"""
Pre-Metric Substrate Module

Implements the foundational pre-metric manifold M∅ that lacks any a priori metric
structure but contains the protofields and directional vectors that seed the
emergence of spacetime geometry and consciousness dimension.

Based on CUE Framework Axiom 1-6.
"""

from typing import Dict, Any, Optional, Tuple
import torch
import numpy as np
from cueai_architect.base import CUEGeometricModule, CUEConfiguration


class PreMetricSubstrate(CUEGeometricModule):
    """
    Pre-metric substrate M∅ implementation.

    The foundational manifold that lacks metric structure but contains
    protofields Ψ and Φ, directional vectors ξμ, ζμ, and the proto-coherence
    constant Λ that govern emergence dynamics.

    Attributes:
        proto_coherence_lambda: Global constant Λ modulating alignment intensity
        psi_protocoherence: Cognitive protocoherence scalar field
        phi_dark_precursor: Dark scalar precursor field
        xi_vector_field: First directional vector field
        zeta_vector_field: Second directional vector field
        topological_tension: Scalar functional τ encoding misalignment energy
        relational_oscillator: Bidirectional tensor form Ω
    """

    def __init__(
        self,
        manifold_resolution: int = 64,
        proto_coherence_lambda: float = 1.0,
        config: Optional[CUEConfiguration] = None,
        **kwargs
    ):
        super().__init__(manifold_dim=4, config=config, **kwargs)

        self.manifold_resolution = manifold_resolution
        self.proto_coherence_lambda = proto_coherence_lambda

        # Initialize protofields
        self.psi_protocoherence = None
        self.phi_dark_precursor = None
        self.xi_vector_field = None
        self.zeta_vector_field = None
        self.topological_tension = None
        self.relational_oscillator = None

        # Proto-action components
        self.proto_action_components = {}

        self.logger.info(
            f"PreMetricSubstrate initialized with resolution {manifold_resolution}"
        )

    def initialize(self) -> None:
        """Initialize the pre-metric substrate with protofields."""
        if self._is_initialized:
            return

        self.logger.info("Initializing pre-metric substrate...")

        # Initialize cognitive protocoherence scalar Ψ
        self.psi_protocoherence = self._initialize_scalar_field(
            "psi", amplitude=0.1, coherence_pattern=True
        )

        # Initialize dark scalar precursor Φ  
        self.phi_dark_precursor = self._initialize_scalar_field(
            "phi", amplitude=0.05, coherence_pattern=False
        )

        # Initialize directional vector fields (lack norms/inner products)
        self.xi_vector_field = self._initialize_vector_field("xi")
        self.zeta_vector_field = self._initialize_vector_field("zeta")

        # Initialize topological tension functional
        self.topological_tension = self._compute_topological_tension()

        # Initialize relational entanglement oscillator
        self.relational_oscillator = self._initialize_relational_oscillator()

        self._is_initialized = True
        self.logger.info("Pre-metric substrate initialization complete")

    def _initialize_scalar_field(
        self, 
        field_type: str, 
        amplitude: float,
        coherence_pattern: bool = True
    ) -> torch.Tensor:
        """Initialize scalar field with specified characteristics."""
        # Create spatial grid
        grid_shape = (self.manifold_resolution,) * self.manifold_dim

        if coherence_pattern:
            # Create coherent standing wave pattern for Ψ
            coords = torch.meshgrid([
                torch.linspace(-np.pi, np.pi, self.manifold_resolution)
                for _ in range(self.manifold_dim)
            ], indexing='ij')

            field = amplitude * torch.prod(torch.stack([
                torch.sin(coord) for coord in coords
            ]), dim=0)
        else:
            # Create more random pattern for Φ
            field = amplitude * torch.randn(grid_shape, device=self.device)

        self.logger.debug(f"Initialized {field_type} field with shape {field.shape}")
        return self.to_device(field)

    def _initialize_vector_field(self, field_type: str) -> torch.Tensor:
        """Initialize directional vector field without norms."""
        grid_shape = (self.manifold_resolution,) * self.manifold_dim

        # Create vector field components (one for each dimension)
        vector_field = torch.randn(
            *grid_shape, self.manifold_dim, device=self.device
        )

        # Note: Deliberately NOT normalizing as these lack norms/inner products
        self.logger.debug(f"Initialized {field_type} vector field")
        return vector_field

    def _compute_topological_tension(self) -> torch.Tensor:
        """
        Compute topological tension τ(Φ, Ψ) encoding misalignment energy.

