{"version":3,"file":"index.cjs","sources":["../node_modules/@rec-math/math/esm/index.js","../../src/physical-constants.ts","../../src/stretch-range.ts","../../src/survey-parameters.ts","../../src/model.ts","../../src/index.ts"],"sourcesContent":["/*! @rec-math/math v1.3.0 2022-06-28 23:54:20\n * https://github.com/rec-math/ts-math#readme\n * Copyright pbuk (https://github.com/pb-uk) MIT license.\n */\n\n// rec-math/src/version.ts\r\nconst version = '1.3.0';\n\n// rec-math/src/numerical/quad/adaptive-quadrature.ts\r\n/** Defaults for integration. */\r\nconst defaults = {\r\n /**\r\n * Target error estimate for a step: if this is smaller it can lead to\r\n * accumulation of roundoff errors.\r\n */\r\n epsilon: Number.EPSILON * 16,\r\n /**\r\n * Maximum depth \\\\( d_{max} \\\\)for integration: the maximum number of steps\r\n * can be \\\\( 2^{d_{max}} \\\\).\r\n * */\r\n maxDepth: Infinity,\r\n};\r\n/**\r\n * Perform a substitution with an appropriate change of variables to deal with\r\n * infinite ranges.\r\n *\r\n * @param f Integrand callback.\r\n * @param a Lower limit.\r\n * @param b Upper limit.\r\n * @returns An array with any necessary substitution.\r\n */\r\nconst changeOfVariables = (f, a, b) => {\r\n if (!isFinite(b)) {\r\n if (!isFinite(a)) {\r\n // Change variables to integrate between - and + infinity.\r\n const _f = (t) => {\r\n const tSquared = t * t;\r\n const oneOverOneMinusTSquared = 1 / (1 - tSquared);\r\n return (f(t * oneOverOneMinusTSquared) *\r\n (1 + tSquared) *\r\n oneOverOneMinusTSquared *\r\n oneOverOneMinusTSquared);\r\n };\r\n return [_f, -1, 1];\r\n }\r\n // Change variables to integrate up to infinity.\r\n const _f = (t) => {\r\n const oneOverOneMinusT = 1 / (1 - t);\r\n return f(a + t * oneOverOneMinusT) * oneOverOneMinusT * oneOverOneMinusT;\r\n };\r\n return [_f, 0, 1];\r\n }\r\n if (!isFinite(a)) {\r\n // Change variables to integrate up from negative infinity.\r\n const _f = (t) => {\r\n return f(b - (1 - t) / t) / (t * t);\r\n };\r\n return [_f, 0, 1];\r\n }\r\n return [f, a, b];\r\n};\r\nconst integrate = (integrationStep, f, a, b, options = {}) => {\r\n // Establish settings.\r\n const settings = Object.assign(Object.assign({}, defaults), options);\r\n const { epsilon, maxDepth } = settings;\r\n const info = { steps: 0, errorEstimate: 0, depth: 1 };\r\n // Allow for a change of variables to deal with infinite limits.\r\n const [_f, _a, _b] = changeOfVariables(f, a, b);\r\n // Get estimate so we can work out the acceptable global error.\r\n // Use a depth of 1 to calculate a 15 point Kronrod quadrature.\r\n let [result, errorEstimate] = integrate_part(integrationStep, _f, // Integrand.\r\n _a, // Lower limit.\r\n _b, // Upper limit.\r\n 1, // New depth.\r\n 1, // Maximum depth.\r\n 0, Object.assign({}, info));\r\n // Now calculate using the target global error.\r\n const acceptableUnitError = Math.abs((epsilon * result) / (_b - _a));\r\n [result, errorEstimate] = integrate_part(integrationStep, _f, // Integrand.\r\n _a, // Lower limit.\r\n _b, // Upper limit.\r\n 1, // New depth.\r\n maxDepth, // Maximum depth.\r\n acceptableUnitError, // Acceptable error per unit step.\r\n info);\r\n return [result, Object.assign(Object.assign({}, info), { errorEstimate })];\r\n};\r\nconst integrate_part = (integrationStep, f, a, // Lower limit.\r\nb, // Upper limit.\r\ndepth, // New depth.\r\nmaxDepth, // Maximum depth.\r\nacceptableUnitError, // Acceptable error per unit step.\r\ninfo) => {\r\n // Initialize things.\r\n const [currentEstimate, poorEstimate] = integrationStep(f, // Integrand.\r\n a, // Lower limit.