ENH: expose correction and weights parameters in cov

Resolves #688. Adds `axis`, `correction`, `frequency_weights`, and
`weights` to `cov`, giving users control over the degrees-of-freedom
correction and the observation-axis / weighted variants that
`numpy.cov` and `torch.cov` already support.

Naming follows array-api conventions (`axis`, `correction`) rather
than numpy's (`rowvar`, `bias`, `ddof`); the docstring includes a
one-to-one mapping. The delegation moves observations to the last
axis via `xp.moveaxis`, collapsing `rowvar` out of the backend
dispatch — only `ddof` vs `correction` differs between branches.

Dask's native `cov` forces `.compute()` on a lazy scalar when any
weights are given, so weighted dask inputs fall through to the
generic implementation, which is fully lazy.

Author: bruAristimunha

src/array_api_extra/_delegation.py

@@ -81,7 +81,16 @@ def atleast_nd(x: Array, /, *, ndim: int, xp: ModuleType | None = None) -> Array
     return _funcs.atleast_nd(x, ndim=ndim, xp=xp)
 
 
-def cov(m: Array, /, *, xp: ModuleType | None = None) -> Array:
+def cov(
+    m: Array,
+    /,
+    *,
+    axis: int = -1,
+    correction: int | float = 1,
+    frequency_weights: Array | None = None,
+    weights: Array | None = None,
+    xp: ModuleType | None = None,
+) -> Array:
     """
     Estimate a covariance matrix (or a stack of covariance matrices).
 
@@ -92,16 +101,37 @@ def cov(m: Array, /, *, xp: ModuleType | None = None) -> Array:
     :math:`x_i` and :math:`x_j`. The element :math:`C_{ii}` is the variance
     of :math:`x_i`.
 
-    With the exception of supporting batch input, this provides a subset of
-    the functionality of ``numpy.cov``.
+    Extends ``numpy.cov`` with support for batch input and array-api
+    backends. Naming follows the array-api conventions used elsewhere in
+    this library (``axis``, ``correction``) rather than the numpy spellings
+    (``rowvar``, ``bias``, ``ddof``); see Notes for the mapping.
 
     Parameters
     ----------
     m : array
         An array of shape ``(..., N, M)`` whose innermost two dimensions
-        contain *M* observations of *N* variables. That is,
-        each row of `m` represents a variable, and each column a single
-        observation of all those variables.
+        contain *M* observations of *N* variables by default. The axis of
+        observations is controlled by `axis`.
+    axis : int, optional
+        Axis of `m` containing the observations. Default: ``-1`` (the last
+        axis), matching the array-api convention. Use ``axis=-2`` (or ``0``
+        for 2-D input) to treat each column as a variable, which
+        corresponds to ``rowvar=False`` in ``numpy.cov``.
+    correction : int or float, optional
+        Degrees of freedom correction: normalization divides by
+        ``N - correction`` (for unweighted input). Default: ``1``, which
+        gives the unbiased estimate (matches ``numpy.cov`` default of
+        ``bias=False``). Set to ``0`` for the biased estimate (``N``
+        normalization). Corresponds to ``ddof`` in ``numpy.cov`` and to
+        ``correction`` in ``numpy.var``/``std`` and ``torch.cov``.
+    frequency_weights : array, optional
+        1-D array of integer frequency weights: the number of times each
+        observation is repeated. Corresponds to ``fweights`` in
+        ``numpy.cov``/``torch.cov``.
+    weights : array, optional
+        1-D array of observation-vector weights (analytic weights). Larger
+        values mark more important observations. Corresponds to
+        ``aweights`` in ``numpy.cov``/``torch.cov``.
     xp : array_namespace, optional
         The standard-compatible namespace for `m`. Default: infer.
 
@@ -111,6 +141,23 @@ def cov(m: Array, /, *, xp: ModuleType | None = None) -> Array:
         An array having shape (..., N, N) whose innermost two dimensions represent
         the covariance matrix of the variables.
 
