feat:node-modules

node_modules/mathjs/lib/esm/function/special/erf.js

@@ -0,0 +1,155 @@
+/* eslint-disable no-loss-of-precision */
+
+import { deepMap } from '../../utils/collection.js';
+import { sign } from '../../utils/number.js';
+import { factory } from '../../utils/factory.js';
+var name = 'erf';
+var dependencies = ['typed'];
+export var createErf = /* #__PURE__ */factory(name, dependencies, _ref => {
+  var {
+    typed
+  } = _ref;
+  /**
+   * Compute the erf function of a value using a rational Chebyshev
+   * approximations for different intervals of x.
+   *
+   * This is a translation of W. J. Cody's Fortran implementation from 1987
+   * ( https://www.netlib.org/specfun/erf ). See the AMS publication
+   * "Rational Chebyshev Approximations for the Error Function" by W. J. Cody
+   * for an explanation of this process.
+   *
+   * For matrices, the function is evaluated element wise.
+   *
+   * Syntax:
+   *
+   *    math.erf(x)
+   *
+   * Examples:
+   *
+   *    math.erf(0.2)    // returns 0.22270258921047847
+   *    math.erf(-0.5)   // returns -0.5204998778130465
+   *    math.erf(4)      // returns 0.9999999845827421
+   *
+   * See also:
+   *    zeta
+   *
+   * @param {number | Array | Matrix} x   A real number
+   * @return {number | Array | Matrix}    The erf of `x`
+   */
+  return typed('name', {
+    number: function number(x) {
+      var y = Math.abs(x);
+      if (y >= MAX_NUM) {
+        return sign(x);
+      }
+      if (y <= THRESH) {
+        return sign(x) * erf1(y);
+      }
+      if (y <= 4.0) {
+        return sign(x) * (1 - erfc2(y));
+      }
+      return sign(x) * (1 - erfc3(y));
+    },
+    'Array | Matrix': typed.referToSelf(self => n => deepMap(n, self))
+
+    // TODO: For complex numbers, use the approximation for the Faddeeva function
+    //  from "More Efficient Computation of the Complex Error Function" (AMS)
+  });
+
+  /**
+   * Approximates the error function erf() for x <= 0.46875 using this function:
+   *               n
+   * erf(x) = x * sum (p_j * x^(2j)) / (q_j * x^(2j))
+   *              j=0
+   */
+  function erf1(y) {
+    var ysq = y * y;
+    var xnum = P[0][4] * ysq;
+    var xden = ysq;
+    var i;
+    for (i = 0; i < 3; i += 1) {
+      xnum = (xnum + P[0][i]) * ysq;
+      xden = (xden + Q[0][i]) * ysq;
+    }
+    return y * (xnum + P[0][3]) / (xden + Q[0][3]);
+  }
+
+  /**
+   * Approximates the complement of the error function erfc() for
+   * 0.46875 <= x <= 4.0 using this function:
+   *                       n
+   * erfc(x) = e^(-x^2) * sum (p_j * x^j) / (q_j * x^j)
+   *                      j=0
+   */
+  function erfc2(y) {
+    var xnum = P[1][8] * y;
+    var xden = y;
+    var i;
+    for (i = 0; i < 7; i += 1) {
+      xnum = (xnum + P[1][i]) * y;
+      xden = (xden + Q[1][i]) * y;
+    }
+    var result = (xnum + P[1][7]) / (xden + Q[1][7]);
+    var ysq = parseInt(y * 16) / 16;
+    var del = (y - ysq) * (y + ysq);
+    return Math.exp(-ysq * ysq) * Math.exp(-del) * result;
+  }
+
+  /**
+   * Approximates the complement of the error function erfc() for x > 4.0 using
+   * this function:
+   *
+   * erfc(x) = (e^(-x^2) / x) * [ 1/sqrt(pi) +
+   *               n
+   *    1/(x^2) * sum (p_j * x^(-2j)) / (q_j * x^(-2j)) ]
+   *              j=0
