"""Independent small mathematical oracles for Section 9's coordinate contract.""" from fractions import Fraction from hashlib import sha256 import importlib.util import json import os from pathlib import Path import shutil import subprocess import sys from types import SimpleNamespace import zipfile import mpmath as mp import numpy as np import pytest from ideal_poly_volume_toolkit import variational as var ROOT = Path(__file__).resolve().parents[3] EXPERIMENT = ROOT / "experiments/section9" FIXTURE = json.loads((EXPERIMENT / "fixture.json").read_text()) POINTS = np.array(FIXTURE["points"]) FACES = np.array(FIXTURE["triangles"]) INTERIOR = FIXTURE["interior_vertices"] BOUNDARY = FIXTURE["boundary_vertices"] def experiment_module(): spec = importlib.util.spec_from_file_location("section9_fixture_oracle", EXPERIMENT / "run.py") module = importlib.util.module_from_spec(spec) spec.loader.exec_module(module) return module def test_integer_mesh_fem_and_volume_hessian(): base = var.corner_angles(POINTS, FACES) incidence = var.leading_trailing_matrix(FACES, INTERIOR) gradient, hessian = var.angle_volume_derivatives(base, incidence, [0, 0]) fem = var.fem_stiffness(POINTS, FACES) cot = var.cotangent_stiffness(len(POINTS), FACES, base) expected = np.array([[4., -1.], [-1., 4.]]) np.testing.assert_allclose(fem[np.ix_(INTERIOR, INTERIOR)], expected, atol=1e-14, rtol=0) np.testing.assert_allclose(cot, fem, atol=1e-14, rtol=0) np.testing.assert_allclose(-hessian, 2*expected, atol=1e-14, rtol=0) np.testing.assert_allclose(gradient, 0, atol=1e-14, rtol=0) assert var.angle_volume(base, incidence, [0, 0]) == pytest.approx(float(12*mp.catalan), abs=1e-12) def test_off_origin_hessian_against_high_precision_volume_derivative(): base = var.corner_angles(POINTS, FACES) incidence = var.leading_trailing_matrix(FACES, INTERIOR) u = FIXTURE["off_origin_parameters"] alpha = var.deformed_angles(base, incidence, u) # Preserve both kinds of affine constraints, without asserting realization. np.testing.assert_allclose(alpha.sum(axis=1), np.pi, atol=1e-14, rtol=0) sums = [{}, {}] for values, total in zip((base, alpha), sums): for face, angles in zip(FACES, values): for k in range(3): edge = tuple(sorted((face[(k+1) % 3], face[(k+2) % 3]))) total[edge] = total.get(edge, 0.) + angles[k] for edge in sums[0]: assert sums[0][edge] == pytest.approx(sums[1][edge], abs=1e-14) _, hessian = var.angle_volume_derivatives(base, incidence, u) previous_precision = mp.mp.dps oracle = experiment_module().high_precision_hessian(POINTS, FACES, incidence, u) assert mp.mp.dps == previous_precision np.testing.assert_allclose(hessian, oracle, atol=1e-11, rtol=0) def test_exact_rational_matrix_tree_and_schur_identities(): experiment = experiment_module() matrix = experiment.rational_fem(FIXTURE["points"], FIXTURE["triangles"]) grounded = [[matrix[i][j] for j in INTERIOR] for i in INTERIOR] assert grounded == [[Fraction(4), Fraction(-1)], [Fraction(-1), Fraction(4)]] assert experiment.rooted_forest_sum(matrix, BOUNDARY) == (Fraction(15), 15) effective = var.schur_complement(2*np.array(grounded, dtype=float), [0]) np.testing.assert_allclose(effective, [[7.5]], atol=0, rtol=0) assert 8*effective[0, 0] == 60 def test_dirichlet_response_against_linear_harmonic_function(): matrix = var.fem_stiffness(POINTS, FACES) response = var.schur_complement(matrix, INTERIOR) boundary_voltage = POINTS[BOUNDARY, 0] / 3 grounded = matrix[np.ix_(INTERIOR, INTERIOR)] voltage = -np.linalg.solve(grounded, matrix[np.ix_(INTERIOR, BOUNDARY)] @ boundary_voltage) np.testing.assert_allclose(voltage, [1/3, 2/3], atol=1e-14, rtol=0) np.testing.assert_allclose(response @ np.ones(len(BOUNDARY)), 0, atol=1e-14, rtol=0) np.testing.assert_allclose(response, response.T, atol=1e-14, rtol=0) for scale in (-2., 0., 1.5): v = scale*boundary_voltage assert v @ response @ v == pytest.approx(2*scale**2/3, abs=1e-13) assert np.linalg.eigvalsh(response).min() >= -1e-14 def test_cyclic_face_order_and_vertex_relabeling_preserve_fem(): rotated = np.roll(FACES, 1, axis=1) np.testing.assert_allclose(var.fem_stiffness(POINTS, rotated), var.fem_stiffness(POINTS, FACES)) incidence = var.leading_trailing_matrix(rotated, INTERIOR) _, hessian = var.angle_volume_derivatives(var.corner_angles(POINTS, rotated), incidence, [0, 0]) np.testing.assert_allclose(-hessian, [[8, -2], [-2, 8]], atol=1e-14, rtol=0) permutation = np.array([5, 3, 9, 0, 11, 1, 7, 2, 10, 6, 4, 8]) new_points = np.empty_like(POINTS) new_points[permutation] = POINTS relabeled = var.fem_stiffness(new_points, permutation[FACES]) np.testing.assert_allclose(relabeled[np.ix_(permutation, permutation)], var.fem_stiffness(POINTS, FACES)) def test_zero_dimensional_single_triangle_is_supported(): faces = np.array([[0, 1, 2]]) points = np.array([[0., 0.], [1., 0.], [0., 1.]]) base = var.corner_angles(points, faces) incidence = var.leading_trailing_matrix(faces, []) gradient, hessian = var.angle_volume_derivatives(base, incidence, []) assert incidence.shape == (3, 