+    Notes
+    -----
+    Mapping from ``numpy.cov`` to this function::
+
+        numpy.cov(m, rowvar=True)           -> cov(m, axis=-1)   # default
+        numpy.cov(m, rowvar=False)          -> cov(m, axis=-2)
+        numpy.cov(m, bias=True)             -> cov(m, correction=0)
+        numpy.cov(m, ddof=k)                -> cov(m, correction=k)
+        numpy.cov(m, fweights=f)            -> cov(m, frequency_weights=f)
+        numpy.cov(m, aweights=a)            -> cov(m, weights=a)
+
+    Unlike ``numpy.cov``, a ``RuntimeWarning`` for non-positive effective
+    degrees of freedom is only emitted on the unweighted path. The
+    weighted path omits the check so that lazy backends (e.g. Dask) can
+    stay lazy end-to-end; choose ``correction`` and weights such that the
+    effective normalizer is positive.
+
     Examples
     --------
     >>> import array_api_strict as xp
@@ -164,16 +211,57 @@ def cov(m: Array, /, *, xp: ModuleType | None = None) -> Array:
     if xp is None:
         xp = array_namespace(m)
 
-    if (
-        is_numpy_namespace(xp)
-        or is_cupy_namespace(xp)
-        or is_torch_namespace(xp)
-        or is_dask_namespace(xp)
-        or is_jax_namespace(xp)
-    ) and m.ndim <= 2:
-        return xp.cov(m)
-
-    return _funcs.cov(m, xp=xp)
+    # Validate axis against m.ndim.
+    ndim = max(m.ndim, 1)
+    if not -ndim <= axis < ndim:
+        msg = f"axis {axis} is out of bounds for array of dimension {m.ndim}"
+        raise IndexError(msg)
+
+    # Normalize: observations on the last axis. After this, every backend
+    # sees the same convention and we never need to deal with `rowvar`.
+    if m.ndim >= 2 and axis not in (-1, m.ndim - 1):
+        m = xp.moveaxis(m, axis, -1)
+
+    # `numpy.cov` (and cupy/dask/jax) require integer `ddof`; `torch.cov`
+    # requires integer `correction`. For non-integer-valued `correction`,
+    # fall through to the generic implementation.
+    integer_correction = isinstance(correction, int) or correction.is_integer()
+    has_weights = frequency_weights is not None or weights is not None
+
+    if m.ndim <= 2 and integer_correction:
+        if is_torch_namespace(xp):
+            device = get_device(m)
+            fw = (
+                None
+                if frequency_weights is None
+                else xp.asarray(frequency_weights, device=device)
+            )
+            aw = None if weights is None else xp.asarray(weights, device=device)
+            return xp.cov(m, correction=int(correction), fweights=fw, aweights=aw)
+        # `dask.array.cov` forces `.compute()` whenever weights are given:
+        # its internal `if fact <= 0` check on a lazy 0-D scalar triggers
+        # materialization. Route to the generic impl, which is fully lazy
+        # because it only does sum/matmul and skips that scalar check.
+        if (
+            is_numpy_namespace(xp)
+            or is_cupy_namespace(xp)
+            or is_jax_namespace(xp)
+            or (is_dask_namespace(xp) and not has_weights)
+        ):
+            return xp.cov(
+                m,
+                ddof=int(correction),
+                fweights=frequency_weights,
+                aweights=weights,
+            )
+
+    return _funcs.cov(
+        m,
+        correction=correction,
+        frequency_weights=frequency_weights,
+        weights=weights,
+        xp=xp,
+    )
 
 
 def create_diagonal(

src/array_api_extra/_lib/_funcs.py

@@ -281,31 +281,67 @@ def broadcast_shapes(*shapes: tuple[float | None, ...]) -> tuple[int | None, ...
     return tuple(out)
 
 
-def cov(m: Array, /, *, xp: ModuleType) -> Array:  # numpydoc ignore=PR01,RT01
+def cov(
+    m: Array,
+    /,
+    *,
+    correction: int | float = 1,
+    frequency_weights: Array | None = None,
+    weights: Array | None = None,
+    xp: ModuleType,
+) -> Array:  # numpydoc ignore=PR01,RT01
     """See docstring in array_api_extra._delegation."""
-    m = xp.asarray(m, copy=True)
+    m = xp.asarray(m)
     dtype = (
         xp.float64 if xp.isdtype(m.dtype, "integral") else xp.result_type(m, xp.float64)
     )
 
     m = atleast_nd(m, ndim=2, xp=xp)
     m = xp.astype(m, dtype)
 
-    avg = xp.mean(m, axis=-1, keepdims=True)
+    device = _compat.device(m)
+    fw = (
+        None
+        if frequency_weights is None
+        else xp.astype(xp.asarray(frequency_weights, device=device), dtype)
+    )
+    aw = (
+        None
+        if weights is None
+        else xp.astype(xp.asarray(weights, device=device), dtype)
+    )
+    if fw is None and aw is None:
+        w = None
+    elif fw is None:
+        w = aw
+    elif aw is None:
+        w = fw
+    else:
+        w = fw * aw
 
     m_shape = eager_shape(m)
-    fact = m_shape[-1] - 1
-
-    if fact <= 0:
-        warnings.warn("Degrees of freedom <= 0 for slice", RuntimeWarning, stacklevel=2)
-        fact = 0
-
-    m -= avg
-    m_transpose = xp.matrix_transpose(m)
-    if xp.isdtype(m_transpose.dtype, "complex floating"):
-        m_transpose = xp.conj(m_transpose)
-    c = xp.matmul(m, m_transpose)
-    c /= fact
+    if w is None:
+        avg = xp.mean(m, axis=-1, keepdims=True)
+        fact = m_shape[-1] - correction
+        if fact <= 0:
+            warnings.warn(
+                "Degrees of freedom <= 0 for slice", RuntimeWarning, stacklevel=2
+            )
+            fact = 0
+    else:
+        v1 = xp.sum(w, axis=-1)
+        avg = xp.sum(m * w, axis=-1, keepdims=True) / v1
+        if aw is None:
+            fact = v1 - correction
+        else:
+            fact = v1 - correction * xp.sum(w * aw, axis=-1) / v1
+
+    m_c = m - avg
+    m_w = m_c if w is None else m_c * w
+    m_cT = xp.matrix_transpose(m_c)
+    if xp.isdtype(m_cT.dtype, "complex floating"):
+        m_cT = xp.conj(m_cT)
+    c = xp.matmul(m_w, m_cT) / fact
     axes = tuple(axis for axis, length in enumerate(c.shape) if length == 1)
     return xp.squeeze(c, axis=axes)
 

tests/test_funcs.py

@@ -608,6 +608,97 @@ def test_batch(self, xp: ModuleType):
         ref = np.reshape(np.stack(ref_list), (*batch_shape, n_var, n_var))
         xp_assert_close(res, xp.asarray(ref))
 
