# 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 as `u @ 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, where `K = 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.