Complete dpnp.cov implementation (IntelPython#2303)

The PR proposes to rework implementation of `dpnp.cov` and to add
support of all missing keywords, replace TODO with already supported
functionality and to remove any fallback on numpy call.
Also this PR update documentation and adds extra tests to improve the
coverage.

dpnp/dpnp_iface_statistics.py

@@ -54,7 +54,7 @@
     to_supported_dtypes,
 )
 
-from .dpnp_utils import call_origin, get_usm_allocations
+from .dpnp_utils import get_usm_allocations
 from .dpnp_utils.dpnp_utils_reduction import dpnp_wrap_reduction_call
 from .dpnp_utils.dpnp_utils_statistics import dpnp_cov, dpnp_median
 
@@ -748,61 +748,175 @@ def cov(
 
     For full documentation refer to :obj:`numpy.cov`.
 
+    Parameters
+    ----------
+    m : {dpnp.ndarray, usm_ndarray}
+        A 1-D or 2-D array containing multiple variables and observations.
+        Each row of `m` represents a variable, and each column a single
+        observation of all those variables. Also see `rowvar` below.
+    y : {None, dpnp.ndarray, usm_ndarray}, optional
+        An additional set of variables and observations. `y` has the same form
+        as that of `m`.
+
+        Default: ``None``.
+    rowvar : bool, optional
+        If `rowvar` is ``True``, then each row represents a variable, with
+        observations in the columns. Otherwise, the relationship is transposed:
+        each column represents a variable, while the rows contain observations.
+
+        Default: ``True``.
+    bias : bool, optional
+        Default normalization is by ``(N - 1)``, where ``N`` is the number of
+        observations given (unbiased estimate). If `bias` is ``True``, then
+        normalization is by ``N``. These values can be overridden by using the
+        keyword `ddof`.
+
+        Default: ``False``.
+    ddof : {None, int}, optional
+        If not ``None`` the default value implied by `bias` is overridden. Note
+        that ``ddof=1`` will return the unbiased estimate, even if both
+        `fweights` and `aweights` are specified, and ``ddof=0`` will return the
+        simple average. See the notes for the details.
+
+        Default: ``None``.
+    fweights : {None, dpnp.ndarray, usm_ndarray}, optional
+        1-D array of integer frequency weights; the number of times each
+        observation vector should be repeated.
+        It is required that ``fweights >= 0``. However, the function will not
+        raise an error when ``fweights < 0`` for performance reasons.
+
+        Default: ``None``.
+    aweights : {None, dpnp.ndarray, usm_ndarray}, optional
+        1-D array of observation vector weights. These relative weights are
+        typically large for observations considered "important" and smaller for
+        observations considered less "important". If ``ddof=0`` the array of
+        weights can be used to assign probabilities to observation vectors.
+        It is required that ``aweights >= 0``. However, the function will not
+        error when ``aweights < 0`` for performance reasons.
+
+        Default: ``None``.
+    dtype : {None, str, dtype object}, optional
+        Data-type of the result. By default, the return data-type will have
+        at least floating point type based on the capabilities of the device on
+        which the input arrays reside.
+
+        Default: ``None``.
+
     Returns
     -------
     out : dpnp.ndarray
         The covariance matrix of the variables.
 
-    Limitations
-    -----------
-    Input array ``m`` is supported as :obj:`dpnp.ndarray`.
-    Dimension of input array ``m`` is limited by ``m.ndim <= 2``.
-    Size and shape of input arrays are supported to be equal.
-    Parameter `y` is supported only with default value ``None``.
-    Parameter `bias` is supported only with default value ``False``.
-    Parameter `ddof` is supported only with default value ``None``.
-    Parameter `fweights` is supported only with default value ``None``.
-    Parameter `aweights` is supported only with default value ``None``.
-    Otherwise the function will be executed sequentially on CPU.
-    Input array data types are limited by supported DPNP :ref:`Data types`.
-
     See Also
     --------
-    :obj:`dpnp.corrcoef` : Normalized covariance matrix
+    :obj:`dpnp.corrcoef` : Normalized covariance matrix.
+
+    Notes
+    -----
+    Assume that the observations are in the columns of the observation array `m`
+    and let ``f = fweights`` and ``a = aweights`` for brevity. The steps to
+    compute the weighted covariance are as follows::
+
+        >>> import dpnp as np
+        >>> m = np.arange(10, dtype=np.float32)
+        >>> f = np.arange(10) * 2
+        >>> a = np.arange(10) ** 2.0
+        >>> ddof = 1
+        >>> w = f * a
+        >>> v1 = np.sum(w)
+        >>> v2 = np.sum(w * a)
+        >>> m -= np.sum(m * w, axis=None, keepdims=True) / v1
+        >>> cov = np.dot(m * w, m.T) * v1 / (v1**2 - ddof * v2)
+
+    Note that when ``a == 1``, the normalization factor
+    ``v1 / (v1**2 - ddof * v2)`` goes over to ``1 / (np.sum(f) - ddof)``
+    as it should.
 