        This functional measures the misalignment between proto-scalar
        configurations and marks zones of geometric instability.
        """
        if self.psi_protocoherence is None or self.phi_dark_precursor is None:
            raise ValueError("Proto-fields must be initialized first")

        # Compute field gradients
        psi_grad = self._compute_field_gradient(self.psi_protocoherence)
        phi_grad = self._compute_field_gradient(self.phi_dark_precursor)

        # Misalignment measure: |∇Ψ|² - |∇Φ|² + Ψ·Φ interaction
        psi_grad_norm = torch.sum(psi_grad**2, dim=-1)
        phi_grad_norm = torch.sum(phi_grad**2, dim=-1)

        cross_interaction = self.psi_protocoherence * self.phi_dark_precursor

        tension = psi_grad_norm - phi_grad_norm + 0.5 * cross_interaction**2

        self.logger.debug("Computed topological tension functional")
        return tension

    def _compute_field_gradient(self, field: torch.Tensor) -> torch.Tensor:
        """Compute gradient of scalar field using finite differences."""
        gradients = []

        for dim in range(self.manifold_dim):
            # Use torch.gradient for numerical differentiation
            grad_dim = torch.gradient(field, dim=dim)[0]
            gradients.append(grad_dim)

        return torch.stack(gradients, dim=-1)

    def _initialize_relational_oscillator(self) -> torch.Tensor:
        """
        Initialize relational entanglement oscillator Ω.

        Bidirectional tensor form mediating coherence flux between
        pre-metric directions, functioning as informational oscillator.
        """
        # Create oscillator tensor Ω: TM∅ × TM∅ → ℝ
        oscillator_shape = (
            self.manifold_resolution,
            self.manifold_resolution,
            self.manifold_dim,
            self.manifold_dim
        )

        # Initialize with coherent oscillatory patterns
        oscillator = torch.zeros(oscillator_shape, device=self.device)

        for i in range(self.manifold_dim):
            for j in range(self.manifold_dim):
                # Create oscillatory coupling pattern
                phase = 2 * np.pi * (i + j) / self.manifold_dim
                oscillator[:, :, i, j] = torch.sin(
                    torch.linspace(0, 4*np.pi, self.manifold_resolution).unsqueeze(1) + phase
                ).repeat(1, self.manifold_resolution)

        self.logger.debug("Initialized relational entanglement oscillator")
        return oscillator

    def compute_proto_action(self) -> torch.Tensor:
        """
        Compute the proto-action integral according to CUE Equation (1).

        S_pre = ∫_M∅ d⁴x L_pre
        where L_pre = Λ·Ω(ξ,ζ) - ∇_ξΦ·∇_ζΨ + τ(Φ,Ψ)·δ(R)

        Returns:
            Proto-action scalar value
        """
        if not self._is_initialized:
            self.initialize()

        # Compute oscillator contribution: Λ·Ω(ξ,ζ)
        oscillator_term = self._compute_oscillator_contribution()

        # Compute directional derivative term: -∇_ξΦ·∇_ζΨ  
        derivative_term = self._compute_directional_derivative_term()

        # Compute tension localization term: τ(Φ,Ψ)·δ(R)
        # Note: δ(R) localizes at curvature-null zones (simplified as uniform here)
        tension_term = self.topological_tension

        # Combine terms for proto-Lagrangian density
        proto_lagrangian = (
            self.proto_coherence_lambda * oscillator_term
            - derivative_term
            + tension_term
        )

        # Integrate over manifold (sum approximation)
        proto_action = torch.sum(proto_lagrangian)

        self.proto_action_components = {
            "oscillator_term": torch.sum(oscillator_term),
            "derivative_term": torch.sum(derivative_term),
            "tension_term": torch.sum(tension_term),
            "total_action": proto_action
        }

        self.log_computation("proto_action", proto_action)
        return proto_action

    def _compute_oscillator_contribution(self) -> torch.Tensor:
        """Compute Ω(ξ,ζ) oscillator contribution."""
        # Contract oscillator with vector fields
        # Ω(ξ,ζ) = Ω_μν ξ^μ ζ^ν (Einstein summation)

        contribution = torch.zeros(
            self.manifold_resolution**self.manifold_dim, device=self.device
        ).reshape((self.manifold_resolution,) * self.manifold_dim)

