tensor/integrate/filon_test.go

// Copyright (c) 2026 Petr Balvín <opensource@petrbalvin.org> (https://petrbalvin.org)
// SPDX-License-Identifier: MIT

package integrate

import (
	"math"
	"testing"

	"sourcedock.dev/petrbalvin/tensor/internal/base"
)

// intFilon closed forms: the antiderivatives the referents come from.
// intFilon1 integrates 1·cos(kx) and 1·sin(kx); intFilonX integrates x
// against the same kernels; intFilonExp integrates e^{ax} against
// them. All are exact calculus, evaluated independently of the code
// under test.
func intFilon1(a, b, k float64) (c, s float64) {
	return (math.Sin(k*b) - math.Sin(k*a)) / k,
		(math.Cos(k*a) - math.Cos(k*b)) / k
}

func intFilonX(a, b, k float64) (c, s float64) {
	cb, sb := math.Cos(k*b), math.Sin(k*b)
	ca, sa := math.Cos(k*a), math.Sin(k*a)
	c = (cb+k*b*sb)/k/k - (ca+k*a*sa)/k/k
	s = (sb-k*b*cb)/k/k - (sa-k*a*ca)/k/k
	return c, s
}

func intFilonExp(a, b, amp, k float64) (c, s float64) {
	cb, sb := math.Cos(k*b), math.Sin(k*b)
	ca, sa := math.Cos(k*a), math.Sin(k*a)
	eb, ea := math.Exp(amp*b), math.Exp(amp*a)
	c = eb*(amp*cb+k*sb)/(amp*amp+k*k) - ea*(amp*ca+k*sa)/(amp*amp+k*k)
	s = eb*(amp*sb-k*cb)/(amp*amp+k*k) - ea*(amp*sa-k*ca)/(amp*amp+k*k)
	return c, s
}

func wantFilon(t *testing.T, label string, gotC, gotS, wantC, wantS, tol float64) {
	t.Helper()
	if d := math.Abs(gotC - wantC); d > tol*math.Max(1, math.Abs(wantC)) {
		t.Fatalf("%s: cos part = %.17g, want %.17g (absolute %.3g)", label, gotC, wantC, d)
	}
	if d := math.Abs(gotS - wantS); d > tol*math.Max(1, math.Abs(wantS)) {
		t.Fatalf("%s: sin part = %.17g, want %.17g (absolute %.3g)", label, gotS, wantS, d)
	}
}

// TestIntegrateFilonExactAmplitudes pins the exactness the method
// promises: unit and linear amplitudes are polynomials below the
// default degree, so every frequency from one to a thousand must land
// on the closed form at the rounding floor, whatever the carrier does
// between the samples.
func TestIntegrateFilonExactAmplitudes(t *testing.T) {
	one := func(float64) (float64, error) { return 1, nil }
	identity := func(x float64) (float64, error) { return x, nil }
	for _, c := range []struct {
		label string
		a, b  float64
		k     float64
		f     func(float64) (float64, error)
		ref   func(a, b, k float64) (c, s float64)
	}{
		{"unit on [0, π]", 0, math.Pi, 1, one, intFilon1},
		{"unit on [2, 7]", 2, 7, 100, one, intFilon1},
		{"unit on [0, 1]", 0, 1, 1000, one, intFilon1},
		{"x on [0, π]", 0, math.Pi, 1, identity, intFilonX},
		{"x on [2, 7]", 2, 7, 500, identity, intFilonX},
	} {
		gotC, gotS, err := IntegrateFilon(c.f, c.a, c.b, c.k, FilonOptions{})
		if err != nil {
			t.Fatalf("%s: %v", c.label, err)
		}
		wantC, wantS := c.ref(c.a, c.b, c.k)
		wantFilon(t, c.label, gotC, gotS, wantC, wantS, 1e-12)
	}
}

// TestIntegrateFilonZeroFrequency pins the degeneration at k = 0: the
// sine part is exactly zero and the cosine part is the plain integral
// of the amplitude.
func TestIntegrateFilonZeroFrequency(t *testing.T) {
	f := func(x float64) (float64, error) { return x * x, nil }
	gotC, gotS, err := IntegrateFilon(f, 0, 3, 0, FilonOptions{})
	if err != nil {
		t.Fatalf("IntegrateFilon: %v", err)
	}
	if gotS != 0 {
		t.Fatalf("the sine part at k = 0 is %g, want 0", gotS)
	}
	if d := math.Abs(gotC - 9); d > 1e-12 {
		t.Fatalf("the cosine part at k = 0 is %.17g, want 9", gotC)
	}
}

// TestIntegrateFilonExponential holds a non-polynomial amplitude
// against the exact antiderivative at a frequency whose carrier the
// automatic panel count must respect: two hundred and fifty
// oscillations over the interval, answered from a few thousand
// amplitude samples.
func TestIntegrateFilonExponential(t *testing.T) {
	const amp = 0.5
	f := func(x float64) (float64, error) { return math.Exp(amp * x), nil }
	gotC, gotS, err := IntegrateFilon(f, 2, 7, 500, FilonOptions{})
	if err != nil {
		t.Fatalf("IntegrateFilon: %v", err)
	}
	wantC, wantS := intFilonExp(2, 7, amp, 500)
	wantFilon(t, "exp amplitude", gotC, gotS, wantC, wantS, 1e-11)
}

// TestIntegrateFilonOrientation pins the reversed interval and the
// empty one: reversing negates both parts and an empty interval
// integrates to nothing.
func TestIntegrateFilonOrientation(t *testing.T) {
	f := func(x float64) (float64, error) { return math.Exp(0.2 * x), nil }
	fc, fs, err := IntegrateFilon(f, 0, 3, 40, FilonOptions{})
	if err != nil {
		t.Fatal(err)
	}
	rc, rs, err := IntegrateFilon(f, 3, 0, 40, FilonOptions{})
	if err != nil {
		t.Fatal(err)
	}
	if rc != -fc || rs != -fs {
		t.Fatalf("the reversed interval gave (%.17g, %.17g), want the negation of (%.17g, %.17g)", rc, rs, fc, fs)
	}
	if ec, es, err := IntegrateFilon(f, 2, 2, 40, FilonOptions{}); err != nil || ec != 0 || es != 0 {
		t.Fatalf("the empty interval gave (%g, %g, %v)", ec, es, err)
	}
}

// TestIntegrateFilonDeterministic redraws one integral and requires
// the same bits, the contract every entry point here carries.
func TestIntegrateFilonDeterministic(t *testing.T) {
	f := func(x float64) (float64, error) { return math.Exp(0.1 * x), nil }
	one := func() (float64, float64) {
		c, s, err := IntegrateFilon(f, 0, 5, 300, FilonOptions{})
		if err != nil {
			t.Fatal(err)
		}
		return c, s
	}
	c1, s1 := one()
	c2, s2 := one()
	if c1 != c2 || s1 != s2 {
		t.Fatalf("the same call moved: (%.17g, %.17g) against (%.17g, %.17g)", c1, s1, c2, s2)
	}
}

// TestIntegrateFilonErrors pins the contract: NaN bounds or frequency,
// a node count out of range, a forced panel count whose panels carry
// more carrier than the weights can be built within, and a failing or
// non-finite amplitude all surface as errors naming themselves.
func TestIntegrateFilonErrors(t *testing.T) {
	f := func(x float64) (float64, error) { return 1, nil }
	if _, _, err := IntegrateFilon(f, math.NaN(), 1, 10, FilonOptions{}); err == nil {
		t.Fatal("a NaN bound: want an error")
	}
	if _, _, err := IntegrateFilon(f, 0, 1, math.NaN(), FilonOptions{}); err == nil {
		t.Fatal("a NaN frequency: want an error")
	}
	if _, _, err := IntegrateFilon(f, 0, 1, math.Inf(1), FilonOptions{}); err == nil {
		t.Fatal("an infinite frequency: want an error")
	}
	if _, _, err := IntegrateFilon(f, 0, 1, 10, FilonOptions{Nodes: 1}); err == nil {
		t.Fatal("one node: want an error")
	}
	if _, _, err := IntegrateFilon(f, 0, 1, 10, FilonOptions{Nodes: 33}); err == nil {
		t.Fatal("33 nodes: want an error")
	}
	if _, _, err := IntegrateFilon(f, 0, 1, 1e6, FilonOptions{Panels: 2}); err == nil {
		t.Fatal("two panels under a carrier of 1e6: want an error")
	}
	boom := func(float64) (float64, error) { return 0, base.Errf("amplitude failed") }
	if _, _, err := IntegrateFilon(boom, 0, 1, 10, FilonOptions{}); err == nil {
		t.Fatal("a failing amplitude: want the error to propagate")
	}
	bad := func(x float64) (float64, error) {
		if x > 0.5 {
			return math.NaN(), nil
		}
		return 1, nil
	}
	if _, _, err := IntegrateFilon(bad, 0, 1, 10, FilonOptions{}); err == nil {
		t.Fatal("a non-finite amplitude value: want an error")
	}
}