253 lines
9.5 KiB
Go
253 lines
9.5 KiB
Go
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package basic
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import (
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"math"
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"testing"
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)
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// 根数表口径：经典贝塞尔符号、NASA 式三次拟合，以及与已发布表的 μ 时间自变量换算。
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const (
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besselianNASAT0JDE = 2460409.25
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besselianNASADeltaT = 70.6
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besselianNASASeed = 2460409.262835
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)
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func nasa2024BesselianElements(t *testing.T) SolarEclipseBesselianElementsResult {
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t.Helper()
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result, ok := SolarEclipseBesselianElements(besselianNASASeed, SolarEclipseBesselianElementsOptions{
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DeltaTSeconds: besselianNASADeltaT,
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ReferenceJDE: besselianNASAT0JDE,
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})
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if !ok {
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t.Fatal("2024-04-08 should have a solar eclipse")
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}
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return result
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}
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func TestSolarEclipseBesselianElementsMatchesNASA2024(t *testing.T) {
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result := nasa2024BesselianElements(t)
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cases := []struct {
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label string
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got SolarEclipseBesselianPolynomial
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want SolarEclipseBesselianPolynomial
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tol [4]float64
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}{
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{"x", result.X, SolarEclipseBesselianPolynomial{-0.318157, 0.5117105, 0.0000326, -0.0000085}, [4]float64{2e-4, 1e-5, 1e-6, 1e-6}},
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{"y", result.Y, SolarEclipseBesselianPolynomial{0.219747, 0.2709586, -0.0000594, -0.0000047}, [4]float64{2e-4, 1e-5, 1e-6, 1e-6}},
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{"d", result.D, SolarEclipseBesselianPolynomial{7.58620, 0.014844, -0.000002, 0}, [4]float64{1e-4, 1e-5, 1e-5, 1e-5}},
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{"l1", result.L1, SolarEclipseBesselianPolynomial{0.535813, 0.0000618, -0.0000128, 0}, [4]float64{1e-4, 1e-5, 1e-5, 1e-5}},
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{"l2", result.L2, SolarEclipseBesselianPolynomial{-0.010274, 0.0000615, -0.0000127, 0}, [4]float64{1e-4, 1e-5, 1e-5, 1e-5}},
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}
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for _, item := range cases {
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for n := range item.want {
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if math.Abs(item.got[n]-item.want[n]) > item.tol[n] {
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t.Errorf("%s[%d] = %.8f, want %.8f (tol %.1e)", item.label, n, item.got[n], item.want[n], item.tol[n])
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}
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}
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}
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published := SolarEclipseBesselianMuForPublishedTable(result.Mu, result.DeltaTSeconds)
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for n, want := range [4]float64{89.59122, 15.004084, 0, 0} {
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if math.Abs(published[n]-want) > 1e-4 {
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t.Errorf("published mu[%d] = %.6f, want %.6f", n, published[n], want)
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}
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}
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if math.Abs(result.TanF1-0.0046683) > 1e-6 || math.Abs(result.TanF2-0.0046450) > 1e-6 {
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t.Errorf("tan f = %.8f / %.8f, want 0.0046683 / 0.0046450", result.TanF1, result.TanF2)
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}
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if math.Abs(result.Gamma-0.3431) > 1e-4 {
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t.Errorf("gamma = %.6f, want 0.3431", result.Gamma)
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}
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if math.Abs(result.Magnitude-1.0566) > 1e-3 {
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t.Errorf("magnitude = %.6f, want 1.0566", result.Magnitude)
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}
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if result.T0JDE != besselianNASAT0JDE || result.ValidHours != 3 {
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t.Errorf("t0 = %.6f validHours = %g, want %.6f / 3", result.T0JDE, result.ValidHours, besselianNASAT0JDE)
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}
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if result.Model != SolarEclipseModelNASABulletinSplitK {
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t.Errorf("model = %q, want %q", result.Model, SolarEclipseModelNASABulletinSplitK)
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}
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if result.PenumbralK != solarEclipsePenumbralK || result.UmbralK != solarEclipseUmbralK {
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t.Errorf("k = %g / %g, want %g / %g", result.PenumbralK, result.UmbralK, solarEclipsePenumbralK, solarEclipseUmbralK)
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}
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if math.Abs(result.DeltaTSeconds-besselianNASADeltaT) > 1e-9 {
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t.Errorf("deltaT = %g, want %g", result.DeltaTSeconds, besselianNASADeltaT)
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}
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}
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func TestSolarEclipseBesselianElementsFollowsSampledElements(t *testing.T) {
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result := nasa2024BesselianElements(t)
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solver := newSolarEclipseSolver(
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CalcMoonSHByJDE(besselianNASASeed, 0),
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SolarEclipseModelNASABulletinSplitK,
