SparseArray

An abstract base class for all the sparse array classes.

Attributes:

Name	Type	Description
dtype	dtype	The data type of this array.
fill_value	scalar	The fill value of this array.

Source code in sparse/numba_backend/_sparse_array.py

class SparseArray:
    """
    An abstract base class for all the sparse array classes.

    Attributes
    ----------
    dtype : numpy.dtype
        The data type of this array.
    fill_value : scalar
        The fill value of this array.
    """

    __metaclass__ = ABCMeta

    def __init__(self, shape, fill_value=None):
        if not isinstance(shape, Iterable):
            shape = (shape,)

        if not all(isinstance(sh, Integral) and int(sh) >= 0 for sh in shape):
            raise ValueError("shape must be an non-negative integer or a tuple of non-negative integers.")

        self.shape = tuple(int(sh) for sh in shape)

        if fill_value is not None:
            if not hasattr(fill_value, "dtype") or fill_value.dtype != self.dtype:
                self.fill_value = self.dtype.type(fill_value)
            else:
                self.fill_value = fill_value
        else:
            self.fill_value = _zero_of_dtype(self.dtype)

    dtype = None

    @property
    def device(self):
        data = getattr(self, "data", None)
        return getattr(data, "device", "cpu")

    def to_device(self, device, /, *, stream=None):
        if device != "cpu":
            raise ValueError("Only `device='cpu'` is supported.")

        return self

    @property
    @abstractmethod
    def nnz(self):
        """
        The number of nonzero elements in this array. Note that any duplicates in
        `coords` are counted multiple times.

        Returns
        -------
        int
            The number of nonzero elements in this array.

        See Also
        --------
        - [`sparse.DOK.nnz`][] : Equivalent [`sparse.DOK`][] array property.
        - [`numpy.count_nonzero`][] : A similar Numpy function.
        - [`scipy.sparse.coo_matrix.nnz`][] : The Scipy equivalent property.

        Examples
        --------
        >>> import numpy as np
        >>> from sparse import COO
        >>> x = np.array([0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 0])
        >>> np.count_nonzero(x)
        6
        >>> s = COO.from_numpy(x)
        >>> s.nnz
        6
        >>> np.count_nonzero(x) == s.nnz
        True
        """

    @property
    def ndim(self):
        """
        The number of dimensions of this array.

        Returns
        -------
        int
            The number of dimensions of this array.

        See Also
        --------
        - [`sparse.DOK.ndim`][] : Equivalent property for [`sparse.DOK`][] arrays.
        - [`numpy.ndarray.ndim`][] : Numpy equivalent property.

        Examples
        --------
        >>> from sparse import COO
        >>> import numpy as np
        >>> x = np.random.rand(1, 2, 3, 1, 2)
        >>> s = COO.from_numpy(x)
        >>> s.ndim
        5
        >>> s.ndim == x.ndim
        True
        """
        return len(self.shape)

    @property
    def size(self):
        """
        The number of all elements (including zeros) in this array.

        Returns
        -------
        int
            The number of elements.

        See Also
        --------
        [`numpy.ndarray.size`][] : Numpy equivalent property.

        Examples
        --------
        >>> from sparse import COO
        >>> import numpy as np
        >>> x = np.zeros((10, 10))
        >>> s = COO.from_numpy(x)
        >>> s.size
        100
        """
        # We use this instead of np.prod because np.prod
        # returns a float64 for an empty shape.
        return reduce(operator.mul, self.shape, 1)

    @property
    def density(self):
        """
        The ratio of nonzero to all elements in this array.

        Returns
        -------
        float
            The ratio of nonzero to all elements.

        See Also
        --------
        - [`sparse.COO.size`][] : Number of elements.
        - [`sparse.COO.nnz`][] : Number of nonzero elements.

        Examples
        --------
        >>> import numpy as np
        >>> from sparse import COO
        >>> x = np.zeros((8, 8))
        >>> x[0, :] = 1
        >>> s = COO.from_numpy(x)
        >>> s.density
        0.125
        """
        with warnings.catch_warnings():
            warnings.filterwarnings("ignore", category=RuntimeWarning)
            return float(np.float64(self.nnz) / np.float64(self.size))

    def _repr_html_(self):
        """
        Diagnostic report about this array.
        Renders in Jupyter.
        """
        try:
            from matrepr import to_html
            from matrepr.adapters.sparse_driver import PyDataSparseDriver

            return to_html(PyDataSparseDriver.adapt(self), notebook=True)
        except (ImportError, ValueError):
            return html_table(self)

    def _str_impl(self, summary):
        """
        A human-readable representation of this array, including a metadata summary
        and a tabular view of the array values.

        Values view only included if `matrepr` is available.

        Parameters
        ----------
        summary
            A type-specific summary of this array, used as the first line of return value.

        Returns
        -------
        str
            A human-readable representation of this array.
        """
        try:
            from matrepr import to_str
            from matrepr.adapters.sparse_driver import PyDataSparseDriver

            values = to_str(
                PyDataSparseDriver.adapt(self),
                title=False,  # disable matrepr description
                width_str=0,  # autodetect terminal width
                max_cols=9999,
            )
            return f"{summary}\n{values}"
        except (ImportError, ValueError):
            return summary

    @abstractmethod
    def asformat(self, format):
        """
        Convert this sparse array to a given format.

        Parameters
        ----------
        format : str
            A format string.

        Returns
        -------
        out : SparseArray
            The converted array.

        Raises
        ------
        NotImplementedError
            If the format isn't supported.
        """

    @abstractmethod
    def todense(self):
        """
        Convert this [`sparse.SparseArray`][] array to a dense [`numpy.ndarray`][]. Note that
        this may take a large amount of memory and time.

        Returns
        -------
        numpy.ndarray
            The converted dense array.

        See Also
        --------
        - [`sparse.DOK.todense`][] : Equivalent `DOK` array method.
        - [`sparse.COO.todense`][] : Equivalent `COO` array method.
        - [`scipy.sparse.coo_matrix.todense`][] : Equivalent Scipy method.

        Examples
        --------
        >>> import sparse
        >>> x = np.random.randint(100, size=(7, 3))
        >>> s = sparse.COO.from_numpy(x)
        >>> x2 = s.todense()
        >>> np.array_equal(x, x2)
        True
        """

    def _make_shallow_copy_of(self, other):
        self.__dict__ = other.__dict__.copy()

    def __array__(self, *args, **kwargs):
        from ._settings import AUTO_DENSIFY

        if not AUTO_DENSIFY:
            raise RuntimeError(
                "Cannot convert a sparse array to dense automatically. To manually densify, use the todense method."
            )

        return np.asarray(self.todense(), *args, **kwargs)

    def __array_function__(self, func, types, args, kwargs):
        import sparse as module

        sparse_func = None
        try:
            submodules = getattr(func, "__module__", "numpy").split(".")[1:]
            for submodule in submodules:
                module = getattr(module, submodule)
            sparse_func = getattr(module, func.__name__)
        except AttributeError:
            pass
        else:
            return sparse_func(*args, **kwargs)

        with contextlib.suppress(AttributeError):
            sparse_func = getattr(type(self), func.__name__)

        if not isinstance(sparse_func, Callable) and len(args) == 1 and len(kwargs) == 0:
            try:
                return getattr(self, func.__name__)
            except AttributeError:
                pass

        if sparse_func is None:
            return NotImplemented

        return sparse_func(*args, **kwargs)

