tensor/signal/poissondirichlet_test.go

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

package signal

import (
	"math"
	"testing"

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

// poissonManufactured builds f = −Δu for u = sin(πx)·sin(πy) on the
// unit square over an (n × n) grid including the boundary, so the
// exact solution is known everywhere.
func poissonManufactured(t *testing.T, n int) (f, exact *core.Array) {
	t.Helper()
	flatF := make([]float64, n*n)
	flatU := make([]float64, n*n)
	for r := range n {
		for c := range n {
			x := float64(c) / float64(n-1)
			y := float64(r) / float64(n-1)
			i := r*n + c
			flatU[i] = math.Sin(math.Pi*x) * math.Sin(math.Pi*y)
			flatF[i] = 2 * math.Pi * math.Pi * flatU[i]
		}
	}
	f = mustFloats(t, flatF, n, n)
	exact = mustFloats(t, flatU, n, n)
	return f, exact
}

// TestSolvePoissonDirichletManufactured checks the sine-solve against
// the manufactured solution: second-order convergence, with the
// coarse grid already inside 5e-3.
func TestSolvePoissonDirichletManufactured(t *testing.T) {
	for _, n := range []int{9, 17, 33} {
		f, exact := poissonManufactured(t, n)
		u, err := SolvePoissonDirichlet(f, 1, 1)
		if err != nil {
			t.Fatalf("SolvePoissonDirichlet(%d): %v", n, err)
		}
		worst := 0.0
		for i := range exact.Len() {
			if e := math.Abs(u.FloatAt(i) - exact.FloatAt(i)); e > worst {
				worst = e
			}
		}
		h := 1 / float64(n-1)
		if worst > 3*h*h {
			t.Fatalf("grid %d: worst error %.3g above the O(h²) budget %.3g", n, worst, 3*h*h)
		}
		// The boundary is exactly zero by construction.
		for c := range n {
			if u.FloatAt(c) != 0 || u.FloatAt((n-1)*n+c) != 0 {
				t.Fatalf("grid %d: boundary came back nonzero", n)
			}
		}
	}
}

// TestSolvePoissonNeumannManufactured checks the cosine solve with a
// zero-mean source whose solution is u = cos(πx)·cos(πy), the
// derivative-free data the Neumann solve exists for.
func TestSolvePoissonNeumannManufactured(t *testing.T) {
	const n = 17
	flatF := make([]float64, n*n)
	flatU := make([]float64, n*n)
	for r := range n {
		for c := range n {
			x := float64(c) / float64(n-1)
			y := float64(r) / float64(n-1)
			i := r*n + c
			flatU[i] = math.Cos(math.Pi*x) * math.Cos(math.Pi*y)
			flatF[i] = 2 * math.Pi * math.Pi * flatU[i]
		}
	}
	// Zero-mean shift: subtract the mean, which also shifts u by a
	// constant the Neumann problem cannot see.
	meanF := 0.0
	for _, v := range flatF {
		meanF += v
	}
	meanF /= float64(n * n)
	for i := range flatF {
		flatF[i] -= meanF
	}
	f := mustFloats(t, flatF, n, n)
	exact := mustFloats(t, flatU, n, n)
	u, err := SolvePoissonNeumann(f, 1, 1)
	if err != nil {
		t.Fatalf("SolvePoissonNeumann: %v", err)
	}
	// Compare up to the free constant: recentre both to zero mean.
	got := 0.0
	for i := range u.Len() {
		got += u.FloatAt(i)
	}
	got /= float64(u.Len())
	worst := 0.0
	for i := range u.Len() {
		if e := math.Abs(u.FloatAt(i) - got - exact.FloatAt(i)); e > worst {
			worst = e
		}
	}
	h := 1 / float64(n-1)
	if worst > 3*h*h {
		t.Fatalf("worst error %.3g above the O(h²) budget %.3g", worst, 3*h*h)
	}
}

// TestSolvePoissonNeumannMeanRefusal checks the compatibility
// condition: a nonzero-mean source has no Neumann solution.
func TestSolvePoissonNeumannMeanRefusal(t *testing.T) {
	f := mustFloats(t, []float64{
		1, 1, 1,
		1, 1, 1,
		1, 1, 1,
	}, 3, 3)
	if _, err := SolvePoissonNeumann(f, 1, 1); err == nil {
		t.Fatal("nonzero-mean source accepted")
	}
	if _, err := SolvePoissonDirichlet(mustFloats(t, []float64{1, 1}, 1, 2), 1, 1); err == nil {
		t.Fatal("grid under 3×3 accepted")
	}
	if _, err := SolvePoissonDirichlet(f, 0, 1); err == nil {
		t.Fatal("non-positive length accepted")
	}
}