import operator
import warnings
from collections.abc import Iterable
from functools import reduce
from typing import Any, NamedTuple
import numba
import numpy as np
from .._sparse_array import SparseArray
from .._utils import (
can_store,
check_consistent_fill_value,
check_zero_fill_value,
is_unsigned_dtype,
isscalar,
normalize_axis,
)
[docs]
def asCOO(x, name="asCOO", check=True):
"""
Convert the input to :obj:`COO`. Passes through :obj:`COO` objects as-is.
Parameters
----------
x : Union[SparseArray, scipy.sparse.spmatrix, numpy.ndarray]
The input array to convert.
name : str, optional
The name of the operation to use in the exception.
check : bool, optional
Whether to check for a dense input.
Returns
-------
COO
The converted :obj:`COO` array.
Raises
------
ValueError
If ``check`` is true and a dense input is supplied.
"""
from .._common import _is_sparse
from .core import COO
if check and not _is_sparse(x):
raise ValueError(f"Performing this operation would produce a dense result: {name}")
if not isinstance(x, COO):
x = COO(x)
return x
def linear_loc(coords, shape):
if shape == () and len(coords) == 0:
# `np.ravel_multi_index` is not aware of arrays, so cannot produce a
# sensible result here (https://github.com/numpy/numpy/issues/15690).
# Since `coords` is an array and not a sequence, we know the correct
# dimensions.
return np.zeros(coords.shape[1:], dtype=np.intp)
return np.ravel_multi_index(coords, shape)
[docs]
def kron(a, b):
"""Kronecker product of 2 sparse arrays.
Parameters
----------
a, b : SparseArray, scipy.sparse.spmatrix, or np.ndarray
The arrays over which to compute the Kronecker product.
Returns
-------
res : COO
The kronecker product
Raises
------
ValueError
If all arguments are dense or arguments have nonzero fill-values.
Examples
--------
>>> from sparse import eye
>>> a = eye(3, dtype="i8")
>>> b = np.array([1, 2, 3], dtype="i8")
>>> res = kron(a, b)
>>> res.todense() # doctest: +SKIP
array([[1, 2, 3, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 2, 3, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 1, 2, 3]], dtype=int64)
"""
from .._common import _is_sparse
from .._umath import _cartesian_product
from .core import COO
check_zero_fill_value(a, b)
a_sparse = _is_sparse(a)
b_sparse = _is_sparse(b)
a_ndim = np.ndim(a)
b_ndim = np.ndim(b)
if not (a_sparse or b_sparse):
raise ValueError("Performing this operation would produce a dense result: kron")
if a_ndim == 0 or b_ndim == 0:
return a * b
a = asCOO(a, check=False)
b = asCOO(b, check=False)
# Match dimensions
max_dim = max(a.ndim, b.ndim)
a = a.reshape((1,) * (max_dim - a.ndim) + a.shape)
b = b.reshape((1,) * (max_dim - b.ndim) + b.shape)
a_idx, b_idx = _cartesian_product(np.arange(a.nnz), np.arange(b.nnz))
a_expanded_coords = a.coords[:, a_idx]
b_expanded_coords = b.coords[:, b_idx]
o_coords = a_expanded_coords * np.asarray(b.shape)[:, None] + b_expanded_coords
o_data = a.data[a_idx] * b.data[b_idx]
o_shape = tuple(i * j for i, j in zip(a.shape, b.shape, strict=True))
return COO(o_coords, o_data, shape=o_shape, has_duplicates=False)
def concatenate(arrays, axis=0):
"""
Concatenate the input arrays along the given dimension.
Parameters
----------
arrays : Iterable[SparseArray]
The input arrays to concatenate.
axis : int, optional
The axis along which to concatenate the input arrays. The default is zero.
Returns
-------
COO
The output concatenated array.
Raises
------
ValueError
If all elements of :code:`arrays` don't have the same fill-value.
See Also
--------
numpy.concatenate : NumPy equivalent function
"""
from .core import COO
check_consistent_fill_value(arrays)
if axis is None:
arrays = [x.flatten() for x in arrays]
arrays = [x if isinstance(x, COO) else COO(x) for x in arrays]
axis = normalize_axis(axis, arrays[0].ndim)
assert all(x.shape[ax] == arrays[0].shape[ax] for x in arrays for ax in set(range(arrays[0].ndim)) - {axis})
nnz = 0
dim = sum(x.shape[axis] for x in arrays)
shape = list(arrays[0].shape)
shape[axis] = dim
data = np.concatenate([x.data for x in arrays])
coords = np.concatenate([x.coords for x in arrays], axis=1)
if not can_store(coords.dtype, max(shape)):
coords = coords.astype(np.min_scalar_type(max(shape)))
dim = 0
for x in arrays:
if dim:
coords[axis, nnz : x.nnz + nnz] += dim
dim += x.shape[axis]
nnz += x.nnz
return COO(
coords,
data,
shape=shape,
has_duplicates=False,
sorted=(axis == 0),
fill_value=arrays[0].fill_value,
)
def stack(arrays, axis=0):
"""
Stack the input arrays along the given dimension.
