Function _is_matrix_spd

linear_algebra/src/conjugate_gradient.py:12–45

Returns True if input matrix is symmetric positive definite. Returns False otherwise. For a matrix to be SPD, all eigenvalues must be positive. >>> import numpy as np >>> matrix = np.array([ ... [4.12401784, -5.01453636, -0.63865857], ... [-5.01453636, 12.33347422, -3.

(matrix: np.ndarray)

def _is_matrix_spd(matrix: np.ndarray) -> bool:
    """
    Returns True if input matrix is symmetric positive definite.
    Returns False otherwise.

    For a matrix to be SPD, all eigenvalues must be positive.

    >>> import numpy as np
    >>> matrix = np.array([
    ... [4.12401784, -5.01453636, -0.63865857],
    ... [-5.01453636, 12.33347422, -3.40493586],
    ... [-0.63865857, -3.40493586,  5.78591885]])
    >>> _is_matrix_spd(matrix)
    True
    >>> matrix = np.array([
    ... [0.34634879,  1.96165514,  2.18277744],
    ... [0.74074469, -1.19648894, -1.34223498],
    ... [-0.7687067 ,  0.06018373, -1.16315631]])
    >>> _is_matrix_spd(matrix)
    False
    """
    # Ensure matrix is square.
    assert np.shape(matrix)[0] == np.shape(matrix)[1]

    # If matrix not symmetric, exit right away.
    if np.allclose(matrix, matrix.T) is False:
        return False

    # Get eigenvalues and eignevectors for a symmetric matrix.
    eigen_values, _ = np.linalg.eigh(matrix)

    # Check sign of all eigenvalues.
    # np.all returns a value of type np.bool_
    return bool(np.all(eigen_values > 0))


def _create_spd_matrix(dimension: int) -> Any: