Published
Edited
Nov 28, 2020
3 forks
Importers
19 stars
Seat optimization by simulated annealing algorithmSIR simulation of infection (WebGL)Babylonian method visualized - computing sqrtSupertoroidUmbilic TorusBilinear interpolation of tileBox-Muller transformBroken Calabi-Yau Manifold 3DCircle InversionCalabi-Yau Manifold 3D
Multivariate Normal Distribution
function multivariateNormal(mean, covArray) {
const n = mean.length;
const cov = math.matrix(covArray);
return {
// Probability Density Function
pdf: x => {
const c = 1 / (math.sqrt(2*math.PI)**n * math.sqrt(math.det(cov)));
return c * math.exp(
-(1/2) * math.multiply(
math.subtract(math.matrix(x), math.matrix(mean)),
math.inv(cov),
math.subtract(math.matrix(x), math.matrix(mean))
)
);
},
// Differential entropy
entropy: 0.5*math.log(math.det(cov)) + 0.5*n*(1 + math.log(2*math.PI)),
// Generate n samples using Cholesky Decomposition
sample: n_samples => Array(n_samples).fill().map(_ => {
const L = choleskyDecomposition(cov);
const z = boxMuller(n);
return math.add(
math.matrix(mean),
math.multiply(cov, math.matrix(z))
).toArray();
}),
};
}
// Usage example
{
const norm = multivariateNormal([0, 0], [[1, 0], [0, 2]]);
return [norm.entropy, norm.pdf([0, 0]), norm.sample(3)]
}
A = math.matrix([[1, cov12], [cov12, v2]])
// mean: [0, 0]
normal = multivariateNormal([0, 0], A)
samples2D = normal.sample(1000).map(d => ({x: d[0], y: d[1]}))
import {chart as densityChart} with {samples2D as data} from "@sw1227/fork-density-contours"
// Values of PDF in x: (-5, 5), y: (-5, 5)
data = d3.range(-5, 5, 0.1).map(y => (
d3.range(-5, 5, 0.1).map(x => (
normal.pdf([x, y])
))
))
imshow(data.reverse(), Math.min(width/100, 4), d3.interpolateViridis)
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