"""Tests for Phase 2 algorithm analysis and improvements.

This module contains tests to analyze current algorithm issues and validate
improvements made in Phase 2.
"""

import jax
import jax.numpy as jnp
import pytest

from polytopax.algorithms.approximation import approximate_convex_hull


class TestCurrentAlgorithmIssues:
    """Test current algorithm to identify and document issues."""

    def test_vertex_count_violation(self):
        """Test that demonstrates the vertex count violation issue."""
        # Simple 2D square (4 input points)
        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, hull_indices = approximate_convex_hull(
            points, n_directions=20, random_key=jax.random.PRNGKey(42)
        )

        input_count = points.shape[0]
        output_count = hull_vertices.shape[0]

        # Document the current issue: output vertices > input vertices
        print(f"Input vertices: {input_count}")
        print(f"Output vertices: {output_count}")
        print(f"Violation: {output_count > input_count}")

        # This test documents the current problematic behavior
        # In a correct convex hull algorithm, output_count <= input_count should always hold
        # Currently this fails, which is what we need to fix

    def test_triangle_vertex_count_violation(self):
        """Test vertex count violation with a simple triangle."""
        # Simple triangle (3 input points)
        points = jnp.array([
            [0.0, 0.0],  # Origin
            [1.0, 0.0],  # Right
            [0.5, 1.0]   # Top
        ])

        hull_vertices, _ = approximate_convex_hull(
            points, n_directions=15, random_key=jax.random.PRNGKey(123)
        )

        input_count = points.shape[0]
        output_count = hull_vertices.shape[0]

        print(f"Triangle - Input: {input_count}, Output: {output_count}")

        # Mathematical violation: triangle convex hull should have ≤ 3 vertices
        # Current algorithm produces many more due to soft selection interpolation

    def test_soft_selection_interpolation_issue(self):
        """Analyze how soft selection creates non-vertex points."""
        points = jnp.array([
            [0.0, 0.0],
            [1.0, 0.0],
            [0.0, 1.0]
        ])

        # Get hull with different temperatures to see interpolation effect
        hull_low_temp, _ = approximate_convex_hull(
            points, temperature=0.01, random_key=jax.random.PRNGKey(42)
        )
        hull_high_temp, _ = approximate_convex_hull(
            points, temperature=1.0, random_key=jax.random.PRNGKey(42)
        )

        print(f"Low temp vertices: {hull_low_temp.shape[0]}")
        print(f"High temp vertices: {hull_high_temp.shape[0]}")

        # Check if any hull vertices are exact matches to input points
        # Soft selection creates weighted combinations, not exact vertices
        exact_matches_low = 0
        exact_matches_high = 0

        for hull_vertex in hull_low_temp:
            for input_point in points:
                if jnp.allclose(hull_vertex, input_point, atol=1e-6):
                    exact_matches_low += 1
                    break

        for hull_vertex in hull_high_temp:
            for input_point in points:
                if jnp.allclose(hull_vertex, input_point, atol=1e-6):
                    exact_matches_high += 1
                    break

        print(f"Exact matches low temp: {exact_matches_low}")
        print(f"Exact matches high temp: {exact_matches_high}")

    def test_mathematical_properties_violation(self):
        """Test violations of fundamental convex hull properties."""
        points = jnp.array([
            [0.0, 0.0],
            [1.0, 0.0],
            [1.0, 1.0],
            [0.0, 1.0]
        ])

        hull_vertices, _ = approximate_convex_hull(points)

        # Property 1: All hull vertices should be on the convex hull boundary
        # Property 2: All input points should be inside or on the hull
        # Property 3: Hull should be the minimal convex set containing all points

        # For now, just document what we get
        print(f"Input points shape: {points.shape}")
        print(f"Hull vertices shape: {hull_vertices.shape}")
        print(f"Hull vertices sample:\n{hull_vertices[:5]}")

        # The current algorithm fails these properties due to soft interpolation


class TestImprovedAlgorithmRequirements:
    """Define requirements for the improved algorithm through tests."""

    def test_vertex_count_constraint_requirement(self):
        """Test that improved algorithm must satisfy vertex count constraint."""
        jnp.array([
            [0.0, 0.0],
            [1.0, 0.0],
            [0.0, 1.0]
        ])

        # This test will pass once we implement the improved algorithm
        # For now, it serves as a specification

        # hull_vertices = improved_approximate_convex_hull(points)
        # assert hull_vertices.shape[0] <= points.shape[0]

        # Placeholder for future implementation
        pytest.skip("Will be implemented with improved algorithm")

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

        # The improved algorithm must still be differentiable for ML applications
        # def volume_objective(pts):
        #     hull = improved_approximate_convex_hull(pts)
        #     return compute_hull_volume(hull)
        #
        # grad_fn = jax.grad(volume_objective)
        # gradients = grad_fn(points)
        # assert gradients.shape == points.shape

        pytest.skip("Will be implemented with improved algorithm")

    def test_accuracy_requirement(self):
        """Test accuracy requirements for the improved algorithm."""
        # Known geometric shapes with exact convex hulls

        # Unit square
        jnp.array([
            [0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0]
        ])
        # Expected: exactly these 4 vertices, area = 1.0

        # Regular triangle
        jnp.array([
            [0.0, 0.0], [1.0, 0.0], [0.5, jnp.sqrt(3)/2]
        ])
        # Expected: exactly these 3 vertices, area = √3/4

        pytest.skip("Will be validated with improved algorithm")


class TestStagedSelectionMethodDesign:
    """Design tests for the staged selection improvement method."""

    def test_stage1_coarse_approximation(self):
        """Test Stage 1: Coarse approximation to filter candidate points."""
        jnp.array([
            [0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0],
            [0.5, 0.5]  # Interior point that should be filtered out
        ])

        # Stage 1 should identify that the interior point is not on the hull
        # and focus on the boundary points

        # candidates = coarse_hull_approximation(points)
        # Expected: candidates should prefer boundary points

        pytest.skip("Stage 1 implementation pending")

    def test_stage2_fine_adjustment(self):
        """Test Stage 2: Fine adjustment with differentiable selection."""
        # After coarse selection, fine-tune with soft selection
        # but constrain to not exceed input vertex count

        pytest.skip("Stage 2 implementation pending")

    def test_stage3_vertex_limiting(self):
        """Test Stage 3: Enforce vertex count constraint."""
        # Final stage must guarantee output_vertices <= input_vertices

        pytest.skip("Stage 3 implementation pending")


if __name__ == "__main__":
    # Run analysis tests to understand current issues
    test_instance = TestCurrentAlgorithmIssues()

    print("=== Analyzing Current Algorithm Issues ===")
    test_instance.test_vertex_count_violation()
    print()
    test_instance.test_triangle_vertex_count_violation()
    print()
    test_instance.test_soft_selection_interpolation_issue()
    print()
    test_instance.test_mathematical_properties_violation()