    @staticmethod
    def _reduce(method, *args, **kwargs):
        from ._common import _is_scipy_sparse_obj

        assert len(args) == 1

        self = args[0]
        if _is_scipy_sparse_obj(self):
            self = type(self).from_scipy_sparse(self)

        return self.reduce(method, **kwargs)

    def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
        out = kwargs.pop("out", None)
        if out is not None and not all(isinstance(x, type(self)) for x in out):
            return NotImplemented

        if getattr(ufunc, "signature", None) is not None:
            return self.__array_function__(ufunc, (np.ndarray, type(self)), inputs, kwargs)

        if out is not None:
            test_args = [np.empty((1,), dtype=a.dtype) if hasattr(a, "dtype") else a for a in inputs]
            test_kwargs = kwargs.copy()
            if method == "reduce":
                test_kwargs["axis"] = None
            test_out = tuple(np.empty((1,), dtype=a.dtype) for a in out)
            if len(test_out) == 1:
                test_out = test_out[0]
            getattr(ufunc, method)(*test_args, out=test_out, **test_kwargs)
            kwargs["dtype"] = out[0].dtype

        if method == "outer":
            method = "__call__"

            cum_ndim = 0
            inputs_transformed = []
            for inp in reversed(inputs):
                inputs_transformed.append(inp[(Ellipsis,) + (None,) * cum_ndim])
                cum_ndim += inp.ndim

            inputs = tuple(reversed(inputs_transformed))

        if method == "__call__":
            result = elemwise(ufunc, *inputs, **kwargs)
        elif method == "reduce":
            result = SparseArray._reduce(ufunc, *inputs, **kwargs)
        else:
            return NotImplemented

        if out is not None:
            (out,) = out
            if out.shape != result.shape:
                raise ValueError(
                    f"non-broadcastable output operand with shape {out.shape} "
                    f"doesn't match the broadcast shape {result.shape}"
                )

            out._make_shallow_copy_of(result)
            return out

        return result

    def reduce(self, method, axis=(0,), keepdims=False, **kwargs):
        """
        Performs a reduction operation on this array.

        Parameters
        ----------
        method : numpy.ufunc
            The method to use for performing the reduction.
        axis : Union[int, Iterable[int]], optional
            The axes along which to perform the reduction. Uses all axes by default.
        keepdims : bool, optional
            Whether or not to keep the dimensions of the original array.
        **kwargs : dict
            Any extra arguments to pass to the reduction operation.

        See Also
        --------
        - [`numpy.ufunc.reduce`][] : A similar Numpy method.
        - [`sparse.COO.reduce`][] : This method implemented on COO arrays.
        - [`sparse.GCXS.reduce`][] : This method implemented on GCXS arrays.
        """
        axis = normalize_axis(axis, self.ndim)
        zero_reduce_result = method.reduce([self.fill_value, self.fill_value], **kwargs)
        reduce_super_ufunc = _reduce_super_ufunc.get(method)
        if not equivalent(zero_reduce_result, self.fill_value) and reduce_super_ufunc is None:
            raise ValueError(f"Performing this reduction operation would produce a dense result: {method!s}")

        if not isinstance(axis, tuple):
            axis = (axis,)
        out = self._reduce_calc(method, axis, keepdims, **kwargs)
        if len(out) == 1:
            return out[0]
        data, counts, axis, n_cols, arr_attrs = out
        result_fill_value = self.fill_value
        if reduce_super_ufunc is None:
            missing_counts = counts != n_cols
            data[missing_counts] = method(data[missing_counts], self.fill_value, **kwargs)
        else:
            data = method(
                data,
                reduce_super_ufunc(self.fill_value, n_cols - counts),
            ).astype(data.dtype)
            result_fill_value = reduce_super_ufunc(self.fill_value, n_cols)

        out = self._reduce_return(data, arr_attrs, result_fill_value)

        if keepdims:
            shape = list(self.shape)
            for ax in axis:
                shape[ax] = 1
            out = out.reshape(shape)

        if out.ndim == 0:
            return out[()]

        return out

    def _reduce_calc(self, method, axis, keepdims, **kwargs):
        raise NotImplementedError

    def _reduce_return(self, data, arr_attrs, result_fill_value):
        raise NotImplementedError

    def sum(self, axis=None, keepdims=False, dtype=None, out=None):
        """
        Performs a sum operation along the given axes. Uses all axes by default.

        Parameters
        ----------
        axis : Union[int, Iterable[int]], optional
            The axes along which to sum. Uses all axes by default.
        keepdims : bool, optional
            Whether or not to keep the dimensions of the original array.
        dtype : numpy.dtype
            The data type of the output array.

        Returns
        -------
        SparseArray
            The reduced output sparse array.

        See Also
        --------
        - [`numpy.sum`][] : Equivalent numpy function.
        - [`scipy.sparse.coo_matrix.sum`][] : Equivalent Scipy function.
        """
        return np.add.reduce(self, out=out, axis=axis, keepdims=keepdims, dtype=dtype)

    def max(self, axis=None, keepdims=False, out=None):
        """
        Maximize along the given axes. Uses all axes by default.

        Parameters
        ----------
        axis : Union[int, Iterable[int]], optional
            The axes along which to maximize. Uses all axes by default.
        keepdims : bool, optional
            Whether or not to keep the dimensions of the original array.
        out : numpy.dtype
            The data type of the output array.

        Returns
        -------
        SparseArray
            The reduced output sparse array.

        See Also
        --------
        - [`numpy.max`][] : Equivalent numpy function.
        - [`scipy.sparse.coo_matrix.max`][] : Equivalent Scipy function.
        """
        return np.maximum.reduce(self, out=out, axis=axis, keepdims=keepdims)

    amax = max

    def any(self, axis=None, keepdims=False, out=None):
        """
        See if any values along array are ``True``. Uses all axes by default.

        Parameters
        ----------
        axis : Union[int, Iterable[int]], optional
            The axes along which to minimize. Uses all axes by default.
        keepdims : bool, optional
            Whether or not to keep the dimensions of the original array.

        Returns
        -------
        SparseArray
            The reduced output sparse array.

        See Also
        --------
        [`numpy.any`][] : Equivalent numpy function.
        """
        return np.logical_or.reduce(self, out=out, axis=axis, keepdims=keepdims)

    def all(self, axis=None, keepdims=False, out=None):
        """
        See if all values in an array are ``True``. Uses all axes by default.

        Parameters
        ----------
        axis : Union[int, Iterable[int]], optional
            The axes along which to minimize. Uses all axes by default.
        keepdims : bool, optional
            Whether or not to keep the dimensions of the original array.

        Returns
        -------
        SparseArray
            The reduced output sparse array.

        See Also
        --------
        [`numpy.all`][] : Equivalent numpy function.
        """
        return np.logical_and.reduce(self, out=out, axis=axis, keepdims=keepdims)

    def min(self, axis=None, keepdims=False, out=None):
        """
        Minimize along the given axes. Uses all axes by default.

        Parameters
        ----------
        axis : Union[int, Iterable[int]], optional
            The axes along which to minimize. Uses all axes by default.
        keepdims : bool, optional
            Whether or not to keep the dimensions of the original array.
        out : numpy.dtype
            The data type of the output array.

        Returns
        -------
        SparseArray
            The reduced output sparse array.

