torch.symeig¶
-
torch.
symeig
(input, eigenvectors=False, upper=True, *, out=None)¶ This function returns eigenvalues and eigenvectors of a real symmetric or complex Hermitian matrix
input
or a batch thereof, represented by a namedtuple (eigenvalues, eigenvectors).This function calculates all eigenvalues (and vectors) of
input
such that .The boolean argument
eigenvectors
defines computation of both eigenvectors and eigenvalues or eigenvalues only.If it is
False
, only eigenvalues are computed. If it isTrue
, both eigenvalues and eigenvectors are computed.Since the input matrix
input
is supposed to be symmetric or Hermitian, only the upper triangular portion is used by default.If
upper
isFalse
, then lower triangular portion is used.Warning
torch.symeig()
is deprecated in favor oftorch.linalg.eigh()
and will be removed in a future PyTorch release. The default behavior has changed from using the upper triangular portion of the matrix by default to using the lower triangular portion.L, _ = torch.symeig(A, upper=upper)
should be replaced withUPLO = "U" if upper else "L" L = torch.linalg.eigvalsh(A, UPLO=UPLO)
L, V = torch.symeig(A, eigenvectors=True, upper=upper)
should be replaced withUPLO = "U" if upper else "L" L, V = torch.linalg.eigh(A, UPLO=UPLO)
Note
The eigenvalues are returned in ascending order. If
input
is a batch of matrices, then the eigenvalues of each matrix in the batch is returned in ascending order.Note
Irrespective of the original strides, the returned matrix V will be transposed, i.e. with strides V.contiguous().transpose(-1, -2).stride().
Warning
Extra care needs to be taken when backward through outputs. Such operation is only stable when all eigenvalues are distinct and becomes less stable the smaller is.
- Parameters
input (Tensor) – the input tensor of size where * is zero or more batch dimensions consisting of symmetric or Hermitian matrices.
eigenvectors (bool, optional) – controls whether eigenvectors have to be computed
upper (boolean, optional) – controls whether to consider upper-triangular or lower-triangular region
- Keyword Arguments
out (tuple, optional) – the output tuple of (Tensor, Tensor)
- Returns
A namedtuple (eigenvalues, eigenvectors) containing
eigenvalues (Tensor): Shape . The eigenvalues in ascending order.
eigenvectors (Tensor): Shape . If
eigenvectors=False
, it’s an empty tensor. Otherwise, this tensor contains the orthonormal eigenvectors of theinput
.
- Return type
Examples:
>>> a = torch.randn(5, 5) >>> a = a + a.t() # To make a symmetric >>> a tensor([[-5.7827, 4.4559, -0.2344, -1.7123, -1.8330], [ 4.4559, 1.4250, -2.8636, -3.2100, -0.1798], [-0.2344, -2.8636, 1.7112, -5.5785, 7.1988], [-1.7123, -3.2100, -5.5785, -2.6227, 3.1036], [-1.8330, -0.1798, 7.1988, 3.1036, -5.1453]]) >>> e, v = torch.symeig(a, eigenvectors=True) >>> e tensor([-13.7012, -7.7497, -2.3163, 5.2477, 8.1050]) >>> v tensor([[ 0.1643, 0.9034, -0.0291, 0.3508, 0.1817], [-0.2417, -0.3071, -0.5081, 0.6534, 0.4026], [-0.5176, 0.1223, -0.0220, 0.3295, -0.7798], [-0.4850, 0.2695, -0.5773, -0.5840, 0.1337], [ 0.6415, -0.0447, -0.6381, -0.0193, -0.4230]]) >>> a_big = torch.randn(5, 2, 2) >>> a_big = a_big + a_big.transpose(-2, -1) # To make a_big symmetric >>> e, v = a_big.symeig(eigenvectors=True) >>> torch.allclose(torch.matmul(v, torch.matmul(e.diag_embed(), v.transpose(-2, -1))), a_big) True