r"""Base classes for spectral mixing layers.

Provides base classes for spectral mixing layers, extending a base MixingLayer
with domain-specific functionality for token mixing operations using spectral
transforms. These classes define mathematical interfaces and computational
requirements for spectral transformers.

Mixing layers implement core token mixing operations that replace traditional
attention mechanisms in spectral transformers, providing linear or log-linear
computational complexity for sequence modeling tasks.

Classes
-------
MixingLayer
    Base class for spectral mixing operations.
UnitaryMixingLayer
    Base class for mixing layers that preserve energy (unitary operations).
FilterMixingLayer
    Base class for frequency-domain filtering operations.

Examples
--------
Implementing a custom spectral mixing layer:

>>> from spectrans.layers.mixing.base import MixingLayer
>>> class CustomMixing(MixingLayer):
...     def forward(self, x):
...         # Custom spectral mixing implementation
...         return self.apply_spectral_operation(x)

Creating a unitary mixing layer:

>>> from spectrans.layers.mixing.base import UnitaryMixingLayer
>>> class OrthogonalMixing(UnitaryMixingLayer):
...     def forward(self, x):
...         return self.apply_unitary_transform(x)
...     def verify_unitarity(self, x):
...         # Custom verification logic
...         return True

Notes
-----
Mathematical Properties:

All spectral mixing layers preserve shape where output equals input shape for sequence
modeling, support batched processing with consistent behavior, and maintain full gradient
flow for end-to-end training.

Unitary mixing layers additionally satisfy energy preservation $||f(\mathbf{x})||^2 = ||\mathbf{x}||^2$
following Parseval's theorem and preserve inner products through orthogonality.

Filter mixing layers operate in frequency domain, applying learned filters to frequency
components with localized operations in frequency space.


See Also
--------
spectrans.core.base : Core base classes for all spectral components
spectrans.transforms : Spectral transform implementations used by mixing layers
"""

from abc import abstractmethod
from typing import Any

import torch
import torch.nn as nn

from ...core.base import SpectralComponent


class MixingLayer(SpectralComponent):
    """Base class for spectral mixing operations.

    Mixing layers perform token mixing operations using various
    spectral transforms instead of traditional attention mechanisms.
    This class provides spectral-specific functionality including
    mathematical property verification and standardized interfaces
    for spectral transform operations.

    Parameters
    ----------
    hidden_dim : int
        Hidden dimension of the model.
    dropout : float, default=0.0
        Dropout probability for regularization.
    norm_eps : float, default=1e-5
        Epsilon for numerical stability in normalization.

    Attributes
    ----------
    hidden_dim : int
        Hidden dimension of the model.
    dropout : torch.nn.Module
        Dropout layer for regularization.
    norm_eps : float
        Epsilon for numerical stability.
    """

    def __init__(
        self,
        hidden_dim: int,
        dropout: float = 0.0,
        norm_eps: float = 1e-5,
    ):
        super().__init__()
        self.hidden_dim = hidden_dim
        self.dropout = nn.Dropout(dropout) if dropout > 0 else nn.Identity()
        self.norm_eps = norm_eps

    @abstractmethod
    def get_spectral_properties(self) -> dict[str, Any]:
        """Get mathematical properties of the spectral operation.

        Returns
        -------
        dict[str, Any]
            Dictionary containing mathematical properties such as:
            - 'unitary': bool, whether the transform is unitary
            - 'real_output': bool, whether output is guaranteed real
            - 'frequency_domain': bool, whether operation occurs in frequency domain
            - 'energy_preserving': bool, whether energy is preserved
        """
        pass

    def verify_shape_consistency(
        self, input_tensor: torch.Tensor, output_tensor: torch.Tensor
    ) -> bool:
        """Verify that input and output shapes are consistent.

        Parameters
        ----------
        input_tensor : torch.Tensor
            Input tensor to the mixing layer.
        output_tensor : torch.Tensor
            Output tensor from the mixing layer.

        Returns
        -------
        bool
            True if shapes are consistent, False otherwise.
        """
        if input_tensor.shape != output_tensor.shape:
            return False

        # Verify batch dimension consistency
        if input_tensor.size(0) != output_tensor.size(0):
            return False

        # Verify sequence length consistency
        if input_tensor.size(1) != output_tensor.size(1):
            return False

        # Verify hidden dimension consistency
        return input_tensor.size(2) == output_tensor.size(2)

    def compute_spectral_norm(self, tensor: torch.Tensor) -> torch.Tensor:
        """Compute spectral norm for analysis and regularization.

        Parameters
        ----------
        tensor : torch.Tensor
            Input tensor to compute spectral norm for.

        Returns
        -------
        torch.Tensor
            Spectral norm of the input tensor.
        """
        # Reshape to matrix for spectral norm computation
        batch_size, seq_len, hidden_dim = tensor.shape
        matrix = tensor.view(batch_size * seq_len, hidden_dim)

        # Compute singular values
        _, s, _ = torch.svd(matrix)

        # Return maximum singular value (spectral norm)
        return torch.max(s, dim=-1)[0].mean()


class UnitaryMixingLayer(MixingLayer):
    """Base class for unitary mixing operations.

    Unitary mixing layers preserve energy and inner products, maintaining
    mathematical properties essential for stable training and theoretical
    guarantees in spectral transformers.

    Parameters
    ----------
    hidden_dim : int
        Hidden dimension of the model.
    dropout : float, default=0.0
        Dropout probability for regularization.
    norm_eps : float, default=1e-5
        Epsilon for numerical stability.
    energy_tolerance : float, default=1e-4
        Tolerance for energy preservation verification.

    Attributes
    ----------
    energy_tolerance : float
        Tolerance for energy preservation checks.
    """

    def __init__(
        self,
        hidden_dim: int,
        dropout: float = 0.0,
        norm_eps: float = 1e-5,
        energy_tolerance: float = 1e-4,
    ):
        super().__init__(hidden_dim, dropout, norm_eps)
        self.energy_tolerance = energy_tolerance

    def get_spectral_properties(self) -> dict[str, Any]:
        """Get properties specific to unitary transforms.

        Returns
        -------
        dict[str, Any]
            Dictionary containing unitary transform properties.
        """
        return {
            "unitary": True,
            "energy_preserving": True,
            "invertible": True,
            "orthogonal": True,
            "spectrum_preserving": True,
        }

    def verify_energy_preservation(
        self, input_tensor: torch.Tensor, output_tensor: torch.Tensor
    ) -> bool:
        r"""Verify energy preservation (Parseval's theorem).

        Checks that $||\mathbf{output}||^2 \approx ||\mathbf{input}||^2$ within tolerance.

        Parameters
        ----------
        input_tensor : torch.Tensor
            Input tensor before transformation.
        output_tensor : torch.Tensor
            Output tensor after transformation.

        Returns
        -------
        bool
            True if energy is preserved within tolerance.
        """
        input_energy = torch.norm(input_tensor, p=2, dim=-1) ** 2
        output_energy = torch.norm(output_tensor, p=2, dim=-1) ** 2

        energy_diff = torch.abs(input_energy - output_energy)
        max_energy = torch.max(input_energy, output_energy)

        # Relative error should be within tolerance
        relative_error = energy_diff / (max_energy + self.norm_eps)

        return bool(torch.all(relative_error < self.energy_tolerance))

    def verify_orthogonality(self, transform_matrix: torch.Tensor) -> bool:
        r"""Verify orthogonality of the transform matrix.

        Checks that $\mathbf{T} \mathbf{T}^H \approx \mathbf{I}$ (identity matrix).

        Parameters
        ----------
        transform_matrix : torch.Tensor
            Transform matrix to verify.

        Returns
        -------
        bool
            True if matrix is orthogonal within tolerance.
        """
        # Compute T @ T^H
        product = torch.matmul(transform_matrix, transform_matrix.conj().transpose(-2, -1))

        # Expected identity matrix
        identity = torch.eye(
            transform_matrix.size(-1), device=transform_matrix.device, dtype=transform_matrix.dtype
        )

        # Check deviation from identity
        deviation = torch.norm(product - identity, p="fro")

        return bool(deviation < self.energy_tolerance)


class FilterMixingLayer(MixingLayer):
    """Base class for frequency-domain filtering operations.

    Filter mixing layers apply learnable filters in the frequency domain,
    enabling selective emphasis or suppression of frequency components
    for improved sequence modeling capabilities.

    Parameters
    ----------
    hidden_dim : int
        Hidden dimension of the model.
    sequence_length : int
        Expected sequence length for filter initialization.
    dropout : float, default=0.0
        Dropout probability for regularization.
    norm_eps : float, default=1e-5
        Epsilon for numerical stability.
    learnable_filters : bool, default=True
        Whether filters are learnable parameters.

    Attributes
    ----------
    sequence_length : int
        Expected sequence length.
    learnable_filters : bool
        Whether filters are learnable.
    """

    def __init__(
        self,
        hidden_dim: int,
        sequence_length: int,
        dropout: float = 0.0,
        norm_eps: float = 1e-5,
        learnable_filters: bool = True,
    ):
        super().__init__(hidden_dim, dropout, norm_eps)
        self.sequence_length = sequence_length
        self.learnable_filters = learnable_filters

    def get_spectral_properties(self) -> dict[str, Any]:
        """Get properties specific to filtering operations.

        Returns
        -------
        dict[str, Any]
            Dictionary containing filter-specific properties.
        """
        return {
            "frequency_domain": True,
            "learnable_filters": self.learnable_filters,
            "selective_filtering": True,
            "complex_valued": True,
            "energy_preserving": False,  # Filtering can change energy
        }

    @abstractmethod
    def get_filter_response(self) -> torch.Tensor:
        """Get the frequency response of the current filters.

        Returns
        -------
        torch.Tensor
            Complex-valued frequency response of shape matching the filter parameters.
        """
        pass

    def analyze_frequency_response(self) -> dict[str, torch.Tensor]:
        """Analyze the frequency response characteristics.

        Returns
        -------
        dict[str, torch.Tensor]
            Dictionary containing:
            - 'magnitude': Magnitude response
            - 'phase': Phase response
            - 'group_delay': Group delay response
            - 'passband_energy': Energy in different frequency bands
        """
        response = self.get_filter_response()

        magnitude = torch.abs(response)
        phase = torch.angle(response)

        # Compute group delay (negative derivative of phase)
        # For discrete signals, use finite differences
        phase_diff = torch.diff(phase, dim=-1)
        group_delay = -phase_diff

        # Analyze energy in different frequency bands
        total_energy = torch.sum(magnitude**2, dim=-1, keepdim=True)
        low_freq_energy = torch.sum(
            magnitude[..., : magnitude.size(-1) // 4] ** 2, dim=-1, keepdim=True
        )
        high_freq_energy = torch.sum(
            magnitude[..., 3 * magnitude.size(-1) // 4 :] ** 2, dim=-1, keepdim=True
        )

        return {
            "magnitude": magnitude,
            "phase": phase,
            "group_delay": group_delay,
            "total_energy": total_energy,
            "low_freq_energy": low_freq_energy / (total_energy + self.norm_eps),
            "high_freq_energy": high_freq_energy / (total_energy + self.norm_eps),
        }


__all__: list[str] = [
    "FilterMixingLayer",
    "MixingLayer",
    "UnitaryMixingLayer",
]
