mlx.core.linalg.eigh

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mlx.core.linalg.eigh#

eigh(a: array, UPLO: str = 'L', *, stream: None | Stream | Device = None) → Tuple[array, array]#

Compute the eigenvalues and eigenvectors of a complex Hermitian or real symmetric matrix.

This function supports arrays with at least 2 dimensions. When the input has more than two dimensions, the eigenvalues and eigenvectors are computed for each matrix in the last two dimensions.

Parameters:

  • a (array) – Input array. Must be a real symmetric or complex Hermitian matrix.

  • UPLO (str, optional) – Whether to use the upper ("U") or lower ("L") triangle of the matrix. Default: "L".

  • stream (Stream, optional) – Stream or device. Defaults to None in which case the default stream of the default device is used.

Returns:

A tuple containing the eigenvalues in ascending order and the normalized eigenvectors. The column v[:, i] is the eigenvector corresponding to the i-th eigenvalue.

Return type:

Tuple[array, array]

Note

The input matrix is assumed to be symmetric (or Hermitian). Only the selected triangle is used. No checks for symmetry are performed.

Example

>>> A = mx.array([[1., -2.], [-2., 1.]])
>>> w, v = mx.linalg.eigh(A, stream=mx.cpu)
>>> w
array([-1., 3.], dtype=float32)
>>> v
array([[ 0.707107, -0.707107],
      [ 0.707107,  0.707107]], dtype=float32)
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