0) assert gradient.shape == (0,) assert hessian.shape == (0, 0) assert var.angle_volume(base, incidence, []) == pytest.approx(float(mp.catalan), abs=1e-13) matrix = var.fem_stiffness(points, faces) np.testing.assert_array_equal(var.schur_complement(matrix, []), matrix) def test_bad_domains_and_singular_elimination_are_explicit_failures(): base = var.corner_angles(POINTS, FACES) incidence = var.leading_trailing_matrix(FACES, INTERIOR) with pytest.raises(ValueError, match="strictly between"): var.deformed_angles(base, incidence, [10, 0]) with pytest.raises(ValueError, match="finite"): var.deformed_angles(base, incidence, [float('nan'), 0]) with pytest.raises(ValueError, match="nonboundary"): var.leading_trailing_matrix(FACES, [0, 5, 6]) with pytest.raises(ValueError, match="counterclockwise"): var.corner_angles(POINTS, FACES[:, ::-1]) with pytest.raises(ValueError, match="distinct"): var.schur_complement(np.eye(3), [1, 1]) with pytest.raises(np.linalg.LinAlgError): var.schur_complement(np.zeros((2, 2)), [0]) def test_unsigned_label_overflow_cannot_alias_the_last_vertex(): oversized = np.array([[0, 1, 2**64-1]], dtype=np.uint64) with pytest.raises(ValueError, match="representable"): var.corner_angles([[0, 0], [1, 0], [0, 1]], oversized) with pytest.raises(ValueError, match="representable"): var.leading_trailing_matrix(FACES, np.array([5, 2**64-1], dtype=np.uint64)) with pytest.raises(ValueError, match="representable"): var.schur_complement(np.eye(2), np.array([2**64-1], dtype=np.uint64)) def test_external_fixture_and_installed_module_provenance(tmp_path, monkeypatch): experiment = experiment_module() external_fixture = tmp_path / "external-fixture.json" shutil.copyfile(EXPERIMENT / "fixture.json", external_fixture) external_package = tmp_path / "site-packages/ideal_poly_volume_toolkit" external_package.mkdir(parents=True) for name in ("variational.py", "geometry.py"): shutil.copyfile(Path(var.__file__).with_name(name), external_package / name) monkeypatch.setattr(experiment, "var", SimpleNamespace(__file__=str(external_package / "variational.py"))) report = experiment.source_provenance(external_fixture) records = {row['role']: row for row in report['source_files']} for role, path in [('experiment.fixture', external_fixture), ('toolkit.variational', external_package / 'variational.py'), ('toolkit.geometry', external_package / 'geometry.py')]: assert records[role]['location_kind'] == 'external' assert records[role]['sha256'] == sha256(path.read_bytes()).hexdigest() assert report['source_sha256'][role] == records[role]['sha256'] (external_package / 'geometry.py').unlink() with pytest.raises(FileNotFoundError, match="toolkit.geometry"): experiment.source_provenance(external_fixture) def test_detached_bundle_runs_outside_checkout_without_book(tmp_path): experiment = experiment_module() origin = experiment.source_provenance(EXPERIMENT / 'fixture.json') archive_path = tmp_path / 'reproduction.zip' experiment.create_reproduction_bundle({'provenance': origin}, EXPERIMENT / 'fixture.json', archive_path) with zipfile.ZipFile(archive_path) as archive: archive.extractall(tmp_path / 'extracted') bundle = tmp_path / 'extracted/section9-reproduction' arbitrary_cwd = tmp_path / 'elsewhere' arbitrary_cwd.mkdir() env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1') env.pop('PYTHONPATH', None) completed = subprocess.run([sys.executable, str(bundle / 'experiments/section9/run.py')], cwd=arbitrary_cwd, env=env, text=True, capture_output=True, timeout=60) assert completed.returncode == 0, completed.stdout + completed.stderr report = json.loads((bundle / 'artifacts/section9/result.json').read_text()) assert report['all_checks_passed'] provenance = report['provenance'] assert provenance['execution_context'] == 'detached-bundle' assert provenance['source_commit'] is None assert provenance['repository_dirty_at_start'] is None assert provenance['bundle_payload_hashes_match'] is True records = {row['role']: row for row in provenance['source_files']} assert records['toolkit.variational']['path'] == 'packages/volume-toolkit/ideal_poly_volume_toolkit/variational.py' assert records['book.tex']['available'] is False assert records['book.reference_pdf']['available'] is False assert (bundle / 'LICENSES/volume-toolkit-MIT.txt').is_file() requirements = (bundle / 'requirements.txt').read_text().splitlines() assert {line.split('==')[0] for line in requirements} == {'numpy', 'scipy', 'mpmath'} page = (bundle / 'site/section9/index.html').read_text() assert 'Monograph source and PDF are not included' in page assert 'href="downloads/polyhedral_volumes_and_geodesic_identities.pdf"' not in page def test_external_fixture_contract_rejects_a_changed_experiment(tmp_path): experiment = experiment_module() changed = dict(FIXTURE) changed['off_origin_parameters'] = [0.01, 0.02] path = tmp_path / 'changed.json' path.write_text(json.dumps(changed)) with pytest.raises(ValueError, match="not a general mesh experiment"): experiment.build_report(path)