        See Also
        --------
        - [`numpy.min`][] : Equivalent numpy function.
        - [`scipy.sparse.coo_matrix.min`][] : Equivalent Scipy function.
        """
        return np.minimum.reduce(self, out=out, axis=axis, keepdims=keepdims)

    amin = min

    def prod(self, axis=None, keepdims=False, dtype=None, out=None):
        """
        Performs a product operation along the given axes. Uses all axes by default.

        Parameters
        ----------
        axis : Union[int, Iterable[int]], optional
            The axes along which to multiply. Uses all axes by default.
        keepdims : bool, optional
            Whether or not to keep the dimensions of the original array.
        dtype : numpy.dtype
            The data type of the output array.

        Returns
        -------
        SparseArray
            The reduced output sparse array.

        See Also
        --------
        [`numpy.prod`][] : Equivalent numpy function.
        """
        return np.multiply.reduce(self, out=out, axis=axis, keepdims=keepdims, dtype=dtype)

    def round(self, decimals=0, out=None):
        """
        Evenly round to the given number of decimals.

        See Also
        --------
        - [`numpy.round`][] :
            NumPy equivalent ufunc.
        - [`sparse.elemwise`][] :
            Apply an arbitrary element-wise function to one or two
            arguments.
        """
        if out is not None and not isinstance(out, tuple):
            out = (out,)
        return self.__array_ufunc__(np.round, "__call__", self, decimals=decimals, out=out)

    round_ = round

    def clip(self, min=None, max=None, out=None):
        """
        Clip (limit) the values in the array.

        Return an array whose values are limited to ``[min, max]``. One of min
        or max must be given.

        See Also
        --------
        - [sparse.clip][] : For full documentation and more details.
        - [`numpy.clip`][] : Equivalent NumPy function.
        """
        if min is None and max is None:
            raise ValueError("One of max or min must be given.")
        if out is not None and not isinstance(out, tuple):
            out = (out,)
        return self.__array_ufunc__(np.clip, "__call__", self, a_min=min, a_max=max, out=out)

    def astype(self, dtype, casting="unsafe", copy=True):
        """
        Copy of the array, cast to a specified type.

        See Also
        --------
        - [`scipy.sparse.coo_matrix.astype`][] :
            SciPy sparse equivalent function
        - [`numpy.ndarray.astype`][] :
            NumPy equivalent ufunc.
        - [`sparse.elemwise`][] :
            Apply an arbitrary element-wise function to one or two
            arguments.
        """
        # this matches numpy's behavior
        if self.dtype == dtype and not copy:
            return self
        return self.__array_ufunc__(np.ndarray.astype, "__call__", self, dtype=dtype, copy=copy, casting=casting)

    def mean(self, axis=None, keepdims=False, dtype=None, out=None):
        """
        Compute the mean along the given axes. Uses all axes by default.

        Parameters
        ----------
        axis : Union[int, Iterable[int]], optional
            The axes along which to compute the mean. Uses all axes by default.
        keepdims : bool, optional
            Whether or not to keep the dimensions of the original array.
        dtype : numpy.dtype
            The data type of the output array.

        Returns
        -------
        SparseArray
            The reduced output sparse array.

        See Also
        --------
        - [`numpy.ndarray.mean`][] : Equivalent numpy method.
        - [`scipy.sparse.coo_matrix.mean`][] : Equivalent Scipy method.

        Notes
        -----
        * The `out` parameter is provided just for compatibility with
          Numpy and isn't actually supported.

        Examples
        --------
        You can use [`sparse.COO.mean`][] to compute the mean of an array across any
        dimension.

        >>> from sparse import COO
        >>> x = np.array([[1, 2, 0, 0], [0, 1, 0, 0]], dtype="i8")
        >>> s = COO.from_numpy(x)
        >>> s2 = s.mean(axis=1)
        >>> s2.todense()  # doctest: +SKIP
        array([0.5, 1.5, 0., 0.])

        You can also use the `keepdims` argument to keep the dimensions
        after the mean.

        >>> s3 = s.mean(axis=0, keepdims=True)
        >>> s3.shape
        (1, 4)

        You can pass in an output datatype, if needed.

        >>> s4 = s.mean(axis=0, dtype=np.float16)
        >>> s4.dtype
        dtype('float16')

        By default, this reduces the array down to one number, computing the
        mean along all axes.

        >>> s.mean()
        np.float64(0.5)
        """

        if axis is None:
            axis = tuple(range(self.ndim))
        elif not isinstance(axis, tuple):
            axis = (axis,)
        den = reduce(operator.mul, (self.shape[i] for i in axis), 1)

        if dtype is None:
            if issubclass(self.dtype.type, np.integer | np.bool_):
                dtype = inter_dtype = np.dtype("f8")
            else:
                dtype = self.dtype
                inter_dtype = np.dtype("f4") if issubclass(dtype.type, np.float16) else dtype
        else:
            inter_dtype = dtype

        num = self.sum(axis=axis, keepdims=keepdims, dtype=inter_dtype)

        if num.ndim:
            out = np.true_divide(num, den, casting="unsafe")
            return out.astype(dtype) if out.dtype != dtype else out
        return np.divide(num, den, dtype=dtype, out=out)

    def var(self, axis=None, dtype=None, out=None, ddof=0, keepdims=False):
        """
        Compute the variance along the given axes. Uses all axes by default.

        Parameters
        ----------
        axis : Union[int, Iterable[int]], optional
            The axes along which to compute the variance. Uses all axes by default.
        dtype : numpy.dtype, optional
            The output datatype.
        out : SparseArray, optional
            The array to write the output to.
        ddof : int
            The degrees of freedom.
        keepdims : bool, optional
            Whether or not to keep the dimensions of the original array.

        Returns
        -------
        SparseArray
            The reduced output sparse array.

        See Also
        --------
        [`numpy.ndarray.var`][] : Equivalent numpy method.

        Examples
        --------
        You can use [`sparse.COO.var`][] to compute the variance of an array across any
        dimension.

        >>> from sparse import COO
        >>> x = np.array([[1, 2, 0, 0], [0, 1, 0, 0]], dtype="i8")
        >>> s = COO.from_numpy(x)
        >>> s2 = s.var(axis=1)
        >>> s2.todense()  # doctest: +SKIP
        array([0.6875, 0.1875])

        You can also use the `keepdims` argument to keep the dimensions
        after the variance.

        >>> s3 = s.var(axis=0, keepdims=True)
        >>> s3.shape
        (1, 4)

        You can pass in an output datatype, if needed.

        >>> s4 = s.var(axis=0, dtype=np.float16)
        >>> s4.dtype
        dtype('float16')

        By default, this reduces the array down to one number, computing the
        variance along all axes.

        >>> s.var()
        np.float64(0.5)
        """
        axis = normalize_axis(axis, self.ndim)

        if axis is None:
            axis = tuple(range(self.ndim))

        if not isinstance(axis, tuple):
            axis = (axis,)

        rcount = reduce(operator.mul, (self.shape[a] for a in axis), 1)
        # Make this warning show up on top.
        if ddof >= rcount:
            warnings.warn("Degrees of freedom <= 0 for slice", RuntimeWarning, stacklevel=1)

        # Cast bool, unsigned int, and int to float64 by default
        if dtype is None and issubclass(self.dtype.type, np.integer | np.bool_):
            dtype = np.dtype("f8")

        arrmean = self.sum(axis, dtype=dtype, keepdims=True)[...]
        np.divide(arrmean, rcount, out=arrmean)
        x = self - arrmean
        if issubclass(self.dtype.type, np.complexfloating):
            x = x.real * x.real + x.imag * x.imag
        else:
            x = np.multiply(x, x, out=x)

        ret = x.sum(axis=axis, dtype=dtype, out=out, keepdims=keepdims)

        # Compute degrees of freedom and make sure it is not negative.
        rcount = max([rcount - ddof, 0])

        ret = ret[...]
        np.divide(ret, rcount, out=ret, casting="unsafe")
        return ret[()]

    def std(self, axis=None, dtype=None, out=None, ddof=0, keepdims=False):
        """
        Compute the standard deviation along the given axes. Uses all axes by default.