Parameters
----------
arrays : Iterable[SparseArray]
The input arrays to stack.
axis : int, optional
The axis along which to stack the input arrays.
Returns
-------
COO
The output stacked array.
Raises
------
ValueError
If all elements of :code:`arrays` don't have the same fill-value.
See Also
--------
numpy.stack : NumPy equivalent function
"""
from .core import COO
check_consistent_fill_value(arrays)
assert len({x.shape for x in arrays}) == 1
arrays = [x if isinstance(x, COO) else COO(x) for x in arrays]
axis = normalize_axis(axis, arrays[0].ndim + 1)
data = np.concatenate([x.data for x in arrays])
coords = np.concatenate([x.coords for x in arrays], axis=1)
shape = list(arrays[0].shape)
shape.insert(axis, len(arrays))
nnz = 0
new = np.empty(shape=(coords.shape[1],), dtype=np.intp)
for dim, x in enumerate(arrays):
new[nnz : x.nnz + nnz] = dim
nnz += x.nnz
coords = [coords[i] for i in range(coords.shape[0])]
coords.insert(axis, new)
coords = np.stack(coords, axis=0)
return COO(
coords,
data,
shape=shape,
has_duplicates=False,
sorted=(axis == 0),
fill_value=arrays[0].fill_value,
)
[docs]
def triu(x, k=0):
"""
Returns an array with all elements below the k-th diagonal set to zero.
Parameters
----------
x : COO
The input array.
k : int, optional
The diagonal below which elements are set to zero. The default is
zero, which corresponds to the main diagonal.
Returns
-------
COO
The output upper-triangular matrix.
Raises
------
ValueError
If :code:`x` doesn't have zero fill-values.
See Also
--------
numpy.triu : NumPy equivalent function
"""
from .core import COO
check_zero_fill_value(x)
if not x.ndim >= 2:
raise NotImplementedError("sparse.triu is not implemented for scalars or 1-D arrays.")
mask = x.coords[-2] + k <= x.coords[-1]
coords = x.coords[:, mask]
data = x.data[mask]
return COO(coords, data, shape=x.shape, has_duplicates=False, sorted=True)
[docs]
def tril(x, k=0):
"""
Returns an array with all elements above the k-th diagonal set to zero.
Parameters
----------
x : COO
The input array.
k : int, optional
The diagonal above which elements are set to zero. The default is
zero, which corresponds to the main diagonal.
Returns
-------
COO
The output lower-triangular matrix.
Raises
------
ValueError
If :code:`x` doesn't have zero fill-values.
See Also
--------
numpy.tril : NumPy equivalent function
"""
from .core import COO
check_zero_fill_value(x)
if not x.ndim >= 2:
raise NotImplementedError("sparse.tril is not implemented for scalars or 1-D arrays.")
mask = x.coords[-2] + k >= x.coords[-1]
coords = x.coords[:, mask]
data = x.data[mask]
return COO(coords, data, shape=x.shape, has_duplicates=False, sorted=True)
[docs]
def nansum(x, axis=None, keepdims=False, dtype=None, out=None):
"""
Performs a ``NaN`` skipping sum operation along the given axes. Uses all axes by default.
Parameters
----------
x : SparseArray
The array to perform the reduction on.
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
-------
COO
The reduced output sparse array.
See Also
--------
:obj:`COO.sum` : Function without ``NaN`` skipping.
numpy.nansum : Equivalent Numpy function.
"""
assert out is None
x = asCOO(x, name="nansum")
return nanreduce(x, np.add, axis=axis, keepdims=keepdims, dtype=dtype)
[docs]
def nanmean(x, axis=None, keepdims=False, dtype=None, out=None):
"""
Performs a ``NaN`` skipping mean operation along the given axes. Uses all axes by default.
Parameters
----------
x : SparseArray
The array to perform the reduction on.
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
-------
COO
The reduced output sparse array.
See Also
--------
:obj:`COO.mean` : Function without ``NaN`` skipping.
numpy.nanmean : Equivalent Numpy function.
"""
assert out is None
x = asCOO(x, name="nanmean")
if not (np.issubdtype(x.dtype, np.floating) or np.issubdtype(x.dtype, np.complexfloating)):
return x.mean(axis=axis, keepdims=keepdims, dtype=dtype)
mask = np.isnan(x)
x2 = where(mask, 0, x)
# Count the number non-nan elements along axis
nancount = mask.sum(axis=axis, dtype="i8", keepdims=keepdims)
if axis is None:
axis = tuple(range(x.ndim))
elif not isinstance(axis, tuple):
axis = (axis,)
den = reduce(operator.mul, (x.shape[i] for i in axis), 1)
den -= nancount
if (den == 0).any():
warnings.warn("Mean of empty slice", RuntimeWarning, stacklevel=2)
num = np.sum(x2, axis=axis, dtype=dtype, keepdims=keepdims)
with np.errstate(invalid="ignore", divide="ignore"):
if num.ndim:
return np.true_divide(num, den, casting="unsafe")
return (num / den).astype(dtype if dtype is not None else x.dtype)
[docs]
def nanmax(x, axis=None, keepdims=False, dtype=None, out=None):
"""
Maximize along the given axes, skipping ``NaN`` values. Uses all axes by default.
