringify([seq[0], seq[1]]))); } svg .selectAll("circle") .data(dataset) .enter() .append("circle") .attr("cx", function(d) { return x(d[0]); }) .attr("cy", function(d) { return y(d[1]); }) .attr("r", 3); // Once we append the vis elments to it, we return the DOM element for Observable to display above. return svg.node(); }3a:T807,{ var margin = { top: 20, right: 20, bottom: 30, left: 40 }, width = 500 - margin.left - margin.right, height = 500 - margin.top - margin.bottom; // DOM.svg() is a Observables specific convenience method which creates an SVG DOM element. const svg = d3 .select( DOM.svg( width + margin.left + margin.right, height + margin.top + margin.bottom ) ) .attr("transform", "translate(" + margin.left + "," + margin.top + ")") .style("overflow", "visible"); //Set up scales that we can use to draw the axes var x = d3 .scaleLinear() .domain([0.0, 1.0]) .range([0, width]); var y = d3 .scaleLinear() .domain([0.0, 1.0]) .range([height, 0]); //Setting up the axes var xAxis = d3 .axisBottom() .scale(x) .ticks(5); var yAxis = d3 .axisLeft() .scale(y) .ticks(5); //Add the axis to our svg element // x-axis svg .append("g") .attr("class", "x axis label") .attr("transform", "translate(" + 0 + "," + height + ")") .call(xAxis) .append("text") .text("x") .attr("x", width) .attr("y", -6) .attr("fill", "currentColor") .style("text-anchor", "end"); // y-axis svg .append("g") .attr("class", "y axis label") .call(yAxis) .append("text") .text("y") .attr("transform", "rotate(-90)") .attr("x", 6) .attr("y", 6) .attr("fill", "currentColor") .style("text-anchor", "end"); // sobol data set var rng = new ql.SobolRsg().init(5000, 242656); var dataset = []; for (var i = 0; i < 512; i++) { var seq = rng.nextSequence().value; dataset.push(JSON.parse(JSON.stringify([seq[2499], seq[2500]]))); } svg .selectAll("circle") .data(dataset) .enter() .append("circle") .attr("cx", function(d) { return x(d[0]); }) .attr("cy", function(d) { return y(d[1]); }) .attr("r", 3); // Once we append the vis elments to it, we return the DOM element for Observable to display above. return svg.node(); }3b:T807,{ var margin = { top: 20, right: 20, bottom: 30, left: 40 }, width = 500 - margin.left - margin.right, height = 500 - margin.top - margin.bottom; // DOM.svg() is a Observables specific convenience method which creates an SVG DOM element. const svg = d3 .select( DOM.svg( width + margin.left + margin.right, height + margin.top + margin.bottom ) ) .attr("transform", "translate(" + margin.left + "," + margin.top + ")") .style("overflow", "visible"); //Set up scales that we can use to draw the axes var x = d3 .scaleLinear() .domain([0.0, 1.0]) .range([0, width]); var y = d3 .scaleLinear() .domain([0.0, 1.0]) .range([height, 0]); //Setting up the axes var xAxis = d3 .axisBottom() .scale(x) .ticks(5); var yAxis = d3 .axisLeft() .scale(y) .ticks(5); //Add the axis to our svg element // x-axis svg .append("g") .attr("class", "x axis label") .attr("transform", "translate(" + 0 + "," + height + ")") .call(xAxis) .append("text") .text("x") .attr("x", width) .attr("y", -6) .attr("fill", "currentColor") .style("text-anchor", "end"); // y-axis svg .append("g") .attr("class", "y axis label") .call(yAxis) .append("text") .text("y") .attr("transform", "rotate(-90)") .attr("x", 6) .attr("y", 6) .attr("fill", "currentColor") .style("text-anchor", "end"); // sobol data set var rng = new ql.SobolRsg().init(5000, 242656); var dataset = []; for (var i = 0; i < 512; i++) { var seq = rng.nextSequence().value; dataset.push(JSON.parse(JSON.stringify([seq[4998], seq[4999]]))); } svg .selectAll("circle") .data(dataset) .enter() .append("circle") .attr("cx", function(d) { return x(d[0]); }) .attr("cy", function(d) { return y(d[1]); }) .attr("r", 