\r\n b);\r\n const errorEstimate = Math.abs(poorEstimate - currentEstimate);\r\n if (depth >= maxDepth) {\r\n // Reached the maximum allowable depth so return the partial sum.\r\n ++info.steps;\r\n return [currentEstimate, errorEstimate];\r\n }\r\n const acceptableError = acceptableUnitError * (b - a);\r\n if (errorEstimate <= acceptableError) {\r\n // Error is acceptable for the size of step so return the partial sum.\r\n ++info.steps;\r\n return [currentEstimate, errorEstimate];\r\n }\r\n const mid = (a + b) / 2;\r\n if (a >= mid || mid >= b) {\r\n // We can't make this step any smaller: looks like a discontinuity.\r\n info.isUnreliable = true;\r\n const safeErrorEstimate = isNaN(errorEstimate) ? 0 : errorEstimate;\r\n if (isNaN(currentEstimate) || Math.abs(currentEstimate) === Infinity) {\r\n return [0, safeErrorEstimate];\r\n }\r\n return [currentEstimate, safeErrorEstimate];\r\n }\r\n // Recurse deeper.\r\n ++depth;\r\n if (depth > info.depth) {\r\n info.depth = depth;\r\n }\r\n const [leftEstimate, leftErrorEstimate] = integrate_part(integrationStep, f, // Integrand.\r\n a, // Lower limit.\r\n mid, // Upper limit.\r\n depth, // New depth.\r\n maxDepth, // Maximum depth.\r\n acceptableUnitError, // Acceptable error per unit step.\r\n info);\r\n const [rightEstimate, rightErrorEstimate] = integrate_part(integrationStep, f, // Integrand.\r\n mid, // Lower limit.\r\n b, // Upper limit.\r\n depth, // New depth.\r\n maxDepth, // Maximum depth.\r\n acceptableUnitError, // Acceptable error per unit step.\r\n info);\r\n return [leftEstimate + rightEstimate, leftErrorEstimate + rightErrorEstimate];\r\n};\n\n// rec-math/src/numerical/quad/gauss-kronrod-g7k15.ts\r\n// Gauss-Kronrod constants (G7, K15) on [-1, 1].\r\n// https://www.advanpix.com/2011/11/07/gauss-kronrod-quadrature-nodes-weights/\r\n// node_g0k0 = 0;\r\n// node_g1k2 = 4.058451513773971669066064120769615e-01 exact;\r\nconst node_g1k2 = 0.4058451513773972;\r\n// node_g2k4 = 7.415311855993944398638647732807884e-01 exact;\r\nconst node_g2k4 = 0.7415311855993945;\r\n// node_g3k6 = 9.491079123427585245261896840478513e-01 exact;\r\nconst node_g3k6 = 0.9491079123427585;\r\n// node_k1 = 2.077849550078984676006894037732449e-01 exact;\r\nconst node_k1 = 0.20778495500789848;\r\n// node_k3 = 5.860872354676911302941448382587296e-01 exact;\r\nconst node_k3 = 0.5860872354676911;\r\n// node_k5 = 8.648644233597690727897127886409262e-01 exact;\r\nconst node_k5 = 0.8648644233597691;\r\n// node_k7 = 9.914553711208126392068546975263285e-01 exact;\r\nconst node_k7 = 0.9914553711208126;\r\n// weight_g0 = 4.179591836734693877551020408163265e-01 exact;\r\nconst weight_g0 = 0.4179591836734694;\r\n// weight_g1 = 3.818300505051189449503697754889751e-01 exact;\r\nconst weight_g1 = 0.3818300505051189;\r\n// weight_g2 = 2.797053914892766679014677714237796e-01 exact;\r\nconst weight_g2 = 0.27970539148927664;\r\n// weight_g3 = 1.294849661688696932706114326790820e-01 exact;\r\nconst weight_g3 = 0.1294849661688697;\r\n// weight_k0 = 2.094821410847278280129991748917143e-01 exact;\r\nconst weight_k0 = 0.20948214108472782;\r\n// weight_k1 = 2.044329400752988924141619992346491e-01 exact;\r\nconst weight_k1 = 0.20443294007529889;\r\n// weight_k2 = 1.903505780647854099132564024210137e-01 exact;\r\nconst weight_k2 = 0.19035057806478542;\r\n// weight_k3 = 1.690047266392679028265834265985503e-01 exact;\r\nconst weight_k3 = 0.1690047266392679;\r\n// weight_k4 = 1.406532597155259187451895905102379e-01 exact;\r\nconst weight_k4 = 0.14065325971552592;\r\n// weight_k5 = 1.047900103222501838398763225415180e-01 exact;\r\nconst weight_k5 = 0.10479001032225019;\r\n// weight_k6 = 6.309209262997855329070066318920429e-02 exact;\r\nconst weight_k6 = 0.06309209262997856;\r\n// weight_k7 = 2.293532201052922496373200805896959e-02 exact;\r\nconst weight_k7 = 0.022935322010529224;\r\n/**\r\n * Perform a single integration step.