        Parameters
        ----------
        axis : Union[int, Iterable[int]], optional
            The axes along which to compute the standard deviation. Uses
            all axes by default.
        dtype : numpy.dtype, optional
            The output datatype.
        out : SparseArray, optional
            The array to write the output to.
        ddof : int
            The degrees of freedom.
        keepdims : bool, optional
            Whether or not to keep the dimensions of the original array.

        Returns
        -------
        SparseArray
            The reduced output sparse array.

        See Also
        --------
        [`numpy.ndarray.std`][] : Equivalent numpy method.

        Examples
        --------
        You can use [`sparse.COO.std`][] to compute the standard deviation of an array
        across any dimension.

        >>> from sparse import COO
        >>> x = np.array([[1, 2, 0, 0], [0, 1, 0, 0]], dtype="i8")
        >>> s = COO.from_numpy(x)
        >>> s2 = s.std(axis=1)
        >>> s2.todense()  # doctest: +SKIP
        array([0.8291562, 0.4330127])

        You can also use the `keepdims` argument to keep the dimensions
        after the standard deviation.

        >>> s3 = s.std(axis=0, keepdims=True)
        >>> s3.shape
        (1, 4)

        You can pass in an output datatype, if needed.

        >>> s4 = s.std(axis=0, dtype=np.float16)
        >>> s4.dtype
        dtype('float16')

        By default, this reduces the array down to one number, computing the
        standard deviation along all axes.

        >>> s.std()  # doctest: +SKIP
        0.7071067811865476
        """
        ret = self.var(axis=axis, dtype=dtype, out=out, ddof=ddof, keepdims=keepdims)

        return np.sqrt(ret)

    @property
    def real(self):
        """The real part of the array.

        Examples
        --------
        >>> from sparse import COO
        >>> x = COO.from_numpy([1 + 0j, 0 + 1j])
        >>> x.real.todense()  # doctest: +SKIP
        array([1., 0.])
        >>> x.real.dtype
        dtype('float64')

        Returns
        -------
        out : SparseArray
            The real component of the array elements. If the array dtype is
            real, the dtype of the array is used for the output. If the array
            is complex, the output dtype is float.

        See Also
        --------
        - [`numpy.ndarray.real`][] : NumPy equivalent attribute.
        - [`numpy.real`][] : NumPy equivalent function.
        """
        return self.__array_ufunc__(np.real, "__call__", self)

    @property
    def imag(self):
        """The imaginary part of the array.

        Examples
        --------
        >>> from sparse import COO
        >>> x = COO.from_numpy([1 + 0j, 0 + 1j])
        >>> x.imag.todense()  # doctest: +SKIP
        array([0., 1.])
        >>> x.imag.dtype
        dtype('float64')

        Returns
        -------
        out : SparseArray
            The imaginary component of the array elements. If the array dtype
            is real, the dtype of the array is used for the output. If the
            array is complex, the output dtype is float.

        See Also
        --------
        - [`numpy.ndarray.imag`][] : NumPy equivalent attribute.
        - [`numpy.imag`][] : NumPy equivalent function.
        """
        return self.__array_ufunc__(np.imag, "__call__", self)

    def conj(self):
        """Return the complex conjugate, element-wise.

        The complex conjugate of a complex number is obtained by changing the
        sign of its imaginary part.

        Examples
        --------
        >>> from sparse import COO
        >>> x = COO.from_numpy([1 + 2j, 2 - 1j])
        >>> res = x.conj()
        >>> res.todense()  # doctest: +SKIP
        array([1.-2.j, 2.+1.j])
        >>> res.dtype
        dtype('complex128')

        Returns
        -------
        out : SparseArray
            The complex conjugate, with same dtype as the input.

        See Also
        --------
        - [`numpy.ndarray.conj`][] : NumPy equivalent method.
        - [`numpy.conj`][] : NumPy equivalent function.
        """
        return np.conj(self)

    def __array_namespace__(self, *, api_version=None):
        if api_version is None:
            api_version = "2022.12"

        if api_version not in {"2021.12", "2022.12"}:
            raise ValueError(f'"{api_version}" Array API version not supported.')
        import sparse

        return sparse

    def __bool__(self):
        """ """
        return self._to_scalar(bool)

    def __float__(self):
        """ """
        return self._to_scalar(float)

    def __int__(self):
        """ """
        return self._to_scalar(int)

    def __index__(self):
        """ """
        return self._to_scalar(int)

    def __complex__(self):
        """ """
        return self._to_scalar(complex)

    def _to_scalar(self, builtin):
        if self.size != 1 or self.shape != ():
            raise ValueError(f"{builtin} can be computed for one-element arrays only.")
        return builtin(self.todense().flatten()[0])

    @abstractmethod
    def isinf(self):
        """ """

    @abstractmethod
    def isnan(self):
        """ """

Attributes

shape = tuple(int(sh) for sh in shape) instance-attribute

fill_value = self.dtype.type(fill_value) instance-attribute

dtype = None class-attribute instance-attribute

device property

nnz abstractmethod property

The number of nonzero elements in this array. Note that any duplicates in coords are counted multiple times.

Returns:

Type	Description
int	The number of nonzero elements in this array.

See Also

• sparse.DOK.nnz : Equivalent sparse.DOK array property.
• numpy.count_nonzero : A similar Numpy function.
• scipy.sparse.coo_matrix.nnz : The Scipy equivalent property.

Examples:

>>> import numpy as np
>>> from sparse import COO
>>> x = np.array([0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 0])
>>> np.count_nonzero(x)
6
>>> s = COO.from_numpy(x)
>>> s.nnz
6
>>> np.count_nonzero(x) == s.nnz
True

ndim property

The number of dimensions of this array.

Returns:

Type	Description
int	The number of dimensions of this array.

See Also

• sparse.DOK.ndim : Equivalent property for sparse.DOK arrays.
• numpy.ndarray.ndim : Numpy equivalent property.

Examples:

>>> from sparse import COO
>>> import numpy as np
>>> x = np.random.rand(1, 2, 3, 1, 2)
>>> s = COO.from_numpy(x)
>>> s.ndim
5
>>> s.ndim == x.ndim
True

size property

The number of all elements (including zeros) in this array.

Returns:

Type	Description
int	The number of elements.

See Also

numpy.ndarray.size : Numpy equivalent property.

Examples:

>>> from sparse import COO
>>> import numpy as np
>>> x = np.zeros((10, 10))
>>> s = COO.from_numpy(x)
>>> s.size
100

density property

The ratio of nonzero to all elements in this array.

Returns:

Type	Description
float	The ratio of nonzero to all elements.

See Also

• sparse.COO.size : Number of elements.
• sparse.COO.nnz : Number of nonzero elements.

