{"ast":null,"code":"/**\n * @license Complex.js v2.0.12 11/02/2016\n *\n * Copyright (c) 2016, Robert Eisele (robert@xarg.org)\n * Dual licensed under the MIT or GPL Version 2 licenses.\n **/\n\n/**\n *\n * This class allows the manipulation of complex numbers.\n * You can pass a complex number in different formats. Either as object, double, string or two integer parameters.\n *\n * Object form\n * { re: , im: }\n * { arg: , abs: }\n * { phi: , r: }\n *\n * Array / Vector form\n * [ real, imaginary ]\n *\n * Double form\n * 99.3 - Single double value\n *\n * String form\n * '23.1337' - Simple real number\n * '15+3i' - a simple complex number\n * '3-i' - a simple complex number\n *\n * Example:\n *\n * var c = new Complex('99.3+8i');\n * c.mul({r: 3, i: 9}).div(4.9).sub(3, 2);\n *\n */\n\n'use strict';\n\nvar cosh = function (x) {\n return (Math.exp(x) + Math.exp(-x)) * 0.5;\n};\nvar sinh = function (x) {\n return (Math.exp(x) - Math.exp(-x)) * 0.5;\n};\n\n/**\n * Calculates cos(x) - 1 using Taylor series if x is small.\n *\n * @param {number} x\n * @returns {number} cos(x) - 1\n */\n\nvar cosm1 = function (x) {\n var limit = Math.PI / 4;\n if (x < -limit || x > limit) {\n return Math.cos(x) - 1.0;\n }\n var xx = x * x;\n return xx * (-0.5 + xx * (1 / 24 + xx * (-1 / 720 + xx * (1 / 40320 + xx * (-1 / 3628800 + xx * (1 / 4790014600 + xx * (-1 / 87178291200 + xx * (1 / 20922789888000))))))));\n};\nvar hypot = function (x, y) {\n var a = Math.abs(x);\n var b = Math.abs(y);\n if (a < 3000 && b < 3000) {\n return Math.sqrt(a * a + b * b);\n }\n if (a < b) {\n a = b;\n b = x / y;\n } else {\n b = y / x;\n }\n return a * Math.sqrt(1 + b * b);\n};\nvar parser_exit = function () {\n throw SyntaxError('Invalid Param');\n};\n\n/**\n * Calculates log(sqrt(a^2+b^2)) in a way to avoid overflows\n *\n * @param {number} a\n * @param {number} b\n * @returns {number}\n */\nfunction logHypot(a, b) {\n var _a = Math.abs(a);\n var _b = Math.abs(b);\n if (a === 0) {\n return Math.log(_b);\n }\n if (b === 0) {\n return Math.log(_a);\n }\n if (_a < 3000 && _b < 3000) {\n return Math.log(a * a + b * b) * 0.5;\n }\n\n /* I got 4 ideas to compute this property without overflow:\n *\n * Testing 1000000 times with random samples for a,b ∈ [1, 1000000000] against a big decimal library to get an error estimate\n *\n * 1. Only eliminate the square root: (OVERALL ERROR: 3.9122483030951116e-11)\n Math.log(a * a + b * b) / 2\n *\n *\n * 2. Try to use the non-overflowing pythagoras: (OVERALL ERROR: 8.889760039210159e-10)\n var fn = function(a, b) {\n a = Math.abs(a);\n b = Math.abs(b);\n var t = Math.min(a, b);\n a = Math.max(a, b);\n t = t / a;\n return Math.log(a) + Math.log(1 + t * t) / 2;\n };\n * 3. Abuse the identity cos(atan(y/x) = x / sqrt(x^2+y^2): (OVERALL ERROR: 3.4780178737037204e-10)\n Math.log(a / Math.cos(Math.atan2(b, a)))\n * 4. Use 3. and apply log rules: (OVERALL ERROR: 1.2014087502620896e-9)\n Math.log(a) - Math.log(Math.cos(Math.atan2(b, a)))\n */\n\n return Math.log(a / Math.cos(Math.atan2(b, a)));\n}\nvar parse = function (a, b) {\n var z = {\n 're': 0,\n 'im': 0\n };\n if (a === undefined || a === null) {\n z['re'] = z['im'] = 0;\n } else if (b !== undefined) {\n z['re'] = a;\n z['im'] = b;\n } else switch (typeof a) {\n case 'object':\n if ('im' in a && 're' in a) {\n z['re'] = a['re'];\n z['im'] = a['im'];\n } else if ('abs' in a && 'arg' in a) {\n if (!Number.isFinite(a['abs']) && Number.isFinite(a['arg'])) {\n return Complex['INFINITY'];\n }\n z['re'] = a['abs'] * Math.cos(a['arg']);\n z['im'] = a['abs'] * Math.sin(a['arg']);\n } else if ('r' in a && 'phi' in a) {\n if (!Number.isFinite(a['r']) && Number.isFinite(a['phi'])) {\n return Complex['INFINITY'];\n }\n z['re'] = a['r'] * Math.cos(a['phi']);\n z['im'] = a['r'] * Math.sin(a['phi']);\n } else if (a.length === 2) {\n // Quick array check\n z['re'] = a[0];\n z['im'] = a[1];\n } else {\n parser_exit();\n }\n break;\n case 'string':\n z['im'] = /* void */\n z['re'] = 0;\n var tokens = a.match(/\\d+\\.?\\d*e[+-]?\\d+|\\d+\\.?\\d*|\\.\\d+|./g);\n var plus = 1;\n var minus = 0;\n if (tokens === null) {\n parser_exit();\n }\n for (var i = 0; i < tokens.length; i++) {\n var c = tokens[i];\n if (c === ' ' || c === '\\t' || c === '\\n') {\n /* void */\n } else if (c === '+') {\n plus++;\n } else if (c === '-') {\n minus++;\n } else if (c === 'i' || c === 'I') {\n if (plus + minus === 0) {\n parser_exit();\n }\n if (tokens[i + 1] !== ' ' && !isNaN(tokens[i + 1])) {\n z['im'] += parseFloat((minus % 2 ? '-' : '') + tokens[i + 1]);\n i++;\n } else {\n z['im'] += parseFloat((minus % 2 ? '-' : '') + '1');\n }\n plus = minus = 0;\n } else {\n if (plus + minus === 0 || isNaN(c)) {\n parser_exit();\n }\n if (tokens[i + 1] === 'i' || tokens[i + 1] === 'I') {\n z['im'] += parseFloat((minus % 2 ? '-' : '') + c);\n i++;\n } else {\n z['re'] += parseFloat((minus % 2 ? '-' : '') + c);\n }\n plus = minus = 0;\n }\n }\n\n // Still something on the stack\n if (plus + minus > 0) {\n parser_exit();\n }\n break;\n case 'number':\n z['im'] = 0;\n z['re'] = a;\n break;\n default:\n parser_exit();\n }\n if (isNaN(z['re']) || isNaN(z['im'])) {\n // If a calculation is NaN, we treat it as NaN and don't throw\n //parser_exit();\n }\n return z;\n};\n\n/**\n * @constructor\n * @returns {Complex}\n */\nfunction Complex(a, b) {\n if (!(this instanceof Complex)) {\n return new Complex(a, b);\n }\n var z = parse(a, b);\n this['re'] = z['re'];\n this['im'] = z['im'];\n}\n_c = Complex;\nComplex.prototype = {\n 're': 0,\n 'im': 0,\n /**\n * Calculates the sign of a complex number, which is a normalized complex\n *\n * @returns {Complex}\n */\n 'sign': function () {\n var abs = this['abs']();\n return new Complex(this['re'] / abs, this['im'] / abs);\n },\n /**\n * Adds two complex numbers\n *\n * @returns {Complex}\n */\n 'add': function (a, b) {\n var z = new Complex(a, b);\n\n // Infinity + Infinity = NaN\n if (this['isInfinite']() && z['isInfinite']()) {\n return Complex['NAN'];\n }\n\n // Infinity + z = Infinity { where z != Infinity }\n if (this['isInfinite']() || z['isInfinite']()) {\n return Complex['INFINITY'];\n }\n return new Complex(this['re'] + z['re'], this['im'] + z['im']);\n },\n /**\n * Subtracts two complex numbers\n *\n * @returns {Complex}\n */\n 'sub': function (a, b) {\n var z = new Complex(a, b);\n\n // Infinity - Infinity = NaN\n if (this['isInfinite']() && z['isInfinite']()) {\n return Complex['NAN'];\n }\n\n // Infinity - z = Infinity { where z != Infinity }\n if (this['isInfinite']() || z['isInfinite']()) {\n return Complex['INFINITY'];\n }\n return new Complex(this['re'] - z['re'], this['im'] - z['im']);\n },\n /**\n * Multiplies two complex numbers\n *\n * @returns {Complex}\n */\n 'mul': function (a, b) {\n var z = new Complex(a, b);\n\n // Infinity * 0 = NaN\n if (this['isInfinite']() && z['isZero']() || this['isZero']() && z['isInfinite']()) {\n return Complex['NAN'];\n }\n\n // Infinity * z = Infinity { where z != 0 }\n if (this['isInfinite']() || z['isInfinite']()) {\n return Complex['INFINITY'];\n }\n\n // Short circuit for real values\n if (z['im'] === 0 && this['im'] === 0) {\n return new Complex(this['re'] * z['re'], 0);\n }\n return new Complex(this['re'] * z['re'] - this['im'] * z['im'], this['re'] * z['im'] + this['im'] * z['re']);\n },\n /**\n * Divides two complex numbers\n *\n * @returns {Complex}\n */\n 'div': function (a, b) {\n var z = new Complex(a, b);\n\n // 0 / 0 = NaN and Infinity / Infinity = NaN\n if (this['isZero']() && z['isZero']() || this['isInfinite']() && z['isInfinite']()) {\n return Complex['NAN'];\n }\n\n // Infinity / 0 = Infinity\n if (this['isInfinite']() || z['isZero']()) {\n return Complex['INFINITY'];\n }\n\n // 0 / Infinity = 0\n if (this['isZero']() || z['isInfinite']()) {\n return Complex['ZERO'];\n }\n a = this['re'];\n b = this['im'];\n var c = z['re'];\n var d = z['im'];\n var t, x;\n if (0 === d) {\n // Divisor is real\n return new Complex(a / c, b / c);\n }\n if (Math.abs(c) < Math.abs(d)) {\n x = c / d;\n t = c * x + d;\n return new Complex((a * x + b) / t, (b * x - a) / t);\n } else {\n x = d / c;\n t = d * x + c;\n return new Complex((a + b * x) / t, (b - a * x) / t);\n }\n },\n /**\n * Calculate the power of two complex numbers\n *\n * @returns {Complex}\n */\n 'pow': function (a, b) {\n var z = new Complex(a, b);\n a = this['re'];\n b = this['im'];\n if (z['isZero']()) {\n return Complex['ONE'];\n }\n\n // If the exponent is real\n if (z['im'] === 0) {\n if (b === 0) {\n return new Complex(Math.pow(a, z['re']), 0);\n } else if (a === 0) {\n // If base is fully imaginary\n\n switch ((z['re'] % 4 + 4) % 4) {\n case 0:\n return new Complex(Math.pow(b, z['re']), 0);\n case 1:\n return new Complex(0, Math.pow(b, z['re']));\n case 2:\n return new Complex(-Math.pow(b, z['re']), 0);\n case 3:\n return new Complex(0, -Math.pow(b, z['re']));\n }\n }\n }\n\n /* I couldn't find a good formula, so here is a derivation and optimization\n *\n * z_1^z_2 = (a + bi)^(c + di)\n * = exp((c + di) * log(a + bi)\n * = pow(a^2 + b^2, (c + di) / 2) * exp(i(c + di)atan2(b, a))\n * =>...\n * Re = (pow(a^2 + b^2, c / 2) * exp(-d * atan2(b, a))) * cos(d * log(a^2 + b^2) / 2 + c * atan2(b, a))\n * Im = (pow(a^2 + b^2, c / 2) * exp(-d * atan2(b, a))) * sin(d * log(a^2 + b^2) / 2 + c * atan2(b, a))\n *\n * =>...\n * Re = exp(c * log(sqrt(a^2 + b^2)) - d * atan2(b, a)) * cos(d * log(sqrt(a^2 + b^2)) + c * atan2(b, a))\n * Im = exp(c * log(sqrt(a^2 + b^2)) - d * atan2(b, a)) * sin(d * log(sqrt(a^2 + b^2)) + c * atan2(b, a))\n *\n * =>\n * Re = exp(c * logsq2 - d * arg(z_1)) * cos(d * logsq2 + c * arg(z_1))\n * Im = exp(c * logsq2 - d * arg(z_1)) * sin(d * logsq2 + c * arg(z_1))\n *\n */\n\n if (a === 0 && b === 0 && z['re'] > 0 && z['im'] >= 0) {\n return Complex['ZERO'];\n }\n var arg = Math.atan2(b, a);\n var loh = logHypot(a, b);\n a = Math.exp(z['re'] * loh - z['im'] * arg);\n b = z['im'] * loh + z['re'] * arg;\n return new Complex(a * Math.cos(b), a * Math.sin(b));\n },\n /**\n * Calculate the complex square root\n *\n * @returns {Complex}\n */\n 'sqrt': function () {\n var a = this['re'];\n var b = this['im'];\n var r = this['abs']();\n var re, im;\n if (a >= 0) {\n if (b === 0) {\n return new Complex(Math.sqrt(a), 0);\n }\n re = 0.5 * Math.sqrt(2.0 * (r + a));\n } else {\n re = Math.abs(b) / Math.sqrt(2 * (r - a));\n }\n if (a <= 0) {\n im = 0.5 * Math.sqrt(2.0 * (r - a));\n } else {\n im = Math.abs(b) / Math.sqrt(2 * (r + a));\n }\n return new Complex(re, b < 0 ? -im : im);\n },\n /**\n * Calculate the complex exponent\n *\n * @returns {Complex}\n */\n 'exp': function () {\n var tmp = Math.exp(this['re']);\n if (this['im'] === 0) {\n //return new Complex(tmp, 0);\n }\n return new Complex(tmp * Math.cos(this['im']), tmp * Math.sin(this['im']));\n },\n /**\n * Calculate the complex exponent and subtracts one.\n *\n * This may be more accurate than `Complex(x).exp().sub(1)` if\n * `x` is small.\n *\n * @returns {Complex}\n */\n 'expm1': function () {\n /**\n * exp(a + i*b) - 1\n = exp(a) * (cos(b) + j*sin(b)) - 1\n = expm1(a)*cos(b) + cosm1(b) + j*exp(a)*sin(b)\n */\n\n var a = this['re'];\n var b = this['im'];\n return new Complex(Math.expm1(a) * Math.cos(b) + cosm1(b), Math.exp(a) * Math.sin(b));\n },\n /**\n * Calculate the natural log\n *\n * @returns {Complex}\n */\n 'log': function () {\n var a = this['re'];\n var b = this['im'];\n if (b === 0 && a > 0) {\n //return new Complex(Math.log(a), 0);\n }\n return new Complex(logHypot(a, b), Math.atan2(b, a));\n },\n /**\n * Calculate the magnitude of the complex number\n *\n * @returns {number}\n */\n 'abs': function () {\n return hypot(this['re'], this['im']);\n },\n /**\n * Calculate the angle of the complex number\n *\n * @returns {number}\n */\n 'arg': function () {\n return Math.atan2(this['im'], this['re']);\n },\n /**\n * Calculate the sine of the complex number\n *\n * @returns {Complex}\n */\n 'sin': function () {\n // sin(c) = (e^b - e^(-b)) / (2i)\n\n var a = this['re'];\n var b = this['im'];\n return new Complex(Math.sin(a) * cosh(b), Math.cos(a) * sinh(b));\n },\n /**\n * Calculate the cosine\n *\n * @returns {Complex}\n */\n 'cos': function () {\n // cos(z) = (e^b + e^(-b)) / 2\n\n var a = this['re'];\n var b = this['im'];\n return new Complex(Math.cos(a) * cosh(b), -Math.sin(a) * sinh(b));\n },\n /**\n * Calculate the tangent\n *\n * @returns {Complex}\n */\n 'tan': function () {\n // tan(c) = (e^(ci) - e^(-ci)) / (i(e^(ci) + e^(-ci)))\n\n var a = 2 * this['re'];\n var b = 2 * this['im'];\n var d = Math.cos(a) + cosh(b);\n return new Complex(Math.sin(a) / d, sinh(b) / d);\n },\n /**\n * Calculate the cotangent\n *\n * @returns {Complex}\n */\n 'cot': function () {\n // cot(c) = i(e^(ci) + e^(-ci)) / (e^(ci) - e^(-ci))\n\n var a = 2 * this['re'];\n var b = 2 * this['im'];\n var d = Math.cos(a) - cosh(b);\n return new Complex(-Math.sin(a) / d, sinh(b) / d);\n },\n /**\n * Calculate the secant\n *\n * @returns {Complex}\n */\n 'sec': function () {\n // sec(c) = 2 / (e^(ci) + e^(-ci))\n\n var a = this['re'];\n var b = this['im'];\n var d = 0.5 * cosh(2 * b) + 0.5 * Math.cos(2 * a);\n return new Complex(Math.cos(a) * cosh(b) / d, Math.sin(a) * sinh(b) / d);\n },\n /**\n * Calculate the cosecans\n *\n * @returns {Complex}\n */\n 'csc': function () {\n // csc(c) = 2i / (e^(ci) - e^(-ci))\n\n var a = this['re'];\n var b = this['im'];\n var d = 0.5 * cosh(2 * b) - 0.5 * Math.cos(2 * a);\n return new Complex(Math.sin(a) * cosh(b) / d, -Math.cos(a) * sinh(b) / d);\n },\n /**\n * Calculate the complex arcus sinus\n *\n * @returns {Complex}\n */\n 'asin': function () {\n // asin(c) = -i * log(ci + sqrt(1 - c^2))\n\n var a = this['re'];\n var b = this['im'];\n var t1 = new Complex(b * b - a * a + 1, -2 * a * b)['sqrt']();\n var t2 = new Complex(t1['re'] - b, t1['im'] + a)['log']();\n return new Complex(t2['im'], -t2['re']);\n },\n /**\n * Calculate the complex arcus cosinus\n *\n * @returns {Complex}\n */\n 'acos': function () {\n // acos(c) = i * log(c - i * sqrt(1 - c^2))\n\n var a = this['re'];\n var b = this['im'];\n var t1 = new Complex(b * b - a * a + 1, -2 * a * b)['sqrt']();\n var t2 = new Complex(t1['re'] - b, t1['im'] + a)['log']();\n return new Complex(Math.PI / 2 - t2['im'], t2['re']);\n },\n /**\n * Calculate the complex arcus tangent\n *\n * @returns {Complex}\n */\n 'atan': function () {\n // atan(c) = i / 2 log((i + x) / (i - x))\n\n var a = this['re'];\n var b = this['im'];\n if (a === 0) {\n if (b === 1) {\n return new Complex(0, Infinity);\n }\n if (b === -1) {\n return new Complex(0, -Infinity);\n }\n }\n var d = a * a + (1.0 - b) * (1.0 - b);\n var t1 = new Complex((1 - b * b - a * a) / d, -2 * a / d).log();\n return new Complex(-0.5 * t1['im'], 0.5 * t1['re']);\n },\n /**\n * Calculate the complex arcus cotangent\n *\n * @returns {Complex}\n */\n 'acot': function () {\n // acot(c) = i / 2 log((c - i) / (c + i))\n\n var a = this['re'];\n var b = this['im'];\n if (b === 0) {\n return new Complex(Math.atan2(1, a), 0);\n }\n var d = a * a + b * b;\n return d !== 0 ? new Complex(a / d, -b / d).atan() : new Complex(a !== 0 ? a / 0 : 0, b !== 0 ? -b / 0 : 0).atan();\n },\n /**\n * Calculate the complex arcus secant\n *\n * @returns {Complex}\n */\n 'asec': function () {\n // asec(c) = -i * log(1 / c + sqrt(1 - i / c^2))\n\n var a = this['re'];\n var b = this['im'];\n if (a === 0 && b === 0) {\n return new Complex(0, Infinity);\n }\n var d = a * a + b * b;\n return d !== 0 ? new Complex(a / d, -b / d).acos() : new Complex(a !== 0 ? a / 0 : 0, b !== 0 ? -b / 0 : 0).acos();\n },\n /**\n * Calculate the complex arcus cosecans\n *\n * @returns {Complex}\n */\n 'acsc': function () {\n // acsc(c) = -i * log(i / c + sqrt(1 - 1 / c^2))\n\n var a = this['re'];\n var b = this['im'];\n if (a === 0 && b === 0) {\n return new Complex(Math.PI / 2, Infinity);\n }\n var d = a * a + b * b;\n return d !== 0 ? new Complex(a / d, -b / d).asin() : new Complex(a !== 0 ? a / 0 : 0, b !== 0 ? -b / 0 : 0).asin();\n },\n /**\n * Calculate the complex sinh\n *\n * @returns {Complex}\n */\n 'sinh': function () {\n // sinh(c) = (e^c - e^-c) / 2\n\n var a = this['re'];\n var b = this['im'];\n return new Complex(sinh(a) * Math.cos(b), cosh(a) * Math.sin(b));\n },\n /**\n * Calculate the complex cosh\n *\n * @returns {Complex}\n */\n 'cosh': function () {\n // cosh(c) = (e^c + e^-c) / 2\n\n var a = this['re'];\n var b = this['im'];\n return new Complex(cosh(a) * Math.cos(b), sinh(a) * Math.sin(b));\n },\n /**\n * Calculate the complex tanh\n *\n * @returns {Complex}\n */\n 'tanh': function () {\n // tanh(c) = (e^c - e^-c) / (e^c + e^-c)\n\n var a = 2 * this['re'];\n var b = 2 * this['im'];\n var d = cosh(a) + Math.cos(b);\n return new Complex(sinh(a) / d, Math.sin(b) / d);\n },\n /**\n * Calculate the complex coth\n *\n * @returns {Complex}\n */\n 'coth': function () {\n // coth(c) = (e^c + e^-c) / (e^c - e^-c)\n\n var a = 2 * this['re'];\n var b = 2 * this['im'];\n var d = cosh(a) - Math.cos(b);\n return new Complex(sinh(a) / d, -Math.sin(b) / d);\n },\n /**\n * Calculate the complex coth\n *\n * @returns {Complex}\n */\n 'csch': function () {\n // csch(c) = 2 / (e^c - e^-c)\n\n var a = this['re'];\n var b = this['im'];\n var d = Math.cos(2 * b) - cosh(2 * a);\n return new Complex(-2 * sinh(a) * Math.cos(b) / d, 2 * cosh(a) * Math.sin(b) / d);\n },\n /**\n * Calculate the complex sech\n *\n * @returns {Complex}\n */\n 'sech': function () {\n // sech(c) = 2 / (e^c + e^-c)\n\n var a = this['re'];\n var b = this['im'];\n var d = Math.cos(2 * b) + cosh(2 * a);\n return new Complex(2 * cosh(a) * Math.cos(b) / d, -2 * sinh(a) * Math.sin(b) / d);\n },\n /**\n * Calculate the complex asinh\n *\n * @returns {Complex}\n */\n 'asinh': function () {\n // asinh(c) = log(c + sqrt(c^2 + 1))\n\n var tmp = this['im'];\n this['im'] = -this['re'];\n this['re'] = tmp;\n var res = this['asin']();\n this['re'] = -this['im'];\n this['im'] = tmp;\n tmp = res['re'];\n res['re'] = -res['im'];\n res['im'] = tmp;\n return res;\n },\n /**\n * Calculate the complex acosh\n *\n * @returns {Complex}\n */\n 'acosh': function () {\n // acosh(c) = log(c + sqrt(c^2 - 1))\n\n var res = this['acos']();\n if (res['im'] <= 0) {\n var tmp = res['re'];\n res['re'] = -res['im'];\n res['im'] = tmp;\n } else {\n var tmp = res['im'];\n res['im'] = -res['re'];\n res['re'] = tmp;\n }\n return res;\n },\n /**\n * Calculate the complex atanh\n *\n * @returns {Complex}\n */\n 'atanh': function () {\n // atanh(c) = log((1+c) / (1-c)) / 2\n\n var a = this['re'];\n var b = this['im'];\n var noIM = a > 1 && b === 0;\n var oneMinus = 1 - a;\n var onePlus = 1 + a;\n var d = oneMinus * oneMinus + b * b;\n var x = d !== 0 ? new Complex((onePlus * oneMinus - b * b) / d, (b * oneMinus + onePlus * b) / d) : new Complex(a !== -1 ? a / 0 : 0, b !== 0 ? b / 0 : 0);\n var temp = x['re'];\n x['re'] = logHypot(x['re'], x['im']) / 2;\n x['im'] = Math.atan2(x['im'], temp) / 2;\n if (noIM) {\n x['im'] = -x['im'];\n }\n return x;\n },\n /**\n * Calculate the complex acoth\n *\n * @returns {Complex}\n */\n 'acoth': function () {\n // acoth(c) = log((c+1) / (c-1)) / 2\n\n var a = this['re'];\n var b = this['im'];\n if (a === 0 && b === 0) {\n return new Complex(0, Math.PI / 2);\n }\n var d = a * a + b * b;\n return d !