\r\n *\r\n * @param f Integrand callback.\r\n * @param a Lower limit.\r\n * @param b Upper limit.\r\n * @returns [current best estimate, poor estimate]\r\n */\r\nconst integrationStep = (f, // Integrand.\r\na, // Lower limit.\r\nb) => {\r\n // Gauss-Kronrod (G7, K15).\r\n const scale = (b - a) / 2;\r\n const offset = (a + b) / 2;\r\n // const scaled_g0k0 = 0;\r\n const scaled_k1 = node_k1 * scale;\r\n const scaled_g1k2 = node_g1k2 * scale;\r\n const scaled_k3 = node_k3 * scale;\r\n const scaled_g2k4 = node_g2k4 * scale;\r\n const scaled_k5 = node_k5 * scale;\r\n const scaled_g3k6 = node_g3k6 * scale;\r\n const scaled_k7 = node_k7 * scale;\r\n const scaled_weight_g0 = weight_g0 * scale;\r\n const scaled_weight_g1 = weight_g1 * scale;\r\n const scaled_weight_g2 = weight_g2 * scale;\r\n const scaled_weight_g3 = weight_g3 * scale;\r\n const scaled_weight_k0 = weight_k0 * scale;\r\n const scaled_weight_k1 = weight_k1 * scale;\r\n const scaled_weight_k2 = weight_k2 * scale;\r\n const scaled_weight_k3 = weight_k3 * scale;\r\n const scaled_weight_k4 = weight_k4 * scale;\r\n const scaled_weight_k5 = weight_k5 * scale;\r\n const scaled_weight_k6 = weight_k6 * scale;\r\n const scaled_weight_k7 = weight_k7 * scale;\r\n const f_g0k0 = f(offset);\r\n const f_k1_h = f(offset + scaled_k1);\r\n const f_k1_l = f(offset - scaled_k1);\r\n const f_g1k2_h = f(offset + scaled_g1k2);\r\n const f_g1k2_l = f(offset - scaled_g1k2);\r\n const f_k3_h = f(offset + scaled_k3);\r\n const f_k3_l = f(offset - scaled_k3);\r\n const f_g2k4_h = f(offset + scaled_g2k4);\r\n const f_g2k4_l = f(offset - scaled_g2k4);\r\n const f_k5_h = f(offset + scaled_k5);\r\n const f_k5_l = f(offset - scaled_k5);\r\n const f_g3k6_h = f(offset + scaled_g3k6);\r\n const f_g3k6_l = f(offset - scaled_g3k6);\r\n const f_k7_h = f(offset + scaled_k7);\r\n const f_k7_l = f(offset - scaled_k7);\r\n const poorEstimate = scaled_weight_g0 * f_g0k0 + // g0\r\n scaled_weight_g1 * (f_g1k2_h + f_g1k2_l) + // g1\r\n scaled_weight_g2 * (f_g2k4_h + f_g2k4_l) + // g2\r\n scaled_weight_g3 * (f_g3k6_h + f_g3k6_l); // g3\r\n const currentEstimate = scaled_weight_k0 * f_g0k0 + // k0\r\n scaled_weight_k1 * (f_k1_h + f_k1_l) + // k1\r\n scaled_weight_k2 * (f_g1k2_h + f_g1k2_l) + // k2\r\n scaled_weight_k3 * (f_k3_h + f_k3_l) + // k3\r\n scaled_weight_k4 * (f_g2k4_h + f_g2k4_l) + // k4\r\n scaled_weight_k5 * (f_k5_h + f_k5_l) + // k5\r\n scaled_weight_k6 * (f_g3k6_h + f_g3k6_l) + // k6\r\n scaled_weight_k7 * (f_k7_h + f_k7_l); // k7\r\n return [currentEstimate, poorEstimate];\r\n};\n\n// rec-math/src/numerical/quad/index.ts\r\nconst rangeErrorMessage = 'integration range must be an array of at least two endpoints';\r\n/**\r\n * Numerically compute a definite integral.\r\n *\r\n * @param f Callback returning value of integrand.\r\n * @param range A range of at least 2 endpoints.\r\n * @param options Options for the computation.\r\n *\r\n * @returns The results of the computation.\r\n */\r\nconst quad = (f, range, options = {}) => {\r\n // Interpret the range.\r\n if (!Array.isArray(range)) {\r\n throw new RangeError(rangeErrorMessage);\r\n }\r\n if (range.length === 2) {\r\n // Integrate over a single range.\r\n const [a, b] = range;\r\n return integrate(integrationStep, f, a, b, options);\r\n }\r\n if (range.length < 2) {\r\n // Can't integrate at a point!\r\n throw new RangeError(rangeErrorMessage);\r\n }\r\n // Integrate over multiple ranges.