Parameters
----------
x : SparseArray
The array to perform the reduction on.
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
-------
COO
The reduced output sparse array.
See Also
--------
:obj:`COO.max` : Function without ``NaN`` skipping.
numpy.nanmax : Equivalent Numpy function.
"""
assert out is None
x = asCOO(x, name="nanmax")
ar = x.reduce(np.fmax, axis=axis, keepdims=keepdims, dtype=dtype)
if (isscalar(ar) and np.isnan(ar)) or np.isnan(ar.data).any():
warnings.warn("All-NaN slice encountered", RuntimeWarning, stacklevel=2)
return ar
[docs]
def nanmin(x, axis=None, keepdims=False, dtype=None, out=None):
"""
Minimize along the given axes, skipping ``NaN`` values. Uses all axes by default.
Parameters
----------
x : SparseArray
The array to perform the reduction on.
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
-------
COO
The reduced output sparse array.
See Also
--------
:obj:`COO.min` : Function without ``NaN`` skipping.
numpy.nanmin : Equivalent Numpy function.
"""
assert out is None
x = asCOO(x, name="nanmin")
ar = x.reduce(np.fmin, axis=axis, keepdims=keepdims, dtype=dtype)
if (isscalar(ar) and np.isnan(ar)) or np.isnan(ar.data).any():
warnings.warn("All-NaN slice encountered", RuntimeWarning, stacklevel=2)
return ar
[docs]
def nanprod(x, axis=None, keepdims=False, dtype=None, out=None):
"""
Performs a product operation along the given axes, skipping ``NaN`` values.
Uses all axes by default.
Parameters
----------
x : SparseArray
The array to perform the reduction on.
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
-------
COO
The reduced output sparse array.
See Also
--------
:obj:`COO.prod` : Function without ``NaN`` skipping.
numpy.nanprod : Equivalent Numpy function.
"""
assert out is None
x = asCOO(x)
return nanreduce(x, np.multiply, axis=axis, keepdims=keepdims, dtype=dtype)
[docs]
def where(condition, x=None, y=None):
"""
Select values from either ``x`` or ``y`` depending on ``condition``.
If ``x`` and ``y`` are not given, returns indices where ``condition``
is nonzero.
Performs the equivalent of :obj:`numpy.where`.
Parameters
----------
condition : SparseArray
The condition based on which to select values from
either ``x`` or ``y``.
x : SparseArray, optional
The array to select values from if ``condition`` is nonzero.
y : SparseArray, optional
The array to select values from if ``condition`` is zero.
Returns
-------
COO
The output array with selected values if ``x`` and ``y`` are given;
else where the array is nonzero.
Raises
------
ValueError
If the operation would produce a dense result; or exactly one of
``x`` and ``y`` are given.
See Also
--------
numpy.where : Equivalent Numpy function.
"""
from .._umath import elemwise
x_given = x is not None
y_given = y is not None
if not (x_given or y_given):
check_zero_fill_value(condition)
condition = asCOO(condition, name=str(np.where))
return tuple(condition.coords)
if x_given != y_given:
raise ValueError("either both or neither of x and y should be given")
return elemwise(np.where, condition, x, y)
[docs]
def argwhere(a):
"""
Find the indices of array elements that are non-zero, grouped by element.
Parameters
----------
a : array_like
Input data.
Returns
-------
index_array : numpy.ndarray
See Also
--------
:obj:`where`, :obj:`COO.nonzero`
Examples
--------
>>> import sparse
>>> x = sparse.COO(np.arange(6).reshape((2, 3)))
>>> sparse.argwhere(x > 1)
array([[0, 2],
[1, 0],
[1, 1],
[1, 2]])
"""
return np.transpose(a.nonzero())
[docs]
def argmax(x, /, *, axis=None, keepdims=False):
"""
Returns the indices of the maximum values along a specified axis.
When the maximum value occurs multiple times, only the indices
corresponding to the first occurrence are returned.
Parameters
----------
x : SparseArray
Input array. The fill value must be ``0.0`` and all non-zero values
must be greater than ``0.0``.
axis : int, optional
Axis along which to search. If ``None``, the function must return
the index of the maximum value of the flattened array. Default: ``None``.
keepdims : bool, optional
If ``True``, the reduced axes (dimensions) must be included in the result
as singleton dimensions, and, accordingly, the result must be compatible
with the input array. Otherwise, if ``False``, the reduced axes (dimensions)
must not be included in the result. Default: ``False``.
Returns
-------
out : numpy.ndarray
If ``axis`` is ``None``, a zero-dimensional array containing the index of
the first occurrence of the maximum value. Otherwise, a non-zero-dimensional
array containing the indices of the maximum values.