3); // Once we append the vis elments to it, we return the DOM element for Observable to display above. return svg.node(); }3c:T807,{ var margin = { top: 20, right: 20, bottom: 30, left: 40 }, width = 500 - margin.left - margin.right, height = 500 - margin.top - margin.bottom; // DOM.svg() is a Observables specific convenience method which creates an SVG DOM element. const svg = d3 .select( DOM.svg( width + margin.left + margin.right, height + margin.top + margin.bottom ) ) .attr("transform", "translate(" + margin.left + "," + margin.top + ")") .style("overflow", "visible"); //Set up scales that we can use to draw the axes var x = d3 .scaleLinear() .domain([0.0, 1.0]) .range([0, width]); var y = d3 .scaleLinear() .domain([0.0, 1.0]) .range([height, 0]); //Setting up the axes var xAxis = d3 .axisBottom() .scale(x) .ticks(5); var yAxis = d3 .axisLeft() .scale(y) .ticks(5); //Add the axis to our svg element // x-axis svg .append("g") .attr("class", "x axis label") .attr("transform", "translate(" + 0 + "," + height + ")") .call(xAxis) .append("text") .text("x") .attr("x", width) .attr("y", -6) .attr("fill", "currentColor") .style("text-anchor", "end"); // y-axis svg .append("g") .attr("class", "y axis label") .call(yAxis) .append("text") .text("y") .attr("transform", "rotate(-90)") .attr("x", 6) .attr("y", 6) .attr("fill", "currentColor") .style("text-anchor", "end"); // sobol data set var rng = new ql.SobolRsg().init(5000, 242656); var dataset = []; for (var i = 0; i < 512; i++) { var seq = rng.nextSequence().value; dataset.push(JSON.parse(JSON.stringify([seq[1738], seq[2889]]))); } svg .selectAll("circle") .data(dataset) .enter() .append("circle") .attr("cx", function(d) { return x(d[0]); }) .attr("cy", function(d) { return y(d[1]); }) .attr("r", 3); // Once we append the vis elments to it, we return the DOM element for Observable to display above. return svg.node(); }3d:T807,{ var margin = { top: 20, right: 20, bottom: 30, left: 40 }, width = 500 - margin.left - margin.right, height = 500 - margin.top - margin.bottom; // DOM.svg() is a Observables specific convenience method which creates an SVG DOM element. const svg = d3 .select( DOM.svg( width + margin.left + margin.right, height + margin.top + margin.bottom ) ) .attr("transform", "translate(" + margin.left + "," + margin.top + ")") .style("overflow", "visible"); //Set up scales that we can use to draw the axes var x = d3 .scaleLinear() .domain([0.0, 1.0]) .range([0, width]); var y = d3 .scaleLinear() .domain([0.0, 1.0]) .range([height, 0]); //Setting up the axes var xAxis = d3 .axisBottom() .scale(x) .ticks(5); var yAxis = d3 .axisLeft() .scale(y) .ticks(5); //Add the axis to our svg element // x-axis svg .append("g") .attr("class", "x axis label") .attr("transform", "translate(" + 0 + "," + height + ")") .call(xAxis) .append("text") .text("x") .attr("x", width) .attr("y", -6) .attr("fill", "currentColor") .style("text-anchor", "end"); // y-axis svg .append("g") .attr("class", "y axis label") .call(yAxis) .append("text") .text("y") .attr("transform", "rotate(-90)") .attr("x", 6) .attr("y", 6) .attr("fill", "currentColor") .style("text-anchor", "end"); // sobol data set var rng = new ql.SobolRsg().init(5000, 242656); var dataset = []; for (var i = 0; i < 512; i++) { var seq = rng.nextSequence().value; dataset.push(JSON.parse(JSON.stringify([seq[2295], seq[4350]]))); } svg .selectAll("circle") .data(dataset) .enter() .append("circle") .attr("cx", function(d) { return x(d[0]); }) .attr("cy", function(d) { return y(d[1]); }) .attr("r", 3); // Once we append the vis elments to it, we return the DOM element for Observable to display above. return svg.node(); }3e:T806,{ var margin = { top: 20, right: 20, bottom: 