\r\n let result = 0;\r\n const points = [];\r\n const info = {\r\n steps: 0,\r\n errorEstimate: 0,\r\n points,\r\n depth: 0,\r\n };\r\n for (let i = 0; i < range.length - 1; ++i) {\r\n const single = integrate(integrationStep, f, range[i], range[i + 1], options);\r\n info.points.push(single);\r\n // Update the result.\r\n result += single[0];\r\n // Update the cumulative statistics.\r\n info.steps += single[1].steps;\r\n info.errorEstimate += single[1].errorEstimate;\r\n info.depth = Math.max(info.depth, single[1].depth);\r\n }\r\n return [result, info];\r\n};\n\n// rec-math/src/numerical/index.ts\n\nvar index = /*#__PURE__*/Object.freeze({\n __proto__: null,\n quad: quad\n});\n\nexport { index as numerical, version };\n//# sourceMappingURL=index.js.map\n","/**\n * Speed of light (c).\n *\n * c = 299,792,458 m/s by definition.\n */\nexport const c = 299792458;\n\n/**\n * Gravitational constant G.\n *\n * G = 6.674 30(15)e-11 m^3 kg-1 s-2 (https://physics.nist.gov/constants)\n */\nexport const g = 6.6743e-11;\n\n/**\n * \\\\( \\frac{3}{8 \\pi G} \\\\)\n * ~1.78844 53398 69671 75324 24796 9868579134180130851632893841\n */\nexport const rhoConst = 1.7884453398696718e9;\n\n// Conversions -----------------------------------------------------------------\n/**\n * Convert astornomical units to metres.\n *\n * 1 AU = 149,597,870,700 m by definition.\n */\nexport const auToM = 149597870700;\n\n/**\n * Convert gigayears to seconds.\n *\n * Calculated as 1e9 years * 365.25 days * 86,400 s using a Julian Year.\n *\n * @see https://www.iau.org/public/themes/measuring/\n */\nexport const gyrToSeconds = 3.15576e16;\n\n/**\n * Conversion factor for the Hubble parameter.\n *\n * Convert from \\\\( km.s^{-1}Mpsc^{-1} \\\\) to Gyr. Calculation:\n * - 1 parsec = \\\\( 648,000 / \\pi \\\\) au.\n * - 1 au = 149,597,870,700 m.\n * - 1 parsec = \\\\( \\frac{96,939,420,213,600,000}\\pi \\\\) m\n * - 1 Gyr = \\\\( 1e9 \\times 365.25 \\times 86,400 \\\\) s.\n * \\\\( \\frac{3.15576e16 \\pi }{96,939,420,213,600,000} \\\\)\n * \\\\( \\frac{3.15576e16 \\pi }{1495978707} \\\\)\n * $$\\frac{487,000}{1,495,978,707} \\pi \\approx 1.02271 21650 45694 937 e-3$$\n */\nexport const kmsmpscToGyr = 1.022712165045695e-3;\n\n/**\n * Convert light years to metres.\n *\n * 299792458 * 365.25 * 86400 = 9,460,730,472,580,800. This is larger than\n * MAX_SAFE_INTEGER but is stored exactly as a float.\n */\nexport const lyToM = 9.4607304725808e15;\n\n/**\n * Convert parsecs to light years.\n * \\\\(\\frac{149,597,870,700 \\times 648,000}{(299,792,458 \\times 365.25 \\times 86400)\\pi}\\\\)\n * \\\\(\\frac{969,394,202,136,000}{94,607,304,725,808\\pi}\\\\)\n * ~3.26156 37771 67433 56213\n * Note the last digit is not an error, it is a 7 due to machine epsilon.\n */\nexport const parsecToLy = 3.2615637771674337;\n\n/**\n * Convert parsecs to metres.\n *\n * - 1 parsec = \\\\( 648,000 / \\pi \\\\) au.\n * - 1 au = 149,597,870,700 m.\n * - 1 parsec = \\\\( \\frac{648,000 \\times 149,597,870,700}\\pi \\\\) m\n * \\\\( \\frac{96,939,420,213,600,000}\\pi \\\\)\n * ~3.08567 75814 91367 27891 e16\n */\nexport const parsecToM = 3.085677581491367e16;\n","// cosmic-expansion/src/stretch-range.ts\n\n/**\n * Compute stretch range.\n */\ninterface StretchInputs {\n exponentialSteps?: boolean;\n stretch: [upper: number, lower: number] | number[];\n steps?: number;\n}\n\n/**\n * Add values to an existing array of steps, decreasing linearly.\n *\n * @param steps Existing steps to add new values to.\n * @param upper Upper bound (already in `steps`).\n * @param lower Lower bound.\n * @param count Number of steps to add.