Information Coefficient

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/** D17 reference algorithms. JSON boundary validation is deliberate and shared.
 * Arrays are copied before sorting; callers' inputs are never mutated.
 * QR solves least squares without forming normal equations.
 */
type Data = Record<string, any>;
type Result = Record<string, any>;
class ContractError extends Error {
}
const fail = (code: string): never => { throw new ContractError(code); };
const num = (x: unknown): number => typeof x === 'number' && Number.isFinite(x) ? x : fail('INVALID_NUMBER');
function integer(x: unknown, lo: number, hi: number): number { const v = num(x); return Number.isInteger(v) && v >= lo && v <= hi ? v : fail('INVALID_PARAMETER'); }
function vec(x: unknown, min = 1): number[] { if (!Array.isArray(x))
    fail('INVALID_SHAPE'); const a = x as unknown[]; if (a.length < min)
    fail('INSUFFICIENT_DATA'); return a.map(num); }
function mat(x: unknown, min = 1): number[][] { if (!Array.isArray(x) || x.length < min)
    fail('INSUFFICIENT_DATA'); const a = (x as unknown[]).map(v => vec(v)); if (new Set(a.map(r => r.length)).size !== 1)
    fail('LENGTH_MISMATCH'); return a; }
function same(...x: {
    length: number;
}[]): void { if (new Set(x.map(a => a.length)).size !== 1)
    fail('LENGTH_MISMATCH'); }
function ids(d: Data, n: number): string[] { required(d, ['ids']); if (!Array.isArray(d.ids) || d.ids.length !== n)
    fail('LENGTH_MISMATCH'); if (d.ids.some((v: unknown) => typeof v !== 'string' || !/^[A-Za-z0-9_.-]+$/.test(v)))
    fail('INVALID_ID'); if (new Set(d.ids).size !== n)
    fail('DUPLICATE_ID'); return [...d.ids]; }
function required(d: Data, keys: string[]): void { for (const key of keys)
    if (!Object.hasOwn(d, key))
        fail('MISSING_FIELD'); }
function validDate(v: unknown): boolean { if (typeof v !== 'string' || !/^\d{4}-\d{2}-\d{2}$/.test(v) || v.startsWith('0000'))
    return false; const date = new Date(v + 'T00:00:00Z'); return Number.isFinite(date.valueOf()) && date.toISOString().slice(0, 10) === v; }
function context(d: Data, op: string): void {
    const keys = ['as_of', 'formation_at', 'inputs_available_at'];
    const evaluation = ['ic', 'rank_ic', 'spread', 'decay'].includes(op);
    if (evaluation)
        keys.push('outcomes_start_at', 'outcomes_end_at', 'outcomes_available_at');
    required(d, keys);
    if (keys.some(k => !validDate(d[k])))
        fail('INVALID_DATE');
    if (d.formation_at > d.as_of || d.inputs_available_at > d.formation_at)
        fail('FUTURE_INPUT');
    if (evaluation) {
        if (d.outcomes_start_at < d.formation_at || d.outcomes_end_at < d.outcomes_start_at)
            fail('INVALID_OUTCOME_WINDOW');
        if (d.outcomes_available_at < d.outcomes_end_at)
            fail('INVALID_DATE_ORDER');
        if (d.outcomes_available_at > d.as_of)
            fail('IMMATURE_OUTCOME');
    }
}
const sum = (a: number[]): number => a.reduce((s, v) => s + v, 0);
const mean = (a: number[]): number => sum(a) / a.length;
const dot = (a: number[], b: number[]): number => sum(a.map((v, i) => v * b[i]));
const tr = (a: number[][]): number[][] => a[0].map((_, j) => a.map(r => r[j]));
const mm = (a: number[][], b: number[][]): number[][] => { const cols = tr(b); return a.map(row => cols.map(col => dot(row, col))); };
function sd(x: number[], ddof = 0): number { const m = mean(x); return Math.sqrt(sum(x.map(v => (v - m) ** 2)) / (x.length - ddof)); }
function standard(x: number[]): number[] { const m = mean(x), s = sd(x); if (s <= 1e-14 * Math.max(1, ...x.map(Math.abs)))
    fail('CONSTANT_CROSS_SECTION'); return x.map(v => (v - m) / s); }
function corr(x: number[], y: number[]): number | null { same(x, y); if (Math.max(...x) === Math.min(...x) || Math.max(...y) === Math.min(...y))
    return null; const xm = mean(x), ym = mean(y), a = x.map(v => v - xm), b = y.map(v => v - ym), den = Math.sqrt(dot(a, a) * dot(b, b)); return den <= 0 ? null : Math.max(-1, Math.min(1, dot(a, b) / den)); }
