/**
 * earth-now.co
 * Author:  Simon-Pierre Boucher
 * Contact: contact@spboucher.ai
 * File:    packages/models/test/fourier.test.ts
 * Purpose: Golden recovery tests — the Fourier fitter must recover a known synthetic Keeling-style signal
 */

import { describe, expect, it } from "vitest";
import { SEASONAL_EPOCH_MS, YEAR_SECONDS } from "@earth-now/counter";
import { fitFourier } from "../src/index";

/** Synthetic Keeling curve: 400 ppm at epoch + 2.5 ppm/yr + 3 ppm annual cycle. */
function syntheticCo2(tMs: number): number {
  const tau = (tMs - SEASONAL_EPOCH_MS) / 1000;
  const omega = (2 * Math.PI) / YEAR_SECONDS;
  return 400 + (2.5 / YEAR_SECONDS) * tau + 3 * Math.cos(omega * tau - 0.7);
}

function monthlySeries(fromYear: number, years: number): Array<{ time: string; value: number }> {
  const out: Array<{ time: string; value: number }> = [];
  for (let y = 0; y < years; y++) {
    for (let m = 0; m < 12; m++) {
      const t = Date.UTC(fromYear + y, m, 15);
      out.push({ time: new Date(t).toISOString(), value: syntheticCo2(t) });
    }
  }
  return out;
}

describe("fitFourier — synthetic Keeling recovery", () => {
  const observations = monthlySeries(2020, 5);
  const fit = fitFourier({
    observations,
    harmonics: [
      { period: "year", order: 1 },
      { period: "year", order: 2 },
    ],
  });

  it("recovers the linear trend (~2.5 ppm/yr)", () => {
    expect(fit.trendPerSecond * YEAR_SECONDS).toBeCloseTo(2.5, 2);
  });

  it("reproduces the signal within 0.05 ppm at arbitrary instants", () => {
    for (const iso of [
      "2021-03-07T12:00:00Z",
      "2022-08-19T00:00:00Z",
      "2024-11-30T06:30:00Z",
      "2025-05-15T00:00:00Z",
    ]) {
      const t = Date.parse(iso);
      expect(fit.valueAt(t)).toBeCloseTo(syntheticCo2(t), 1);
      expect(Math.abs(fit.valueAt(t) - syntheticCo2(t))).toBeLessThan(0.05);
    }
  });

  it("fits with near-zero residual on noiseless input", () => {
    expect(fit.rmse).toBeLessThan(0.02);
  });

  it("converts the annual cycle to rate harmonics with the right amplitude", () => {
    // Value amplitude 3 ppm → rate amplitude 3·ω.
    const omega = (2 * Math.PI) / YEAR_SECONDS;
    const fundamental = fit.rateHarmonics.find((h) => h.order === 1);
    expect(fundamental).toBeDefined();
    expect(fundamental!.amplitude).toBeCloseTo(3 * omega, 6);
  });

  it("rejects underdetermined fits", () => {
    expect(() =>
      fitFourier({
        observations: observations.slice(0, 3),
        harmonics: [
          { period: "year", order: 1 },
          { period: "year", order: 2 },
        ],
      }),
    ).toThrow(/need at least/);
  });
});