        # Simplified computation (full tensor contraction)
        for mu in range(self.manifold_dim):
            for nu in range(self.manifold_dim):
                contribution += (
                    self.relational_oscillator[..., mu, nu] *
                    self.xi_vector_field[..., mu] *
                    self.zeta_vector_field[..., nu]
                )

        return contribution

    def _compute_directional_derivative_term(self) -> torch.Tensor:
        """Compute ∇_ξΦ·∇_ζΨ directional derivative term."""
        # Compute directional derivatives
        phi_grad = self._compute_field_gradient(self.phi_dark_precursor)
        psi_grad = self._compute_field_gradient(self.psi_protocoherence)

        # Contract with vector fields
        xi_dot_phi_grad = torch.sum(
            self.xi_vector_field * phi_grad, dim=-1
        )
        zeta_dot_psi_grad = torch.sum(
            self.zeta_vector_field * psi_grad, dim=-1
        )

        return xi_dot_phi_grad * zeta_dot_psi_grad

    def compute(self, *args, **kwargs) -> Dict[str, torch.Tensor]:
        """Main computation method - compute full pre-metric analysis."""
        proto_action = self.compute_proto_action()

        results = {
            "proto_action": proto_action,
            "psi_field": self.psi_protocoherence,
            "phi_field": self.phi_dark_precursor,
            "topological_tension": self.topological_tension,
            "action_components": self.proto_action_components
        }

        return results

    def detect_geometric_instabilities(self) -> torch.Tensor:
        """
        Detect zones of geometric instability where spacetime emergence occurs.

        These are regions where topological tension exceeds threshold,
        marking potential bifurcation points for metric generation.
        """
        if not self._is_initialized:
            self.initialize()

        # Find high-tension regions
        tension_threshold = torch.std(self.topological_tension)
        instability_mask = self.topological_tension > tension_threshold

        self.logger.info(
            f"Found {torch.sum(instability_mask)} instability zones "
            f"out of {instability_mask.numel()} total points"
        )

        return instability_mask

    def visualize_substrate(self, slice_dim: int = 0, slice_index: Optional[int] = None):
        """Create visualization of the pre-metric substrate."""
        if not self._is_initialized:
            self.initialize()

        try:
            import matplotlib.pyplot as plt

            if slice_index is None:
                slice_index = self.manifold_resolution // 2

            # Create slices for visualization
            fig, axes = plt.subplots(2, 2, figsize=(12, 10))
            fig.suptitle("Pre-Metric Substrate Visualization", fontsize=16)

            # Get 2D slices
            slices = [slice(None)] * self.manifold_dim
            slices[slice_dim] = slice_index
            slice_tuple = tuple(slices)

            # Plot Ψ field
            im1 = axes[0,0].imshow(
                self.psi_protocoherence[slice_tuple].cpu().numpy(),
                cmap='viridis'
            )
            axes[0,0].set_title("Ψ Cognitive Protocoherence")
            plt.colorbar(im1, ax=axes[0,0])

            # Plot Φ field  
            im2 = axes[0,1].imshow(
                self.phi_dark_precursor[slice_tuple].cpu().numpy(),
                cmap='plasma'
            )
            axes[0,1].set_title("Φ Dark Precursor")
            plt.colorbar(im2, ax=axes[0,1])

            # Plot topological tension
            im3 = axes[1,0].imshow(
                self.topological_tension[slice_tuple].cpu().numpy(),
                cmap='hot'
            )
            axes[1,0].set_title("Topological Tension τ(Φ,Ψ)")
            plt.colorbar(im3, ax=axes[1,0])

            # Plot instability zones
            instabilities = self.detect_geometric_instabilities()[slice_tuple]
            axes[1,1].imshow(
                instabilities.cpu().numpy(),
                cmap='binary'
            )
            axes[1,1].set_title("Geometric Instability Zones")

            plt.tight_layout()
            return fig

        except ImportError:
            self.logger.warning("matplotlib not available for visualization")
            return None
