xorbits.numpy.linalg.eigvals

xorbits.numpy.linalg.eigvals(a)

Compute the eigenvalues of a general matrix.

Main difference between eigvals and eig: the eigenvectors aren’t returned.

参数

a ((..., M, M) array_like) – A complex- or real-valued matrix whose eigenvalues will be computed.

返回

w – The eigenvalues, each repeated according to its multiplicity. They are not necessarily ordered, nor are they necessarily real for real matrices.

返回类型

(…, M,) ndarray

引发

LinAlgError – If the eigenvalue computation does not converge.

参见

eig

eigenvalues and right eigenvectors of general arrays

eigvalsh

eigenvalues of real symmetric or complex Hermitian (conjugate symmetric) arrays.

eigh

eigenvalues and eigenvectors of real symmetric or complex Hermitian (conjugate symmetric) arrays.

scipy.linalg.eigvals

Similar function in SciPy.

提示

1.8.0(numpy.linalg) 新版功能.

Broadcasting rules apply, see the numpy.linalg documentation for details.

This is implemented using the _geev LAPACK routines which compute the eigenvalues and eigenvectors of general square arrays.

实际案例

Illustration, using the fact that the eigenvalues of a diagonal matrix are its diagonal elements, that multiplying a matrix on the left by an orthogonal matrix, Q, and on the right by Q.T (the transpose of Q), preserves the eigenvalues of the “middle” matrix. In other words, if Q is orthogonal, then Q * A * Q.T has the same eigenvalues as A:

>>> from numpy import linalg as LA  
>>> x = np.random.random()  
>>> Q = np.array([[np.cos(x), -np.sin(x)], [np.sin(x), np.cos(x)]])  
>>> LA.norm(Q[0, :]), LA.norm(Q[1, :]), np.dot(Q[0, :],Q[1, :])  
(1.0, 1.0, 0.0)

Now multiply a diagonal matrix by Q on one side and by Q.T on the other:

>>> D = np.diag((-1,1))  
>>> LA.eigvals(D)  
array([-1.,  1.])
>>> A = np.dot(Q, D)  
>>> A = np.dot(A, Q.T)  
>>> LA.eigvals(A)  
array([ 1., -1.]) # random

警告

This method has not been implemented yet. Xorbits will try to execute it with numpy.linalg.

This docstring was copied from numpy.linalg.