import get from 'lodash-es/get.js'
import each from 'lodash-es/each.js'
import map from 'lodash-es/map.js'
import size from 'lodash-es/size.js'
import filter from 'lodash-es/filter.js'
import sum from 'lodash-es/sum.js'
import isNumber from 'lodash-es/isNumber.js'
import isarr from 'wsemi/src/isarr.mjs'
import ispint from 'wsemi/src/ispint.mjs'
import cint from 'wsemi/src/cint.mjs'
import arrFilterByNum from 'wsemi/src/arrFilterByNum.mjs'
import nelderMead from 'w-optimization/src/nelderMead.mjs'
import bin from './bin.mjs'
import jt from './jStat.mjs'
/**
* 計算擬合Gamma分布之參數
*
* Unit Test: {@link https://github.com/yuda-lyu/w-statistic/blob/master/test/arrGammaFit.test.js Github}
* @memberOf w-statistic
* @param {Array} arr 輸入陣列，只提取有效數字(或為字串的數字)進行計算
* @returns {Object} 回傳參數物件
* @example
*
* async function test() {
*
* let arr
* let r
*
* arr = [12, 36, 9, 13, 6, 17, 7, 12, 31, 57, 44, 32, 16, 11, 10, 38, 31, 28, 26, 7, 16, 16, 16, 13, 7, 8, 12, 17, 11, 20, 7, 6, 14, 7, 37, 11, 7, 8, 8, 32, 29, 52, 20, 6, 11, 12, 33, 48, 10, 27, 11, 24, 17, 11, 23, 20, 13, 16, 16, 17, 13, 15, 13, 26, 11, 13, 29, 18, 18, 13, 11, 12, 9, 17, 19, 14, 19, 9, 37, 32, 14, 20, 13, 22, 12, 14, 33, 15, 20, 37, 24, 19, 15, 15, 5, 11, 13, 60, 39, 17, 6, 18, 40, 21, 18, 17, 12, 12, 10, 39, 27, 10, 8, 44, 36, 18, 11, 8, 13, 9, 25, 11, 10, 55, 54, 13, 8, 19, 38, 9, 17, 14, 9, 12, 54, 22, 11, 19, 50, 18, 12, 40, 52, 12, 15, 7, 12, 15, 18, 19, 11, 43, 23, 14, 25, 32, 23, 15, 12, 20, 14, 10, 12, 24, 50, 40, 16, 14, 9, 27, 9, 11, 17, 19, 12, 17, 14, 5, 24, 22, 60, 20, 9, 11, 11, 6, 7, 8, 31, 10, 12, 9, 11, 26, 14, 7, 14, 57, 19, 9, 10, 9, 19, 19, 15, 21, 48, 23, 26, 14, 46, 51, 10, 10, 9, 7, 19, 46, 27, 18, 12, 10, 36, 15, 5, 11, 13, 21, 15, 15, 16, 29, 44, 42, 7, 14, 9, 6, 22, 24, 18, 39, 7, 50, 33, 11, 20, 17, 18, 48, 8, 21, 20, 12, 41, 11, 18, 11, 58, 18, 21, 23, 12, 67, 35]
* r = await arrGammaFit(arr, {
* n: 69,
* min: 1,
* max: 70,
* })
* console.log(r)
* // => {
* // shape: 3.8362965388539396,
* // scale: 4.074897568773075,
* // arrPdf: [
* // [ 1.5, 0, 0.002034542900938358 ],
* // [ 2.5, 0, 0.006778251528074013 ],
* // [ 3.5, 0, 0.013772161615714786 ],
* // [ 4.5, 0.011320754716981131, 0.02197810173523445 ],
* // [ 5.5, 0.022641509433962263, 0.030380569392341527 ],
* // [ 6.5, 0.045283018867924525, 0.03817623569640994 ],
* // [ 7.5, 0.03018867924528302, 0.044821355259143096 ],
* // [ 8.5, 0.052830188679245285, 0.05001282903727686 ],
* // [ 9.5, 0.04150943396226415, 0.053642598229888455 ],
* // [ 10.5, 0.07924528301886792, 0.05574595886606071 ],
* // [ 11.5, 0.07169811320754717, 0.05645381775460518 ],
* // [ 12.5, 0.045283018867924525, 0.05595305000100274 ],
* // [ 13.5, 0.04905660377358491, 0.05445596204835303 ],
* // [ 14.5, 0.04150943396226415, 0.05217827444112463 ],
* // [ 15.5, 0.03018867924528302, 0.04932434550769117 ],
* // [ 16.5, 0.04150943396226415, 0.04607816130381367 ],
* // [ 17.5, 0.045283018867924525, 0.04259868048491963 ],
* // [ 18.5, 0.04150943396226415, 0.03901830570786497 ],
* // [ 19.5, 0.033962264150943396, 0.03544347629738162 ],
* // [ 20.5, 0.018867924528301886, 0.031956597426761706 ],
* // [ 21.5, 0.01509433962264151, 0.028618718038250914 ],
* // [ 22.5, 0.018867924528301886, 0.025472535008409646 ],
* // [ 23.5, 0.018867924528301886, 0.0225454335944075 ],
* // [ 24.5, 0.007547169811320755, 0.019852376582105462 ],
* // [ 25.5, 0.01509433962264151, 0.017398531002249633 ],
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* // [ 33.5, 0, 0.005296667950862123 ],
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* // [ 51.5, 0.007547169811320755, 0.00021642735070210298 ],
* // [ 52.5, 0, 0.00017882288240340192 ],
* // [ 53.5, 0.007547169811320755, 0.00014760023544158093 ],
* // [ 54.5, 0.0037735849056603774, 0.00012170840693236135 ],
* // [ 55.5, 0, 0.0001002626841944302 ],
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* // [ 58.5, 0, 0.000055750813268511874 ],
* // [ 59.5, 0.007547169811320755, 0.00004576689576865875 ],
* // [ 60.5, 0, 0.000037540816896368505 ],
* // [ 61.5, 0, 0.00003076942665494607 ],
* // [ 62.5, 0, 0.000025200512318922518 ],
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* // [ 68.5, 0, 0.000007496453216403037 ],
