Function sfqr

dask/array/linalg.py:514–619

Direct Short-and-Fat QR Currently, this is a quick hack for non-tall-and-skinny matrices which are one chunk tall and (unless they are one chunk wide) have chunks that are wider than they are tall Q [R_1 R_2 ...] = [A_1 A_2 ...] it computes the factorization Q R_1 = A_1, then

(data, name=None)

def sfqr(data, name=None):
    """Direct Short-and-Fat QR

    Currently, this is a quick hack for non-tall-and-skinny matrices which
    are one chunk tall and (unless they are one chunk wide) have chunks
    that are wider than they are tall

    Q [R_1 R_2 ...] = [A_1 A_2 ...]

    it computes the factorization Q R_1 = A_1, then computes the other
    R_k's in parallel.

    Parameters
    ----------
    data: Array

    See Also
    --------
    dask.array.linalg.qr
        Main user API that uses this function
    dask.array.linalg.tsqr
        Variant for tall-and-skinny case
    """
    nr, nc = len(data.chunks[0]), len(data.chunks[1])
    cr, cc = data.chunks[0][0], data.chunks[1][0]

    if not (
        (data.ndim == 2)
        and (nr == 1)  # Is a matrix
        and (  # Has exactly one block row
            (cr <= cc)
            or (nc == 1)  # Chunking dimension on rows is at least that on cols or...
        )
    ):  # ... only one block col
        raise ValueError(
            "Input must have the following properties:\n"
            "  1. Have two dimensions\n"
            "  2. Have only one row of blocks\n"
            "  3. Either one column of blocks or (first) chunk size on cols\n"
            "     is at most that on rows (e.g.: for a 5x20 matrix,\n"
            "     chunks=((5), (8,4,8)) is fine, but chunks=((5), (4,8,8)) is not;\n"
            "     still, prefer something simple like chunks=(5,10) or chunks=5)\n\n"
            "Note: This function (sfqr) supports QR decomposition in the case\n"
            "of short-and-fat matrices (single row chunk/block; see qr)"
        )

    prefix = name or "sfqr-" + tokenize(data)
    prefix += "_"

    m, n = data.shape

    qq, rr = np.linalg.qr(np.ones(shape=(1, 1), dtype=data.dtype))

    layers = data.__dask_graph__().layers.copy()
    dependencies = data.__dask_graph__().dependencies.copy()

    # data = A = [A_1 A_rest]
    name_A_1 = f"{prefix}A_1"