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).withDeltaTSeconds(besselianNASADeltaT)
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for _, hours := range []float64{-2.7, -0.8, 0.4, 2.3} {
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point := solver.besselianElementsAt(result.T0JDE + hours/24)
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if math.Abs(result.X.At(hours)-point.x) > 1e-5 ||
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math.Abs(result.Y.At(hours)-point.y) > 1e-5 ||
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math.Abs(result.L1.At(hours)-point.l1) > 1e-5 ||
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math.Abs(result.L2.At(hours)-point.l2) > 1e-5 ||
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math.Abs(result.D.At(hours)-point.d) > 1e-5 {
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t.Errorf("t=%+.2fh polynomial (%g,%g,%g,%g,%g) does not track elements (%g,%g,%g,%g,%g)",
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hours, result.X.At(hours), result.Y.At(hours), result.D.At(hours), result.L1.At(hours), result.L2.At(hours),
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point.x, point.y, point.d, point.l1, point.l2)
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}
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if math.Abs(math.Mod(result.Mu.At(hours)-point.mu, 360)) > 1e-4 {
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t.Errorf("t=%+.2fh mu = %g does not track %g", hours, result.Mu.At(hours), point.mu)
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}
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}
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}
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func TestSolarEclipseBesselianElementsMuStaysContinuousAcrossZero(t *testing.T) {
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// 2013-11-03 的食甚点在格林尼治附近，μ 的采样点会跨过 0°，是展开逻辑的边界用例。
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for _, seed := range []float64{besselianNASASeed, JDCalc(2013, 11, 3)} {
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result, ok := SolarEclipseBesselianElements(seed, SolarEclipseBesselianElementsOptions{
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DeltaTSeconds: besselianNASADeltaT,
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})
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if !ok {
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t.Fatalf("seed %.4f should have a solar eclipse", seed)
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}
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if result.Mu.At(0) < 0 || result.Mu.At(0) >= 360 {
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t.Errorf("seed %.4f: mu(0) = %g, want [0,360)", seed, result.Mu.At(0))
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}
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if math.Abs(result.Mu[1]-15.041067) > 0.05 {
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t.Errorf("seed %.4f: mu rate = %.6f, want about 15.041067", seed, result.Mu[1])
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}
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for _, hours := range []float64{-3, -1.5, 1.5, 3} {
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drift := result.Mu.At(hours) - (result.Mu.At(0) + 15.041067*hours)
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if math.Abs(drift) > 0.5 {
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t.Errorf("seed %.4f: mu(%+.1f) is not a continuous continuation, drift %.4f", seed, hours, drift)
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}
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}
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}
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}
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func TestSolarEclipseBesselianElementsDefaultsToWholeHour(t *testing.T) {
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result, ok := SolarEclipseBesselianElements(besselianNASASeed, SolarEclipseBesselianElementsOptions{
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DeltaTSeconds: besselianNASADeltaT,
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})
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if !ok {
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t.Fatal("2024-04-08 should have a solar eclipse")
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}
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if math.Abs(result.T0JDE*24-math.Round(result.T0JDE*24)) > 1e-9 {
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t.Errorf("t0 = %.9f is not a whole TT hour", result.T0JDE)
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}
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if math.Abs(result.T0JDE*24-besselianNASASeed*24) > 0.5 {
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t.Errorf("t0 = %.6f is not the whole hour nearest greatest eclipse %.6f", result.T0JDE, besselianNASASeed)
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}
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if result.ValidHours != 3 {
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t.Errorf("validHours = %g, want 3", result.ValidHours)
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}
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// 食甚落在半小时之后的事件取下一个整小时：NASA 2009-07-22 表食甚 02:36:24 TDT，t0 记 03:00 TDT。
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forward, ok := SolarEclipseBesselianElements(JDCalc(2009, 7, 22), SolarEclipseBesselianElementsOptions{
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DeltaTSeconds: 65.9,
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})
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if !ok {
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t.Fatal("2009-07-22 should have a solar eclipse")
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}
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if math.Abs(forward.T0JDE-2455034.625) > 1e-9 {
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t.Errorf("t0 = %.9f, want 2455034.625 (03:00 TDT)", forward.T0JDE)
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}
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}
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func TestSolarEclipseBesselianElementsMatchesPublishedHours(t *testing.T) {
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testCases := []struct {
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name string
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date [3]int
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delta float64
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t0 float64
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want [6]SolarEclipseBesselianPolynomial
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}{
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{
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name: "2009-07-22 total", date: [3]int{2009, 7, 22}, delta: 65.9, t0: 2455034.625,
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want: [6]SolarEclipseBesselianPolynomial{
