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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 degreen
given bywhere 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’
.
- A (Tensor) – tensor of shape
- 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)
- If
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https://pytorch.org/docs/2.1/generated/torch.linalg.eigvalsh.html