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import { Mapper } from './types'; | ||
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export function all(...fns: Mapper[]): Mapper { | ||
return x => { | ||
for (const fn of fns) { | ||
x = fn(x); | ||
} | ||
return x; | ||
}; | ||
} |
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import { Mapper } from './types'; | ||
import { abs } from './utils'; | ||
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/** | ||
* Cumulative distribution function for Gaussian distribution. | ||
* | ||
* @param m Mean of the input value. | ||
* @param d Standard deviation of the input value. | ||
*/ | ||
export function cdf(m = 0, d = 1): Mapper { | ||
return x => { | ||
let p; | ||
let z = (x - m) / d; | ||
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if (z !== z) { | ||
return NaN; | ||
} | ||
if (z === 0) { | ||
return 0.5; | ||
} | ||
if (z <= -3.5) { | ||
return 0; | ||
} | ||
if (z >= 3.5) { | ||
return 1; | ||
} | ||
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p = abs(z); | ||
p = zTable[(p * 10) | 0][((p * 100) | 0) - ((p * 10) | 0) * 10]; | ||
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return z < 0 ? 1 - p : p; | ||
}; | ||
} | ||
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const zTable = [ | ||
[0.5, 0.504, 0.508, 0.512, 0.516, 0.5199, 0.5239, 0.5279, 0.5319, 0.5359], | ||
[0.5398, 0.5438, 0.5478, 0.5517, 0.5557, 0.5596, 0.5636, 0.5675, 0.5714, 0.5753], | ||
[0.5793, 0.5832, 0.5871, 0.591, 0.5948, 0.5987, 0.6026, 0.6064, 0.6103, 0.6141], | ||
[0.6179, 0.6217, 0.6255, 0.6293, 0.6331, 0.6368, 0.6406, 0.6443, 0.648, 0.6517], | ||
[0.6554, 0.6591, 0.6628, 0.6664, 0.67, 0.6736, 0.6772, 0.6808, 0.6844, 0.6879], | ||
[0.6915, 0.695, 0.6985, 0.7019, 0.7054, 0.7088, 0.7123, 0.7157, 0.719, 0.7224], | ||
[0.7257, 0.7291, 0.7324, 0.7357, 0.7389, 0.7422, 0.7454, 0.7486, 0.7517, 0.7549], | ||
[0.758, 0.7611, 0.7642, 0.7673, 0.7704, 0.7734, 0.7764, 0.7794, 0.7823, 0.7852], | ||
[0.7881, 0.791, 0.7939, 0.7967, 0.7995, 0.8023, 0.8051, 0.8078, 0.8106, 0.8133], | ||
[0.8159, 0.8186, 0.8212, 0.8238, 0.8264, 0.8289, 0.8315, 0.834, 0.8365, 0.8389], | ||
[0.8413, 0.8438, 0.8461, 0.8485, 0.8508, 0.8531, 0.8554, 0.8577, 0.8599, 0.8621], | ||
[0.8643, 0.8665, 0.8686, 0.8708, 0.8729, 0.8749, 0.877, 0.879, 0.881, 0.883], | ||
[0.8849, 0.8869, 0.8888, 0.8907, 0.8925, 0.8944, 0.8962, 0.898, 0.8997, 0.9015], | ||
[0.9032, 0.9049, 0.9066, 0.9082, 0.9099, 0.9115, 0.9131, 0.9147, 0.9162, 0.9177], | ||
[0.9192, 0.9207, 0.9222, 0.9236, 0.9251, 0.9265, 0.9279, 0.9292, 0.9306, 0.9319], | ||
[0.9332, 0.9345, 0.9357, 0.937, 0.9382, 0.9394, 0.9406, 0.9418, 0.9429, 0.9441], | ||
[0.9452, 0.9463, 0.9474, 0.9484, 0.9495, 0.9505, 0.9515, 0.9525, 0.9535, 0.9545], | ||
[0.9554, 0.9564, 0.9573, 0.9582, 0.9591, 0.9599, 0.9608, 0.9616, 0.9625, 0.9633], | ||
[0.9641, 0.9649, 0.9656, 0.9664, 0.9671, 0.9678, 0.9686, 0.9693, 0.9699, 0.9706], | ||
[0.9713, 0.9719, 0.9726, 0.9732, 0.9738, 0.9744, 0.975, 0.9756, 0.9761, 0.9767], | ||
[0.9772, 0.9778, 0.9783, 0.9788, 0.9793, 0.9798, 0.9803, 0.9808, 0.9812, 0.9817], | ||
[0.9821, 0.9826, 0.983, 0.9834, 0.9838, 0.9842, 0.9846, 0.985, 0.9854, 0.9857], | ||
[0.9861, 0.9864, 0.9868, 0.9871, 0.9875, 0.9878, 0.9881, 0.9884, 0.9887, 0.989], | ||
[0.9893, 0.9896, 0.9898, 0.9901, 0.9904, 0.9906, 0.9909, 0.9911, 0.9913, 0.9916], | ||
[0.9918, 0.992, 0.9922, 0.9925, 0.9927, 0.9929, 0.9931, 0.9932, 0.9934, 0.9936], | ||
[0.9938, 0.994, 0.9941, 0.9943, 0.9945, 0.9946, 0.9948, 0.9949, 0.9951, 0.9952], | ||
[0.9953, 0.9955, 0.9956, 0.9957, 0.9959, 0.996, 0.9961, 0.9962, 0.9963, 0.9964], | ||
[0.9965, 0.9966, 0.9967, 0.9968, 0.9969, 0.997, 0.9971, 0.9972, 0.9973, 0.9974], | ||
[0.9974, 0.9975, 0.9976, 0.9977, 0.9977, 0.9978, 0.9979, 0.9979, 0.998, 0.9981], | ||
[0.9981, 0.9982, 0.9982, 0.9983, 0.9984, 0.9984, 0.9985, 0.9985, 0.9986, 0.9986], | ||
[0.9987, 0.9987, 0.9987, 0.9988, 0.9988, 0.9989, 0.9989, 0.9989, 0.999, 0.999], | ||
[0.999, 0.9991, 0.9991, 0.9991, 0.9992, 0.9992, 0.9992, 0.9992, 0.9993, 0.9993], | ||
[0.9993, 0.9993, 0.9994, 0.9994, 0.9994, 0.9994, 0.9994, 0.9995, 0.9995, 0.9995], | ||
[0.9995, 0.9995, 0.9995, 0.9996, 0.9996, 0.9996, 0.9996, 0.9996, 0.9996, 0.9997], | ||
