qfeval_functions.functions.eigh

eigh(tensor, uplo='L')[source]

Compute eigenvalues and eigenvectors of a symmetric/Hermitian matrix.

This function computes the eigenvalues and eigenvectors of a real symmetric or complex Hermitian matrix. The eigenvalues are returned in ascending order, and the corresponding eigenvectors are normalized. This implementation uses NumPy for CPU tensors and CuPy for CUDA tensors.

Note

This function does not support automatic differentiation (autograd).

Parameters:

  • tensor (Tensor) – A symmetric (if real) or Hermitian (if complex) matrix of shape (..., N, N). Only the upper or lower triangular part is used, depending on the uplo parameter.

  • uplo (str) –

    Indicates which triangular part of the matrix is used:

    • ’L’ or ‘l’: Use the lower triangular part (default)

    • ’U’ or ‘u’: Use the upper triangular part

Returns:

A tuple containing:

  • Eigenvalues: A tensor of shape (..., N) containing eigenvalues in ascending order

  • Eigenvectors: A tensor of shape (..., N, N) where the columns are the normalized eigenvectors corresponding to the eigenvalues

Return type:

Tuple[Tensor, Tensor]

Example

>>> # Create a symmetric matrix
>>> A = torch.tensor([[4.0, -2.0],
...                   [-2.0, 3.0]])
>>> eigenvalues, eigenvectors = QF.eigh(A)
>>> eigenvalues
tensor([1.4384, 5.5616])

>>> # Verify: A @ v = λ @ v
>>> torch.allclose(A @ eigenvectors, eigenvectors @ torch.diag(eigenvalues))
True

>>> # Using upper triangular part
>>> B = torch.tensor([[1.0, 2.0, 3.0],
...                   [0.0, 4.0, 5.0],
...                   [0.0, 0.0, 6.0]])
>>> eigenvalues, eigenvectors = QF.eigh(B, uplo='U')