\n * @returns\n */\nconst addLinearStretchValues = (\n steps: number[],\n upper: number,\n lower: number,\n count: number\n) => {\n for (let i = 1; i < count; ++i) {\n steps.push(upper - ((upper - lower) * i) / count);\n }\n steps.push(lower);\n\n return steps;\n};\n\n/**\n * Add values to an existing array of steps, decreasing exponentially.\n *\n * @param steps Existing steps to add new values to.\n * @param upper Upper bound (already in `steps`).\n * @param lower Lower bound.\n * @param count Number of steps to add.\n * @returns\n */\nconst addStretchValues = (\n steps: number[],\n upper: number,\n lower: number,\n count: number\n) => {\n const factor = (lower / upper) ** (1 / count);\n let current = upper;\n for (let i = 0; i < count - 1; ++i) {\n current *= factor;\n steps.push(current);\n }\n steps.push(lower);\n\n return steps;\n};\n\n/**\n * Get a list of values for stretch factor s (i.e. 1 + redshift (z)).\n *\n * @todo Implement linear steps (currently only exponential).\n * @todo Deal with negative step values.\n * @param inputs Sanitized inputs.\n * @returns Sanitized inputs.\n */\nexport const getStretchValues = (inputs: StretchInputs): number[] => {\n const { stretch, steps: stepCount, exponentialSteps } = inputs;\n\n // If there is no count we must have the values already.\n if (!stepCount) {\n return stretch;\n }\n\n // Get the bounds and add the first value.\n const [upper, lower] = stretch;\n const steps = [upper];\n\n if (lower >= 1 || upper <= 1) {\n // If s = 1 is not spanned by the range just do even steps all the way down.\n if (exponentialSteps) {\n addStretchValues(steps, upper, lower, stepCount);\n return steps;\n }\n addLinearStretchValues(steps, upper, lower, stepCount);\n return steps;\n }\n\n if (exponentialSteps) {\n // Add steps separately above and below 1 to ensure s = 1 is included exactly.\n const factor = (lower / upper) ** (1 / stepCount);\n const countLower = Math.round(Math.log(lower) / Math.log(factor));\n // From upper down to 1.\n addStretchValues(steps, upper, 1, stepCount - countLower);\n // From 1 down to lower.\n addStretchValues(steps, 1, lower, countLower);\n return steps;\n }\n\n // Add steps separately above and below 1 to ensure s = 1 is included exactly.\n const step = (upper - lower) / stepCount;\n const countLower = Math.round((1 - lower) / step);\n // From upper down to 1.\n addLinearStretchValues(steps, upper, 1, stepCount - countLower);\n // From 1 down to lower.\n addLinearStretchValues(steps, 1, lower, countLower);\n return steps;\n};\n","export interface CosmicExpansionSurvey {\n h0: number;\n omegaLambda0?: number;\n omegaM0?: number;\n zEq: number;\n sigma8?: number;\n omega0: number;\n temperature0: number;\n age?: number;\n}\n\n/**\n * Parameters from the Planck 2018 survey with baryon acoustic oscillations\n * (BAO) data.\n *\n * Planck 2018: https://arxiv.org/abs/1807.06209\n */\nexport const planck2018Bao: CosmicExpansionSurvey = {\n h0: 67.66,\n omegaM0: 0.3111,\n zEq: 3387,\n omega0: 1,\n temperature0: 2.72548,\n age: 13.787,\n};\n\n/**\n * Parameters from the Planck 2018 survey.\n *\n * Planck 2018: https://arxiv.org/abs/1807.06209\n */\nexport const planck2018: CosmicExpansionSurvey = {\n h0: 67.36,\n // omegaLambda0: 0.6847,\n omegaM0: 0.3153,\n sigma8: 0.8111,\n zEq: 3402,\n omega0: 1,\n temperature0: 2.72548,\n age: 13.797,\n};\n\n/**\n * Parameters from the Planck 2015 survey - unverified.\n *\n * @todo Verify Planck 2015 parameters.\n */\nexport const planck2015: CosmicExpansionSurvey = {\n h0: 67.74,\n omegaLambda0: 0.691,\n zEq: 3370,\n omega0: 1,\n temperature0: 2.72548,\n};\n\n/**\n * Parameters from the WMAP 2013 survey - unverified.