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mathjs

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Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser with support for symbolic computation, comes with a large set of built-in functions and constants, and offers an integrated solution to work with dif

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import { deepMap } from '../../utils/collection.js'; import { factory } from '../../utils/factory.js'; import { gammaG, gammaNumber, gammaP } from '../../plain/number/index.js'; var name = 'gamma'; var dependencies = ['typed', 'config', 'multiplyScalar', 'pow', 'BigNumber', 'Complex']; export var createGamma = /* #__PURE__ */factory(name, dependencies, _ref => { var { typed, config, multiplyScalar, pow, BigNumber: _BigNumber, Complex: _Complex } = _ref; /** * Compute the gamma function of a value using Lanczos approximation for * small values, and an extended Stirling approximation for large values. * * For matrices, the function is evaluated element wise. * * Syntax: * * math.gamma(n) * * Examples: * * math.gamma(5) // returns 24 * math.gamma(-0.5) // returns -3.5449077018110335 * math.gamma(math.i) // returns -0.15494982830180973 - 0.49801566811835596i * * See also: * * combinations, factorial, permutations * * @param {number | Array | Matrix} n A real or complex number * @return {number | Array | Matrix} The gamma of `n` */ return typed(name, { number: gammaNumber, Complex: function Complex(n) { if (n.im === 0) { return this(n.re); } n = new _Complex(n.re - 1, n.im); var x = new _Complex(gammaP[0], 0); for (var i = 1; i < gammaP.length; ++i) { var real = n.re + i; // x += p[i]/(n+i) var den = real * real + n.im * n.im; if (den !== 0) { x.re += gammaP[i] * real / den; x.im += -(gammaP[i] * n.im) / den; } else { x.re = gammaP[i] < 0 ? -Infinity : Infinity; } } var t = new _Complex(n.re + gammaG + 0.5, n.im); var twoPiSqrt = Math.sqrt(2 * Math.PI); n.re += 0.5; var result = pow(t, n); if (result.im === 0) { // sqrt(2*PI)*result result.re *= twoPiSqrt; } else if (result.re === 0) { result.im *= twoPiSqrt; } else { result.re *= twoPiSqrt; result.im *= twoPiSqrt; } var r = Math.exp(-t.re); // exp(-t) t.re = r * Math.cos(-t.im); t.im = r * Math.sin(-t.im); return multiplyScalar(multiplyScalar(result, t), x); }, BigNumber: function BigNumber(n) { if (n.isInteger()) { return n.isNegative() || n.isZero() ? new _BigNumber(Infinity) : bigFactorial(n.minus(1)); } if (!n.isFinite()) { return new _BigNumber(n.isNegative() ? NaN : Infinity); } throw new Error('Integer BigNumber expected'); }, 'Array | Matrix': function ArrayMatrix(n) { return deepMap(n, this); } }); /** * Calculate factorial for a BigNumber * @param {BigNumber} n * @returns {BigNumber} Returns the factorial of n */ function bigFactorial(n) { if (n < 8) { return new _BigNumber([1, 1, 2, 6, 24, 120, 720, 5040][n]); } var precision = config.precision + (Math.log(n.toNumber()) | 0); var Big = _BigNumber.clone({ precision: precision }); if (n % 2 === 1) { return n.times(bigFactorial(new _BigNumber(n - 1))); } var p = n; var prod = new Big(n); var sum = n.toNumber(); while (p > 2) { p -= 2; sum += p; prod = prod.times(sum); } return new _BigNumber(prod.toPrecision(_BigNumber.precision)); } });