Examples:

>>> import numpy as np
>>> from sparse import COO
>>> x = np.zeros((8, 8))
>>> x[0, :] = 1
>>> s = COO.from_numpy(x)
>>> s.density
0.125

amax = max class-attribute instance-attribute

amin = min class-attribute instance-attribute

round_ = round class-attribute instance-attribute

real property

The real part of the array.

Examples:

>>> from sparse import COO
>>> x = COO.from_numpy([1 + 0j, 0 + 1j])
>>> x.real.todense()
array([1., 0.])
>>> x.real.dtype
dtype('float64')

Returns:

Name	Type	Description
out	SparseArray	The real component of the array elements. If the array dtype is real, the dtype of the array is used for the output. If the array is complex, the output dtype is float.

See Also

• numpy.ndarray.real : NumPy equivalent attribute.
• numpy.real : NumPy equivalent function.

imag property

The imaginary part of the array.

Examples:

>>> from sparse import COO
>>> x = COO.from_numpy([1 + 0j, 0 + 1j])
>>> x.imag.todense()
array([0., 1.])
>>> x.imag.dtype
dtype('float64')

Returns:

Name	Type	Description
out	SparseArray	The imaginary component of the array elements. If the array dtype is real, the dtype of the array is used for the output. If the array is complex, the output dtype is float.

See Also

• numpy.ndarray.imag : NumPy equivalent attribute.
• numpy.imag : NumPy equivalent function.

Functions

to_device(device, /, *, stream=None)

Source code in sparse/numba_backend/_sparse_array.py

def to_device(self, device, /, *, stream=None):
    if device != "cpu":
        raise ValueError("Only `device='cpu'` is supported.")

    return self

asformat(format) abstractmethod

Convert this sparse array to a given format.

Parameters:

Name	Type	Description	Default
format	str	A format string.	required

Returns:

Name	Type	Description
out	SparseArray	The converted array.

Raises:

Type	Description
NotImplementedError	If the format isn't supported.

Source code in sparse/numba_backend/_sparse_array.py

@abstractmethod
def asformat(self, format):
    """
    Convert this sparse array to a given format.

    Parameters
    ----------
    format : str
        A format string.

    Returns
    -------
    out : SparseArray
        The converted array.

    Raises
    ------
    NotImplementedError
        If the format isn't supported.
    """

todense() abstractmethod

Convert this sparse.SparseArray array to a dense numpy.ndarray. Note that this may take a large amount of memory and time.

Returns:

Type	Description
ndarray	The converted dense array.

See Also

• sparse.DOK.todense : Equivalent DOK array method.
• sparse.COO.todense : Equivalent COO array method.
• scipy.sparse.coo_matrix.todense : Equivalent Scipy method.

Examples:

>>> import sparse
>>> x = np.random.randint(100, size=(7, 3))
>>> s = sparse.COO.from_numpy(x)
>>> x2 = s.todense()
>>> np.array_equal(x, x2)
True

Source code in sparse/numba_backend/_sparse_array.py

@abstractmethod
def todense(self):
    """
    Convert this [`sparse.SparseArray`][] array to a dense [`numpy.ndarray`][]. Note that
    this may take a large amount of memory and time.

    Returns
    -------
    numpy.ndarray
        The converted dense array.

    See Also
    --------
    - [`sparse.DOK.todense`][] : Equivalent `DOK` array method.
    - [`sparse.COO.todense`][] : Equivalent `COO` array method.
    - [`scipy.sparse.coo_matrix.todense`][] : Equivalent Scipy method.

    Examples
    --------
    >>> import sparse
    >>> x = np.random.randint(100, size=(7, 3))
    >>> s = sparse.COO.from_numpy(x)
    >>> x2 = s.todense()
    >>> np.array_equal(x, x2)
    True
    """

reduce(method, axis=(0,), keepdims=False, **kwargs)

Performs a reduction operation on this array.

Parameters:

Name	Type	Description	Default
method	ufunc	The method to use for performing the reduction.	required
axis	Union[int, Iterable[int]]	The axes along which to perform the reduction. Uses all axes by default.	(0,)
keepdims	bool_	Whether or not to keep the dimensions of the original array.	False
**kwargs	dict	Any extra arguments to pass to the reduction operation.	{}

See Also

• numpy.ufunc.reduce : A similar Numpy method.
• sparse.COO.reduce : This method implemented on COO arrays.
• sparse.GCXS.reduce : This method implemented on GCXS arrays.

Source code in sparse/numba_backend/_sparse_array.py

def reduce(self, method, axis=(0,), keepdims=False, **kwargs):
    """
    Performs a reduction operation on this array.

    Parameters
    ----------
    method : numpy.ufunc
        The method to use for performing the reduction.
    axis : Union[int, Iterable[int]], optional
        The axes along which to perform the reduction. Uses all axes by default.
    keepdims : bool, optional
        Whether or not to keep the dimensions of the original array.
    **kwargs : dict
        Any extra arguments to pass to the reduction operation.

    See Also
    --------
    - [`numpy.ufunc.reduce`][] : A similar Numpy method.
    - [`sparse.COO.reduce`][] : This method implemented on COO arrays.
    - [`sparse.GCXS.reduce`][] : This method implemented on GCXS arrays.
    """
    axis = normalize_axis(axis, self.ndim)
    zero_reduce_result = method.reduce([self.fill_value, self.fill_value], **kwargs)
    reduce_super_ufunc = _reduce_super_ufunc.get(method)
    if not equivalent(zero_reduce_result, self.fill_value) and reduce_super_ufunc is None:
        raise ValueError(f"Performing this reduction operation would produce a dense result: {method!s}")

    if not isinstance(axis, tuple):
        axis = (axis,)
    out = self._reduce_calc(method, axis, keepdims, **kwargs)
    if len(out) == 1:
        return out[0]
    data, counts, axis, n_cols, arr_attrs = out
    result_fill_value = self.fill_value
    if reduce_super_ufunc is None:
        missing_counts = counts != n_cols
        data[missing_counts] = method(data[missing_counts], self.fill_value, **kwargs)
    else:
        data = method(
            data,
            reduce_super_ufunc(self.fill_value, n_cols - counts),
        ).astype(data.dtype)
        result_fill_value = reduce_super_ufunc(self.fill_value, n_cols)

    out = self._reduce_return(data, arr_attrs, result_fill_value)

    if keepdims:
        shape = list(self.shape)
        for ax in axis:
            shape[ax] = 1
        out = out.reshape(shape)

    if out.ndim == 0:
        return out[()]

    return out

sum(axis=None, keepdims=False, dtype=None, out=None)

Performs a sum operation along the given axes. Uses all axes by default.

Parameters:

Name	Type	Description	Default
axis	Union[int, Iterable[int]]	The axes along which to sum. Uses all axes by default.	None
keepdims	bool_	Whether or not to keep the dimensions of the original array.	False
dtype	dtype	The data type of the output array.	None

Returns:

Type	Description
SparseArray	The reduced output sparse array.

See Also

• numpy.sum : Equivalent numpy function.
• scipy.sparse.coo_matrix.sum : Equivalent Scipy function.

Source code in sparse/numba_backend/_sparse_array.py

def sum(self, axis=None, keepdims=False, dtype=None, out=None):
    """
    Performs a sum operation along the given axes. Uses all axes by default.

    Parameters
    ----------
    axis : Union[int, Iterable[int]], optional
        The axes along which to sum. Uses all axes by default.
    keepdims : bool, optional
        Whether or not to keep the dimensions of the original array.
    dtype : numpy.dtype
        The data type of the output array.

