合計/平均/分散/中央値/etc を計算する【JavaScript】
合計
１行実装
const sumValue = array.reduce((pre, cr) => pre+cr);簡易実装
const sum = (array) => {
const len = array.length;
let sum = 0
for (let i=0; i<len; i++) {
sum = sum + array[i];
}
return sum;
};サンプル
var array = [1, 3, 5, 7, 9, 8, 6, 4, 2];
var sumValue = array.reduce((pre, cr) => pre+cr);
console.log(sumValue); // 45
console.log(sum(array)); // 45
console.log(sum([2])); // 2
console.log(sum([2, 3])); // 5
console.log(sum([2, 3, 5])); // 10平均
１行実装
const avgValue = array.reduce((pre, cr) => pre+cr) / array.length;簡易実装
const average = (array) => {
const len = array.length;
if (len === 0) { return 0; }
let sum = 0
for (let i=0; i<len; i++) {
sum = sum + array[i];
}
return sum / len;
};サンプル
var array = [1, 3, 5, 7, 9, 8, 6, 4, 2];
var avgValue = array.reduce((pre, cr) => pre+cr) / array.length;
console.log(avgValue); // 5
console.log(average(array)); // 5
console.log(average([2])); // 2
console.log(average([2, 3])); // 2.5
console.log(average([2, 3, 5]));// 3.3333333333333335分散
簡易実装
const variance = (array) => {
const len = array.length;
if (len === 0) { throw new Error('Cannot calculate variance of an empty array.'); }
let sum = 0
for (let i=0; i<len; i++) {
sum = sum + array[i];
}
const avg = sum / len;
let vsum = 0;
for (let i=0; i<len; i++) {
vsum = vsum + (array[i] - avg)**2
}
return vsum / len; // 標本分散
//return vsum / (len-1); // 不偏分散
};サンプル
console.log(variance([1, 2, 3])); // 0.6666666666666666
console.log(variance([1, 5, 9])); // 10.666666666666666
console.log(variance([9, 7, 5, 3, 1, 2, 4, 6, 8])); // 6.666666666666667
console.log(variance([9, 7, 5, 3, 1, 0, 2, 4, 6, 8])); // 8.25標準偏差
簡易実装
const stdev = (array, normalize) => {
const len = array.length;
if (len === 0) { throw new Error('Cannot calculate standard deviation of an empty array.'); }
let sum = 0
for (let i=0; i<len; i++) {
sum = sum + array[i];
}
const avg = sum / len;
let vsum = 0;
for (let i=0; i<len; i++) {
vsum = vsum + (array[i] - avg)**2
}
return Math.sqrt(vsum / len); // 母集団標準偏差
//return Math.sqrt(vsum / (len-1)); // 標本標準偏差
};サンプル
console.log(stdev([1, 2, 3])); // 0.816496580927726
console.log(stdev([1, 5, 9])); // 3.265986323710904
console.log(stdev([9, 7, 5, 3, 1, 2, 4, 6, 8])); // 2.581988897471611
console.log(stdev([9, 7, 5, 3, 1, 0, 2, 4, 6, 8])); // 2.8722813232690143最大値
１行実装
const maxValue = array.reduce((pre, cr) => pre > cr ? pre : cr);const maxValue = Math.max(...array);簡易実装
const max = function(array) {
const len = array.length;
if (len === 0) { throw new Error('Cannot calculate min of an empty array.'); }
let max = array[0];
for (let i=1; i<len; i++) {
if (max < array[i]) {
max = array[i];
}
}
return max;
};サンプル
var array = [1, 3, 5, 7, 9, 8, 6, 4, 2];
var maxValue = array.reduce((pre, cr) => pre > cr ? pre : cr);
console.log(maxValue); // 9
console.log(max(array)); // 9最小値
１行実装
const minValue = array.reduce((pre, cr) => pre < cr ? pre : cr);const minValue = Math.min(...array);簡易実装
const min = function(array) {
const len = array.length;
if (len === 0) { throw new Error('Cannot calculate max of an empty array.'); }
