jax.numpy.linalg.svd#
- jax.numpy.linalg.svd(a, full_matrices=True, compute_uv=True, hermitian=False)[source]#
Singular Value Decomposition.
LAX-backend implementation of
numpy.linalg.svd()
.Original docstring below.
When a is a 2D array, and
full_matrices=False
, then it is factorized asu @ np.diag(s) @ vh = (u * s) @ vh
, where u and the Hermitian transpose of vh are 2D arrays with orthonormal columns and s is a 1D array of a’s singular values. When a is higher-dimensional, SVD is applied in stacked mode as explained below.- Parameters
a ((..., M, N) array_like) – A real or complex array with
a.ndim >= 2
.full_matrices (bool, optional) – If True (default), u and vh have the shapes
(..., M, M)
and(..., N, N)
, respectively. Otherwise, the shapes are(..., M, K)
and(..., K, N)
, respectively, whereK = min(M, N)
.compute_uv (bool, optional) – Whether or not to compute u and vh in addition to s. True by default.
hermitian (bool, optional) – If True, a is assumed to be Hermitian (symmetric if real-valued), enabling a more efficient method for finding singular values. Defaults to False.
- Return type
- Returns
When compute_uv is True, the result is a namedtuple with the following
attribute names
U ({ (…, M, M), (…, M, K) } array) – Unitary array(s). The first
a.ndim - 2
dimensions have the same size as those of the input a. The size of the last two dimensions depends on the value of full_matrices. Only returned when compute_uv is True.S ((…, K) array) – Vector(s) with the singular values, within each vector sorted in descending order. The first
a.ndim - 2
dimensions have the same size as those of the input a.Vh ({ (…, N, N), (…, K, N) } array) – Unitary array(s). The first
a.ndim - 2
dimensions have the same size as those of the input a. The size of the last two dimensions depends on the value of full_matrices. Only returned when compute_uv is True.