     Examples
     --------
     >>> import dpnp as np
     >>> x = np.array([[0, 2], [1, 1], [2, 0]]).T
-    >>> x.shape
-    (2, 3)
-    >>> [i for i in x]
-    [0, 1, 2, 2, 1, 0]
-    >>> out = np.cov(x)
-    >>> out.shape
-    (2, 2)
-    >>> [i for i in out]
-    [1.0, -1.0, -1.0, 1.0]
+
+    Consider two variables, :math:`x_0` and  :math:`x_1`, which correlate
+    perfectly, but in opposite directions:
+
+    >>> x
+    array([[0, 1, 2],
+           [2, 1, 0]])
+
+    Note how :math:`x_0` increases while :math:`x_1` decreases. The covariance
+    matrix shows this clearly:
+
+    >>> np.cov(x)
+    array([[ 1., -1.],
+           [-1.,  1.]])
+
+    Note that element :math:`C_{0,1}`, which shows the correlation between
+    :math:`x_0` and :math:`x_1`, is negative.
+
+    Further, note how `x` and `y` are combined:
+
+    >>> x = np.array([-2.1, -1,  4.3])
+    >>> y = np.array([3,  1.1,  0.12])
+    >>> X = np.stack((x, y), axis=0)
+    >>> np.cov(X)
+    array([[11.71      , -4.286     ], # may vary
+           [-4.286     ,  2.14413333]])
+    >>> np.cov(x, y)
+    array([[11.71      , -4.286     ], # may vary
+           [-4.286     ,  2.14413333]])
+    >>> np.cov(x)
+    array(11.71)
 
     """
 
-    if not dpnp.is_supported_array_type(m):
-        pass
-    elif m.ndim > 2:
-        pass
-    elif bias:
-        pass
-    elif ddof is not None:
-        pass
-    elif fweights is not None:
-        pass
-    elif aweights is not None:
-        pass
+    arrays = [m]
+    if y is not None:
+        arrays.append(y)
+    dpnp.check_supported_arrays_type(*arrays)
+
+    if m.ndim > 2:
+        raise ValueError("m has more than 2 dimensions")
+
+    if y is not None:
+        if y.ndim > 2:
+            raise ValueError("y has more than 2 dimensions")
+
+    if ddof is not None:
+        if not isinstance(ddof, int):
+            raise ValueError("ddof must be integer")
     else:
-        return dpnp_cov(m, y=y, rowvar=rowvar, dtype=dtype)
+        ddof = 0 if bias else 1
+
+    def_float = dpnp.default_float_type(m.sycl_queue)
+    if dtype is None:
+        dtype = dpnp.result_type(*arrays, def_float)
+
+    if fweights is not None:
+        dpnp.check_supported_arrays_type(fweights)
+        if not dpnp.issubdtype(fweights.dtype, numpy.integer):
+            raise TypeError("fweights must be integer")
+
+        if fweights.ndim > 1:
+            raise ValueError("cannot handle multidimensional fweights")
+
+        fweights = dpnp.astype(fweights, dtype=def_float)
+
+    if aweights is not None:
+        dpnp.check_supported_arrays_type(aweights)
+        if aweights.ndim > 1:
+            raise ValueError("cannot handle multidimensional aweights")
+
+        aweights = dpnp.astype(aweights, dtype=def_float)
 
-    return call_origin(
-        numpy.cov, m, y, rowvar, bias, ddof, fweights, aweights, dtype=dtype
+    return dpnp_cov(
+        m,
+        y=y,
+        rowvar=rowvar,
+        ddof=ddof,
+        dtype=dtype,
+        fweights=fweights,
+        aweights=aweights,
     )
 
 

dpnp/dpnp_utils/dpnp_utils_statistics.py

@@ -32,7 +32,6 @@
 
 import dpnp
 from dpnp.dpnp_array import dpnp_array
-from dpnp.dpnp_utils import get_usm_allocations, map_dtype_to_device
 
 __all__ = ["dpnp_cov", "dpnp_median"]
 
@@ -119,66 +118,77 @@ def _flatten_array_along_axes(a, axes_to_flatten, overwrite_input):
     return a_flatten, overwrite_input
 
 
-def dpnp_cov(m, y=None, rowvar=True, dtype=None):
+def dpnp_cov(
+    m, y=None, rowvar=True, ddof=1, dtype=None, fweights=None, aweights=None
+):
     """
-    dpnp_cov(m, y=None, rowvar=True, dtype=None)
-
     Estimate a covariance matrix based on passed data.
-    No support for given weights is provided now.
 
