torch.linalg.eigvalsh¶
- torch.linalg.eigvalsh(A, UPLO='L', *, out=None) Tensor ¶
Computes the eigenvalues of a complex Hermitian or real symmetric matrix.
Letting be or , the eigenvalues of a complex Hermitian or real symmetric matrix are defined as the roots (counted with multiplicity) of the polynomial p of degree n given by
where is the n-dimensional identity matrix. The eigenvalues of a real symmetric or complex Hermitian matrix are always real.
Supports input of float, double, cfloat and cdouble dtypes. Also supports batches of matrices, and if
A
is a batch of matrices then the output has the same batch dimensions.The eigenvalues are returned in ascending order.
A
is assumed to be Hermitian (resp. symmetric), but this is not checked internally, instead:If
UPLO
= ‘L’ (default), only the lower triangular part of the matrix is used in the computation.If
UPLO
= ‘U’, only the upper triangular part of the matrix is used.
Note
When inputs are on a CUDA device, this function synchronizes that device with the CPU.
See also
torch.linalg.eigh()
computes the full eigenvalue decomposition.- Parameters
A (Tensor) – tensor of shape (*, n, n) where * is zero or more batch dimensions consisting of symmetric or Hermitian matrices.
UPLO ('L', 'U', optional) – controls whether to use the upper or lower triangular part of
A
in the computations. Default: ‘L’.
- Keyword Arguments
out (Tensor, optional) – output tensor. Ignored if None. Default: None.
- Returns
A real-valued tensor containing the eigenvalues even when
A
is complex. The eigenvalues are returned in ascending order.
Examples:
>>> A = torch.randn(2, 2, dtype=torch.complex128) >>> A = A + A.T.conj() # creates a Hermitian matrix >>> A tensor([[2.9228+0.0000j, 0.2029-0.0862j], [0.2029+0.0862j, 0.3464+0.0000j]], dtype=torch.complex128) >>> torch.linalg.eigvalsh(A) tensor([0.3277, 2.9415], dtype=torch.float64) >>> A = torch.randn(3, 2, 2, dtype=torch.float64) >>> A = A + A.mT # creates a batch of symmetric matrices >>> torch.linalg.eigvalsh(A) tensor([[ 2.5797, 3.4629], [-4.1605, 1.3780], [-3.1113, 2.7381]], dtype=torch.float64)