linal-labs/matrix_decompostion.py at main · Tew1s/linal-labs · GitHub

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import numpy as np
from scipy.linalg import lu

def lu_decomposition(x: np.ndarray) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
    """
    Perform LU decomposition of a matrix.

    Args:
        x (np.ndarray): The input matrix to decompose.

    Returns:
        tuple[np.ndarray, np.ndarray, np.ndarray]:
            The permutation matrix P, lower triangular matrix L, and upper triangular matrix U.
    """
    return lu(x)


def qr_decomposition(x: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
    """
    Perform QR decomposition of a matrix.

    Args:
        x (np.ndarray): The input matrix to decompose.

    Returns:
        tuple[np.ndarray, np.ndarray]: The orthogonal matrix Q and upper triangular matrix R.
    """
    return np.linalg.qr(x)


def determinant(x: np.ndarray) -> np.ndarray:
    """
    Calculate the determinant of a matrix.

    Args:
        x (np.ndarray): The input matrix.

    Returns:
        np.ndarray: The determinant of the matrix.
    """
    return np.linalg.det(x)


def eigen(x: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
    """
    Compute the eigenvalues and right eigenvectors of a matrix.

    Args:
        x (np.ndarray): The input matrix.

    Returns:
        tuple[np.ndarray, np.ndarray]: The eigenvalues and the right eigenvectors of the matrix.
    """
    return np.linalg.eig(x)


def svd(x: np.ndarray) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
    """
    Perform Singular Value Decomposition (SVD) of a matrix.

    Args:
        x (np.ndarray): The input matrix to decompose.

    Returns:
        tuple[np.ndarray, np.ndarray, np.ndarray]: The matrices U, S, and V.
    """
    return np.linalg.svd(x)