129 lines
3.7 KiB
JavaScript
129 lines
3.7 KiB
JavaScript
import { deepMap } from '../../utils/collection.js';
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import { factory } from '../../utils/factory.js';
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import { gammaG, gammaNumber, gammaP } from '../../plain/number/index.js';
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var name = 'gamma';
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var dependencies = ['typed', 'config', 'multiplyScalar', 'pow', 'BigNumber', 'Complex'];
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export var createGamma = /* #__PURE__ */factory(name, dependencies, _ref => {
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var {
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typed,
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config,
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multiplyScalar,
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pow,
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BigNumber: _BigNumber,
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Complex: _Complex
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} = _ref;
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/**
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* Compute the gamma function of a value using Lanczos approximation for
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* small values, and an extended Stirling approximation for large values.
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*
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* For matrices, the function is evaluated element wise.
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*
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* Syntax:
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*
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* math.gamma(n)
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*
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* Examples:
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*
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* math.gamma(5) // returns 24
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* math.gamma(-0.5) // returns -3.5449077018110335
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* math.gamma(math.i) // returns -0.15494982830180973 - 0.49801566811835596i
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*
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* See also:
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*
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* combinations, factorial, permutations
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*
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* @param {number | Array | Matrix} n A real or complex number
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* @return {number | Array | Matrix} The gamma of `n`
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*/
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return typed(name, {
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number: gammaNumber,
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Complex: function Complex(n) {
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if (n.im === 0) {
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return this(n.re);
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} // Lanczos approximation doesn't work well with real part lower than 0.5
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// So reflection formula is required
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if (n.re < 0.5) {
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// Euler's reflection formula
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// gamma(1-z) * gamma(z) = PI / sin(PI * z)
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// real part of Z should not be integer [sin(PI) == 0 -> 1/0 - undefined]
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// thanks to imperfect sin implementation sin(PI * n) != 0
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// we can safely use it anyway
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var _t = new _Complex(1 - n.re, -n.im);
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var r = new _Complex(Math.PI * n.re, Math.PI * n.im);
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return new _Complex(Math.PI).div(r.sin()).div(this(_t));
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} // Lanczos approximation
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// z -= 1
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n = new _Complex(n.re - 1, n.im); // x = gammaPval[0]
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var x = new _Complex(gammaP[0], 0); // for (i, gammaPval) in enumerate(gammaP):
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for (var i = 1; i < gammaP.length; ++i) {
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// x += gammaPval / (z + i)
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var gammaPval = new _Complex(gammaP[i], 0);
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x = x.add(gammaPval.div(n.add(i)));
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} // t = z + gammaG + 0.5
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var t = new _Complex(n.re + gammaG + 0.5, n.im); // y = sqrt(2 * pi) * t ** (z + 0.5) * exp(-t) * x
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var twoPiSqrt = Math.sqrt(2 * Math.PI);
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var tpow = t.pow(n.add(0.5));
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var expt = t.neg().exp(); // y = [x] * [sqrt(2 * pi)] * [t ** (z + 0.5)] * [exp(-t)]
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return x.mul(twoPiSqrt).mul(tpow).mul(expt);
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},
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BigNumber: function BigNumber(n) {
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if (n.isInteger()) {
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return n.isNegative() || n.isZero() ? new _BigNumber(Infinity) : bigFactorial(n.minus(1));
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}
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if (!n.isFinite()) {
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return new _BigNumber(n.isNegative() ? NaN : Infinity);
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}
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throw new Error('Integer BigNumber expected');
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},
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'Array | Matrix': function ArrayMatrix(n) {
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return deepMap(n, this);
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}
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});
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/**
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* Calculate factorial for a BigNumber
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* @param {BigNumber} n
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* @returns {BigNumber} Returns the factorial of n
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*/
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function bigFactorial(n) {
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if (n < 8) {
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return new _BigNumber([1, 1, 2, 6, 24, 120, 720, 5040][n]);
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}
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var precision = config.precision + (Math.log(n.toNumber()) | 0);
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var Big = _BigNumber.clone({
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precision: precision
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});
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if (n % 2 === 1) {
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return n.times(bigFactorial(new _BigNumber(n - 1)));
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}
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var p = n;
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var prod = new Big(n);
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var sum = n.toNumber();
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while (p > 2) {
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p -= 2;
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sum += p;
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prod = prod.times(sum);
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}
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return new _BigNumber(prod.toPrecision(_BigNumber.precision));
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}
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}); |