[0.9997, 0.9997, 0.9997, 0.9997, 0.9997, 0.9997, 0.9997, 0.9997, 0.9997, 0.9998], | ||
]; |
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import { log, sqrt } from './utils'; | ||
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/** | ||
* Inverse cumulative distribution function for Gaussian distribution. | ||
* | ||
* @param x The value in range (0, 1). | ||
*/ | ||
export function cdfInv(x: number): number { | ||
let q, r; | ||
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if (x <= 0) { | ||
return -Infinity; | ||
} | ||
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if (x >= 1) { | ||
return Infinity; | ||
} | ||
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if (x < 0.02425 || x > 0.97575) { | ||
q = sqrt(-2 * log(x > 0.97575 ? 1 - x : x)); | ||
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const c = | ||
(((((-0.00778489400243029 * q + -0.322396458041136) * q + -2.40075827716184) * q + -2.54973253934373) * q + | ||
4.37466414146497) * | ||
q + | ||
2.93816398269878) / | ||
((((0.00778469570904146 * q + 0.32246712907004) * q + 2.445134137143) * q + 3.75440866190742) * q + 1); | ||
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return x > 0.97575 ? -c : c; | ||
} | ||
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q = x - 0.5; | ||
r = q * q; | ||
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return ( | ||
((((((-39.6968302866538 * r + 220.946098424521) * r + -275.928510446969) * r + 138.357751867269) * r + | ||
-30.6647980661472) * | ||
r + | ||
2.50662827745924) * | ||
q) / | ||
(((((-54.4760987982241 * r + 161.585836858041) * r + -155.698979859887) * r + 66.8013118877197) * r + | ||
-13.2806815528857) * | ||
r + | ||
1) | ||
); | ||
} |
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import { Mapper } from './types'; | ||
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export function decay(fn: Mapper): Mapper { | ||
return x => 1 - fn(x); | ||
} |
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import { Mapper } from './types'; | ||
import { exp, PI, sqrt } from './utils'; | ||
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/** | ||
* Gaussian distribution. | ||
* | ||
* @param m Mean. | ||
* @param d Standard deviation. | ||
*/ | ||
export function gauss(m = 0, d = 1): Mapper { | ||
const q = d * sqrt(2 * PI); | ||
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return x => { | ||
x = (x - m) / d; | ||
return exp(-0.5 * x * x) / q; | ||
}; | ||
} |
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import { mapRange } from './mapRange'; | ||
import { cdfInv } from './cdfInv'; | ||
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/** | ||
* Distributes `n` numbers normally from `min` to `max`. | ||
* | ||
* @param n The number of numbers to distribute. | ||
* @param a The minimum value. | ||
* @param b The maximum value. | ||
*/ | ||
export function gaussDist(n: number, a: number, b: number): number[] { | ||
const arr = []; | ||
const q = n + 1; | ||
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const gMin = cdfInv(1 / q); | ||
const gMax = cdfInv(n / q); | ||
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const v = mapRange(gMin, gMax, a, b); | ||
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for (let i = 1; i < q; i++) { | ||
arr.push(v(cdfInv(i / q))); | ||
} | ||
return arr; | ||
} |
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import { Mapper } from './types'; | ||
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export function mapRange(a1: number, b1: number, a2 = 0, b2 = 1): Mapper { | ||
return x => a2 + ((b2 - a2) * (x - a1)) / (b1 - a1); | ||
} |
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import { cdf } from '../main/cdf'; | ||
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describe('cdf', () => { | ||
test('', () => { | ||
expect(cdf(0, 1)(2)).toBe(0.9772); | ||
expect(cdf(0, 1)(0)).toBe(0.5); | ||
expect(cdf(4, 2)(-1)).toBe(0.006199999999999983); | ||
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expect(cdf(NaN, 0)(0)).toBe(NaN); | ||
expect(cdf(0, NaN)(0)).toBe(NaN); | ||
expect(cdf(0, 1)(NaN)).toBe(NaN); | ||
}); | ||
}); |