+   */
+  function erfc3(y) {
+    var ysq = 1 / (y * y);
+    var xnum = P[2][5] * ysq;
+    var xden = ysq;
+    var i;
+    for (i = 0; i < 4; i += 1) {
+      xnum = (xnum + P[2][i]) * ysq;
+      xden = (xden + Q[2][i]) * ysq;
+    }
+    var result = ysq * (xnum + P[2][4]) / (xden + Q[2][4]);
+    result = (SQRPI - result) / y;
+    ysq = parseInt(y * 16) / 16;
+    var del = (y - ysq) * (y + ysq);
+    return Math.exp(-ysq * ysq) * Math.exp(-del) * result;
+  }
+});
+
+/**
+ * Upper bound for the first approximation interval, 0 <= x <= THRESH
+ * @constant
+ */
+var THRESH = 0.46875;
+
+/**
+ * Constant used by W. J. Cody's Fortran77 implementation to denote sqrt(pi)
+ * @constant
+ */
+var SQRPI = 5.6418958354775628695e-1;
+
+/**
+ * Coefficients for each term of the numerator sum (p_j) for each approximation
+ * interval (see W. J. Cody's paper for more details)
+ * @constant
+ */
+var P = [[3.16112374387056560e00, 1.13864154151050156e02, 3.77485237685302021e02, 3.20937758913846947e03, 1.85777706184603153e-1], [5.64188496988670089e-1, 8.88314979438837594e00, 6.61191906371416295e01, 2.98635138197400131e02, 8.81952221241769090e02, 1.71204761263407058e03, 2.05107837782607147e03, 1.23033935479799725e03, 2.15311535474403846e-8], [3.05326634961232344e-1, 3.60344899949804439e-1, 1.25781726111229246e-1, 1.60837851487422766e-2, 6.58749161529837803e-4, 1.63153871373020978e-2]];
+
+/**
+ * Coefficients for each term of the denominator sum (q_j) for each approximation
+ * interval (see W. J. Cody's paper for more details)
+ * @constant
+ */
+var Q = [[2.36012909523441209e01, 2.44024637934444173e02, 1.28261652607737228e03, 2.84423683343917062e03], [1.57449261107098347e01, 1.17693950891312499e02, 5.37181101862009858e02, 1.62138957456669019e03, 3.29079923573345963e03, 4.36261909014324716e03, 3.43936767414372164e03, 1.23033935480374942e03], [2.56852019228982242e00, 1.87295284992346047e00, 5.27905102951428412e-1, 6.05183413124413191e-2, 2.33520497626869185e-3]];
+
+/**
+ * Maximum/minimum safe numbers to input to erf() (in ES6+, this number is
+ * Number.[MAX|MIN]_SAFE_INTEGER). erf() for all numbers beyond this limit will
+ * return 1
+ */
+var MAX_NUM = Math.pow(2, 53);

node_modules/mathjs/lib/esm/function/special/zeta.js

@@ -0,0 +1,148 @@
+import { factory } from '../../utils/factory.js';
+var name = 'zeta';
+var dependencies = ['typed', 'config', 'multiply', 'pow', 'divide', 'factorial', 'equal', 'smallerEq', 'isNegative', 'gamma', 'sin', 'subtract', 'add', '?Complex', '?BigNumber', 'pi'];
+export var createZeta = /* #__PURE__ */factory(name, dependencies, _ref => {
+  var {
+    typed,
+    config,
+    multiply,
+    pow,
+    divide,
+    factorial,
+    equal,
+    smallerEq,
+    isNegative,
+    gamma,
+    sin,
+    subtract,
+    add,
+    Complex,
+    BigNumber: _BigNumber,
+    pi
+  } = _ref;
+  /**
+   * Compute the Riemann Zeta function of a value using an infinite series for
+   * all of the complex plane using Riemann's Functional equation.
+   *
+   * Based off the paper by Xavier Gourdon and Pascal Sebah
+   * ( http://numbers.computation.free.fr/Constants/Miscellaneous/zetaevaluations.pdf )
+   *
+   * Implementation and slight modification by Anik Patel
+   *
+   * Note: the implementation is accurate up to about 6 digits.