30, left: 40 }, width = 500 - margin.left - margin.right, height = 500 - margin.top - margin.bottom; // DOM.svg() is a Observables specific convenience method which creates an SVG DOM element. const svg = d3 .select( DOM.svg( width + margin.left + margin.right, height + margin.top + margin.bottom ) ) .attr("transform", "translate(" + margin.left + "," + margin.top + ")") .style("overflow", "visible"); //Set up scales that we can use to draw the axes var x = d3 .scaleLinear() .domain([0.0, 1.0]) .range([0, width]); var y = d3 .scaleLinear() .domain([0.0, 1.0]) .range([height, 0]); //Setting up the axes var xAxis = d3 .axisBottom() .scale(x) .ticks(5); var yAxis = d3 .axisLeft() .scale(y) .ticks(5); //Add the axis to our svg element // x-axis svg .append("g") .attr("class", "x axis label") .attr("transform", "translate(" + 0 + "," + height + ")") .call(xAxis) .append("text") .text("x") .attr("x", width) .attr("y", -6) .attr("fill", "currentColor") .style("text-anchor", "end"); // y-axis svg .append("g") .attr("class", "y axis label") .call(yAxis) .append("text") .text("y") .attr("transform", "rotate(-90)") .attr("x", 6) .attr("y", 6) .attr("fill", "currentColor") .style("text-anchor", "end"); // sobol data set var rng = new ql.SobolRsg().init(5000, 242656); var dataset = []; for (var i = 0; i < 512; i++) { var seq = rng.nextSequence().value; dataset.push(JSON.parse(JSON.stringify([seq[429], seq[3944]]))); } svg .selectAll("circle") .data(dataset) .enter() .append("circle") .attr("cx", function(d) { return x(d[0]); }) .attr("cy", function(d) { return y(d[1]); }) .attr("r", 3); // Once we append the vis elments to it, we return the DOM element for Observable to display above. return svg.node(); }3f:T81c,{ var mt = new ql.MersenneTwisterUniformRng().init1(42); var margin = { top: 20, right: 20, bottom: 30, left: 40 }, width = 500 - margin.left - margin.right, height = 500 - margin.top - margin.bottom; // DOM.svg() is a Observables specific convenience method which creates an SVG DOM element. const svg = d3 .select( DOM.svg( width + margin.left + margin.right, height + margin.top + margin.bottom ) ) .attr("transform", "translate(" + margin.left + "," + margin.top + ")") .style("overflow", "visible"); //Set up scales that we can use to draw the axes var x = d3 .scaleLinear() .domain([0.0, 1.0]) .range([0, width]); var y = d3 .scaleLinear() .domain([0.0, 1.0]) .range([height, 0]); //Setting up the axes var xAxis = d3 .axisBottom() .scale(x) .ticks(5); var yAxis = d3 .axisLeft() .scale(y) .ticks(5); //Add the axis to our svg element // x-axis svg .append("g") .attr("class", "x axis label") .attr("transform", "translate(" + 0 + "," + height + ")") .call(xAxis) .append("text") .text("x") .attr("x", width) .attr("y", -6) .attr("fill", "currentColor") .style("text-anchor", "end"); // y-axis svg .append("g") .attr("class", "y axis label") .call(yAxis) .append("text") .text("y") .attr("transform", "rotate(-90)") .attr("x", 6) .attr("y", 6) .attr("fill", "currentColor") .style("text-anchor", "end"); var dataset = []; for (var i = 0; i < 512; i++) { var xs = new Array(5000); for (let j = 0; j < 5000; j++) { xs[j] = mt.next().value; } dataset.push([xs[1738], xs[2889]]); } svg .selectAll("circle") .data(dataset) .enter() .append("circle") .attr("cx", function(d) { return x(d[0]); }) .attr("cy", function(d) { return y(d[1]); }) .attr("r", 3); // Once we append the vis elments to it, we return the DOM element for Observable to display above. return svg.node(); }40:T81c,{ var mt = new ql.MersenneTwisterUniformRng().init1(42); var margin = { top: 20, right: 20, bottom: 30, left: 40 }, width = 500 - margin.left - margin.right, height = 500 - margin.top - margin.bottom; // DOM.svg() is a Observables