Function svd

dask/array/linalg.py:874–962

Compute the singular value decomposition of a matrix. Parameters ---------- a : (M, N) Array coerce_signs : bool Whether or not to apply sign coercion to singular vectors in order to maintain deterministic results, by default True. Examples --------

(a, coerce_signs=True)

def svd(a, coerce_signs=True):
    """
    Compute the singular value decomposition of a matrix.

    Parameters
    ----------
    a : (M, N) Array
    coerce_signs : bool
        Whether or not to apply sign coercion to singular vectors in
        order to maintain deterministic results, by default True.

    Examples
    --------

    >>> u, s, v = da.linalg.svd(x)  # doctest: +SKIP

    Returns
    -------

    u : (M, K) Array, unitary / orthogonal
        Left-singular vectors of `a` (in columns) with shape (M, K)
        where K = min(M, N).
    s : (K,) Array, singular values in decreasing order (largest first)
        Singular values of `a`.
    v : (K, N) Array, unitary / orthogonal
        Right-singular vectors of `a` (in rows) with shape (K, N)
        where K = min(M, N).

    Warnings
    --------

    SVD is only supported for arrays with chunking in one dimension.
    This requires that all inputs either contain a single column
    of chunks (tall-and-skinny) or a single row of chunks (short-and-fat).
    For arrays with chunking in both dimensions, see da.linalg.svd_compressed.

    See Also
    --------

    np.linalg.svd : Equivalent NumPy Operation
    da.linalg.svd_compressed : Randomized SVD for fully chunked arrays
    dask.array.linalg.tsqr : QR factorization for tall-and-skinny arrays
    dask.array.utils.svd_flip : Sign normalization for singular vectors
    """
    nb = a.numblocks
    if a.ndim != 2:
        raise ValueError(
            f"Array must be 2D.\nInput shape: {a.shape}\nInput ndim: {a.ndim}\n"
        )
    if nb[0] > 1 and nb[1] > 1:
        raise NotImplementedError(
            "Array must be chunked in one dimension only. "
            "This function (svd) only supports tall-and-skinny or short-and-fat "
            "matrices (see da.linalg.svd_compressed for SVD on fully chunked arrays).\n"
            f"Input shape: {a.shape}\n"
            f"Input numblocks: {nb}\n"
        )