Eig and eigh

scipy.linalg 中，有两个用于求特征值的函数：eigeigh。虽然二者长相几乎一样，但

• eigh 按特征值从小到大的顺序
• eig 按特征值从大到小的顺序

class SubspaceLearningMixin():
""" Mixin Class for Linear Subspace Learning Algorithms.
Features in the implementation of __getitem__ method.    """    components: np.ndarray
def __init__(self):
self.mean_ = 0.0
@abstractmethod
def fit(self, X, y):
pass
def transform(self, X, n_components=None):
if n_components: pc = self[n_components]
else: pc=self.components_
X = X - self.mean_
return X @ pc.T
def __getitem__(self, item):
"""Get principal components."""
if isinstance(item, slice):
return self.components_[item]
else:
return self.components_[:item]
class MyPCA(SubspaceLearningMixin):
def __init__(self):
super().__init__()
def fit(self, X, y=None, method="svd"):
self.mean_ = np.mean(X, axis=0)
X = X - self.mean_
if method == 'svd':
U, S, Vt = scipy.linalg.svd(X, full_matrices=False)
U, Vt = svd_flip(U, Vt)
self.variances_ = S # 从大到小
self.components_ = Vt
elif method == 'eigen':
eigval, eigvec = scipy.linalg.eig((X.T @ X) / (n_samples - 1))
self.components_ = eigvec.real.T
self.variances_ = eigval.real
elif method == 'eigen_hermitian':
eigval, eigvec = scipy.linalg.eigh((X.T @ X) / (n_samples - 1))
self.components_ = eigvec.T[::-1]
self.variances_ = eigval[::-1]