function ranks(x: number[]): number[] { const order = x.map((_, i) => i).sort((a, b) => x[a] - x[b]); const out = x.map(() => 0); let start = 0; while (start < x.length) {
    let end = start + 1;
    while (end < x.length && x[order[end]] === x[order[start]])
        end++;
    for (let j = start; j < end; j++)
        out[order[j]] = (start + 1 + end) / 2;
    start = end;
} return out; }
function quantile(x: number[], p: number): number { const y = [...x].sort((a, b) => a - b), h = (y.length - 1) * p, j = Math.floor(h), f = h - j; return y[j] * (1 - f) + y[Math.min(j + 1, y.length - 1)] * f; }
function compound(x: number[]): number { if (x.some(v => v <= -1))
    fail('INVALID_RETURN'); return Math.expm1(sum(x.map(Math.log1p))); }
/** erfc(|z|/sqrt(2)) via regularized Gamma(1/2,x); converged series/CF. */
function normalP(z: number): number {
    const x = z * z / 2, a = 0.5, lg = 0.5723649429247001;
    if (x === 0)
        return 1;
    const factor = Math.exp(-x + a * Math.log(x) - lg);
    if (x < a + 1) {
        let term = 1 / a, total = term, ap = a;
        for (let i = 1; i < 500; i++) {
            ap++;
            term *= x / ap;
            total += term;
            if (Math.abs(term) < Math.abs(total) * 1e-15)
                break;
        }
        return Math.max(0, 1 - total * factor);
    }
    let b = x + 1 - a, c = 1e300, d = 1 / b, h = d;
    for (let i = 1; i < 500; i++) {
        const an = -i * (i - a);
        b += 2;
        d = an * d + b;
        if (Math.abs(d) < 1e-300)
            d = 1e-300;
        c = b + an / c;
        if (Math.abs(c) < 1e-300)
            c = 1e-300;
        d = 1 / d;
        const delta = d * c;
        h *= delta;
        if (Math.abs(delta - 1) < 1e-15)
            break;
    }
    return Math.max(0, Math.min(1, factor * h));
}
export function ols(y: number[], x: number[][], lags = 0): Result {
    const n = y.length, p = x[0].length;
    same(y, x);
    if (n <= p)
        fail('INSUFFICIENT_DATA');
    integer(lags, 0, n - 1);
    const cols = tr(x), scales = cols.map(c => Math.sqrt(dot(c, c)));
    if (scales.some(s => s === 0))
        fail('SINGULAR_DESIGN');
    const q: number[][] = [], r = Array.from({ length: p }, () => Array(p).fill(0) as number[]);
    for (let j = 0; j < p; j++) {
        let v = cols[j].map(z => z / scales[j]);
        for (let pass = 0; pass < 2; pass++)
            for (let i = 0; i < j; i++) {
                const proj = dot(q[i], v);
                r[i][j] += proj;
                v = v.map((z, t) => z - proj * q[i][t]);
            }
        r[j][j] = Math.sqrt(dot(v, v));
        if (r[j][j] < 1e-10)
            fail('SINGULAR_DESIGN');
        q.push(v.map(z => z / r[j][j]));
    }
    const solve = (v: number[]): number[] => { const b = Array(p).fill(0) as number[]; for (let i = p - 1; i >= 0; i--) {
        let s = 0;
        for (let j = i + 1; j < p; j++)
            s += r[i][j] * b[j];
        b[i] = (v[i] - s) / r[i][i];
    } return b; };
    const beta = solve(q.map(c => dot(c, y))).map((b, i) => b / scales[i]), fitted = x.map(row => dot(row, beta)), residuals = y.map((v, i) => v - fitted[i]);
    const invr = tr(Array.from({ length: p }, (_, j) => solve(Array.from({ length: p }, (_, i) => Number(i === j)))));
    const bread = mm(invr, tr(invr)).map((row, i) => row.map((v, j) => v / scales[i] / scales[j]));
    const scores = x.map((row, t) => row.map(v => v * residuals[t])), meat = mm(tr(scores), scores);
    for (let lag = 1; lag <= lags; lag++) {
        const w = 1 - lag / (lags + 1);
        for (let t = lag; t < n; t++)
            for (let i = 0; i < p; i++)
                for (let j = 0; j < p; j++)
                    meat[i][j] += w * (scores[t][i] * scores[t - lag][j] + scores[t - lag][i] * scores[t][j]);
    }
    const cov = mm(mm(bread, meat), bread), se = cov.map((row, i) => Math.sqrt(Math.max(0, row[i]))), sse = dot(residuals, residuals), ym = mean(y), sst = sum(y.map(v => (v - ym) ** 2));
    return { coefficients: beta, standard_errors: se, fitted, residuals, r_squared: sst === 0 ? null : 1 - sse / sst, n, df_residual: n - p, hac_lags: lags, residual_sum_squares: sse, qr_min_diagonal: Math.min(...r.map((row, i) => row[i])) };
}
function evaluate(d: Data, op: string): Result {
    if (op === 'turnover') {
        required(d, ['old_weights', 'target_weights', 'holding_returns']);
        const old = vec(d.old_weights, 2), target = vec(d.target_weights, 2), r = vec(d.holding_returns, 2);
        same(old, target, r);
        const names = ids(d, old.length);
        if (Math.min(...old, ...target) < 0 || Math.abs(sum(old) - 1) > 1e-10 || Math.abs(sum(target) - 1) > 1e-10)
            fail('INVALID_WEIGHTS');
        if (Math.min(...r) <= -1)
            fail('INVALID_RETURN');
        const wealth = 1 + dot(old, r);
        if (wealth <= 0)
            fail('INVALID_WEALTH');
        const pre = old.map((v, i) => v * (1 + r[i]) / wealth), trades = target.map((v, i) => v - pre[i]), t = sum(trades.map(Math.abs)) / 2;
        return { ids: names, pretrade_weights: pre, trades, turnover: t, two_way: 2 * t, wealth, primary: t };
    }
    if (op === 'spread') {
        required(d, ['forward_returns', 'buckets']);
        const r = vec(d.forward_returns, 2), names = ids(d, r.length), buckets = vec(d.buckets, 2);
        same(r, buckets);
        if (buckets.some(v => !Number.isInteger(v) || v < 1))
            fail('INVALID_PARAMETER');
        const lo = Math.min(...buckets), hi = Math.max(...buckets);
        if (lo === hi)
            fail('EMPTY_LEG');
        if (Math.min(...r) < -1)
            fail('INVALID_RETURN');
        const rh = mean(r.filter((_, i) => buckets[i] === hi)), rl = mean(r.filter((_, i) => buckets[i] === lo)), cost = num(d.cost_bps ?? 0), th = num(d.turnover_high ?? 0), tl = num(d.turnover_low ?? 0);
        if (Math.min(cost, th, tl) < 0)
            fail('INVALID_PARAMETER');
        const drag = cost / 10000 * (th + tl);
        return { ids: names, high_return: rh, low_return: rl, gross_spread: rh - rl, cost: drag, net_spread: rh - rl - drag, gross_exposure: 2, primary: rh - rl - drag };
    }
    required(d, ['scores']);
    const s = vec(d.scores, 3), names = ids(d, s.length);
    if (op === 'decay') {
        required(d, ['forward_path']);
        const paths = mat(d.forward_path, 3);
        same(s, paths);
        const h = integer(d.max_horizon ?? paths[0].length, 1, paths[0].length), labels = Array.from({ length: h }, (_, j) => paths.map(row => compound(row.slice(0, j + 1)))), curve = labels.map(row => corr(s, row));
        return { ids: names, horizons: Array.from({ length: h }, (_, j) => j + 1), correlations: curve, labels_by_horizon: labels, n: s.length, primary: curve[h - 1], undefined_horizons: curve.map((v, i) => v === null ? i + 1 : 0).filter(Boolean) };
    }
    required(d, ['forward_returns']);
    const r = vec(d.forward_returns, 3);
    same(s, r);
    if (Math.min(...r) < -1)
        fail('INVALID_RETURN');
    const a = op === 'rank_ic' ? ranks(s) : s, b = op === 'rank_ic' ? ranks(r) : r, c = corr(a, b);
    return { ids: names, correlation: c, score_coordinates: a, return_coordinates: b, n: s.length, primary: c, defined: c !== null };
}
/** D17-F04-A01 public boundary. No mutation, implicit imputation or silent failure. */
export function compute(input: unknown): Result {
    const op = "ic";
    try {
        if (!input || typeof input !== 'object' || Array.isArray(input))
            fail('INVALID_SHAPE');
        const d = input as Data;
        if (Object.values(d).some(v => v === null))
            fail('INVALID_NUMBER');
        context(d, op);
        const result = evaluate(d, op);
        const check = (v: unknown): void => { if (typeof v === 'number' && !Number.isFinite(v))
            fail('NUMERICAL_FAILURE'); if (Array.isArray(v))
            v.forEach(check);
        else if (v && typeof v === 'object')
            Object.values(v).forEach(check); };
        check(result);
        return { status: 'ok', method: op, ...result };
    }
    catch (error) {
        if (error instanceof ContractError)
            return { status: 'error', method: op, code: error.message };
        throw error;
    }
}