\n *\n * @todo Verify WMAP 2013 parameters.\n */\nexport const wmap2013: CosmicExpansionSurvey = {\n h0: 69.8,\n omegaLambda0: 0.72,\n zEq: 3300,\n omega0: 1,\n temperature0: 2.72548,\n};\n","// cosmic-expansion/src/model.ts\nimport { numerical } from '@rec-math/math';\n\nimport * as physicalConstants from './physical-constants.js';\nimport { getStretchValues } from './stretch-range.js';\nimport * as surveyParameters from './survey-parameters.js';\n\nconst defaultSurvey = 'planck2018Bao';\n\n/**\n * H(s)^2 = H_0^2 (\\Omega_m s^3 + \\Omega_{rad} s^4 + \\Omega_\\Lambda s^{3(1+w)} + \\Omega_k s^2 )\n */\n\nexport interface ExpansionInputs {\n /** Upper and lower bounds for stretch, or an array of values. */\n stretch: [upper: number, lower: number] | number[];\n /** The number of steps to take between the upper and lower stretch bounds. */\n steps?: number;\n /** Stretch steps are linear by default, set this to `true` for exponential steps. */\n exponentialSteps?: boolean;\n}\n/**\n * A full result from an expansion calculation.\n */\nexport interface ExpansionResult {\n /** Stretch \\\\( s = z + 1 \\\\). */\n s: number;\n /** Scale factor \\\\( a = 1 / (z + 1) \\\\). */\n a: number;\n /** Redshift. */\n z: number;\n /** Hubble parameter \\\\( kms^{-1}Mpsc^{-1} \\\\). */\n h: number;\n /** Time (Gy). */\n t: number;\n\n /** Hubble radius (Gly). */\n r: number;\n /** Proper distance of a source observed at this redshift (Gly). */\n dNow: number;\n /** Proper distance at this redshift when the light was emitted (Gly). */\n d: number;\n /** Event horizon (largest proper distance that light can ever bridge) (Gly) */\n dHor: number;\n /** Particle horizon (Gly) */\n dPar: number;\n\n /** Recession rate of a source observed at this redshift (c = 1). */\n vNow: number;\n /** Recession rate at this redshift when the light was emitted (c = 1). */\n v: number;\n /** @todo document this! */\n vGen: number;\n\n /** Matter fraction of the critical energy density \\\\( \\rho_{crit}^{-1} \\\\). */\n omegaM: number;\n /** Dark energy fraction of the critical density \\\\( \\rho_{crit}^{-1} \\\\). */\n omegaLambda: number;\n /** Radiation density fraction of the critical density \\\\( \\rho_{crit}^{-1} \\\\). */\n omegaRad: number;\n\n omega: number;\n temperature: number;\n\n /** Critical density. */\n rhoCrit: number;\n}\n\ninterface IntegrationResult {\n s: number;\n t: number;\n dNow: number;\n // r: number;\n dPar: number;\n dHor: number;\n}\n\ninterface CosmicExpansionVariables {\n h: number;\n omega: number;\n omegaM: number;\n omegaLambda: number;\n omegaRad: number;\n temperature: number;\n rhoCrit: number;\n}\n\ninterface CosmicExpansionModelProps {\n /** Redshift when matter and radiation densities were equal \\\\( z_{eq} \\\\). */\n zEq: number;\n\n /** Total density paramater \\\\( \\Omega_{tot} \\\\). */\n omega0: number;\n\n /** Hubble constant \\\\( H_0 \\\\) (in km/s/Mpsc). */\n h0: number;\n h0Gy: number;\n /** Dark energy density parameter \\\\( \\Omega_\\Lambda \\\\). */\n omegaLambda0: number;\n OmegaK0: number;\n omegaM0: number;\n omegaRad0: number;\n rhoCrit0: number;\n /** Temperature of the cosmic microwave background radiation (K). */\n temperature0: number;\n\n /** $$ \\frac{3}{8 \\pi G} \\approx 1.788 445 339 869 671 753 \\times 10^9 $$ */\n rhoConst: number;\n /** Conversion: multiply (a Hubble factor in) km/s/Mpsc to get Gigayears. */\n kmsmpscToGyr: number;\n /** Conversion: multiply Gigayears to get seconds. */\n gyrToSeconds: number;\n}\n\nexport interface CosmicExpansionModelOptions {\n // The key of a survey to use for parameters.