let min = array[0];
for (let i=1; i<len; i++) {
if (array[i] < min) {
min = array[i];
}
}
return min;
};サンプル
var array = [9, 7, 5, 3, 1, 2, 4, 6, 8];
var minValue = array.reduce((pre, cr) => pre - cr < 0 ? pre : cr);
console.log(minValue); // 1
console.log(min(array)); // 1k番目の値
簡易実装
// see https://blog.teamleadnet.com/2012/07/quick-select-algorithm-find-kth-element.html
const selectKth = function(array, k) {
const len = array.length;
if (k < 0 || len <= k) { throw new Error('k is out of bounds.'); }
let count = 0;
let from = 0;
let to = len - 1;
while (from < to) {
let r = from;
let w = to;
let mid = array[(r+w)/2|0];
while (r < w) {
if (array[r] >= mid) {
const tmp = array[w];
array[w] = array[r];
array[r] = tmp;
w--;
} else {
r++;
}
}
if (array[r] > mid) {
r--;
}
if (k <= r) {
to = r;
} else {
from = r + 1;
}
}
return array[k];
};
const small = function(array, k) { return selectKth(array, k); };
const large = function(array, k) { return selectKth(array, array.length-k-1); };※selectKth()は、array を不完全に並び替えます。
サンプル
console.log(small([1, 3, 5, 7, 9, 8, 6, 4, 2], 0)); // 1
console.log(small([1, 3, 5, 7, 9, 8, 6, 4, 2], 1)); // 2
console.log(small([9, 8, 7, 6, 5, 4, 3, 2, 1], 2)); // 3
console.log(small([9, 8, 7, 6, 5, 4, 3, 2, 1], 3)); // 4
console.log(small([9, 7, 5, 3, 1, 2, 4, 6, 8], 4)); // 5
console.log(small([1, 2, 3, 4, 5, 6, 7, 8, 9], 5)); // 6
console.log(small([1, 2, 3, 4, 5, 6, 7, 8, 9], 6)); // 7
console.log(small([9, 7, 5, 3, 1, 2, 4, 6, 8], 7)); // 8
console.log(small([9, 7, 5, 3, 1, 2, 4, 6, 8], 8)); // 9
console.log(large([1, 2, 3, 4, 5, 6, 7, 8, 9], 0)); // 9
console.log(large([1, 2, 3, 4, 5, 6, 7, 8, 9], 1)); // 8
console.log(large([9, 7, 5, 3, 1, 2, 4, 6, 8], 2)); // 7
console.log(large([9, 7, 5, 3, 1, 2, 4, 6, 8], 3)); // 6
console.log(large([9, 7, 5, 3, 1, 2, 4, 6, 8], 4)); // 5
console.log(large([1, 3, 5, 7, 9, 8, 6, 4, 2], 5)); // 4
console.log(large([1, 3, 5, 7, 9, 8, 6, 4, 2], 6)); // 3
console.log(large([9, 8, 7, 6, 5, 4, 3, 2, 1], 7)); // 2
console.log(large([9, 8, 7, 6, 5, 4, 3, 2, 1], 8)); // 1中央値
簡易実装（sort()版）
const median = (array) => {
const len = array.length;
if (len === 0) { throw new Error('Cannot calculate median of an empty array.'); }
array.sort((a, b) => a-b);
if (len % 2) {
return array[(len-1) / 2)];
} else {
const mid = len / 2;
return (array[mid-1] + array[mid]) / 2;
}
};簡易実装（selectKth()版）
const median = (array) => {
const len = array.length;
if (len === 0) { throw new Error('Cannot calculate median of an empty array.'); }
if (len % 2) {
return selectKth(array, (len-1)/2);
} else {
const mid = len/2 - 1;
const large = selectKth(array, mid+1);
let small = array[mid];
for (let i=0; i<mid; i++) {
if (small < array[i]) {
small = array[i]
}
}
return (small + large) / 2;
}
};※完全には並び替えないため、sort()よりselectKth()の方が高速です。
※selectKth()は、「k番目の値」参照
サンプル
console.log(median([2, 3])); // 2.5
console.log(median([5, 2, 3])); // 3
console.log(median([9, 7, 5, 3, 1, 2, 4, 6, 8])); // 5
console.log(median([9, 7, 5, 3, 1, 0, 2, 4, 6, 8])); // 4.5