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{0.240059, 0.5563975, -0.0000583, -0.0000100},
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{-0.003283, -0.1774571, -0.0001346, 0.0000032},
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{20.26424, -0.007873, -0.000004, 0},
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{0.530426, 0.0000063, -0.0000128, 0},
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{-0.015633, 0.0000063, -0.0000127, 0},
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{0, 0, 0, 0},
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},
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},
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{
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name: "2013-11-03 hybrid", date: [3]int{2013, 11, 3}, delta: 67.2, t0: 2456600.041666667,
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want: [6]SolarEclipseBesselianPolynomial{
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{0.183190, 0.5469478, 0.0000282, -0.0000083},
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{0.294721, -0.1200753, 0.0000790, 0.0000017},
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{-15.20965, -0.012636, 0.000003, 0},
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{0.546301, -0.0001121, -0.0000120, 0},
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{0.000143, -0.0001116, -0.0000120, 0},
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{0, 0, 0, 0},
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},
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},
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}
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tolerances := [6][4]float64{
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{2e-4, 1e-5, 1e-6, 1e-6},
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{2e-4, 1e-5, 1e-6, 1e-6},
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{1e-4, 1e-5, 1e-5, 1e-5},
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{1e-4, 1e-5, 1e-5, 1e-5},
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{1e-4, 1e-5, 1e-5, 1e-5},
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{1e-4, 1e-5, 1e-5, 1e-5},
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}
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labels := [6]string{"x", "y", "d", "l1", "l2", "mu"}
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for _, tc := range testCases {
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t.Run(tc.name, func(t *testing.T) {
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result, ok := SolarEclipseBesselianElements(JDCalc(tc.date[0], tc.date[1], float64(tc.date[2])),
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SolarEclipseBesselianElementsOptions{DeltaTSeconds: tc.delta})
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if !ok {
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t.Fatalf("%s should have a solar eclipse", tc.name)
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}
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if math.Abs(result.T0JDE-tc.t0) > 1e-9 {
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t.Fatalf("t0 = %.9f, want %.9f", result.T0JDE, tc.t0)
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}
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got := [6]SolarEclipseBesselianPolynomial{result.X, result.Y, result.D, result.L1, result.L2, result.Mu}
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for index := range got {
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if index == 5 {
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continue
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}
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for n := range tc.want[index] {
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if math.Abs(got[index][n]-tc.want[index][n]) > tolerances[index][n] {
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t.Errorf("%s[%d] = %.8f, want %.8f (tol %.1e)", labels[index], n,
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got[index][n], tc.want[index][n], tolerances[index][n])
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}
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}
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}
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})
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}
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}
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func TestSolarEclipseBesselianElementsIAUSingleKUsesOneK(t *testing.T) {
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result, ok := SolarEclipseBesselianElements(besselianNASASeed, SolarEclipseBesselianElementsOptions{
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Model: SolarEclipseModelIAUSingleK,
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DeltaTSeconds: besselianNASADeltaT,
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})
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if !ok {
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t.Fatal("2024-04-08 should have a solar eclipse")
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}
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if result.Model != SolarEclipseModelIAUSingleK {
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t.Errorf("model = %q, want %q", result.Model, SolarEclipseModelIAUSingleK)
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}
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if result.UmbralK != result.PenumbralK {
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t.Errorf("k2 = %g, want k1 = %g", result.UmbralK, result.PenumbralK)
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}
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}
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func TestSolarEclipseBesselianElementsWithoutEclipse(t *testing.T) {
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if _, ok := SolarEclipseBesselianElements(JDCalc(2024, 5, 8), SolarEclipseBesselianElementsOptions{}); ok {
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t.Fatal("2024-05-08 has no solar eclipse")
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}
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}
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func TestSolarEclipseBesselianElementsRejectsShortSampleSet(t *testing.T) {
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if got := solarEclipseFitCubic([]float64{-1, 0, 1}, []float64{1, 2, 3}); got != (SolarEclipseBesselianPolynomial{}) {
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t.Errorf("fit with three samples = %v, want zero", got)
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}
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if got := solarEclipseFitCubic([]float64{-3, -1.5, 0, 1.5, 3}, []float64{0, 0, 0, 0, 0}); got != (SolarEclipseBesselianPolynomial{}) {
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t.Errorf("fit of a zero column = %v, want zero", got)
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}
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}
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