    Returns
    -------
    SparseArray
        The reduced output sparse array.

    See Also
    --------
    - [`numpy.sum`][] : Equivalent numpy function.
    - [`scipy.sparse.coo_matrix.sum`][] : Equivalent Scipy function.
    """
    return np.add.reduce(self, out=out, axis=axis, keepdims=keepdims, dtype=dtype)

max(axis=None, keepdims=False, out=None)

Maximize along the given axes. Uses all axes by default.

Parameters:

Name	Type	Description	Default
axis	Union[int, Iterable[int]]	The axes along which to maximize. Uses all axes by default.	None
keepdims	bool_	Whether or not to keep the dimensions of the original array.	False
out	dtype	The data type of the output array.	None

Returns:

Type	Description
SparseArray	The reduced output sparse array.

See Also

• numpy.max : Equivalent numpy function.
• scipy.sparse.coo_matrix.max : Equivalent Scipy function.

Source code in sparse/numba_backend/_sparse_array.py

def max(self, axis=None, keepdims=False, out=None):
    """
    Maximize along the given axes. Uses all axes by default.

    Parameters
    ----------
    axis : Union[int, Iterable[int]], optional
        The axes along which to maximize. Uses all axes by default.
    keepdims : bool, optional
        Whether or not to keep the dimensions of the original array.
    out : numpy.dtype
        The data type of the output array.

    Returns
    -------
    SparseArray
        The reduced output sparse array.

    See Also
    --------
    - [`numpy.max`][] : Equivalent numpy function.
    - [`scipy.sparse.coo_matrix.max`][] : Equivalent Scipy function.
    """
    return np.maximum.reduce(self, out=out, axis=axis, keepdims=keepdims)

any(axis=None, keepdims=False, out=None)

See if any values along array are True. Uses all axes by default.

Parameters:

Name	Type	Description	Default
axis	Union[int, Iterable[int]]	The axes along which to minimize. Uses all axes by default.	None
keepdims	bool_	Whether or not to keep the dimensions of the original array.	False

Returns:

Type	Description
SparseArray	The reduced output sparse array.

See Also

numpy.any : Equivalent numpy function.

Source code in sparse/numba_backend/_sparse_array.py

def any(self, axis=None, keepdims=False, out=None):
    """
    See if any values along array are ``True``. Uses all axes by default.

    Parameters
    ----------
    axis : Union[int, Iterable[int]], optional
        The axes along which to minimize. Uses all axes by default.
    keepdims : bool, optional
        Whether or not to keep the dimensions of the original array.

    Returns
    -------
    SparseArray
        The reduced output sparse array.

    See Also
    --------
    [`numpy.any`][] : Equivalent numpy function.
    """
    return np.logical_or.reduce(self, out=out, axis=axis, keepdims=keepdims)

all(axis=None, keepdims=False, out=None)

See if all values in an array are True. Uses all axes by default.

Parameters:

Name	Type	Description	Default
axis	Union[int, Iterable[int]]	The axes along which to minimize. Uses all axes by default.	None
keepdims	bool_	Whether or not to keep the dimensions of the original array.	False

Returns:

Type	Description
SparseArray	The reduced output sparse array.

See Also

numpy.all : Equivalent numpy function.

Source code in sparse/numba_backend/_sparse_array.py

def all(self, axis=None, keepdims=False, out=None):
    """
    See if all values in an array are ``True``. Uses all axes by default.

    Parameters
    ----------
    axis : Union[int, Iterable[int]], optional
        The axes along which to minimize. Uses all axes by default.
    keepdims : bool, optional
        Whether or not to keep the dimensions of the original array.

    Returns
    -------
    SparseArray
        The reduced output sparse array.

    See Also
    --------
    [`numpy.all`][] : Equivalent numpy function.
    """
    return np.logical_and.reduce(self, out=out, axis=axis, keepdims=keepdims)

min(axis=None, keepdims=False, out=None)

Minimize along the given axes. Uses all axes by default.

Parameters:

Name	Type	Description	Default
axis	Union[int, Iterable[int]]	The axes along which to minimize. Uses all axes by default.	None
keepdims	bool_	Whether or not to keep the dimensions of the original array.	False
out	dtype	The data type of the output array.	None

Returns:

Type	Description
SparseArray	The reduced output sparse array.

See Also

• numpy.min : Equivalent numpy function.
• scipy.sparse.coo_matrix.min : Equivalent Scipy function.

Source code in sparse/numba_backend/_sparse_array.py

def min(self, axis=None, keepdims=False, out=None):
    """
    Minimize along the given axes. Uses all axes by default.

    Parameters
    ----------
    axis : Union[int, Iterable[int]], optional
        The axes along which to minimize. Uses all axes by default.
    keepdims : bool, optional
        Whether or not to keep the dimensions of the original array.
    out : numpy.dtype
        The data type of the output array.

    Returns
    -------
    SparseArray
        The reduced output sparse array.

    See Also
    --------
    - [`numpy.min`][] : Equivalent numpy function.
    - [`scipy.sparse.coo_matrix.min`][] : Equivalent Scipy function.
    """
    return np.minimum.reduce(self, out=out, axis=axis, keepdims=keepdims)

prod(axis=None, keepdims=False, dtype=None, out=None)

Performs a product operation along the given axes. Uses all axes by default.

Parameters:

Name	Type	Description	Default
axis	Union[int, Iterable[int]]	The axes along which to multiply. Uses all axes by default.	None
keepdims	bool_	Whether or not to keep the dimensions of the original array.	False
dtype	dtype	The data type of the output array.	None

Returns:

Type	Description
SparseArray	The reduced output sparse array.

See Also

numpy.prod : Equivalent numpy function.

Source code in sparse/numba_backend/_sparse_array.py

def prod(self, axis=None, keepdims=False, dtype=None, out=None):
    """
    Performs a product operation along the given axes. Uses all axes by default.

    Parameters
    ----------
    axis : Union[int, Iterable[int]], optional
        The axes along which to multiply. Uses all axes by default.
    keepdims : bool, optional
        Whether or not to keep the dimensions of the original array.
    dtype : numpy.dtype
        The data type of the output array.

    Returns
    -------
    SparseArray
        The reduced output sparse array.

    See Also
    --------
    [`numpy.prod`][] : Equivalent numpy function.
    """
    return np.multiply.reduce(self, out=out, axis=axis, keepdims=keepdims, dtype=dtype)

round(decimals=0, out=None)

Evenly round to the given number of decimals.

See Also

• numpy.round : NumPy equivalent ufunc.
• sparse.elemwise : Apply an arbitrary element-wise function to one or two arguments.

Source code in sparse/numba_backend/_sparse_array.py

def round(self, decimals=0, out=None):
    """
    Evenly round to the given number of decimals.

    See Also
    --------
    - [`numpy.round`][] :
        NumPy equivalent ufunc.
    - [`sparse.elemwise`][] :
        Apply an arbitrary element-wise function to one or two
        arguments.
    """
    if out is not None and not isinstance(out, tuple):
        out = (out,)
    return self.__array_ufunc__(np.round, "__call__", self, decimals=decimals, out=out)

clip(min=None, max=None, out=None)

Clip (limit) the values in the array.

Return an array whose values are limited to [min, max]. One of min or max must be given.

See Also

• sparse.clip : For full documentation and more details.
• numpy.clip : Equivalent NumPy function.

Source code in sparse/numba_backend/_sparse_array.py

def clip(self, min=None, max=None, out=None):
    """
    Clip (limit) the values in the array.