\n survey?: 'planck2018Bao' | 'planck2018' | 'planck2015' | 'wmap2013';\n // We can override any of the other model properties.\n [key: string]: number | string | undefined;\n}\n\nexport class CosmicExpansionModel {\n /** Current age of the universe for this model. */\n age: number;\n\n props: CosmicExpansionModelProps;\n\n getESquaredAtStretch: (s: number) => number;\n getVariablesAtStretch: (s: number) => CosmicExpansionVariables;\n\n constructor(options: CosmicExpansionModelOptions = {}) {\n // The next three must be done first, in this order.\n this.props = this.createProps(options);\n this.getESquaredAtStretch = this.createESquaredAtStretchFunction();\n this.getVariablesAtStretch = this.createVariablesAtStretchFunction();\n\n // Now we are set up we can get going.\n this.age = this.getAge();\n }\n\n createProps(options: CosmicExpansionModelOptions): CosmicExpansionModelProps {\n // Constants derived from inputs\n const survey =\n options.survey && surveyParameters[options.survey]\n ? surveyParameters[options.survey]\n : surveyParameters[defaultSurvey];\n const props = {\n ...physicalConstants,\n ...survey,\n ...options,\n };\n\n const { kmsmpscToGyr, h0, omega0, gyrToSeconds, rhoConst, zEq } = props;\n\n const sEq = zEq + 1;\n\n let omegaM0, omegaLambda0;\n\n // Use omegaLambda0 if it is provided.\n if (props.omegaLambda0 != null) {\n omegaLambda0 = props.omegaLambda0;\n omegaM0 = (omega0 - omegaLambda0) * (sEq / (sEq + 1));\n } else if (props.omegaM0 != null) {\n omegaM0 = props.omegaM0;\n omegaLambda0 = omega0 - omegaM0 * ((sEq + 1) / sEq);\n } else {\n throw new Error('Must provide either omegaM0 or omegaLambda0');\n }\n\n const omegaRad0 = omegaM0 / sEq;\n\n const h0Gy = h0 * kmsmpscToGyr;\n const h0Seconds = (h0 * kmsmpscToGyr) / gyrToSeconds;\n\n // Calculate current density parameters.\n const rhoCrit0 = rhoConst * h0Seconds * h0Seconds;\n const OmegaK0 = 1 - omegaM0 - omegaRad0 - omegaLambda0;\n\n return {\n ...props,\n h0Gy,\n rhoCrit0,\n OmegaK0,\n zEq,\n omegaLambda0,\n omegaM0,\n omegaRad0,\n };\n }\n\n /**\n * Hubble constant as a function of stretch.\n *\n * @param s stretch = 1/a, where a is the usual FLRW scale factor.\n * @returns The Hubble constant at stretch s.\n */\n createESquaredAtStretchFunction() {\n const { omegaLambda0, OmegaK0, omegaM0, omegaRad0 } = this.props;\n return (s: number) => {\n const s2 = s * s;\n return (\n omegaLambda0 + OmegaK0 * s2 + omegaM0 * s2 * s + omegaRad0 * s2 * s2\n );\n };\n }\n\n createVariablesAtStretchFunction() {\n const { h0, temperature0, omegaLambda0, omegaM0, omegaRad0, rhoCrit0 } =\n this.props;\n return (s: number): CosmicExpansionVariables => {\n const eSquared = this.getESquaredAtStretch(s);\n const s2 = s * s;\n const h = h0 * Math.sqrt(eSquared);\n const omegaM = (omegaM0 * s2 * s) / eSquared;\n const omegaLambda = omegaLambda0 / eSquared;\n const omegaRad = (omegaRad0 * s2 * s2) / eSquared;\n return {\n h,\n omegaM,\n omegaLambda,\n omegaRad,\n omega: omegaM + omegaLambda + omegaRad,\n temperature: temperature0 * s,\n rhoCrit: rhoCrit0 * eSquared,\n };\n };\n }\n\n getIntegralFunctions() {\n const { getESquaredAtStretch } = this;\n return {\n TH: (s: number): number => 1 / Math.sqrt(getESquaredAtStretch(s)),\n THs: (s: number): number => 1 / (s * Math.sqrt(getESquaredAtStretch(s))),\n };\n }\n\n /**\n * Get a list of cosmic expansion results for a range of stretch values.\n *\n * @param stretchValues Points to calculate at.\n * @returns An array of integration results.\n */\n calculateExpansionForStretchValues(\n stretchValues: number[]\n ): IntegrationResult[] {\n // Convert stretch values in descending order into integration points in\n // ascending order.