"""
return _arg_minmax_common(x, axis=axis, keepdims=keepdims, mode="max")
[docs]
def argmin(x, /, *, axis=None, keepdims=False):
"""
Returns the indices of the minimum values along a specified axis.
When the minimum value occurs multiple times, only the indices
corresponding to the first occurrence are returned.
Parameters
----------
x : SparseArray
Input array. The fill value must be ``0.0`` and all non-zero values
must be less than ``0.0``.
axis : int, optional
Axis along which to search. If ``None``, the function must return
the index of the minimum value of the flattened array. Default: ``None``.
keepdims : bool, optional
If ``True``, the reduced axes (dimensions) must be included in the result
as singleton dimensions, and, accordingly, the result must be compatible
with the input array. Otherwise, if ``False``, the reduced axes (dimensions)
must not be included in the result. Default: ``False``.
Returns
-------
out : numpy.ndarray
If ``axis`` is ``None``, a zero-dimensional array containing the index of
the first occurrence of the minimum value. Otherwise, a non-zero-dimensional
array containing the indices of the minimum values.
"""
return _arg_minmax_common(x, axis=axis, keepdims=keepdims, mode="min")
def _replace_nan(array, value):
"""
Replaces ``NaN``s in ``array`` with ``value``.
Parameters
----------
array : COO
The input array.
value : numpy.number
The values to replace ``NaN`` with.
Returns
-------
COO
A copy of ``array`` with the ``NaN``s replaced.
"""
if not np.issubdtype(array.dtype, np.floating):
return array
return where(np.isnan(array), value, array)
[docs]
def nanreduce(x, method, identity=None, axis=None, keepdims=False, **kwargs):
"""
Performs an ``NaN`` skipping reduction on this array. See the documentation
on :obj:`COO.reduce` for examples.
Parameters
----------
x : COO
The array to reduce.
method : numpy.ufunc
The method to use for performing the reduction.
identity : numpy.number
The identity value for this reduction. Inferred from ``method`` if not given.
Note that some ``ufunc`` objects don't have this, so it may be necessary to give it.
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.
Returns
-------
COO
The result of the reduction operation.
Raises
------
ValueError
If reducing an all-zero axis would produce a nonzero result.
See Also
--------
COO.reduce : Similar method without ``NaN`` skipping functionality.
"""
arr = _replace_nan(x, method.identity if identity is None else identity)
return arr.reduce(method, axis, keepdims, **kwargs)
[docs]
def roll(a, shift, axis=None):
"""
Shifts elements of an array along specified axis. Elements that roll beyond
the last position are circulated and re-introduced at the first.
Parameters
----------
a : COO
Input array
shift : int or tuple of ints
Number of index positions that elements are shifted. If a tuple is
provided, then axis must be a tuple of the same size, and each of the
given axes is shifted by the corresponding number. If an int while axis
is a tuple of ints, then broadcasting is used so the same shift is
applied to all axes.
axis : int or tuple of ints, optional
Axis or tuple specifying multiple axes. By default, the
array is flattened before shifting, after which the original shape is
restored.
Returns
-------
res : ndarray
Output array, with the same shape as a.
"""
from numpy.core._exceptions import UFuncTypeError
from .core import COO, as_coo
a = as_coo(a)
# roll flattened array
if axis is None:
return roll(a.reshape((-1,)), shift, 0).reshape(a.shape)
# roll across specified axis
# parse axis input, wrap in tuple
axis = normalize_axis(axis, a.ndim)
if not isinstance(axis, tuple):
axis = (axis,)
# make shift iterable
if not isinstance(shift, Iterable):
shift = (shift,)
elif np.ndim(shift) > 1:
raise ValueError("'shift' and 'axis' must be integers or 1D sequences.")
# handle broadcasting
if len(shift) == 1:
shift = np.full(len(axis), shift)
# check if dimensions are consistent
if len(axis) != len(shift):
raise ValueError("If 'shift' is a 1D sequence, 'axis' must have equal length.")
if not can_store(a.coords.dtype, max(a.shape + shift)):
raise ValueError(
f"cannot roll with coords.dtype {a.coords.dtype} and shift {shift}. Try casting coords to a larger dtype."
)
# shift elements
coords, data = np.copy(a.coords), np.copy(a.data)
try:
for sh, ax in zip(shift, axis, strict=True):
coords[ax] += sh
coords[ax] %= a.shape[ax]
except UFuncTypeError as e:
if is_unsigned_dtype(coords.dtype):
raise ValueError(
f"rolling with coords.dtype as {coords.dtype} is not safe. Try using a signed dtype."
) from e
return COO(
coords,
data=data,
shape=a.shape,
has_duplicates=False,
fill_value=a.fill_value,
)
[docs]
def diagonal(a, offset=0, axis1=0, axis2=1):
"""
Extract diagonal from a COO array. The equivalent of :obj:`numpy.diagonal`.
Parameters
----------
a : COO
The array to perform the operation on.
offset : int, optional
Offset of the diagonal from the main diagonal. Defaults to main diagonal (0).
axis1 : int, optional
First axis from which the diagonals should be taken.