    Return an array whose values are limited to ``[min, max]``. One of min
    or max must be given.

    See Also
    --------
    - [sparse.clip][] : For full documentation and more details.
    - [`numpy.clip`][] : Equivalent NumPy function.
    """
    if min is None and max is None:
        raise ValueError("One of max or min must be given.")
    if out is not None and not isinstance(out, tuple):
        out = (out,)
    return self.__array_ufunc__(np.clip, "__call__", self, a_min=min, a_max=max, out=out)

astype(dtype, casting='unsafe', copy=True)

Copy of the array, cast to a specified type.

See Also

• scipy.sparse.coo_matrix.astype : SciPy sparse equivalent function
• numpy.ndarray.astype : NumPy equivalent ufunc.
• sparse.elemwise : Apply an arbitrary element-wise function to one or two arguments.

Source code in sparse/numba_backend/_sparse_array.py

def astype(self, dtype, casting="unsafe", copy=True):
    """
    Copy of the array, cast to a specified type.

    See Also
    --------
    - [`scipy.sparse.coo_matrix.astype`][] :
        SciPy sparse equivalent function
    - [`numpy.ndarray.astype`][] :
        NumPy equivalent ufunc.
    - [`sparse.elemwise`][] :
        Apply an arbitrary element-wise function to one or two
        arguments.
    """
    # this matches numpy's behavior
    if self.dtype == dtype and not copy:
        return self
    return self.__array_ufunc__(np.ndarray.astype, "__call__", self, dtype=dtype, copy=copy, casting=casting)

mean(axis=None, keepdims=False, dtype=None, out=None)

Compute the mean along the given axes. Uses all axes by default.

Parameters:

Name	Type	Description	Default
axis	Union[int, Iterable[int]]	The axes along which to compute the mean. Uses all axes by default.	None
keepdims	bool_	Whether or not to keep the dimensions of the original array.	False
dtype	dtype	The data type of the output array.	None

Returns:

Type	Description
SparseArray	The reduced output sparse array.

See Also

• numpy.ndarray.mean : Equivalent numpy method.
• scipy.sparse.coo_matrix.mean : Equivalent Scipy method.

Notes

• The out parameter is provided just for compatibility with Numpy and isn't actually supported.

Examples:

You can use sparse.COO.mean to compute the mean of an array across any dimension.

>>> from sparse import COO
>>> x = np.array([[1, 2, 0, 0], [0, 1, 0, 0]], dtype="i8")
>>> s = COO.from_numpy(x)
>>> s2 = s.mean(axis=1)
>>> s2.todense()
array([0.5, 1.5, 0., 0.])

You can also use the keepdims argument to keep the dimensions after the mean.

>>> s3 = s.mean(axis=0, keepdims=True)
>>> s3.shape
(1, 4)

You can pass in an output datatype, if needed.

>>> s4 = s.mean(axis=0, dtype=np.float16)
>>> s4.dtype
dtype('float16')

By default, this reduces the array down to one number, computing the mean along all axes.

>>> s.mean()
np.float64(0.5)

Source code in sparse/numba_backend/_sparse_array.py

def mean(self, axis=None, keepdims=False, dtype=None, out=None):
    """
    Compute the mean along the given axes. Uses all axes by default.

    Parameters
    ----------
    axis : Union[int, Iterable[int]], optional
        The axes along which to compute the mean. Uses all axes by default.
    keepdims : bool, optional
        Whether or not to keep the dimensions of the original array.
    dtype : numpy.dtype
        The data type of the output array.

    Returns
    -------
    SparseArray
        The reduced output sparse array.

    See Also
    --------
    - [`numpy.ndarray.mean`][] : Equivalent numpy method.
    - [`scipy.sparse.coo_matrix.mean`][] : Equivalent Scipy method.

    Notes
    -----
    * The `out` parameter is provided just for compatibility with
      Numpy and isn't actually supported.

    Examples
    --------
    You can use [`sparse.COO.mean`][] to compute the mean of an array across any
    dimension.

    >>> from sparse import COO
    >>> x = np.array([[1, 2, 0, 0], [0, 1, 0, 0]], dtype="i8")
    >>> s = COO.from_numpy(x)
    >>> s2 = s.mean(axis=1)
    >>> s2.todense()  # doctest: +SKIP
    array([0.5, 1.5, 0., 0.])

    You can also use the `keepdims` argument to keep the dimensions
    after the mean.

    >>> s3 = s.mean(axis=0, keepdims=True)
    >>> s3.shape
    (1, 4)

    You can pass in an output datatype, if needed.

    >>> s4 = s.mean(axis=0, dtype=np.float16)
    >>> s4.dtype
    dtype('float16')

    By default, this reduces the array down to one number, computing the
    mean along all axes.

    >>> s.mean()
    np.float64(0.5)
    """

    if axis is None:
        axis = tuple(range(self.ndim))
    elif not isinstance(axis, tuple):
        axis = (axis,)
    den = reduce(operator.mul, (self.shape[i] for i in axis), 1)

    if dtype is None:
        if issubclass(self.dtype.type, np.integer | np.bool_):
            dtype = inter_dtype = np.dtype("f8")
        else:
            dtype = self.dtype
            inter_dtype = np.dtype("f4") if issubclass(dtype.type, np.float16) else dtype
    else:
        inter_dtype = dtype

    num = self.sum(axis=axis, keepdims=keepdims, dtype=inter_dtype)

    if num.ndim:
        out = np.true_divide(num, den, casting="unsafe")
        return out.astype(dtype) if out.dtype != dtype else out
    return np.divide(num, den, dtype=dtype, out=out)

var(axis=None, dtype=None, out=None, ddof=0, keepdims=False)

Compute the variance along the given axes. Uses all axes by default.

Parameters:

Name	Type	Description	Default
axis	Union[int, Iterable[int]]	The axes along which to compute the variance. Uses all axes by default.	None
dtype	dtype	The output datatype.	None
out	SparseArray	The array to write the output to.	None
ddof	int	The degrees of freedom.	0
keepdims	bool_	Whether or not to keep the dimensions of the original array.	False

Returns:

Type	Description
SparseArray	The reduced output sparse array.

See Also

numpy.ndarray.var : Equivalent numpy method.

Examples:

You can use sparse.COO.var to compute the variance of an array across any dimension.

>>> from sparse import COO
>>> x = np.array([[1, 2, 0, 0], [0, 1, 0, 0]], dtype="i8")
>>> s = COO.from_numpy(x)
>>> s2 = s.var(axis=1)
>>> s2.todense()
array([0.6875, 0.1875])

You can also use the keepdims argument to keep the dimensions after the variance.

>>> s3 = s.var(axis=0, keepdims=True)
>>> s3.shape
(1, 4)

You can pass in an output datatype, if needed.

>>> s4 = s.var(axis=0, dtype=np.float16)
>>> s4.dtype
dtype('float16')

By default, this reduces the array down to one number, computing the variance along all axes.

>>> s.var()
np.float64(0.5)

Source code in sparse/numba_backend/_sparse_array.py

def var(self, axis=None, dtype=None, out=None, ddof=0, keepdims=False):
    """
    Compute the variance along the given axes. Uses all axes by default.

    Parameters
    ----------
    axis : Union[int, Iterable[int]], optional
        The axes along which to compute the variance. Uses all axes by default.
    dtype : numpy.dtype, optional
        The output datatype.
    out : SparseArray, optional
        The array to write the output to.
    ddof : int
        The degrees of freedom.
    keepdims : bool, optional
        Whether or not to keep the dimensions of the original array.

