75 lines
2.8 KiB
JavaScript
75 lines
2.8 KiB
JavaScript
/* eslint-disable no-loss-of-precision */
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import { isInteger } from '../../utils/number.js';
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import { product } from '../../utils/product.js';
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export function gammaNumber(n) {
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var x;
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if (isInteger(n)) {
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if (n <= 0) {
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return isFinite(n) ? Infinity : NaN;
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}
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if (n > 171) {
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return Infinity; // Will overflow
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}
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return product(1, n - 1);
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}
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if (n < 0.5) {
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return Math.PI / (Math.sin(Math.PI * n) * gammaNumber(1 - n));
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}
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if (n >= 171.35) {
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return Infinity; // will overflow
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}
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if (n > 85.0) {
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// Extended Stirling Approx
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var twoN = n * n;
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var threeN = twoN * n;
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var fourN = threeN * n;
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var fiveN = fourN * n;
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return Math.sqrt(2 * Math.PI / n) * Math.pow(n / Math.E, n) * (1 + 1 / (12 * n) + 1 / (288 * twoN) - 139 / (51840 * threeN) - 571 / (2488320 * fourN) + 163879 / (209018880 * fiveN) + 5246819 / (75246796800 * fiveN * n));
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}
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--n;
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x = gammaP[0];
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for (var i = 1; i < gammaP.length; ++i) {
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x += gammaP[i] / (n + i);
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}
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var t = n + gammaG + 0.5;
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return Math.sqrt(2 * Math.PI) * Math.pow(t, n + 0.5) * Math.exp(-t) * x;
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}
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gammaNumber.signature = 'number';
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// TODO: comment on the variables g and p
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export var gammaG = 4.7421875;
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export var gammaP = [0.99999999999999709182, 57.156235665862923517, -59.597960355475491248, 14.136097974741747174, -0.49191381609762019978, 0.33994649984811888699e-4, 0.46523628927048575665e-4, -0.98374475304879564677e-4, 0.15808870322491248884e-3, -0.21026444172410488319e-3, 0.21743961811521264320e-3, -0.16431810653676389022e-3, 0.84418223983852743293e-4, -0.26190838401581408670e-4, 0.36899182659531622704e-5];
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// lgamma implementation ref: https://mrob.com/pub/ries/lanczos-gamma.html#code
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// log(2 * pi) / 2
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export var lnSqrt2PI = 0.91893853320467274178;
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export var lgammaG = 5; // Lanczos parameter "g"
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export var lgammaN = 7; // Range of coefficients "n"
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export var lgammaSeries = [1.000000000190015, 76.18009172947146, -86.50532032941677, 24.01409824083091, -1.231739572450155, 0.1208650973866179e-2, -0.5395239384953e-5];
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export function lgammaNumber(n) {
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if (n < 0) return NaN;
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if (n === 0) return Infinity;
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if (!isFinite(n)) return n;
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if (n < 0.5) {
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// Use Euler's reflection formula:
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// gamma(z) = PI / (sin(PI * z) * gamma(1 - z))
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return Math.log(Math.PI / Math.sin(Math.PI * n)) - lgammaNumber(1 - n);
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}
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// Compute the logarithm of the Gamma function using the Lanczos method
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n = n - 1;
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var base = n + lgammaG + 0.5; // Base of the Lanczos exponential
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var sum = lgammaSeries[0];
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// We start with the terms that have the smallest coefficients and largest denominator
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for (var i = lgammaN - 1; i >= 1; i--) {
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sum += lgammaSeries[i] / (n + i);
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}
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return lnSqrt2PI + (n + 0.5) * Math.log(base) - base + Math.log(sum);
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}
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lgammaNumber.signature = 'number'; |