torch.linalg.eigvalsh — PyTorch 2.7 documentation (original) (raw)
torch.linalg.eigvalsh(A, UPLO='L', *, out=None) → Tensor¶
Computes the eigenvalues of a complex Hermitian or real symmetric matrix.
Letting K\mathbb{K} be R\mathbb{R} or C\mathbb{C}, the eigenvalues of a complex Hermitian or real symmetric matrix A∈Kn×nA \in \mathbb{K}^{n \times n}are defined as the roots (counted with multiplicity) of the polynomial p of degree n given by
p(λ)=det(A−λIn)λ∈Rp(\lambda) = \operatorname{det}(A - \lambda \mathrm{I}_n)\mathrlap{\qquad \lambda \in \mathbb{R}}
where In\mathrm{I}_n 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.
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
Ain 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)