== 0 ? new Complex(a / d, -b / d).atanh() : new Complex(a !== 0 ? a / 0 : 0, b !== 0 ? -b / 0 : 0).atanh();\n },\n /**\n * Calculate the complex acsch\n *\n * @returns {Complex}\n */\n 'acsch': function () {\n // acsch(c) = log((1+sqrt(1+c^2))/c)\n\n var a = this['re'];\n var b = this['im'];\n if (b === 0) {\n return new Complex(a !== 0 ? Math.log(a + Math.sqrt(a * a + 1)) : Infinity, 0);\n }\n var d = a * a + b * b;\n return d !== 0 ? new Complex(a / d, -b / d).asinh() : new Complex(a !== 0 ? a / 0 : 0, b !== 0 ? -b / 0 : 0).asinh();\n },\n /**\n * Calculate the complex asech\n *\n * @returns {Complex}\n */\n 'asech': function () {\n // asech(c) = log((1+sqrt(1-c^2))/c)\n\n var a = this['re'];\n var b = this['im'];\n if (this['isZero']()) {\n return Complex['INFINITY'];\n }\n var d = a * a + b * b;\n return d !== 0 ? new Complex(a / d, -b / d).acosh() : new Complex(a !== 0 ? a / 0 : 0, b !== 0 ? -b / 0 : 0).acosh();\n },\n /**\n * Calculate the complex inverse 1/z\n *\n * @returns {Complex}\n */\n 'inverse': function () {\n // 1 / 0 = Infinity and 1 / Infinity = 0\n if (this['isZero']()) {\n return Complex['INFINITY'];\n }\n if (this['isInfinite']()) {\n return Complex['ZERO'];\n }\n var a = this['re'];\n var b = this['im'];\n var d = a * a + b * b;\n return new Complex(a / d, -b / d);\n },\n /**\n * Returns the complex conjugate\n *\n * @returns {Complex}\n */\n 'conjugate': function () {\n return new Complex(this['re'], -this['im']);\n },\n /**\n * Gets the negated complex number\n *\n * @returns {Complex}\n */\n 'neg': function () {\n return new Complex(-this['re'], -this['im']);\n },\n /**\n * Ceils the actual complex number\n *\n * @returns {Complex}\n */\n 'ceil': function (places) {\n places = Math.pow(10, places || 0);\n return new Complex(Math.ceil(this['re'] * places) / places, Math.ceil(this['im'] * places) / places);\n },\n /**\n * Floors the actual complex number\n *\n * @returns {Complex}\n */\n 'floor': function (places) {\n places = Math.pow(10, places || 0);\n return new Complex(Math.floor(this['re'] * places) / places, Math.floor(this['im'] * places) / places);\n },\n /**\n * Ceils the actual complex number\n *\n * @returns {Complex}\n */\n 'round': function (places) {\n places = Math.pow(10, places || 0);\n return new Complex(Math.round(this['re'] * places) / places, Math.round(this['im'] * places) / places);\n },\n /**\n * Compares two complex numbers\n *\n * **Note:** new Complex(Infinity).equals(Infinity) === false\n *\n * @returns {boolean}\n */\n 'equals': function (a, b) {\n var z = new Complex(a, b);\n return Math.abs(z['re'] - this['re']) <= Complex['EPSILON'] && Math.abs(z['im'] - this['im']) <= Complex['EPSILON'];\n },\n /**\n * Clones the actual object\n *\n * @returns {Complex}\n */\n 'clone': function () {\n return new Complex(this['re'], this['im']);\n },\n /**\n * Gets a string of the actual complex number\n *\n * @returns {string}\n */\n 'toString': function () {\n var a = this['re'];\n var b = this['im'];\n var ret = \"\";\n if (this['isNaN']()) {\n return 'NaN';\n }\n if (this['isInfinite']()) {\n return 'Infinity';\n }\n\n // If is real number\n if (b === 0) {\n return ret + a;\n }\n if (a !== 0) {\n ret += a;\n ret += \" \";\n if (b < 0) {\n b = -b;\n ret += \"-\";\n } else {\n ret += \"+\";\n }\n ret += \" \";\n } else if (b < 0) {\n b = -b;\n ret += \"-\";\n }\n if (1 !== b) {\n // b is the absolute imaginary part\n ret += b;\n }\n return ret + \"i\";\n },\n /**\n * Returns the actual number as a vector\n *\n * @returns {Array}\n */\n 'toVector': function () {\n return [this['re'], this['im']];\n },\n /**\n * Returns the actual real value of the current object\n *\n * @returns {number|null}\n */\n 'valueOf': function () {\n if (this['im'] === 0) {\n return this['re'];\n }\n return null;\n },\n /**\n * Determines whether a complex number is not on the Riemann sphere.\n *\n * @returns {boolean}\n */\n 'isNaN': function () {\n return isNaN(this['re']) || isNaN(this['im']);\n },\n /**\n * Determines whether or not a complex number is at the zero pole of the\n * Riemann sphere.\n *\n * @returns {boolean}\n */\n 'isZero': function () {\n return this['im'] === 0 && this['re'] === 0;\n },\n /**\n * Determines whether a complex number is not at the infinity pole of the\n * Riemann sphere.\n *\n * @returns {boolean}\n */\n 'isFinite': function () {\n return isFinite(this['re']) && isFinite(this['im']);\n },\n /**\n * Determines whether or not a complex number is at the infinity pole of the\n * Riemann sphere.\n *\n * @returns {boolean}\n */\n 'isInfinite': function () {\n return !(this['isNaN']() || this['isFinite']());\n }\n};\nComplex['ZERO'] = new Complex(0, 0);\nComplex['ONE'] = new Complex(1, 0);\nComplex['I'] = new Complex(0, 1);\nComplex['PI'] = new Complex(Math.PI, 0);\nComplex['E'] = new Complex(Math.E, 0);\nComplex['INFINITY'] = new Complex(Infinity, Infinity);\nComplex['NAN'] = new Complex(NaN, NaN);\nComplex['EPSILON'] = 1e-16;\n\n// Since no need to customize the export in React, we can just export the class directly\n\n// if (typeof define === 'function' && define['amd']) {\n// define([], function() {\n// return Complex;\n// });\n// } else if (typeof exports === 'object') {\n// Object.defineProperty(Complex, \"__esModule\", {'value': true});\n// Complex['default'] = Complex;\n// Complex['Complex'] = Complex;\n// module['exports'] = Complex;\n// } else {\n// root['Complex'] = Complex;\n// }\n\nexport { Complex };\nvar _c;\n$RefreshReg$(_c, \"Complex\");","map":{"version":3,"names":["cosh","x","Math","exp","sinh","cosm1","limit","PI","cos","xx","hypot","y","a","abs","b","sqrt","parser_exit","SyntaxError","logHypot","_a","_b","log","atan2","parse","z","undefined","Number","isFinite","Complex","sin","length","tokens","match","plus","minus","i","c","isNaN","parseFloat","_c","prototype","sign","add","sub","mul","div","d","t","pow","arg","loh","r","re","im","tmp","expm1","tan","cot","sec","csc","asin","t1","t2","acos","atan","Infinity","acot","asec","acsc","tanh","coth","csch","sech","asinh","res","acosh","atanh","noIM","oneMinus","onePlus","temp","acoth","acsch","asech","inverse","conjugate","neg","ceil","places","floor","round","equals","clone","toString","ret","toVector","valueOf","isZero","isInfinite","E","NaN","$RefreshReg$"],"sources":["/var/www/gavt/src/gavt/Wave/lib/complex.jsx"],"sourcesContent":["/**\n * @license Complex.js v2.0.12 11/02/2016\n *\n * Copyright (c) 2016, Robert Eisele (robert@xarg.org)\n * Dual licensed under the MIT or GPL Version 2 licenses.