InfoRSI/tests/rules-bits.test.ts

import assert from "node:assert/strict";
import { test } from "node:test";
import {
  authorVsMerged,
  bitWidth,
  cellIndex,
  coverage,
  disagreement,
  placement,
  surprise,
  trackRecord,
  worldBits,
  type Mixture,
} from "../src/rules/index.ts";

// 预期值来源写在每条测试旁边。比特的例子取 ε = 25（Δ = 0.25），格边界在二进制里精确。

function close(actual: number, expected: number, tol = 1e-12): void {
  assert.ok(Math.abs(actual - expected) <= tol, `实际 ${actual}，预期 ${expected}`);
}

/** 很窄的范围 (y − 0.01, y, y + 0.01)，连尾巴 [y − 0.02, y + 0.02]。 */
const narrow = (y: number) => ({ q1: y - 0.01, q5: y, q9: y + 0.01 });

const uniform = (lo: number, hi: number): Mixture => [
  {
    weight: 1,
    knots: [
      [lo, 0],
      [hi, 1],
    ],
  },
];

test("6.9 格宽 Δ = ε/100，跟随 ε", () => {
  assert.equal(bitWidth(0.01), 0.01 / 100);
  assert.equal(bitWidth(25), 0.25);
});

test("6.9 世界比特：从 b 起切；[0,1] 均匀切 4 格是 2 比特，错开 1/8 是 2.25 比特；整个落在一格里是 0", () => {
  // 手算：[0,1] 均匀、b = 0、Δ = 0.25：四格各 1/4，H = 2。
  close(worldBits(uniform(0, 1), 0, 0.25), 2);
  // [0.125, 1.125]：五格 1/8、1/4、1/4、1/4、1/8，H = 2 × (1/8 × 3) + 3 × (1/4 × 2) = 0.75 + 1.5 = 2.25。
  close(worldBits(uniform(0.125, 1.125), 0, 0.25), 2.25);
  // 同一分布、b = 0.125：切口对齐，四格各 1/4，又是 2 比特。说明格从 b 起切。
  close(worldBits(uniform(0.125, 1.125), 0.125, 0.25), 2);
  // [0.3, 0.31] 整个在 [0.25, 0.5) 这一格里：把握 1，0 比特。
  assert.equal(worldBits(uniform(0.3, 0.31), 0, 0.25), 0);
});

test("6.9 惊讶 = −log₂ p；正好在格边界上的实测归右边那格；事前把握为 0 时给明确状态", () => {
  // 手算：[0,1] 均匀，实测 0.3 落在 [0.25, 0.5)，p = 1/4，惊讶 2 比特。
  assert.deepEqual(surprise(uniform(0, 1), 0, 0.25, 0.3), { cell: 1, prior: 0.25, bits: { status: "measured", value: 2 } });
  assert.equal(surprise(uniform(0, 1), 0, 0.25, 0.25).cell, 1);
  assert.deepEqual(surprise(uniform(0, 1), 0, 0.25, 2), {
    cell: 8,
    prior: 0,
    bits: { status: "unmeasured", reason: "事前把握为 0，惊讶算不出" },
  });
});

test("6.9 找实测所在格用和切格同一套边界：b + jΔ 正好落在第 j 格", () => {
  // b = 2.5、Δ = 1e-4：(b + 3Δ − b)/Δ 在浮点里可能是 2.999…，按边界核对后仍是 3。
  for (let j = -5; j <= 50; j++) assert.equal(cellIndex(2.5, 1e-4, 2.5 + j * 1e-4), j);
  for (let j = -5; j <= 50; j++) assert.equal(cellIndex(2.635983, 1e-4, 2.635983 + j * 1e-4), j);
});

test("6.9 分歧量：大家的范围完全一样时为 0；两个窄范围各在一格时为 1 比特", () => {
  const r = { q1: 0.2, q5: 0.5, q9: 0.9 };
  close(
    disagreement(
      [
        { id: "A", author: "A", range: r },
        { id: "B", author: "B", range: r },
      ],
      0,
      0.25,
    ),
    0,
  );
  // 手算：A 交 (0.09, 0.1, 0.11)，连尾巴 [0.08, 0.12]，整个在 [0, 0.25) 里；B 交 (0.59, 0.6, 0.61)，整个在 [0.5, 0.75) 里。
  // 各自 0 比特；平均后两格各一半，1 比特。
  close(
    disagreement(
      [
        { id: "A", author: "A", range: narrow(0.1) },
        { id: "B", author: "B", range: narrow(0.6) },
      ],
      0,
      0.25,
    ),
    1,
  );
});

