_surface_helpers.py 文件源码

def two_by_two_det(mat):
    r"""Compute the determinant of a 2x2 matrix.

    .. note::

       This is used **only** by :func:`quadratic_jacobian_polynomial` and
       :func:`cubic_jacobian_polynomial`.

    This is "needed" because :func:`numpy.linalg.det` uses a more generic
    determinant implementation which can introduce rounding even when the
    simple :math:`a d - b c` will suffice. For example:

    .. doctest:: 2-by-2

       >>> import numpy as np
       >>> mat = np.asfortranarray([
       ...     [-1.5   , 0.1875],
       ...     [-1.6875, 0.0   ],
       ... ])
       >>> actual_det = -mat[0, 1] * mat[1, 0]
       >>> np_det = np.linalg.det(mat)
       >>> np.abs(actual_det - np_det) == np.spacing(actual_det)
       True

    Args:
        mat (numpy.ndarray): A 2x2 matrix.

    Returns:
        float: The determinant of ``mat``.
    """
    return mat[0, 0] * mat[1, 1] - mat[0, 1] * mat[1, 0]