from typing import Tuple

import jax.numpy as jnp
from jax import random


def fastica(
    X: jnp.ndarray, n_components: jnp.ndarray, max_iter: int = 1000, tol: float = 1e-4
) -> Tuple[jnp.ndarray, jnp.ndarray, jnp.ndarray]:
    """
        Perform Independent Component Analysis (ICA) on the input data using the FastICA algorithm.

        Parameters:
        X : jax.numpy.ndarray
            The input data matrix, where each row represents a data point, and each column represents a different signal.
            The input data should be a 2D jax.numpy array with shape (n_samples, n_features).
        n_components : int
            The number of independent components to extract. This should be less than or equal to the number of features in the input data.
        max_iter : int, optional
            The maximum number of iterations for the optimization process. The default value is 1000 iterations.
        tol : float, optional
            The tolerance for convergence. The optimization process stops when the maximum absolute change in the diagonal elements of the
            unmixing matrix from one iteration to the next is less than this tolerance. The default value is 1e-4.

        Returns:
        S : jax.numpy.ndarray
            The separated independent components. This is a 2D jax.numpy array with shape (n_components, n_samples), where each row represents
            a different independent component, and each column represents a data point.
        W : jax.numpy.ndarray
            The unmixing matrix. This is a 2D jax.numpy array with shape (n_components, n_features), representing the estimated inverse of the
            mixing matrix. It is used to transform the input data back into the independent components.
        whitening_matrix : jax.numpy.ndarray
            The whitening matrix used to whiten the input data. This is a 2D jax.numpy array with shape (n_features, n_features), used to decorrelate
            the input data and make its covariance matrix the identity matrix.

        Description:
        The FastICA algorithm aims to separate the mixed input signals into statistically independent components. The function first whitens the input
        data to decorrelate it and normalize its variance. Then, it initializes a random unmixing matrix and uses an optimization process to find
        the optimal unmixing matrix that maximizes the independence of the source signals.

        The optimization process involves iteratively updating the unmixing matrix based on the non-linear function (`tanh` in this case) applied
        to the transformed data (`WX`). The process stops when the unmixing matrix converges according to the specified tolerance (`tol`) or when the
        maximum number of iterations (`max_iter`) is reached.

        Once the optimal unmixing matrix is found, the function applies it to the whitened data to obtain the separated independent components.

        Example usage:
            # Set random seed
            jax.random.PRNGKey(42)

            # Generate synthetic source signals
            n_samples = 2000
            time = jnp.linspace(0, 8, n_samples)
            s1 = jnp.sin(2 * time)
            s2 = jnp.sign(jnp.sin(3 * time))

            # Combine the sources with a mixing matrix
            A = jnp.array([[1, 1], [0.5, 2]])
            X = jnp.dot(A, jnp.array([s1, s2]))

            # Perform ICA
            n_components = 2
            S, W, whitening_matrix = fastica(X.T, n_components)

            # Plot the results
            plt.figure(figsize=(12, 8))

            plt.subplot(3, 1, 1)
            plt.title('Original Source Signals')
            plt.plot(time, s1, label='Source 1 (Sine Wave)')
            plt.plot(time, s2, label='Source 2 (Square Wave)')
            plt.legend()

            plt.subplot(3, 1, 2)
            plt.title('Mixed Signals')
            plt.plot(time, X[0], label='Mixed Signal 1')
            plt.plot(time, X[1], label='Mixed Signal 2')
            plt.legend()

            plt.subplot(3, 1, 3)
            plt.title('Separated Signals (Using ICA)')
            plt.plot(time, S[0], label='Separated Signal 1')
            plt.plot(time, S[1], label='Separated Signal 2')
            plt.legend()
    s
            plt.tight_layout()
            plt.show()
    """
    # Calculate the covariance matrix and perform eigenvalue decomposition
    cov_matrix = jnp.cov(X, rowvar=False)
    eigenvalues, eigenvectors = jnp.linalg.eigh(cov_matrix)

    # Sort the eigenvalues and eigenvectors
    idx = jnp.argsort(eigenvalues)[::-1]
    eigenvalues = eigenvalues[idx]
    eigenvectors = eigenvectors[:, idx]

    # Create the whitening matrix
    D = jnp.diag(1.0 / jnp.sqrt(eigenvalues))
    whitening_matrix = jnp.dot(eigenvectors, D)
    X_whitened = jnp.dot(X, whitening_matrix)

    # Initialize unmixing matrix with random values
    rng = random.PRNGKey(0)  # Set a seed for reproducibility
    W = random.normal(rng, (n_components, n_components))

    # Perform FastICA algorithm
    for _ in range(max_iter):
        WX = jnp.dot(X_whitened, W.T)
        g = jnp.tanh(WX)
        g_prime = 1 - g**2
        W_new = (jnp.dot(X_whitened.T, g) / X.shape[0]) - jnp.diag(
            g_prime.mean(axis=0)
        ).dot(W)

        # Orthogonalize the unmixing matrix
        W_new, _ = jnp.linalg.qr(W_new)

        # Check for convergence
        if jnp.max(jnp.abs(jnp.abs(jnp.diag(jnp.dot(W_new, W.T))) - 1)) < tol:
            W = W_new
            break

        W = W_new

    # Calculate the separated independent components
    S = jnp.dot(W, X_whitened.T)

    return S, W, whitening_matrix