\n **/\n\n/**\n *\n * This class allows the manipulation of complex numbers.\n * You can pass a complex number in different formats. Either as object, double, string or two integer parameters.\n *\n * Object form\n * { re: , im: }\n * { arg: , abs: }\n * { phi: , r: }\n *\n * Array / Vector form\n * [ real, imaginary ]\n *\n * Double form\n * 99.3 - Single double value\n *\n * String form\n * '23.1337' - Simple real number\n * '15+3i' - a simple complex number\n * '3-i' - a simple complex number\n *\n * Example:\n *\n * var c = new Complex('99.3+8i');\n * c.mul({r: 3, i: 9}).div(4.9).sub(3, 2);\n *\n */\n\n'use strict';\n \nvar cosh = function(x) {\n return (Math.exp(x) + Math.exp(-x)) * 0.5;\n};\n\nvar sinh = function(x) {\n return (Math.exp(x) - Math.exp(-x)) * 0.5;\n};\n\n/**\n * Calculates cos(x) - 1 using Taylor series if x is small.\n *\n * @param {number} x\n * @returns {number} cos(x) - 1\n */\n\nvar cosm1 = function(x) {\n var limit = Math.PI/4;\n if (x < -limit || x > limit) {\n return (Math.cos(x) - 1.0);\n }\n\n var xx = x * x;\n return xx *\n (-0.5 + xx *\n (1/24 + xx *\n (-1/720 + xx *\n (1/40320 + xx *\n (-1/3628800 + xx *\n (1/4790014600 + xx *\n (-1/87178291200 + xx *\n (1/20922789888000)\n )\n )\n )\n )\n )\n )\n )\n};\n\nvar hypot = function(x, y) {\n\n var a = Math.abs(x);\n var b = Math.abs(y);\n\n if (a < 3000 && b < 3000) {\n return Math.sqrt(a * a + b * b);\n }\n\n if (a < b) {\n a = b;\n b = x / y;\n } else {\n b = y / x;\n }\n return a * Math.sqrt(1 + b * b);\n};\n\nvar parser_exit = function() {\n throw SyntaxError('Invalid Param');\n};\n\n/**\n * Calculates log(sqrt(a^2+b^2)) in a way to avoid overflows\n *\n * @param {number} a\n * @param {number} b\n * @returns {number}\n */\nfunction logHypot(a, b) {\n\n var _a = Math.abs(a);\n var _b = Math.abs(b);\n\n if (a === 0) {\n return Math.log(_b);\n }\n\n if (b === 0) {\n return Math.log(_a);\n }\n\n if (_a < 3000 && _b < 3000) {\n return Math.log(a * a + b * b) * 0.5;\n }\n\n /* I got 4 ideas to compute this property without overflow:\n *\n * Testing 1000000 times with random samples for a,b ∈ [1, 1000000000] against a big decimal library to get an error estimate\n *\n * 1. Only eliminate the square root: (OVERALL ERROR: 3.9122483030951116e-11)\n\n Math.log(a * a + b * b) / 2\n\n *\n *\n * 2. Try to use the non-overflowing pythagoras: (OVERALL ERROR: 8.889760039210159e-10)\n\n var fn = function(a, b) {\n a = Math.abs(a);\n b = Math.abs(b);\n var t = Math.min(a, b);\n a = Math.max(a, b);\n t = t / a;\n\n return Math.log(a) + Math.log(1 + t * t) / 2;\n };\n\n * 3. Abuse the identity cos(atan(y/x) = x / sqrt(x^2+y^2): (OVERALL ERROR: 3.4780178737037204e-10)\n\n Math.log(a / Math.cos(Math.atan2(b, a)))\n\n * 4. Use 3. and apply log rules: (OVERALL ERROR: 1.2014087502620896e-9)\n\n Math.log(a) - Math.log(Math.cos(Math.atan2(b, a)))\n\n */\n\n return Math.log(a / Math.cos(Math.atan2(b, a)));\n}\n\nvar parse = function(a, b) {\n\n var z = {'re': 0, 'im': 0};\n\n if (a === undefined || a === null) {\n z['re'] =\n z['im'] = 0;\n } else if (b !== undefined) {\n z['re'] = a;\n z['im'] = b;\n } else\n switch (typeof a) {\n\n case 'object':\n\n if ('im' in a && 're' in a) {\n z['re'] = a['re'];\n z['im'] = a['im'];\n } else if ('abs' in a && 'arg' in a) {\n if (!Number.isFinite(a['abs']) && Number.isFinite(a['arg'])) {\n return Complex['INFINITY'];\n }\n z['re'] = a['abs'] * Math.cos(a['arg']);\n z['im'] = a['abs'] * Math.sin(a['arg']);\n } else if ('r' in a && 'phi' in a) {\n if (!Number.isFinite(a['r']) && Number.isFinite(a['phi'])) {\n return Complex['INFINITY'];\n }\n z['re'] = a['r'] * Math.cos(a['phi']);\n z['im'] = a['r'] * Math.sin(a['phi']);\n } else if (a.length === 2) { // Quick array check\n z['re'] = a[0];\n z['im'] = a[1];\n } else {\n parser_exit();\n }\n break;\n\n case 'string':\n\n z['im'] = /* void */\n z['re'] = 0;\n\n var tokens = a.match(/\\d+\\.?\\d*e[+-]?\\d+|\\d+\\.?\\d*|\\.\\d+|./g);\n var plus = 1;\n var minus = 0;\n\n if (tokens === null) {\n parser_exit();\n }\n\n for (var i = 0; i < tokens.length; i++) {\n\n var c = tokens[i];\n\n if (c === ' ' || c === '\\t' || c === '\\n') {\n /* void */\n } else if (c === '+') {\n plus++;\n } else if (c === '-') {\n minus++;\n } else if (c === 'i' || c === 'I') {\n\n if (plus + minus === 0) {\n parser_exit();\n }\n\n if (tokens[i + 1] !== ' ' && !isNaN(tokens[i + 1])) {\n z['im'] += parseFloat((minus % 2 ? '-' : '') + tokens[i + 1]);\n i++;\n } else {\n z['im'] += parseFloat((minus % 2 ? '-' : '') + '1');\n }\n plus = minus = 0;\n\n } else {\n\n if (plus + minus === 0 || isNaN(c)) {\n parser_exit();\n }\n\n if (tokens[i + 1] === 'i' || tokens[i + 1] === 'I') {\n z['im'] += parseFloat((minus % 2 ? '-' : '') + c);\n i++;\n } else {\n z['re'] += parseFloat((minus % 2 ? '-' : '') + c);\n }\n plus = minus = 0;\n }\n }\n\n // Still something on the stack\n if (plus + minus > 0) {\n parser_exit();\n }\n break;\n\n case 'number':\n z['im'] = 0;\n z['re'] = a;\n break;\n\n default:\n parser_exit();\n }\n\n if (isNaN(z['re']) || isNaN(z['im'])) {\n // If a calculation is NaN, we treat it as NaN and don't throw\n //parser_exit();\n }\n\n return z;\n};\n\n/**\n * @constructor\n * @returns {Complex}\n */\nfunction Complex(a, b) {\n\n if (!