specific convenience method which creates an SVG DOM element. const svg = d3 .select( DOM.svg( width + margin.left + margin.right, height + margin.top + margin.bottom ) ) .attr("transform", "translate(" + margin.left + "," + margin.top + ")") .style("overflow", "visible"); //Set up scales that we can use to draw the axes var x = d3 .scaleLinear() .domain([0.0, 1.0]) .range([0, width]); var y = d3 .scaleLinear() .domain([0.0, 1.0]) .range([height, 0]); //Setting up the axes var xAxis = d3 .axisBottom() .scale(x) .ticks(5); var yAxis = d3 .axisLeft() .scale(y) .ticks(5); //Add the axis to our svg element // x-axis svg .append("g") .attr("class", "x axis label") .attr("transform", "translate(" + 0 + "," + height + ")") .call(xAxis) .append("text") .text("x") .attr("x", width) .attr("y", -6) .attr("fill", "currentColor") .style("text-anchor", "end"); // y-axis svg .append("g") .attr("class", "y axis label") .call(yAxis) .append("text") .text("y") .attr("transform", "rotate(-90)") .attr("x", 6) .attr("y", 6) .attr("fill", "currentColor") .style("text-anchor", "end"); var dataset = []; for (var i = 0; i < 512; i++) { var xs = new Array(5000); for (let j = 0; j < 5000; j++) { xs[j] = mt.next().value; } dataset.push([xs[2295], xs[4350]]); } svg .selectAll("circle") .data(dataset) .enter() .append("circle") .attr("cx", function(d) { return x(d[0]); }) .attr("cy", function(d) { return y(d[1]); }) .attr("r", 3); // Once we append the vis elments to it, we return the DOM element for Observable to display above. return svg.node(); }41:T81b,{ var mt = new ql.MersenneTwisterUniformRng().init1(42); var margin = { top: 20, right: 20, bottom: 30, left: 40 }, width = 500 - margin.left - margin.right, height = 500 - margin.top - margin.bottom; // DOM.svg() is a Observables specific convenience method which creates an SVG DOM element. const svg = d3 .select( DOM.svg( width + margin.left + margin.right, height + margin.top + margin.bottom ) ) .attr("transform", "translate(" + margin.left + "," + margin.top + ")") .style("overflow", "visible"); //Set up scales that we can use to draw the axes var x = d3 .scaleLinear() .domain([0.0, 1.0]) .range([0, width]); var y = d3 .scaleLinear() .domain([0.0, 1.0]) .range([height, 0]); //Setting up the axes var xAxis = d3 .axisBottom() .scale(x) .ticks(5); var yAxis = d3 .axisLeft() .scale(y) .ticks(5); //Add the axis to our svg element // x-axis svg .append("g") .attr("class", "x axis label") .attr("transform", "translate(" + 0 + "," + height + ")") .call(xAxis) .append("text") .text("x") .attr("x", width) .attr("y", -6) .attr("fill", "currentColor") .style("text-anchor", "end"); // y-axis svg .append("g") .attr("class", "y axis label") .call(yAxis) .append("text") .text("y") .attr("transform", "rotate(-90)") .attr("x", 6) .attr("y", 6) .attr("fill", "currentColor") .style("text-anchor", "end"); var dataset = []; for (var i = 0; i < 512; i++) { var xs = new Array(5000); for (let j = 0; j < 5000; j++) { xs[j] = mt.next().value; } dataset.push([xs[429], xs[3944]]); } svg .selectAll("circle") .data(dataset) .enter() .append("circle") .attr("cx", function(d) { return x(d[0]); }) .attr("cy", function(d) { return y(d[1]); }) .attr("r", 3); // Once we append the vis elments to it, we return the DOM element for Observable to display above. return svg.node(); }42:[] 31:{"id":"fb240bfc888da4e6","slug":"random-numbers-and-dimensionality","title":"Random Numbers and