Defaults to first axis (0).
axis2 : int, optional
Second axis from which the diagonals should be taken.
Defaults to second axis (1).
Examples
--------
>>> import sparse
>>> x = sparse.as_coo(np.arange(9).reshape(3, 3))
>>> sparse.diagonal(x).todense()
array([0, 4, 8])
>>> sparse.diagonal(x, offset=1).todense()
array([1, 5])
>>> x = sparse.as_coo(np.arange(12).reshape((2, 3, 2)))
>>> x_diag = sparse.diagonal(x, axis1=0, axis2=2)
>>> x_diag.shape
(3, 2)
>>> x_diag.todense()
array([[ 0, 7],
[ 2, 9],
[ 4, 11]])
Returns
-------
out: COO
The result of the operation.
Raises
------
ValueError
If a.shape[axis1] != a.shape[axis2]
See Also
--------
:obj:`numpy.diagonal` : NumPy equivalent function
"""
from .core import COO
if a.shape[axis1] != a.shape[axis2]:
raise ValueError("a.shape[axis1] != a.shape[axis2]")
diag_axes = [axis for axis in range(len(a.shape)) if axis != axis1 and axis != axis2] + [axis1]
diag_shape = [a.shape[axis] for axis in diag_axes]
diag_shape[-1] -= abs(offset)
diag_idx = _diagonal_idx(a.coords, axis1, axis2, offset)
diag_coords = [a.coords[axis][diag_idx] for axis in diag_axes]
diag_data = a.data[diag_idx]
return COO(diag_coords, diag_data, diag_shape)
[docs]
def diagonalize(a, axis=0):
"""
Diagonalize a COO array. The new dimension is appended at the end.
.. WARNING:: :obj:`diagonalize` is not :obj:`numpy` compatible as there is no direct :obj:`numpy` equivalent. The
API may change in the future.
Parameters
----------
a : Union[COO, np.ndarray, scipy.sparse.spmatrix]
The array to diagonalize.
axis : int, optional
The axis to diagonalize. Defaults to first axis (0).
Examples
--------
>>> import sparse
>>> x = sparse.as_coo(np.arange(1, 4))
>>> sparse.diagonalize(x).todense()
array([[1, 0, 0],
[0, 2, 0],
[0, 0, 3]])
>>> x = sparse.as_coo(np.arange(24).reshape((2, 3, 4)))
>>> x_diag = sparse.diagonalize(x, axis=1)
>>> x_diag.shape
(2, 3, 4, 3)
:obj:`diagonalize` is the inverse of :obj:`diagonal`
>>> a = sparse.random((3, 3, 3, 3, 3), density=0.3)
>>> a_diag = sparse.diagonalize(a, axis=2)
>>> (sparse.diagonal(a_diag, axis1=2, axis2=5) == a.transpose([0, 1, 3, 4, 2])).all()
True
Returns
-------
out: COO
The result of the operation.
See Also
--------
:obj:`numpy.diag` : NumPy equivalent for 1D array
"""
from .core import COO, as_coo
a = as_coo(a)
diag_shape = a.shape + (a.shape[axis],)
diag_coords = np.vstack([a.coords, a.coords[axis]])
return COO(diag_coords, a.data, diag_shape)
[docs]
def isposinf(x, out=None):
"""
Test element-wise for positive infinity, return result as sparse ``bool`` array.
Parameters
----------
x
Input
out, optional
Output array
Examples
--------
>>> import sparse
>>> x = sparse.as_coo(np.array([np.inf]))
>>> sparse.isposinf(x).todense()
array([ True])
See Also
--------
numpy.isposinf : The NumPy equivalent
"""
from .core import elemwise
return elemwise(lambda x, out=None, dtype=None: np.isposinf(x, out=out), x, out=out)
[docs]
def isneginf(x, out=None):
"""
Test element-wise for negative infinity, return result as sparse ``bool`` array.
Parameters
----------
x
Input
out, optional
Output array
Examples
--------
>>> import sparse
>>> x = sparse.as_coo(np.array([-np.inf]))
>>> sparse.isneginf(x).todense()
array([ True])
See Also
--------
numpy.isneginf : The NumPy equivalent
"""
from .core import elemwise
return elemwise(lambda x, out=None, dtype=None: np.isneginf(x, out=out), x, out=out)
[docs]
def result_type(*arrays_and_dtypes):
"""Returns the type that results from applying the NumPy type promotion rules to the
arguments.
See Also
--------
numpy.result_type : The NumPy equivalent
"""
return np.result_type(*(_as_result_type_arg(x) for x in arrays_and_dtypes))
def _as_result_type_arg(x):
if not isinstance(x, SparseArray):
return x
if x.ndim > 0:
return x.dtype
# 0-dimensional arrays give different result_type outputs than their dtypes
return x.todense()
@numba.jit(nopython=True, nogil=True)
def _diagonal_idx(coordlist, axis1, axis2, offset):
"""
Utility function that returns all indices that correspond to a diagonal element.
