from abc import ABCMeta, abstractmethod
from collections.abc import Iterable
from numbers import Integral
from typing import Callable
import operator
from functools import reduce
import numpy as np
import scipy.sparse as ss
from ._umath import elemwise
from ._utils import _zero_of_dtype, html_table, equivalent, normalize_axis
_reduce_super_ufunc = {np.add: np.multiply, np.multiply: np.power}
[docs]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(l, Integral) and int(l) >= 0 for l in shape):
raise ValueError(
"shape must be an non-negative integer or a tuple "
"of non-negative integers."
)
self.shape = tuple(int(l) for l 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
@abstractmethod
def nnz(self):
"""
The number of nonzero elements in this array. Note that any duplicates in
:code:`coords` are counted multiple times. To avoid this, call :obj:`COO.sum_duplicates`.
Returns
-------
int
The number of nonzero elements in this array.
See Also
--------
DOK.nnz : Equivalent :obj:`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
--------
DOK.ndim : Equivalent property for :obj:`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
--------
COO.size : Number of elements.
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
"""
return self.nnz / self.size
def _repr_html_(self):
"""
Diagnostic report about this array.
Renders in Jupyter.
"""
return html_table(self)
[docs] @abstractmethod
def todense(self):
"""
Convert this :obj:`SparseArray` array to a dense :obj:`numpy.ndarray`. Note that
this may take a large amount of memory and time.
Returns
-------
numpy.ndarray
The converted dense array.
See Also
--------
DOK.todense : Equivalent :obj:`DOK` array method.
COO.todense : Equivalent :obj:`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)
try:
sparse_func = getattr(type(self), func.__name__)
except AttributeError:
pass
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):
assert len(args) == 1
self = args[0]
if isinstance(self, ss.spmatrix):
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:
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(
"non-broadcastable output operand with shape %s "
"doesn't match the broadcast shape %s" % (out.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.
COO.reduce : This method implemented on COO arrays.
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 = None
if not equivalent(zero_reduce_result, self.fill_value):
reduce_super_ufunc = _reduce_super_ufunc.get(method, None)
if reduce_super_ufunc is None:
raise ValueError(
"Performing this reduction operation would produce "
"a dense result: %s" % str(method)
)
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
--------
:obj:`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.
dtype: numpy.dtype
The data type of the output array.
Returns
-------
SparseArray
The reduced output sparse array.
See Also
--------
:obj:`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
--------
:obj:`numpy.all` : 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
--------
:obj:`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.
dtype: numpy.dtype
The data type of the output array.
Returns
-------
SparseArray
The reduced output sparse array.
See Also
--------
:obj:`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
--------
:obj:`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
--------
:obj:`numpy.round` : NumPy equivalent ufunc.
:obj:`COO.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.
:obj:`COO.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
-----
* This function internally calls :obj:`COO.sum_duplicates` to bring the
array into canonical form.
* The :code:`out` parameter is provided just for compatibility with
Numpy and isn't actually supported.
Examples
--------
You can use :obj:`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 :code:`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()
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 gi66ven 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.
Notes
-----
* This function internally calls :obj:`COO.sum_duplicates` to bring the
array into canonical form.
Examples
--------
You can use :obj:`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 :code:`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()
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)
# 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.
Notes
-----
* This function internally calls :obj:`COO.sum_duplicates` to bring the
array into canonical form.
Examples
--------
You can use :obj:`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 :code:`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)
ret = np.sqrt(ret)
return 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)