+   *
+   * Syntax:
+   *
+   *    math.zeta(n)
+   *
+   * Examples:
+   *
+   *    math.zeta(5)       // returns 1.0369277551433895
+   *    math.zeta(-0.5)    // returns -0.2078862249773449
+   *    math.zeta(math.i)  // returns 0.0033002236853253153 - 0.4181554491413212i
+   *
+   * See also:
+   *    erf
+   *
+   * @param {number | Complex | BigNumber} s   A Real, Complex or BigNumber parameter to the Riemann Zeta Function
+   * @return {number | Complex | BigNumber}    The Riemann Zeta of `s`
+   */
+  return typed(name, {
+    number: s => zetaNumeric(s, value => value, () => 20),
+    BigNumber: s => zetaNumeric(s, value => new _BigNumber(value), () => {
+      // relTol is for example 1e-12. Extract the positive exponent 12 from that
+      return Math.abs(Math.log10(config.relTol));
+    }),
+    Complex: zetaComplex
+  });
+
+  /**
+   * @param {number | BigNumber} s
+   * @param {(value: number) => number | BigNumber} createValue
+   * @param {(value: number | BigNumber | Complex) => number} determineDigits
+   * @returns {number | BigNumber}
+   */
+  function zetaNumeric(s, createValue, determineDigits) {
+    if (equal(s, 0)) {
+      return createValue(-0.5);
+    }
+    if (equal(s, 1)) {
+      return createValue(NaN);
+    }
+    if (!isFinite(s)) {
+      return isNegative(s) ? createValue(NaN) : createValue(1);
+    }
+    return zeta(s, createValue, determineDigits, s => s);
+  }
+
+  /**
+   * @param {Complex} s
+   * @returns {Complex}
+   */
+  function zetaComplex(s) {
+    if (s.re === 0 && s.im === 0) {
+      return new Complex(-0.5);
+    }
+    if (s.re === 1) {
+      return new Complex(NaN, NaN);
+    }
+    if (s.re === Infinity && s.im === 0) {
+      return new Complex(1);
+    }
+    if (s.im === Infinity || s.re === -Infinity) {
+      return new Complex(NaN, NaN);
+    }
+    return zeta(s, value => value, s => Math.round(1.3 * 15 + 0.9 * Math.abs(s.im)), s => s.re);
+  }
+
+  /**
+   * @param {number | BigNumber | Complex} s
+   * @param {(value: number) => number | BigNumber | Complex} createValue
+   * @param {(value: number | BigNumber | Complex) => number} determineDigits
+   * @param {(value: number | BigNumber | Complex) => number} getRe
+   * @returns {*|number}
+   */
+  function zeta(s, createValue, determineDigits, getRe) {
+    var n = determineDigits(s);
+    if (getRe(s) > -(n - 1) / 2) {
+      return f(s, createValue(n), createValue);
+    } else {
+      // Function Equation for reflection to x < 1
+      var c = multiply(pow(2, s), pow(createValue(pi), subtract(s, 1)));
+      c = multiply(c, sin(multiply(divide(createValue(pi), 2), s)));
+      c = multiply(c, gamma(subtract(1, s)));
+      return multiply(c, zeta(subtract(1, s), createValue, determineDigits, getRe));
+    }
+  }
+
+  /**
+   * Calculate a portion of the sum
+   * @param {number | BigNumber} k   a positive integer
+   * @param {number | BigNumber} n   a positive integer
+   * @return {number}    the portion of the sum
+   **/
+  function d(k, n) {
+    var S = k;
+    for (var j = k; smallerEq(j, n); j = add(j, 1)) {
+      var factor = divide(multiply(factorial(add(n, subtract(j, 1))), pow(4, j)), multiply(factorial(subtract(n, j)), factorial(multiply(2, j))));
+      S = add(S, factor);
+    }
+    return multiply(n, S);
+  }
+
+  /**
+   * Calculate the positive Riemann Zeta function
+   * @param {number} s   a real or complex number with s.re > 1
+   * @param {number} n   a positive integer
+   * @param {(number) => number | BigNumber | Complex} createValue
+   * @return {number}    Riemann Zeta of s
+   **/
+  function f(s, n, createValue) {
+    var c = divide(1, multiply(d(createValue(0), n), subtract(1, pow(2, subtract(1, s)))));
+    var S = createValue(0);
+    for (var k = createValue(1); smallerEq(k, n); k = add(k, 1)) {
+      S = add(S, divide(multiply((-1) ** (k - 1), d(k, n)), pow(k, s)));
+    }
+    return multiply(c, S);
+  }
+});