Parameters
----------
coordlist : list of lists
Coordinate indices.
axis1, axis2 : int
The axes of the diagonal.
offset : int
Offset of the diagonal from the main diagonal. Defaults to main diagonal (0).
"""
return np.array([i for i in range(len(coordlist[axis1])) if coordlist[axis1][i] + offset == coordlist[axis2][i]])
[docs]
def clip(a, a_min=None, a_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.
Parameters
----------
a
a_min : scalar or `SparseArray` or `None`
Minimum value. If `None`, clipping is not performed on lower
interval edge.
a_max : scalar or `SparseArray` or `None`
Maximum value. If `None`, clipping is not performed on upper
interval edge.
out : SparseArray, optional
If provided, the results will be placed in this array. It may be
the input array for in-place clipping. `out` must be of the right
shape to hold the output. Its type is preserved.
Returns
-------
clipped_array : SparseArray
An array with the elements of `self`, but where values < `min` are
replaced with `min`, and those > `max` with `max`.
Examples
--------
>>> import sparse
>>> x = sparse.COO.from_numpy([0, 0, 0, 1, 2, 3])
>>> sparse.clip(x, a_min=1).todense() # doctest: +NORMALIZE_WHITESPACE
array([1, 1, 1, 1, 2, 3])
>>> sparse.clip(x, a_max=1).todense() # doctest: +NORMALIZE_WHITESPACE
array([0, 0, 0, 1, 1, 1])
>>> sparse.clip(x, a_min=1, a_max=2).todense() # doctest: +NORMALIZE_WHITESPACE
array([1, 1, 1, 1, 2, 2])
See Also
--------
numpy.clip : Equivalent NumPy function
"""
a = asCOO(a, name="clip")
return a.clip(a_min, a_max)
[docs]
def expand_dims(x, /, *, axis=0):
"""
Expands the shape of an array by inserting a new axis (dimension) of size
one at the position specified by ``axis``.
Parameters
----------
a : COO
Input COO array.
axis : int
Position in the expanded axes where the new axis is placed.
Returns
-------
result : COO
An expanded output COO array having the same data type as ``x``.
Examples
--------
>>> import sparse
>>> x = sparse.COO.from_numpy([[1, 0, 0, 0, 2, -3]])
>>> x.shape
(1, 6)
>>> y1 = sparse.expand_dims(x, axis=1)
>>> y1.shape
(1, 1, 6)
>>> y2 = sparse.expand_dims(x, axis=2)
>>> y2.shape
(1, 6, 1)
"""
x = _validate_coo_input(x)
if not isinstance(axis, int):
raise IndexError(f"Invalid axis position: {axis}")
axis = normalize_axis(axis, x.ndim + 1)
new_coords = np.insert(x.coords, obj=axis, values=np.zeros(x.nnz, dtype=np.intp), axis=0)
new_shape = list(x.shape)
new_shape.insert(axis, 1)
new_shape = tuple(new_shape)
from .core import COO
return COO(
new_coords,
x.data,
shape=new_shape,
fill_value=x.fill_value,
)
[docs]
def flip(x, /, *, axis=None):
"""
Reverses the order of elements in an array along the given axis.
The shape of the array is preserved.
Parameters
----------
a : COO
Input COO array.
axis : int or tuple of ints, optional
Axis (or axes) along which to flip. If ``axis`` is ``None``, the function must
flip all input array axes. If ``axis`` is negative, the function must count from
the last dimension. If provided more than one axis, the function must flip only
the specified axes. Default: ``None``.
Returns
-------
result : COO
An output array having the same data type and shape as ``x`` and whose elements,
relative to ``x``, are reordered.
"""
x = _validate_coo_input(x)
if axis is None:
axis = range(x.ndim)
if not isinstance(axis, Iterable):
axis = (axis,)
new_coords = x.coords.copy()
for ax in axis:
new_coords[ax, :] = x.shape[ax] - 1 - x.coords[ax, :]
from .core import COO
return COO(
new_coords,
x.data,
shape=x.shape,
fill_value=x.fill_value,
)
# Array API set functions
class UniqueCountsResult(NamedTuple):
values: np.ndarray
counts: np.ndarray
[docs]
def unique_counts(x, /):
"""
Returns the unique elements of an input array `x`, and the corresponding
counts for each unique element in `x`.
Parameters
----------
x : COO
Input COO array. It will be flattened if it is not already 1-D.
Returns
-------
out : namedtuple
The result containing:
* values - The unique elements of an input array.
* counts - The corresponding counts for each unique element.
Raises
------
ValueError
If the input array is in a different format than COO.
Examples
--------
>>> import sparse
>>> x = sparse.COO.from_numpy([1, 0, 2, 1, 2, -3])
>>> sparse.unique_counts(x)
UniqueCountsResult(values=array([-3, 0, 1, 2]), counts=array([1, 1, 2, 2]))
"""
x = _validate_coo_input(x)
x = x.flatten()
values, counts = np.unique(x.data, return_counts=True)
if x.nnz < x.size:
values = np.concatenate([[x.fill_value], values])
counts = np.concatenate([[x.size - x.nnz], counts])
sorted_indices = np.argsort(values)
values[sorted_indices] = values.copy()
counts[sorted_indices] = counts.copy()
return UniqueCountsResult(values, counts)
[docs]
def unique_values(x, /):
"""
Returns the unique elements of an input array `x`.
Parameters
----------
x : COO
Input COO array. It will be flattened if it is not already 1-D.
Returns
-------
out : ndarray
The unique elements of an input array.
Raises
------
ValueError
If the input array is in a different format than COO.
Examples
--------
>>> import sparse
>>> x = sparse.COO.from_numpy([1, 0, 2, 1, 2, -3])
>>> sparse.unique_values(x)
array([-3, 0, 1, 2])
"""
x = _validate_coo_input(x)
x = x.flatten()
values = np.unique(x.data)
if x.nnz < x.size:
values = np.sort(np.concatenate([[x.fill_value], values]))
return values
[docs]
def sort(x, /, *, axis=-1, descending=False):
"""
Returns a sorted copy of an input array ``x``.
Parameters
----------
x : SparseArray
Input array. Should have a real-valued data type.
axis : int
Axis along which to sort. If set to ``-1``, the function must sort along
the last axis. Default: ``-1``.
descending : bool
Sort order. If ``True``, the array must be sorted in descending order (by value).
If ``False``, the array must be sorted in ascending order (by value).
Default: ``False``.
Returns
-------
out : COO
A sorted array.
Raises
------
ValueError
If the input array isn't and can't be converted to COO format.
Examples
--------
>>> import sparse
>>> x = sparse.COO.from_numpy([1, 0, 2, 0, 2, -3])
>>> sparse.sort(x).todense()
array([-3, 0, 0, 1, 2, 2])
>>> sparse.sort(x, descending=True).todense()
array([ 2, 2, 1, 0, 0, -3])
"""
from .._common import moveaxis
from .core import COO
x = _validate_coo_input(x)
original_ndim = x.ndim
if x.ndim == 1:
x = x[None, :]
axis = -1
x = moveaxis(x, source=axis, destination=-1)
x_shape = x.shape
x = x.reshape((-1, x_shape[-1]))
new_coords, new_data = _sort_coo(x.coords, x.data, x.fill_value, sort_axis_len=x_shape[-1], descending=descending)
x = COO(new_coords, new_data, x.shape, has_duplicates=False, sorted=True, fill_value=x.fill_value)
x = x.reshape(x_shape[:-1] + (x_shape[-1],))
x = moveaxis(x, source=-1, destination=axis)
return x if original_ndim == x.ndim else x.squeeze()
[docs]
def take(x, indices, /, *, axis=None):
"""
Returns elements of an array along an axis.
Parameters
----------
x : SparseArray
Input array.
indices : ndarray
Array indices. The array must be one-dimensional and have an integer data type.
axis : int
Axis over which to select values. If ``axis`` is negative, the function must
determine the axis along which to select values by counting from the last dimension.
For ``None``, the flattened input array is used. Default: ``None``.
Returns
-------
out : COO
A COO array with requested indices.
Raises
------
ValueError
If the input array isn't and can't be converted to COO format.
"""
x = _validate_coo_input(x)
if axis is None:
x = x.flatten()
return x[indices]
axis = normalize_axis(axis, x.ndim)
full_index = (slice(None),) * axis + (indices, ...)
return x[full_index]
def _validate_coo_input(x: Any):
from .._common import _is_scipy_sparse_obj
from .core import COO
if _is_scipy_sparse_obj(x):
x = COO.from_scipy_sparse(x)
elif not isinstance(x, SparseArray):
raise ValueError(f"Input must be an instance of SparseArray, but it's {type(x)}.")
elif not isinstance(x, COO):
x = x.asformat(COO)
return x
@numba.jit(nopython=True, nogil=True)
def _sort_coo(
coords: np.ndarray,
data: np.ndarray,
fill_value: float,
sort_axis_len: int,
descending: bool,
) -> tuple[np.ndarray, np.ndarray]:
assert coords.shape[0] == 2
group_coords = coords[0, :]
sort_coords = coords[1, :]
data = data.copy()
result_indices = np.empty_like(sort_coords)
# We iterate through all groups and sort each one of them.
# first and last index of a group is tracked.
prev_group = -1
group_first_idx = -1
group_last_idx = -1
# We add `-1` sentinel to know when the last group ends
for idx, group in enumerate(np.append(group_coords, -1)):
if group == prev_group:
continue
if prev_group != -1:
group_last_idx = idx
group_slice = slice(group_first_idx, group_last_idx)
group_size = group_last_idx - group_first_idx
# SORT VALUES
if group_size > 1:
