"""Tests for improved differentiable convex hull algorithm.

These tests define the expected behavior of the improved algorithm
and will drive the TDD implementation.
"""

import jax
import jax.numpy as jnp
import pytest

# Import the improved algorithm implementation
from polytopax.algorithms.approximation import compute_hull_quality_metrics, improved_approximate_convex_hull


class TestImprovedAlgorithmBehavior:
    """Test suite defining the expected behavior of improved algorithm."""

    def test_vertex_count_constraint_simple_triangle(self):
        """Test vertex count constraint with a simple triangle."""
        points = jnp.array([
            [0.0, 0.0],  # A
            [1.0, 0.0],  # B
            [0.5, 1.0]   # C
        ])

        hull_vertices, hull_indices = improved_approximate_convex_hull(
            points, random_key=jax.random.PRNGKey(42)
        )

        # Critical requirement: output vertices <= input vertices
        assert hull_vertices.shape[0] <= points.shape[0]
        assert hull_vertices.shape[0] <= 3  # Triangle has max 3 vertices

        # Test quality metrics
        metrics = compute_hull_quality_metrics(hull_vertices, points)
        assert metrics["constraint_satisfied"] is True
        assert metrics["vertex_count_ratio"] <= 1.0

    def test_vertex_count_constraint_square(self):
        """Test vertex count constraint with a square."""
        points = jnp.array([
            [0.0, 0.0],  # Bottom-left
            [1.0, 0.0],  # Bottom-right
            [1.0, 1.0],  # Top-right
            [0.0, 1.0]   # Top-left
        ])

        hull_vertices, _ = improved_approximate_convex_hull(
            points, random_key=jax.random.PRNGKey(123)
        )
        assert hull_vertices.shape[0] <= 4  # Square has max 4 vertices
        assert hull_vertices.shape[0] >= 3  # At least triangle

        # Verify constraint satisfaction
        metrics = compute_hull_quality_metrics(hull_vertices, points)
        assert metrics["constraint_satisfied"] is True

    def test_vertex_count_constraint_with_interior_points(self):
        """Test that interior points don't increase vertex count."""
        points = jnp.array([
            [0.0, 0.0],  # Corner
            [1.0, 0.0],  # Corner
            [1.0, 1.0],  # Corner
            [0.0, 1.0],  # Corner
            [0.5, 0.5],  # Interior (should not be hull vertex)
            [0.3, 0.3],  # Interior (should not be hull vertex)
        ])

        # Even with interior points, hull should have ≤ 4 vertices (the corners)
        hull_vertices, _ = improved_approximate_convex_hull(
            points, random_key=jax.random.PRNGKey(456)
        )
        assert hull_vertices.shape[0] <= 4

        # Verify the algorithm prefers boundary points
        metrics = compute_hull_quality_metrics(hull_vertices, points)
        assert metrics["constraint_satisfied"] is True
        # Should have good boundary efficiency (hull vertices are mostly input vertices)
        assert metrics["boundary_efficiency"] > 0.5

    def test_differentiability_preservation(self):
        """Test that improved algorithm maintains differentiability."""
        jnp.array([
            [0.0, 0.0],
            [1.0, 0.0],
            [0.5, 1.0]
        ])

        # Define a differentiable objective based on hull area
        # def hull_area_objective(pts):
        #     hull_vertices, _ = improved_approximate_convex_hull(pts)
        #     # Compute area using shoelace formula
        #     x = hull_vertices[:, 0]
        #     y = hull_vertices[:, 1]
        #     return 0.5 * jnp.abs(jnp.sum(x[:-1] * y[1:] - x[1:] * y[:-1]))
        #
        # # Should be differentiable
        # grad_fn = jax.grad(hull_area_objective)
        # gradients = grad_fn(points)
        #
        # assert gradients.shape == points.shape
        # assert not jnp.any(jnp.isnan(gradients))

        pytest.skip("Improved algorithm not yet implemented")

    def test_approximation_quality_vs_exact_hull(self):
        """Test approximation quality against known exact hulls."""
        # Regular triangle - we know the exact hull
        a = 1.0
        h = a * jnp.sqrt(3) / 2
        jnp.array([
            [0.0, 0.0],      # A
            [a, 0.0],        # B
            [a/2, h]         # C
        ])
        a * h / 2  # = a² * sqrt(3) / 4

