jax.numpy.linalg.eigh

jax.numpy.linalg.eigh(a, UPLO=None, symmetrize_input=True)

Compute the eigenvalues and eigenvectors of a Hermitian matrix.

JAX implementation of numpy.linalg.eigh().

Parameters:

• a (ArrayLike) – array of shape (..., M, M), containing the Hermitian (if complex) or symmetric (if real) matrix.

• UPLO (str | None) – specifies whether the calculation is done with the lower triangular part of a ('L', default) or the upper triangular part ('U').

• symmetrize_input (bool) – if True (default) then input is symmetrized, which leads to better behavior under automatic differentiation.

Returns:

A namedtuple (eigenvalues, eigenvectors) where

• eigenvalues: an array of shape (..., M) containing the eigenvalues, sorted in ascending order.

• eigenvectors: an array of shape (..., M, M), where column v[:, i] is the normalized eigenvector corresponding to the eigenvalue w[i].

Return type:

EighResult

See also

• jax.numpy.linalg.eig(): general eigenvalue decomposition.

• jax.numpy.linalg.eigvalsh(): compute eigenvalues only.

• jax.scipy.linalg.eigh(): SciPy API for Hermitian eigendecomposition.

• jax.lax.linalg.eigh(): XLA API for Hermitian eigendecomposition.

Examples

>>> a = jnp.array([[1, -2j],
...                [2j, 1]])
>>> w, v = jnp.linalg.eigh(a)
>>> w
Array([-1.,  3.], dtype=float32)
>>> with jnp.printoptions(precision=3):
...   v
Array([[-0.707+0.j   , -0.707+0.j   ],
       [ 0.   +0.707j,  0.   -0.707j]], dtype=complex64)