-    The implementation is done through existing dpnp and dpctl methods
-    instead of separate function call of dpnp backend.
+    The implementation is done through existing dpnp functions.
 
     """
 
-    def _get_2dmin_array(x, dtype):
-        """
-        Transform an input array to a form required for building a covariance matrix.
-
-        If applicable, it reshapes the input array to have 2 dimensions or greater.
-        If applicable, it transposes the input array when 'rowvar' is False.
-        It casts to another dtype, if the input array differs from requested one.
-
-        """
-        if x.ndim == 0:
-            x = x.reshape((1, 1))
-        elif x.ndim == 1:
-            x = x[dpnp.newaxis, :]
-
-        if not rowvar and x.ndim != 1:
-            x = x.T
-
-        if x.dtype != dtype:
-            x = dpnp.astype(x, dtype)
-        return x
+    # need to create a copy of input, since it will be modified in-place
+    x = dpnp.array(m, ndmin=2, dtype=dtype)
+    if not rowvar and m.ndim != 1:
+        x = x.T
 
-    # input arrays must follow CFD paradigm
-    _, queue = get_usm_allocations((m,) if y is None else (m, y))
+    if x.shape[0] == 0:
+        return dpnp.empty_like(
+            x, shape=(0, 0), dtype=dpnp.default_float_type(m.sycl_queue)
+        )
 
-    # calculate a type of result array if not passed explicitly
-    if dtype is None:
-        dtypes = [m.dtype, dpnp.default_float_type(sycl_queue=queue)]
-        if y is not None:
-            dtypes.append(y.dtype)
-        dtype = dpnp.result_type(*dtypes)
-        # TODO: remove when dpctl.result_type() is returned dtype based on fp64
-        dtype = map_dtype_to_device(dtype, queue.sycl_device)
-
-    X = _get_2dmin_array(m, dtype)
     if y is not None:
-        y = _get_2dmin_array(y, dtype)
-
-        X = dpnp.concatenate((X, y), axis=0)
-
-    avg = X.mean(axis=1)
+        y_ndim = y.ndim
+        y = dpnp.array(y, copy=None, ndmin=2, dtype=dtype)
+        if not rowvar and y_ndim != 1:
+            y = y.T
+        x = dpnp.concatenate((x, y), axis=0)
+
+    # get the product of frequencies and weights
+    w = None
+    if fweights is not None:
+        if fweights.shape[0] != x.shape[1]:
+            raise ValueError("incompatible numbers of samples and fweights")
+
+        w = fweights
+
+    if aweights is not None:
+        if aweights.shape[0] != x.shape[1]:
+            raise ValueError("incompatible numbers of samples and aweights")
+
+        if w is None:
+            w = aweights
+        else:
+            w *= aweights
+
+    avg, w_sum = dpnp.average(x, axis=1, weights=w, returned=True)
+    w_sum = w_sum[0]
+
+    # determine the normalization
+    if w is None:
+        fact = x.shape[1] - ddof
+    elif ddof == 0:
+        fact = w_sum
+    elif aweights is None:
+        fact = w_sum - ddof
+    else:
+        fact = w_sum - ddof * dpnp.sum(w * aweights) / w_sum
 
-    fact = X.shape[1] - 1
-    X -= avg[:, None]
+    if fact <= 0:
+        warnings.warn(
+            "Degrees of freedom <= 0 for slice", RuntimeWarning, stacklevel=2
+        )
+        fact = 0.0
 
-    c = dpnp.dot(X, X.T.conj())
-    c *= 1 / fact if fact != 0 else dpnp.nan
+    x -= avg[:, None]
+    if w is None:
+        x_t = x.T
+    else:
+        x_t = (x * w).T
 
-    return dpnp.squeeze(c)
+    c = dpnp.dot(x, x_t.conj()) / fact
+    return c.squeeze()
 
 
 def dpnp_median(