# np.sort in numba doesn't support `np.sort`'s arguments so `stable`
# keyword can't be supported.
# https://numba.pydata.org/numba-doc/latest/reference/numpysupported.html#other-methods
data[group_slice] = np.sort(data[group_slice])
if descending:
data[group_slice] = data[group_slice][::-1]
# SORT INDICES
fill_value_count = sort_axis_len - group_size
indices = np.arange(group_size)
# find a place where fill_value would be
for pos in range(group_size):
if (not descending and fill_value < data[group_slice][pos]) or (
descending and fill_value > data[group_slice][pos]
):
indices[pos:] += fill_value_count
break
result_indices[group_first_idx:group_last_idx] = indices
prev_group = group
group_first_idx = idx
return np.vstack((group_coords, result_indices)), data
@numba.jit(nopython=True, nogil=True)
def _compute_minmax_args(
coords: np.ndarray,
data: np.ndarray,
reduce_size: int,
fill_value: float,
max_mode_flag: bool,
) -> tuple[np.ndarray, np.ndarray]:
assert coords.shape[0] == 2
reduce_coords = coords[0, :]
index_coords = coords[1, :]
result_indices = np.unique(index_coords)
result_data = []
# we iterate through each trace
for result_index in np.nditer(result_indices):
mask = index_coords == result_index
masked_reduce_coords = reduce_coords[mask]
masked_data = data[mask]
compared_data = operator.gt(masked_data, fill_value) if max_mode_flag else operator.lt(masked_data, fill_value)
if np.any(compared_data) or len(masked_data) == reduce_size:
# best value is a non-fill value
best_arg = np.argmax(masked_data) if max_mode_flag else np.argmin(masked_data)
result_data.append(masked_reduce_coords[best_arg])
else:
# best value is a fill value, find the first occurrence of it
current_coord = np.array(-1, dtype=coords.dtype)
found = False
for idx, new_coord in enumerate(np.nditer(np.sort(masked_reduce_coords))):
# there is at least one fill value between consecutive non-fill values
if new_coord - current_coord > 1:
result_data.append(idx)
found = True
break
current_coord = new_coord
# get the first fill value after all non-fill values
if not found:
result_data.append(current_coord + 1)
return (result_indices, result_data)
def _arg_minmax_common(
x: SparseArray,
axis: int | None,
keepdims: bool,
mode: str,
):
"""
Internal implementation for argmax and argmin functions.
"""
assert mode in ("max", "min")
max_mode_flag = mode == "max"
x = _validate_coo_input(x)
if not isinstance(axis, int | type(None)):
raise ValueError(f"`axis` must be `int` or `None`, but it's: {type(axis)}.")
if isinstance(axis, int) and axis >= x.ndim:
raise ValueError(f"`axis={axis}` is out of bounds for array of dimension {x.ndim}.")
if x.ndim == 0:
raise ValueError("Input array must be at least 1-D, but it's 0-D.")
# If `axis` is None then we need to flatten the input array and memorize
# the original dimensionality for the final reshape operation.
axis_none_original_ndim: int | None = None
if axis is None:
axis_none_original_ndim = x.ndim
x = x.reshape(-1)[:, None]
axis = 0
# A 1-D array must have one more singleton dimension.
if axis == 0 and x.ndim == 1:
x = x[:, None]
# We need to move `axis` to the front.
new_transpose = list(range(x.ndim))
new_transpose.insert(0, new_transpose.pop(axis))
new_transpose = tuple(new_transpose)
# And reshape it to 2-D (reduce axis, the rest of axes flattened)
new_shape = list(x.shape)
new_shape.insert(0, new_shape.pop(axis))
new_shape = tuple(new_shape)
x = x.transpose(new_transpose)
x = x.reshape((new_shape[0], np.prod(new_shape[1:])))
# Compute max/min arguments
result_indices, result_data = _compute_minmax_args(
x.coords.copy(),
x.data.copy(),
reduce_size=x.shape[0],
fill_value=x.fill_value,
max_mode_flag=max_mode_flag,
)
from .core import COO
result = COO(result_indices, result_data, shape=(x.shape[1],), fill_value=0, prune=True)
# Let's reshape the result to the original shape.
result = result.reshape((1, *new_shape[1:]))
new_transpose = list(range(result.ndim))
new_transpose.insert(axis, new_transpose.pop(0))
result = result.transpose(new_transpose)
# If `axis=None` we need to reshape flattened array into original dimensionality.
if axis_none_original_ndim is not None:
result = result.reshape([1 for _ in range(axis_none_original_ndim)])
return result if keepdims else result.squeeze()
[docs]
def matrix_transpose(x, /):
"""
Transposes a matrix or a stack of matrices.
Parameters
----------
x : SparseArray
Input array.
Returns
-------
out : COO
Transposed COO array.
Raises
------
ValueError
If the input array isn't and can't be converted to COO format, or if ``x.ndim < 2``.
"""
if hasattr(x, "ndim") and x.ndim < 2:
raise ValueError("`x.ndim >= 2` must hold.")
x = _validate_coo_input(x)
transpose_axes = list(range(x.ndim))
transpose_axes[-2:] = transpose_axes[-2:][::-1]
return x.transpose(transpose_axes)