test("6.9 落点四段与覆盖率：边界归属；没有样本时覆盖率测不到", () => {
  const r = { q1: 1, q5: 2, q9: 3 };
  assert.equal(placement(r, 0.5), "belowQ1");
  assert.equal(placement(r, 1), "q1ToQ5");
  assert.equal(placement(r, 2), "q5ToQ9");
  assert.equal(placement(r, 3), "q5ToQ9");
  assert.equal(placement(r, 3.5), "aboveQ9");
  const c = coverage([0.5, 1, 2, 3, 3.5].map((value) => ({ range: r, value })));
  assert.deepEqual(c.counts, { belowQ1: 1, q1ToQ5: 1, q5ToQ9: 2, aboveQ9: 1 });
  assert.equal(c.covered, 3);
  assert.deepEqual(c.rate, { status: "measured", value: 0.6 });
  assert.deepEqual(coverage([]).rate, { status: "unmeasured", reason: "没有样本" });
});

test("6.10 战绩：中位数偏高偏低、穿上下沿、包住，按人、按正向与消融分开", () => {
  const r = { q1: 1, q5: 2, q9: 3 };
  const t = trackRecord([
    { researcher: "B", phase: "forward", range: r, value: 2.5 },
    { researcher: "A", phase: "ablation", range: r, value: 2 },
    { researcher: "A", phase: "forward", range: r, value: 0.5 },
    { researcher: "A", phase: "forward", range: r, value: 3.5 },
    { researcher: "A", phase: "forward", range: r, value: 2.5 },
  ]);
  assert.deepEqual(
    t.map((x) => [x.researcher, x.phase]),
    [
      ["A", "forward"],
      ["A", "ablation"],
      ["B", "forward"],
    ],
  );
  // A 正向：0.5 → 中位数偏高、穿下沿；3.5 → 偏低、穿上沿；2.5 → 偏低、包住。
  assert.deepEqual(t[0]!.tally, {
    total: 3,
    medianHigh: 1,
    medianLow: 2,
    aboveTop: 1,
    belowBottom: 1,
    covered: 1,
    placements: { belowQ1: 1, q1ToQ5: 0, q5ToQ9: 1, aboveQ9: 1 },
  });
  // A 消融：实测正好等于 q5，不算偏高也不算偏低。
  assert.equal(t[1]!.tally.medianHigh + t[1]!.tally.medianLow, 0);
});

test("6.10 作者自评 vs 大家合并：作者一半按方向比合并一半好多少，正数是作者更乐观", () => {
  const item = { candidate: "c1", author: "A", authorRange: { q1: 2, q5: 2.5, q9: 3 }, mergedRange: { q1: 1, q5: 2, q9: 3 }, value: 2.25 };
  assert.deepEqual(authorVsMerged([item], "maximize"), [
    { candidate: "c1", author: "A", optimism: 0.5, authorPlacement: "q1ToQ5", mergedPlacement: "q5ToQ9" },
  ]);
  assert.equal(authorVsMerged([item], "minimize")[0]!.optimism, -0.5);
});

test("6.9 分歧量只量人与人之间：同一人几条解释先等权平均成他的折线", () => {
  // 手算：A、B 各交两条解释，都是 (0.09, 0.1, 0.11) 和 (0.59, 0.6, 0.61)，各自整个落在 [0, 0.25)、[0.5, 0.75) 一格里。
  // 每人的折线都是"两格各一半"，各 1 比特；平均后仍是两格各一半，1 比特；分歧量 = 1 − 1 = 0。
  // 若把每条解释各算比特（各 0 比特）再平均，会得出 1。
  close(
    disagreement(
      [
        { id: "e1", author: "A", range: narrow(0.1) },
        { id: "e2", author: "A", range: narrow(0.6) },
        { id: "e3", author: "B", range: narrow(0.1) },
        { id: "e4", author: "B", range: narrow(0.6) },
      ],
      0,
      0.25,
    ),
    0,
  );
});