Dimensionality","thumbnail":"16b485e3ba10ce2deb0c96bdc2b0d9483170bf3262be9883c6bd5d3b98f57191","access_level":"public","create_time":"$D2019-09-13T13:23:59.591Z","update_time":"$D2019-10-07T14:01:13.986Z","view_time":null,"first_public_time":"$D2019-09-13T13:25:56.715Z","has_unpublished_edits":null,"fork":true,"stars":1,"starred":false,"owner":{"type":"team","id":"cdcb47b381942417","login":"quantlib","name":"quantlib.js","avatar_url":"https://avatars-next.observableusercontent.com/29b2ae735eb49fcd254065a6333b9938347cc517e3d57037a5c0d202cc14f0e2","tier":"starter_2024"},"version":211,"publish_version":211,"role":null,"authored":false,"authors":[{"type":"individual","id":"e3ecc7677c479d36","login":"quantlib","name":"quantlib.js","avatar_url":"https://avatars-next.observableusercontent.com/29b2ae735eb49fcd254065a6333b9938347cc517e3d57037a5c0d202cc14f0e2","tier":null}],"members":[{"type":"individual","id":"e3ecc7677c479d36","login":"quantlib","name":"quantlib.js","avatar_url":"https://avatars-next.observableusercontent.com/29b2ae735eb49fcd254065a6333b9938347cc517e3d57037a5c0d202cc14f0e2","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":3,"collection":null,"type":"notebook","body":{"title":"Random Numbers and Dimensionality","cells":[{"id":0,"value":"md`# Random Numbers and Dimensionality`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":29,"value":"ql = import('https://cdn.jsdelivr.net/npm/@quantlib/ql@latest/ql.mjs');","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":9,"value":"d3 = require(\"d3@5\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":59,"value":"md `## Converting a unit square\nThe dimensionality of the problem is 2. With pseudo-random numbers, it doesn't matter much; we can just extract numbers and form pairs from them`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":62,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":79,"value":"md `The same doesn't hold for quasi-random numbers. Each number is correlated to the one that follows it, which ruins the random properties of sequence when used with wrong dimensionality`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":19,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":84,"value":"md `To cover the domain correctly, we have to use the right dimensionality`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":88,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":91,"value":"md `## High dimensionality and quality of randomness\nQuasi-random numbers with hight dimensionality are known to have better randomness in the first components of generated sequences and worse in the last ones. This is not a problem with low numberof dimensions...`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":96,"value":"$36","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":103,"value":"$37","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":105,"value":"$38","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":108,"value":"md `...but with high number of dimensions and not enough draws, it can cause some subspaces to be covered incorrectly`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":113,"value":"$39","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":115,"value":"$3a","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":117,"value":"$3b","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":119,"value":"$3c","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":121,"value":"$3d","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":123,"value":"$3e","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":125,"value":"md `...with pseudo-random numbers, we'd have bad statistics but at least the points would be scatter around randomly`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":128,"value":"$3f","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":132,"value":"$40","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":134,"value":"$41","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W42","stdlib":"1","titling":"auto"}} 32:"$31:body"