(this instanceof Complex)) {\n return new Complex(a, b);\n }\n\n var z = parse(a, b);\n\n this['re'] = z['re'];\n this['im'] = z['im'];\n}\n\nComplex.prototype = {\n\n 're': 0,\n 'im': 0,\n\n /**\n * Calculates the sign of a complex number, which is a normalized complex\n *\n * @returns {Complex}\n */\n 'sign': function() {\n\n var abs = this['abs']();\n\n return new Complex(\n this['re'] / abs,\n this['im'] / abs);\n },\n\n /**\n * Adds two complex numbers\n *\n * @returns {Complex}\n */\n 'add': function(a, b) {\n\n var z = new Complex(a, b);\n\n // Infinity + Infinity = NaN\n if (this['isInfinite']() && z['isInfinite']()) {\n return Complex['NAN'];\n }\n\n // Infinity + z = Infinity { where z != Infinity }\n if (this['isInfinite']() || z['isInfinite']()) {\n return Complex['INFINITY'];\n }\n\n return new Complex(\n this['re'] + z['re'],\n this['im'] + z['im']);\n },\n\n /**\n * Subtracts two complex numbers\n *\n * @returns {Complex}\n */\n 'sub': function(a, b) {\n\n var z = new Complex(a, b);\n\n // Infinity - Infinity = NaN\n if (this['isInfinite']() && z['isInfinite']()) {\n return Complex['NAN'];\n }\n\n // Infinity - z = Infinity { where z != Infinity }\n if (this['isInfinite']() || z['isInfinite']()) {\n return Complex['INFINITY'];\n }\n\n return new Complex(\n this['re'] - z['re'],\n this['im'] - z['im']);\n },\n\n /**\n * Multiplies two complex numbers\n *\n * @returns {Complex}\n */\n 'mul': function(a, b) {\n\n var z = new Complex(a, b);\n\n // Infinity * 0 = NaN\n if ((this['isInfinite']() && z['isZero']()) || (this['isZero']() && z['isInfinite']())) {\n return Complex['NAN'];\n }\n\n // Infinity * z = Infinity { where z != 0 }\n if (this['isInfinite']() || z['isInfinite']()) {\n return Complex['INFINITY'];\n }\n\n // Short circuit for real values\n if (z['im'] === 0 && this['im'] === 0) {\n return new Complex(this['re'] * z['re'], 0);\n }\n\n return new Complex(\n this['re'] * z['re'] - this['im'] * z['im'],\n this['re'] * z['im'] + this['im'] * z['re']);\n },\n\n /**\n * Divides two complex numbers\n *\n * @returns {Complex}\n */\n 'div': function(a, b) {\n\n var z = new Complex(a, b);\n\n // 0 / 0 = NaN and Infinity / Infinity = NaN\n if ((this['isZero']() && z['isZero']()) || (this['isInfinite']() && z['isInfinite']())) {\n return Complex['NAN'];\n }\n\n // Infinity / 0 = Infinity\n if (this['isInfinite']() || z['isZero']()) {\n return Complex['INFINITY'];\n }\n\n // 0 / Infinity = 0\n if (this['isZero']() || z['isInfinite']()) {\n return Complex['ZERO'];\n }\n\n a = this['re'];\n b = this['im'];\n\n var c = z['re'];\n var d = z['im'];\n var t, x;\n\n if (0 === d) {\n // Divisor is real\n return new Complex(a / c, b / c);\n }\n\n if (Math.abs(c) < Math.abs(d)) {\n\n x = c / d;\n t = c * x + d;\n\n return new Complex(\n (a * x + b) / t,\n (b * x - a) / t);\n\n } else {\n\n x = d / c;\n t = d * x + c;\n\n return new Complex(\n (a + b * x) / t,\n (b - a * x) / t);\n }\n },\n\n /**\n * Calculate the power of two complex numbers\n *\n * @returns {Complex}\n */\n 'pow': function(a, b) {\n\n var z = new Complex(a, b);\n\n a = this['re'];\n b = this['im'];\n\n if (z['isZero']()) {\n return Complex['ONE'];\n }\n\n // If the exponent is real\n if (z['im'] === 0) {\n\n if (b === 0) {\n\n return new Complex(Math.pow(a, z['re']), 0);\n\n } else if (a === 0) { // If base is fully imaginary\n\n switch ((z['re'] % 4 + 4) % 4) {\n case 0:\n return new Complex(Math.pow(b, z['re']), 0);\n case 1:\n return new Complex(0, Math.pow(b, z['re']));\n case 2:\n return new Complex(-Math.pow(b, z['re']), 0);\n case 3:\n return new Complex(0, -Math.pow(b, z['re']));\n }\n }\n }\n\n /* I couldn't find a good formula, so here is a derivation and optimization\n *\n * z_1^z_2 = (a + bi)^(c + di)\n * = exp((c + di) * log(a + bi)\n * = pow(a^2 + b^2, (c + di) / 2) * exp(i(c + di)atan2(b, a))\n * =>...\n * Re = (pow(a^2 + b^2, c / 2) * exp(-d * atan2(b, a))) * cos(d * log(a^2 + b^2) / 2 + c * atan2(b, a))\n * Im = (pow(a^2 + b^2, c / 2) * exp(-d * atan2(b, a))) * sin(d * log(a^2 + b^2) / 2 + c * atan2(b, a))\n *\n * =>...\n * Re = exp(c * log(sqrt(a^2 + b^2)) - d * atan2(b, a)) * cos(d * log(sqrt(a^2 + b^2)) + c * atan2(b, a))\n * Im = exp(c * log(sqrt(a^2 + b^2)) - d * atan2(b, a)) * sin(d * log(sqrt(a^2 + b^2)) + c * atan2(b, a))\n *\n * =>\n * Re = exp(c * logsq2 - d * arg(z_1)) * cos(d * logsq2 + c * arg(z_1))\n * Im = exp(c * logsq2 - d * arg(z_1)) * sin(d * logsq2 + c * arg(z_1))\n *\n */\n\n if (a === 0 && b === 0 && z['re'] > 0 && z['im'] >= 0) {\n return Complex['ZERO'];\n }\n\n var arg = Math.atan2(b, a);\n var loh = logHypot(a, b);\n\n a = Math.exp(z['re'] * loh - z['im'] * arg);\n b = z['im'] * loh + z['re'] * arg;\n return new Complex(\n a * Math.cos(b),\n a * Math.sin(b));\n },\n\n /**\n * Calculate the complex square root\n *\n * @returns {Complex}\n */\n 'sqrt': function() {\n\n var a = this['re'];\n var b = this['im'];\n var r = this['abs']();\n\n var re, im;\n\n if (a >= 0) {\n\n if (b === 0) {\n return new Complex(Math.sqrt(a), 0);\n }\n\n re = 0.5 * Math.sqrt(2.0 * (r + a));\n } else {\n re = Math.abs(b) / Math.sqrt(2 * (r - a));\n }\n\n if (a <= 0) {\n im = 0.5 * Math.sqrt(2.0 * (r - a));\n } else {\n im = Math.abs(b) / Math.sqrt(2 * (r + a));\n }\n\n return new Complex(re, b < 0 ? -im : im);\n },\n\n /**\n * Calculate the complex exponent\n *\n * @returns {Complex}\n */\n 'exp': function() {\n\n var tmp = Math.exp(this['re']);\n\n if (this['im'] === 0) {\n //return new Complex(tmp, 0);\n }\n return new Complex(\n tmp * Math.cos(this['im']),\n tmp * Math.sin(this['im']));\n },\n\n /**\n * Calculate the complex exponent and subtracts one.\n *\n * This may be more accurate than `Complex(x).exp().sub(1)` if\n * `x` is small.\n *\n * @returns {Complex}\n */\n 'expm1': function() {\n\n /**\n * exp(a + i*b) - 1\n = exp(a) * (cos(b) + j*sin(b)) - 1\n = expm1(a)*cos(b) + cosm1(b) + j*exp(a)*sin(b)\n */\n\n var a = this['re'];\n var b = this['im'];\n\n return new Complex(\n Math.expm1(a) * Math.cos(b) + cosm1(b),\n Math.exp(a) * Math.sin(b));\n },\n\n /**\n * Calculate the natural log\n *\n * @returns {Complex}\n */\n 'log': function() {\n\n var a = this['re'];\n var b = this['im'];\n\n if (b === 0 && a > 0) {\n //return new Complex(Math.log(a), 0);\n }\n\n return new Complex(\n logHypot(a, b),\n Math.atan2(b, a));\n },\n\n /**\n * Calculate the magnitude of the complex number\n *\n * @returns {number}\n */\n 'abs': function() {\n\n return hypot(this['re'], this['im']);\n },\n\n /**\n * Calculate the angle of the complex number\n *\n * @returns {number}\n */\n 'arg': function() {\n\n return Math.atan2(this['im'], this['re']);\n },\n\n /**\n * Calculate the sine of the complex number\n *\n * @returns {Complex}\n */\n 'sin': function() {\n\n // sin(c) = (e^b - e^(-b)) / (2i)\n\n var a = this['re'];\n var b = this['im'];\n\n return new Complex(\n Math.sin(a) * cosh(b),\n Math.cos(a) * sinh(b));\n },\n\n /**\n * Calculate the cosine\n *\n * @returns {Complex}\n */\n 'cos': function() {\n\n // cos(z) = (e^b + e^(-b)) / 2\n\n var a = this['re'];\n var b = this['im'];\n\n return new Complex(\n Math.cos(a) * cosh(b),\n -Math.sin(a) * sinh(b));\n },\n\n /**\n * Calculate the tangent\n *\n * @returns {Complex}\n */\n 'tan': function() {\n\n // tan(c) = (e^(ci) - e^(-ci)) / (i(e^(ci) + e^(-ci)))\n\n var a = 2 * this['re'];\n var b = 2 * this['im'];\n var d = Math.cos(a) + cosh(b);\n\n return new Complex(\n Math.sin(a) / d,\n sinh(b) / d);\n },\n\n /**\n * Calculate the cotangent\n *\n * @returns {Complex}\n */\n 'cot': function() {\n\n // cot(c) = i(e^(ci) + e^(-ci)) / (e^(ci) - e^(-ci))\n\n var a = 2 * this['re'];\n var b = 2 * this['im'];\n var d = Math.cos(a) - cosh(b);\n\n return new Complex(\n -Math.sin(a) / d,\n sinh(b) / d);\n },\n\n /**\n * Calculate the secant\n *\n * @returns {Complex}\n */\n 'sec': function() {\n\n // sec(c) = 2 / (e^(ci) + e^(-ci))\n\n var a = this['re'];\n var b = this['im'];\n var d = 0.5 * cosh(2 * b) + 0.5 * Math.cos(2 * a);\n\n return new Complex(\n Math.cos(a) * cosh(b) / d,\n Math.sin(a) * sinh(b) / d);\n },\n\n /**\n * Calculate the cosecans\n *\n * @returns {Complex}\n */\n 'csc': function() {\n\n // csc(c) = 2i / (e^(ci) - e^(-ci))\n\n var a = this['re'];\n var b = this['im'];\n var d = 0.5 * cosh(2 * b) - 0.5 * Math.cos(2 * a);\n\n return new Complex(\n Math.sin(a) * cosh(b) / d,\n -Math.cos(a) * sinh(b) / d);\n },\n\n /**\n * Calculate the complex arcus sinus\n *\n * @returns {Complex}\n */\n 'asin': function() {\n\n // asin(c) = -i * log(ci + sqrt(1 - c^2))\n\n var a = this['re'];\n var b = this['im'];\n\n var t1 = new Complex(\n b * b - a * a + 1,\n -2 * a * b)['sqrt']();\n\n var t2 = new Complex(\n t1['re'] - b,\n t1['im'] + a)['log']();\n\n return new Complex(t2['im'], -t2['re']);\n },\n\n /**\n * Calculate the complex arcus cosinus\n *\n * @returns {Complex}\n */\n 'acos': function() {\n\n // acos(c) = i * log(c - i * sqrt(1 - c^2))\n\n var a = this['re'];\n var b = this['im'];\n\n var t1 = new Complex(\n b * b - a * a + 1,\n -2 * a * b)['sqrt']();\n\n var t2 = new Complex(\n t1['re'] - b,\n t1['im'] + a)['log']();\n\n return new Complex(Math.PI / 2 - t2['im'], t2['re']);\n },\n\n /**\n * Calculate the complex arcus tangent\n *\n * @returns {Complex}\n */\n 'atan': function() {\n\n // atan(c) = i / 2 log((i + x) / (i - x))\n\n var a = this['re'];\n var b = this['im'];\n\n if (a === 0) {\n\n if (b === 1) {\n return new Complex(0, Infinity);\n }\n\n if (b === -1) {\n return new Complex(0, -Infinity);\n }\n }\n\n var d = a * a + (1.0 - b) * (1.0 - b);\n\n var t1 = new Complex(\n (1 - b * b - a * a) / d,\n -2 * a / d).log();\n\n return new Complex(-0.5 * t1['im'], 0.5 * t1['re']);\n },\n\n /**\n * Calculate the complex arcus cotangent\n *\n * @returns {Complex}\n */\n 'acot': function() {\n\n // acot(c) = i / 2 log((c - i) / (c + i))\n\n var a = this['re'];\n var b = this['im'];\n\n if (b === 0) {\n return new Complex(Math.atan2(1, a), 0);\n }\n\n var d = a * a + b * b;\n return (d !== 0)\n ? new Complex(\n a / d,\n -b / d).atan()\n : new Complex(\n (a !== 0) ? a / 0 : 0,\n (b !== 0) ? -b / 0 : 0).atan();\n },\n\n /**\n * Calculate the complex arcus secant\n *\n * @returns {Complex}\n */\n 'asec': function() {\n\n // asec(c) = -i * log(1 / c + sqrt(1 - i / c^2))\n\n var a = this['re'];\n var b = this['im'];\n\n if (a === 0 && b === 0) {\n return new Complex(0, Infinity);\n }\n\n var d = a * a + b * b;\n return (d !== 0)\n ? new Complex(\n a / d,\n -b / d).acos()\n : new Complex(\n (a !== 0) ? a / 0 : 0,\n (b !== 0) ? -b / 0 : 0).acos();\n },\n\n /**\n * Calculate the complex arcus cosecans\n *\n * @returns {Complex}\n */\n 'acsc': function() {\n\n // acsc(c) = -i * log(i / c + sqrt(1 - 1 / c^2))\n\n var a = this['re'];\n var b = this['im'];\n\n if (a === 0 && b === 0) {\n return new Complex(Math.PI / 2, Infinity);\n }\n\n var d = a * a + b * b;\n return (d !== 0)\n ? new Complex(\n a / d,\n -b / d).asin()\n : new Complex(\n (a !== 0) ? a / 0 : 0,\n (b !== 0) ? -b / 0 : 0).asin();\n },\n\n /**\n * Calculate the complex sinh\n *\n * @returns {Complex}\n */\n 'sinh': function() {\n\n // sinh(c) = (e^c - e^-c) / 2\n\n var a = this['re'];\n var b = this['im'];\n\n return new Complex(\n sinh(a) * Math.cos(b),\n cosh(a) * Math.sin(b));\n },\n\n /**\n * Calculate the complex cosh\n *\n * @returns {Complex}\n */\n 'cosh': function() {\n\n // cosh(c) = (e^c + e^-c) / 2\n\n var a = this['re'];\n var b = this['im'];\n\n return new Complex(\n cosh(a) * Math.cos(b),\n sinh(a) * Math.sin(b));\n },\n\n /**\n * Calculate the complex tanh\n *\n * @returns {Complex}\n */\n 'tanh': function() {\n\n // tanh(c) = (e^c - e^-c) / (e^c + e^-c)\n\n var a = 2 * this['re'];\n var b = 2 * this['im'];\n var d = cosh(a) + Math.cos(b);\n\n return new Complex(\n sinh(a) / d,\n Math.sin(b) / d);\n },\n\n /**\n * Calculate the complex coth\n *\n * @returns {Complex}\n */\n 'coth': function() {\n\n // coth(c) = (e^c + e^-c) / (e^c - e^-c)\n\n var a = 2 * this['re'];\n var b = 2 * this['im'];\n var d = cosh(a) - Math.cos(b);\n\n return new Complex(\n sinh(a) / d,\n -Math.sin(b) / d);\n },\n\n /**\n * Calculate the complex coth\n *\n * @returns {Complex}\n */\n 'csch': function() {\n\n // csch(c) = 2 / (e^c - e^-c)\n\n var a = this['re'];\n var b = this['im'];\n var d = Math.cos(2 * b) - cosh(2 * a);\n\n return new Complex(\n -2 * sinh(a) * Math.cos(b) / d,\n 2 * cosh(a) * Math.sin(b) / d);\n },\n\n /**\n * Calculate the complex sech\n *\n * @returns {Complex}\n */\n 'sech': function() {\n\n // sech(c) = 2 / (e^c + e^-c)\n\n var a = this['re'];\n var b = this['im'];\n var d = Math.cos(2 * b) + cosh(2 * a);\n\n return new Complex(\n 2 * cosh(a) * Math.cos(b) / d,\n -2 * sinh(a) * Math.sin(b) / d);\n },\n\n /**\n * Calculate the complex asinh\n *\n * @returns {Complex}\n */\n 'asinh': function() {\n\n // asinh(c) = log(c + sqrt(c^2 + 1))\n\n var tmp = this['im'];\n this['im'] = -this['re'];\n this['re'] = tmp;\n var res = this['asin']();\n\n this['re'] = -this['im'];\n this['im'] = tmp;\n tmp = res['re'];\n\n res['re'] = -res['im'];\n res['im'] = tmp;\n return res;\n },\n\n /**\n * Calculate the complex acosh\n *\n * @returns {Complex}\n */\n 'acosh': function() {\n\n // acosh(c) = log(c + sqrt(c^2 - 1))\n\n var res = this['acos']();\n if (res['im'] <= 0) {\n var tmp = res['re'];\n res['re'] = -res['im'];\n res['im'] = tmp;\n } else {\n var tmp = res['im'];\n res['im'] = -res['re'];\n res['re'] = tmp;\n }\n return res;\n },\n\n /**\n * Calculate the complex atanh\n *\n * @returns {Complex}\n */\n 'atanh': function() {\n\n // atanh(c) = log((1+c) / (1-c)) / 2\n\n var a = this['re'];\n var b = this['im'];\n\n var noIM = a > 1 && b === 0;\n var oneMinus = 1 - a;\n var onePlus = 1 + a;\n var d = oneMinus * oneMinus + b * b;\n\n var x = (d !