\n const infty = Number.POSITIVE_INFINITY;\n const sPoints = stretchValues.slice().reverse();\n const isInfinityIncluded = sPoints[sPoints.length - 1] === infty;\n\n if (!isInfinityIncluded) {\n sPoints.push(infty);\n }\n\n // We assume zero is not included.\n sPoints.unshift(0);\n\n const { TH, THs } = this.getIntegralFunctions();\n\n const options = { epsilon: 1e-8 };\n\n const thResults = numerical.quad(TH, sPoints, options);\n const thPoints = thResults[1].points || [thResults];\n\n // Make sure we don't calculate THs at s = 0: discontinuity!\n const thsResults = numerical.quad(THs, sPoints.slice(1), options);\n // We may only have one point so this fix is needed.\n const thsPoints = thsResults[1].points || [thsResults];\n\n // Put in the initial value.\n thsPoints.unshift([0, { steps: 0, errorEstimate: 0, depth: 0 }]);\n\n const thAtOne = numerical.quad(TH, [0, 1], options)[0];\n const thAtInfinity = thResults[0];\n const thsAtInfinity = thsResults[0];\n\n // Create an array to build the return values.\n const results: IntegrationResult[] = [];\n\n // Discard the initial zero start point.\n sPoints.shift();\n const { h0Gy } = this.props;\n\n let th = 0;\n let ths = 0;\n for (let i = 0; i < sPoints.length - (isInfinityIncluded ? 0 : 1); ++i) {\n th += thPoints[i][0];\n ths += thsPoints[i][0];\n const s = sPoints[i];\n\n results.push({\n s,\n t: (thsAtInfinity - ths) / h0Gy,\n dNow: Math.abs(th - thAtOne) / h0Gy,\n dPar: (thAtInfinity - th) / s / h0Gy,\n // ## d_{hor}(s) = \\frac 1 {H_0 s} \\int_{S=0}^s \\frac 1 {\\sqrt {E^2(S)}} dS ##\n dHor: th / s / h0Gy,\n });\n }\n\n return results;\n }\n\n createExpansionResults(\n integrationResults: IntegrationResult[]\n ): ExpansionResult[] {\n const { h0, h0Gy, kmsmpscToGyr } = this.props;\n\n const results: ExpansionResult[] = [];\n\n for (let i = integrationResults.length - 1; i >= 0; --i) {\n const { s, t, dNow: dUnsafe, dHor, dPar } = integrationResults[i];\n\n const params = this.getVariablesAtStretch(s);\n const hGy = params.h * kmsmpscToGyr;\n\n // Force dNow to zero at zero redshift.\n const dNow = s === 1 ? 0 : dUnsafe;\n results.push({\n z: s - 1,\n a: 1 / s,\n s,\n t,\n dNow,\n d: dNow / s,\n r: 1 / hGy,\n dHor,\n dPar,\n vGen: params.h / (s * h0),\n vNow: dNow * h0Gy,\n v: (dNow * hGy) / s,\n ...params,\n });\n }\n\n return results;\n }\n\n /**\n * Calculate the current age of the universe.\n *\n * @param inputs Inputs.\n * @returns\n */\n getAge(): number {\n // Do the integration.\n return this.calculateExpansionForStretchValues([1])[0].t;\n }\n\n /**\n * Get a list of cosmic expansion results.\n *\n * @param inputs Inputs.\n * @returns\n */\n calculateExpansion(inputs: ExpansionInputs): ExpansionResult[] {\n // Calculate the values to calculate at.\n const stretchValues =\n inputs.stretch.length === 1\n ? // Pass the single point to calculate at.\n inputs.stretch\n : // Calculate multiple points.\n getStretchValues(inputs);\n\n // Do the integration.\n const integrationResults =\n this.calculateExpansionForStretchValues(stretchValues);\n\n // Create the tabulated results.\n const results = this.createExpansionResults(integrationResults);\n\n return results;\n }\n}\n\nexport const create = (\n options: CosmicExpansionModelOptions = {}\n): CosmicExpansionModel => {\n return new CosmicExpansionModel(options);\n};\n","// cosmic-expansion/src/index.ts\n\nexport const version = '1.1.1';\nexport { create } from './model.js';\nexport { getStretchValues } from './stretch-range.js';\nexport * as physicalConstants from './physical-constants.js';\nexport * as surveyParameters from 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