        # hull_vertices, _ = improved_approximate_convex_hull(triangle_points)
        #
        # # Compute approximate area
        # x = hull_vertices[:, 0]
        # y = hull_vertices[:, 1]
        # approx_area = 0.5 * jnp.abs(jnp.sum(x[:-1] * y[1:] - x[1:] * y[:-1]))
        #
        # # Should be reasonably close to exact area
        # relative_error = jnp.abs(approx_area - exact_area) / exact_area
        # assert relative_error < 0.1  # Within 10% error

        pytest.skip("Improved algorithm not yet implemented")


class TestStagedSelectionMethodSpecification:
    """Specification tests for the staged selection method."""

    def test_stage1_boundary_point_identification(self):
        """Test Stage 1: Identify points likely to be on boundary."""
        jnp.array([
            [0.0, 0.0],  # Definitely on boundary
            [1.0, 0.0],  # Definitely on boundary
            [1.0, 1.0],  # Definitely on boundary
            [0.0, 1.0],  # Definitely on boundary
            [0.5, 0.5],  # Interior point
            [0.9, 0.9],  # Near boundary but interior
        ])

        # Stage 1 should assign higher scores to boundary points
        # boundary_scores = coarse_boundary_detection(points)
        #
        # # Boundary points should have higher scores than interior points
        # assert boundary_scores[0] > boundary_scores[4]  # Corner vs center
        # assert boundary_scores[1] > boundary_scores[4]  # Corner vs center
        # assert boundary_scores[2] > boundary_scores[5]  # Corner vs near-boundary

        pytest.skip("Stage 1 not yet implemented")

    def test_stage2_differentiable_refinement(self):
        """Test Stage 2: Differentiable refinement while respecting constraints."""
        # Stage 2 should use soft selection but with constraints
        pytest.skip("Stage 2 not yet implemented")

    def test_stage3_hard_vertex_limit(self):
        """Test Stage 3: Hard limit on number of vertices."""
        jnp.array([
            [0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0]  # 4 points
        ])

        # Stage 3 must ensure output has ≤ 4 vertices regardless of intermediate stages
        # final_vertices = enforce_vertex_limit(intermediate_hull, max_vertices=4)
        # assert final_vertices.shape[0] <= 4

        pytest.skip("Stage 3 not yet implemented")


class TestQualityMetrics:
    """Tests for hull quality assessment metrics."""

    def test_coverage_metric(self):
        """Test coverage: how well the hull covers the input points."""
        # Coverage = fraction of input points on or near the hull boundary
        pytest.skip("Quality metrics not yet implemented")

    def test_convexity_metric(self):
        """Test convexity: how close the result is to being convex."""
        # Check if all vertices are on the convex hull of the vertices
        pytest.skip("Quality metrics not yet implemented")

    def test_approximation_error_metric(self):
        """Test approximation error compared to exact hull (when available)."""
        pytest.skip("Quality metrics not yet implemented")


class TestEdgeCases:
    """Test edge cases that the improved algorithm must handle."""

    def test_collinear_points(self):
        """Test handling of collinear points."""
        jnp.array([
            [0.0, 0.0],
            [0.5, 0.0],
            [1.0, 0.0]
        ])

        # Convex hull of collinear points should be a line segment (2 endpoints)
        # hull_vertices, _ = improved_approximate_convex_hull(points)
        # assert hull_vertices.shape[0] <= 2  # At most the two endpoints

        pytest.skip("Improved algorithm not yet implemented")

    def test_duplicate_points(self):
        """Test handling of duplicate points."""
        jnp.array([
            [0.0, 0.0],
            [0.0, 0.0],  # Duplicate
            [1.0, 0.0],
            [0.0, 1.0]
        ])

        # Duplicates shouldn't affect the hull
        # hull_vertices, _ = improved_approximate_convex_hull(points)
        # assert hull_vertices.shape[0] <= 3  # Triangle from unique points

        pytest.skip("Improved algorithm not yet implemented")

    def test_single_point(self):
        """Test degenerate case with single point."""
        jnp.array([[0.0, 0.0]])

        # Hull of single point is the point itself
        # hull_vertices, _ = improved_approximate_convex_hull(points)
        # assert hull_vertices.shape[0] == 1
        # assert jnp.allclose(hull_vertices[0], points[0])

        pytest.skip("Improved algorithm not yet implemented")


if __name__ == "__main__":
    # This will run once we implement the improved algorithm
    print("Improved algorithm test specifications defined.")
    print("Run with pytest once implementation is complete.")