* // [ 69.5, 0, 0.000006111251186318431 ]
* // ],
* // arrCounts: [
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* // [ 2.5, 0, 1.7962366549396136 ],
* // [ 3.5, 0, 3.6496228281644183 ],
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* // [ 15.5, 8, 13.07095155953816 ],
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* // [ 68.5, 0, 0.0019865601023468047 ],
* // [ 69.5, 0, 0.0016194815643743841 ]
* // ],
* // dx: 1,
* // bs: [
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* // { min: 2, max: 3, avg: 2.5, arr: [], counts: 0, pdf: 0 },
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* // {
* // min: 4,
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* // pdf: 0.011320754716981131
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* // pdf: 0.045283018867924525
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* // pdf: 0.045283018867924525
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* // {
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* // pdf: 0.045283018867924525
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* // {
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* // pdf: 0.011320754716981131
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* // {
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* // { min: 60, max: 61, avg: 60.5, arr: [], counts: 0, pdf: 0 },
* // { min: 61, max: 62, avg: 61.5, arr: [], counts: 0, pdf: 0 },
* // { min: 62, max: 63, avg: 62.5, arr: [], counts: 0, pdf: 0 },
* // { min: 63, max: 64, avg: 63.5, arr: [], counts: 0, pdf: 0 },
* // { min: 64, max: 65, avg: 64.5, arr: [], counts: 0, pdf: 0 },
* // { min: 65, max: 66, avg: 65.5, arr: [], counts: 0, pdf: 0 },
* // {
* // min: 66,
* // max: 67,
* // avg: 66.5,
* // arr: [Array],
* // counts: 1,
* // pdf: 0.0037735849056603774
* // },
* // { min: 67, max: 68, avg: 67.5, arr: [], counts: 0, pdf: 0 },
* // { min: 68, max: 69, avg: 68.5, arr: [], counts: 0, pdf: 0 },
* // { min: 69, max: 70, avg: 69.5, arr: [], counts: 0, pdf: 0 }
* // ]
* // }
*
* }
* test()
* .catch((err) => {
* console.log(err)
* })
*
*/
async function arrGammaFit(arr, opt = {}) {
//check arr
if (!isarr(arr)) {
return Promise.reject('arr is not an array')
}
if (size(arr) === 0) {
return Promise.reject('arr is not an effective array')
}
//bin_n
let bin_n = get(opt, 'n')
if (!ispint(bin_n)) {
bin_n = 30
}
bin_n = cint(bin_n)
//bin_min
let bin_min = get(opt, 'min', null)
//bin_max
let bin_max = get(opt, 'max', null)
//rs
let rs = arrFilterByNum(arr)
//需大於0
rs = filter(rs, (v) => {
return v > 0
})
//n
let n = size(rs)
//check
if (n === 0) {
return Promise.reject(`no effective data`)
}
//bin
let bs = bin(rs, bin_n, { min: bin_min, max: bin_max })
// console.log('bs', bs)
//dx
let dx = get(bs, '0.max') - get(bs, '0.min')
// console.log('dx', dx)
//add counts
bs = map(bs, (v) => {
v.counts = size(v.arr)
return v
})
// console.log('bs', bs)
//r
let r = sum(map(bs, 'counts')) * dx //dx大於0, 一定為有效陣列, r必定>0
//check
if (r <= 0) {
throw new Error(`r[${r}<=0]`)
}
//add counts
bs = map(bs, (v) => {
v.pdf = v.counts / r
return v
})
// console.log('bs', bs)
//func
let func = (x, shape, scale) => {
return jt.gamma.pdf(x, shape, scale)
}
//genc
let genc = (shape, scale) => {
let rs = []
each(bs, (v) => {
let x = v.avg
let y = v.pdf
let yf = func(x, shape, scale)
if (!isNumber(yf)) {
console.log('x', x, 'shape', shape, 'scale', scale)
throw new Error(`yf is not number`)
}
rs.push([x, y, yf])
})
return rs
}
//funFit
let funFit = async (params) => {
let shape = params[0]
let scale = params[1]
let fitness = 0
each(genc(shape, scale), (v) => {
let y = v[1]
let yf = v[2]
fitness += (y - yf) ** 2
})
return fitness
}
//nelderMead
let rf = await nelderMead(funFit, [1, 1])
// console.log('rf', rf)
// => {
// count: 225,
// y: 0.004155647100413591,
// x: [ 3.8362965388539396, 4.074897568773075 ]
// }
//shape, scale
let shape = get(rf, 'x.0', null)
let scale = get(rf, 'x.1', null)
// console.log('shape', shape, 'scale', scale)
//genc
let rstPdf = genc(shape, scale)
//rstCounts
let rstCounts = map(rstPdf, (v) => {
return [v[0], v[1] * r, v[2] * r]
})
return {
shape,
scale,
arr: rs,
arrPdf: rstPdf,
arrCounts: rstCounts,
dx,
bs,
}
}
export default arrGammaFit