== 0)\n ? new Complex(\n (onePlus * oneMinus - b * b) / d,\n (b * oneMinus + onePlus * b) / d)\n : new Complex(\n (a !== -1) ? (a / 0) : 0,\n (b !== 0) ? (b / 0) : 0);\n\n var temp = x['re'];\n x['re'] = logHypot(x['re'], x['im']) / 2;\n x['im'] = Math.atan2(x['im'], temp) / 2;\n if (noIM) {\n x['im'] = -x['im'];\n }\n return x;\n },\n\n /**\n * Calculate the complex acoth\n *\n * @returns {Complex}\n */\n 'acoth': function() {\n\n // acoth(c) = log((c+1) / (c-1)) / 2\n\n var a = this['re'];\n var b = this['im'];\n\n if (a === 0 && b === 0) {\n return new Complex(0, Math.PI / 2);\n }\n\n var d = a * a + b * b;\n return (d !== 0)\n ? new Complex(\n a / d,\n -b / d).atanh()\n : new Complex(\n (a !== 0) ? a / 0 : 0,\n (b !== 0) ? -b / 0 : 0).atanh();\n },\n\n /**\n * Calculate the complex acsch\n *\n * @returns {Complex}\n */\n 'acsch': function() {\n\n // acsch(c) = log((1+sqrt(1+c^2))/c)\n\n var a = this['re'];\n var b = this['im'];\n\n if (b === 0) {\n\n return new Complex(\n (a !== 0)\n ? Math.log(a + Math.sqrt(a * a + 1))\n : Infinity, 0);\n }\n\n var d = a * a + b * b;\n return (d !== 0)\n ? new Complex(\n a / d,\n -b / d).asinh()\n : new Complex(\n (a !== 0) ? a / 0 : 0,\n (b !== 0) ? -b / 0 : 0).asinh();\n },\n\n /**\n * Calculate the complex asech\n *\n * @returns {Complex}\n */\n 'asech': function() {\n\n // asech(c) = log((1+sqrt(1-c^2))/c)\n\n var a = this['re'];\n var b = this['im'];\n\n if (this['isZero']()) {\n return Complex['INFINITY'];\n }\n\n var d = a * a + b * b;\n return (d !== 0)\n ? new Complex(\n a / d,\n -b / d).acosh()\n : new Complex(\n (a !== 0) ? a / 0 : 0,\n (b !== 0) ? -b / 0 : 0).acosh();\n },\n\n /**\n * Calculate the complex inverse 1/z\n *\n * @returns {Complex}\n */\n 'inverse': function() {\n\n // 1 / 0 = Infinity and 1 / Infinity = 0\n if (this['isZero']()) {\n return Complex['INFINITY'];\n }\n\n if (this['isInfinite']()) {\n return Complex['ZERO'];\n }\n\n var a = this['re'];\n var b = this['im'];\n\n var d = a * a + b * b;\n\n return new Complex(a / d, -b / d);\n },\n\n /**\n * Returns the complex conjugate\n *\n * @returns {Complex}\n */\n 'conjugate': function() {\n\n return new Complex(this['re'], -this['im']);\n },\n\n /**\n * Gets the negated complex number\n *\n * @returns {Complex}\n */\n 'neg': function() {\n\n return new Complex(-this['re'], -this['im']);\n },\n\n /**\n * Ceils the actual complex number\n *\n * @returns {Complex}\n */\n 'ceil': function(places) {\n\n places = Math.pow(10, places || 0);\n\n return new Complex(\n Math.ceil(this['re'] * places) / places,\n Math.ceil(this['im'] * places) / places);\n },\n\n /**\n * Floors the actual complex number\n *\n * @returns {Complex}\n */\n 'floor': function(places) {\n\n places = Math.pow(10, places || 0);\n\n return new Complex(\n Math.floor(this['re'] * places) / places,\n Math.floor(this['im'] * places) / places);\n },\n\n /**\n * Ceils the actual complex number\n *\n * @returns {Complex}\n */\n 'round': function(places) {\n\n places = Math.pow(10, places || 0);\n\n return new Complex(\n Math.round(this['re'] * places) / places,\n Math.round(this['im'] * places) / places);\n },\n\n /**\n * Compares two complex numbers\n *\n * **Note:** new Complex(Infinity).equals(Infinity) === false\n *\n * @returns {boolean}\n */\n 'equals': function(a, b) {\n\n var z = new Complex(a, b);\n\n return Math.abs(z['re'] - this['re']) <= Complex['EPSILON'] &&\n Math.abs(z['im'] - this['im']) <= Complex['EPSILON'];\n },\n\n /**\n * Clones the actual object\n *\n * @returns {Complex}\n */\n 'clone': function() {\n\n return new Complex(this['re'], this['im']);\n },\n\n /**\n * Gets a string of the actual complex number\n *\n * @returns {string}\n */\n 'toString': function() {\n\n var a = this['re'];\n var b = this['im'];\n var ret = \"\";\n\n if (this['isNaN']()) {\n return 'NaN';\n }\n\n if (this['isInfinite']()) {\n return 'Infinity';\n }\n\n // If is real number\n if (b === 0) {\n return ret + a;\n }\n\n if (a !== 0) {\n ret+= a;\n ret+= \" \";\n if (b < 0) {\n b = -b;\n ret+= \"-\";\n } else {\n ret+= \"+\";\n }\n ret+= \" \";\n } else if (b < 0) {\n b = -b;\n ret+= \"-\";\n }\n\n if (1 !== b) { // b is the absolute imaginary part\n ret+= b;\n }\n return ret + \"i\";\n },\n\n /**\n * Returns the actual number as a vector\n *\n * @returns {Array}\n */\n 'toVector': function() {\n\n return [this['re'], this['im']];\n },\n\n /**\n * Returns the actual real value of the current object\n *\n * @returns {number|null}\n */\n 'valueOf': function() {\n\n if (this['im'] === 0) {\n return this['re'];\n }\n return null;\n },\n\n /**\n * Determines whether a complex number is not on the Riemann sphere.\n *\n * @returns {boolean}\n */\n 'isNaN': function() {\n return isNaN(this['re']) || isNaN(this['im']);\n },\n\n /**\n * Determines whether or not a complex number is at the zero pole of the\n * Riemann sphere.\n *\n * @returns {boolean}\n */\n 'isZero': function() {\n return this['im'] === 0 && this['re'] === 0;\n },\n\n /**\n * Determines whether a complex number is not at the infinity pole of the\n * Riemann sphere.\n *\n * @returns {boolean}\n */\n 'isFinite': function() {\n return isFinite(this['re']) && isFinite(this['im']);\n },\n\n /**\n * Determines whether or not a complex number is at the infinity pole of the\n * Riemann sphere.\n *\n * @returns {boolean}\n */\n 'isInfinite': function() {\n return !(this['isNaN']() || this['isFinite']());\n }\n};\n\nComplex['ZERO'] = new Complex(0, 0);\nComplex['ONE'] = new Complex(1, 0);\nComplex['I'] = new Complex(0, 1);\nComplex['PI'] = new Complex(Math.PI, 0);\nComplex['E'] = new Complex(Math.E, 0);\nComplex['INFINITY'] = new Complex(Infinity, Infinity);\nComplex['NAN'] = new Complex(NaN, NaN);\nComplex['EPSILON'] = 1e-16;\n\n// Since no need to customize the export in React, we can just export the class directly\n\n// if (typeof define === 'function' && define['amd']) {\n// define([], function() {\n// return Complex;\n// });\n// } else if (typeof exports === 'object') {\n// Object.defineProperty(Complex, \"__esModule\", {'value': true});\n// Complex['default'] = Complex;\n// Complex['Complex'] = Complex;\n// module['exports'] = Complex;\n// } else {\n// root['Complex'] = Complex;\n// }\n\nexport 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