    Returns
    -------
    SparseArray
        The reduced output sparse array.

    See Also
    --------
    [`numpy.ndarray.var`][] : Equivalent numpy method.

    Examples
    --------
    You can use [`sparse.COO.var`][] to compute the variance of an array across any
    dimension.

    >>> from sparse import COO
    >>> x = np.array([[1, 2, 0, 0], [0, 1, 0, 0]], dtype="i8")
    >>> s = COO.from_numpy(x)
    >>> s2 = s.var(axis=1)
    >>> s2.todense()  # doctest: +SKIP
    array([0.6875, 0.1875])

    You can also use the `keepdims` argument to keep the dimensions
    after the variance.

    >>> s3 = s.var(axis=0, keepdims=True)
    >>> s3.shape
    (1, 4)

    You can pass in an output datatype, if needed.

    >>> s4 = s.var(axis=0, dtype=np.float16)
    >>> s4.dtype
    dtype('float16')

    By default, this reduces the array down to one number, computing the
    variance along all axes.

    >>> s.var()
    np.float64(0.5)
    """
    axis = normalize_axis(axis, self.ndim)

    if axis is None:
        axis = tuple(range(self.ndim))

    if not isinstance(axis, tuple):
        axis = (axis,)

    rcount = reduce(operator.mul, (self.shape[a] for a in axis), 1)
    # Make this warning show up on top.
    if ddof >= rcount:
        warnings.warn("Degrees of freedom <= 0 for slice", RuntimeWarning, stacklevel=1)

    # Cast bool, unsigned int, and int to float64 by default
    if dtype is None and issubclass(self.dtype.type, np.integer | np.bool_):
        dtype = np.dtype("f8")

    arrmean = self.sum(axis, dtype=dtype, keepdims=True)[...]
    np.divide(arrmean, rcount, out=arrmean)
    x = self - arrmean
    if issubclass(self.dtype.type, np.complexfloating):
        x = x.real * x.real + x.imag * x.imag
    else:
        x = np.multiply(x, x, out=x)

    ret = x.sum(axis=axis, dtype=dtype, out=out, keepdims=keepdims)

    # Compute degrees of freedom and make sure it is not negative.
    rcount = max([rcount - ddof, 0])

    ret = ret[...]
    np.divide(ret, rcount, out=ret, casting="unsafe")
    return ret[()]

std(axis=None, dtype=None, out=None, ddof=0, keepdims=False)

Compute the standard deviation along the given axes. Uses all axes by default.

Parameters:

Name	Type	Description	Default
axis	Union[int, Iterable[int]]	The axes along which to compute the standard deviation. Uses all axes by default.	None
dtype	dtype	The output datatype.	None
out	SparseArray	The array to write the output to.	None
ddof	int	The degrees of freedom.	0
keepdims	bool_	Whether or not to keep the dimensions of the original array.	False

Returns:

Type	Description
SparseArray	The reduced output sparse array.

See Also

numpy.ndarray.std : Equivalent numpy method.

Examples:

You can use sparse.COO.std to compute the standard deviation of an array across any dimension.

>>> from sparse import COO
>>> x = np.array([[1, 2, 0, 0], [0, 1, 0, 0]], dtype="i8")
>>> s = COO.from_numpy(x)
>>> s2 = s.std(axis=1)
>>> s2.todense()
array([0.8291562, 0.4330127])

You can also use the keepdims argument to keep the dimensions after the standard deviation.

>>> s3 = s.std(axis=0, keepdims=True)
>>> s3.shape
(1, 4)

You can pass in an output datatype, if needed.

>>> s4 = s.std(axis=0, dtype=np.float16)
>>> s4.dtype
dtype('float16')

By default, this reduces the array down to one number, computing the standard deviation along all axes.

>>> s.std()
0.7071067811865476

Source code in sparse/numba_backend/_sparse_array.py

def std(self, axis=None, dtype=None, out=None, ddof=0, keepdims=False):
    """
    Compute the standard deviation along the given axes. Uses all axes by default.

    Parameters
    ----------
    axis : Union[int, Iterable[int]], optional
        The axes along which to compute the standard deviation. Uses
        all axes by default.
    dtype : numpy.dtype, optional
        The output datatype.
    out : SparseArray, optional
        The array to write the output to.
    ddof : int
        The degrees of freedom.
    keepdims : bool, optional
        Whether or not to keep the dimensions of the original array.

    Returns
    -------
    SparseArray
        The reduced output sparse array.

    See Also
    --------
    [`numpy.ndarray.std`][] : Equivalent numpy method.

    Examples
    --------
    You can use [`sparse.COO.std`][] to compute the standard deviation of an array
    across any dimension.

    >>> from sparse import COO
    >>> x = np.array([[1, 2, 0, 0], [0, 1, 0, 0]], dtype="i8")
    >>> s = COO.from_numpy(x)
    >>> s2 = s.std(axis=1)
    >>> s2.todense()  # doctest: +SKIP
    array([0.8291562, 0.4330127])

    You can also use the `keepdims` argument to keep the dimensions
    after the standard deviation.

    >>> s3 = s.std(axis=0, keepdims=True)
    >>> s3.shape
    (1, 4)

    You can pass in an output datatype, if needed.

    >>> s4 = s.std(axis=0, dtype=np.float16)
    >>> s4.dtype
    dtype('float16')

    By default, this reduces the array down to one number, computing the
    standard deviation along all axes.

    >>> s.std()  # doctest: +SKIP
    0.7071067811865476
    """
    ret = self.var(axis=axis, dtype=dtype, out=out, ddof=ddof, keepdims=keepdims)

    return np.sqrt(ret)

conj()

Return the complex conjugate, element-wise.

The complex conjugate of a complex number is obtained by changing the sign of its imaginary part.

Examples:

>>> from sparse import COO
>>> x = COO.from_numpy([1 + 2j, 2 - 1j])
>>> res = x.conj()
>>> res.todense()
array([1.-2.j, 2.+1.j])
>>> res.dtype
dtype('complex128')

Returns:

Name	Type	Description
out	SparseArray	The complex conjugate, with same dtype as the input.

See Also

• numpy.ndarray.conj : NumPy equivalent method.
• numpy.conj : NumPy equivalent function.

Source code in sparse/numba_backend/_sparse_array.py

def conj(self):
    """Return the complex conjugate, element-wise.

    The complex conjugate of a complex number is obtained by changing the
    sign of its imaginary part.

    Examples
    --------
    >>> from sparse import COO
    >>> x = COO.from_numpy([1 + 2j, 2 - 1j])
    >>> res = x.conj()
    >>> res.todense()  # doctest: +SKIP
    array([1.-2.j, 2.+1.j])
    >>> res.dtype
    dtype('complex128')

    Returns
    -------
    out : SparseArray
        The complex conjugate, with same dtype as the input.

    See Also
    --------
    - [`numpy.ndarray.conj`][] : NumPy equivalent method.
    - [`numpy.conj`][] : NumPy equivalent function.
    """
    return np.conj(self)

isinf() abstractmethod

Source code in sparse/numba_backend/_sparse_array.py

@abstractmethod
def isinf(self):
    """ """

isnan() abstractmethod

Source code in sparse/numba_backend/_sparse_array.py

@abstractmethod
def isnan(self):
    """ """