+    def test_correction(self, xp: ModuleType):
+        rng = np.random.default_rng(20260417)
+        m = rng.random((3, 20))
+        for correction in (0, 1, 2):
+            ref = np.cov(m, ddof=correction)
+            res = cov(xp.asarray(m), correction=correction)
+            xp_assert_close(res, xp.asarray(ref))
+
+    def test_correction_float(self, xp: ModuleType):
+        # Float correction: reference computed by hand (numpy.cov rejects
+        # non-integer ddof; our generic path supports it).
+        rng = np.random.default_rng(20260417)
+        m = rng.random((3, 20))
+        n = m.shape[-1]
+        centered = m - m.mean(axis=-1, keepdims=True)
+        ref = centered @ centered.T / (n - 1.5)
+        res = cov(xp.asarray(m), correction=1.5)
+        xp_assert_close(res, xp.asarray(ref))
+
+    def test_axis(self, xp: ModuleType):
+        rng = np.random.default_rng(20260417)
+        m = rng.random((20, 3))  # observations on axis 0
+        ref = np.cov(m, rowvar=False)
+        res = cov(xp.asarray(m), axis=0)
+        xp_assert_close(res, xp.asarray(ref))
+        res_neg = cov(xp.asarray(m), axis=-2)
+        xp_assert_close(res_neg, xp.asarray(ref))
+
+    def test_frequency_weights(self, xp: ModuleType):
+        rng = np.random.default_rng(20260417)
+        m = rng.random((3, 10))
+        fw = np.asarray([1, 2, 1, 3, 1, 2, 1, 1, 2, 1], dtype=np.int64)
+        ref = np.cov(m, fweights=fw)
+        res = cov(xp.asarray(m), frequency_weights=xp.asarray(fw))
+        xp_assert_close(res, xp.asarray(ref))
+
+    def test_weights(self, xp: ModuleType):
+        rng = np.random.default_rng(20260417)
+        m = rng.random((3, 10))
+        aw = rng.random(10)
+        ref = np.cov(m, aweights=aw)
+        res = cov(xp.asarray(m), weights=xp.asarray(aw))
+        xp_assert_close(res, xp.asarray(ref))
+
+    def test_both_weights(self, xp: ModuleType):
+        rng = np.random.default_rng(20260417)
+        m = rng.random((3, 10))
+        fw = np.asarray([1, 2, 1, 3, 1, 2, 1, 1, 2, 1], dtype=np.int64)
+        aw = rng.random(10)
+        for correction in (0, 1, 2):
+            ref = np.cov(m, ddof=correction, fweights=fw, aweights=aw)
+            res = cov(
+                xp.asarray(m),
+                correction=correction,
+                frequency_weights=xp.asarray(fw),
+                weights=xp.asarray(aw),
+            )
+            xp_assert_close(res, xp.asarray(ref))
+
+    def test_batch_with_weights(self, xp: ModuleType):
+        rng = np.random.default_rng(20260417)
+        batch_shape = (2, 3)
+        n_var, n_obs = 3, 15
+        m = rng.random((*batch_shape, n_var, n_obs))
+        aw = rng.random(n_obs)
+        res = cov(xp.asarray(m), weights=xp.asarray(aw))
+        ref_list = [np.cov(m_, aweights=aw) for m_ in np.reshape(m, (-1, n_var, n_obs))]
+        ref = np.reshape(np.stack(ref_list), (*batch_shape, n_var, n_var))
+        xp_assert_close(res, xp.asarray(ref))
+
+    def test_axis_with_weights(self, xp: ModuleType):
+        # axis=-2 (observations on first of 2D) combined with weights:
+        # verifies that moveaxis and weight alignment cooperate.
+        rng = np.random.default_rng(20260417)
+        m = rng.random((15, 3))  # observations on axis 0
+        aw = rng.random(15)
+        fw = np.asarray([1, 2, 1, 3, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1], dtype=np.int64)
+        ref = np.cov(m, rowvar=False, fweights=fw, aweights=aw)
+        res = cov(
+            xp.asarray(m),
+            axis=-2,
+            frequency_weights=xp.asarray(fw),
+            weights=xp.asarray(aw),
+        )
+        xp_assert_close(res, xp.asarray(ref))
+
+    def test_axis_out_of_bounds(self, xp: ModuleType):
+        m = xp.asarray([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])
+        with pytest.raises(IndexError):
+            _ = cov(m, axis=5)
+
 
 @pytest.mark.xfail_xp_backend(Backend.SPARSE, reason="no arange", strict=False)
 class TestOneHot: