from functools import reduce, wraps
import operator
import warnings
from collections import Iterable
import numpy as np
import scipy.sparse
import numba
from ..sparse_array import SparseArray
from ..compatibility import range, int
from ..utils import isscalar, normalize_axis, check_zero_fill_value, check_consistent_fill_value
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 .core import COO
if check and not isinstance(x, (SparseArray, scipy.sparse.spmatrix)):
raise ValueError('Performing this operation would produce a dense result: %s' % name)
if not isinstance(x, COO):
x = COO(x)
return x
def linear_loc(coords, shape):
out = np.zeros(coords.shape[1], dtype=np.intp)
tmp = np.zeros(coords.shape[1], dtype=np.intp)
strides = int(1)
for i, d in enumerate(shape[::-1]):
np.multiply(coords[-(i + 1), :], strides, out=tmp)
np.add(tmp, out, out=out)
strides *= d
return out
[docs]def tensordot(a, b, axes=2):
"""
Perform the equivalent of :obj:`numpy.tensordot`.
Parameters
----------
a, b : Union[COO, np.ndarray, scipy.sparse.spmatrix]
The arrays to perform the :code:`tensordot` operation on.
axes : tuple[Union[int, tuple[int], Union[int, tuple[int]], optional
The axes to match when performing the sum.
Returns
-------
Union[COO, numpy.ndarray]
The result of the operation.
Raises
------
ValueError
If all arguments don't have zero fill-values.
See Also
--------
numpy.tensordot : NumPy equivalent function
"""
# Much of this is stolen from numpy/core/numeric.py::tensordot
# Please see license at https://github.com/numpy/numpy/blob/master/LICENSE.txt
check_zero_fill_value(a, b)
if scipy.sparse.issparse(a):
a = asCOO(a)
if scipy.sparse.issparse(b):
b = asCOO(b)
try:
iter(axes)
except TypeError:
axes_a = list(range(-axes, 0))
axes_b = list(range(0, axes))
else:
axes_a, axes_b = axes
try:
na = len(axes_a)
axes_a = list(axes_a)
except TypeError:
axes_a = [axes_a]
na = 1
try:
nb = len(axes_b)
axes_b = list(axes_b)
except TypeError:
axes_b = [axes_b]
nb = 1
# a, b = asarray(a), asarray(b) # <--- modified
as_ = a.shape
nda = a.ndim
bs = b.shape
ndb = b.ndim
equal = True
if na != nb:
equal = False
else:
for k in range(na):
if as_[axes_a[k]] != bs[axes_b[k]]:
equal = False
break
if axes_a[k] < 0:
axes_a[k] += nda
if axes_b[k] < 0:
axes_b[k] += ndb
if not equal:
raise ValueError("shape-mismatch for sum")
# Move the axes to sum over to the end of "a"
# and to the front of "b"
notin = [k for k in range(nda) if k not in axes_a]
newaxes_a = notin + axes_a
N2 = 1
for axis in axes_a:
N2 *= as_[axis]
newshape_a = (-1, N2)
olda = [as_[axis] for axis in notin]
notin = [k for k in range(ndb) if k not in axes_b]
newaxes_b = axes_b + notin
N2 = 1
for axis in axes_b:
N2 *= bs[axis]
newshape_b = (N2, -1)
oldb = [bs[axis] for axis in notin]
at = a.transpose(newaxes_a).reshape(newshape_a)
bt = b.transpose(newaxes_b).reshape(newshape_b)
res = _dot(at, bt)
return res.reshape(olda + oldb)
[docs]def matmul(a, b):
"""Perform the equivalent of :obj:`numpy.matmul` on two arrays.
Parameters
----------
a, b : Union[COO, np.ndarray, scipy.sparse.spmatrix]
The arrays to perform the :code:`matmul` operation on.
Returns
-------
Union[COO, numpy.ndarray]
The result of the operation.
Raises
------
ValueError
If all arguments don't have zero fill-values, or the shape of the two arrays is not broadcastable.
See Also
--------
numpy.matmul : NumPy equivalent function.
COO.__matmul__ : Equivalent function for COO objects.
"""
check_zero_fill_value(a, b)
if not hasattr(a, 'ndim') or not hasattr(b, 'ndim'):
raise TypeError(
"Cannot perform dot product on types %s, %s" %
(type(a), type(b)))
# When b is 2-d, it is equivalent to dot
if b.ndim <= 2:
return dot(a, b)
# when a is 2-d, we need to transpose result after dot
if a.ndim <= 2:
res = dot(a, b)
axes = list(range(res.ndim))
axes.insert(-1, axes.pop(0))
return res.transpose(axes)
# If a can be squeeze to a vector, use dot will be faster
if a.ndim <= b.ndim and np.prod(a.shape[:-1]) == 1:
res = dot(a.reshape(-1), b)
shape = list(res.shape)
shape.insert(-1, 1)
return res.reshape(shape)
# If b can be squeeze to a matrix, use dot will be faster
if b.ndim <= a.ndim and np.prod(b.shape[:-2]) == 1:
return dot(a, b.reshape(b.shape[-2:]))
if a.ndim < b.ndim:
a = a[(None,) * (b.ndim - a.ndim)]
if a.ndim > b.ndim:
b = b[(None,) * (a.ndim - b.ndim)]
for i, j in zip(a.shape[:-2], b.shape[:-2]):
if i != 1 and j != 1 and i != j:
raise ValueError('shapes of a and b are not broadcastable')
def _matmul_recurser(a, b):
if a.ndim == 2:
return dot(a, b)
res = []
for i in range(max(a.shape[0], b.shape[0])):
a_i = a[0] if a.shape[0] == 1 else a[i]
b_i = b[0] if b.shape[0] == 1 else b[i]
res.append(_matmul_recurser(a_i, b_i))
mask = [isinstance(x, SparseArray) for x in res]
if all(mask):
return stack(res)
else:
res = [x.todense() if isinstance(x, SparseArray) else x
for x in res]
return np.stack(res)
return _matmul_recurser(a, b)
[docs]def dot(a, b):
"""
Perform the equivalent of :obj:`numpy.dot` on two arrays.
Parameters
----------
a, b : Union[COO, np.ndarray, scipy.sparse.spmatrix]
The arrays to perform the :code:`dot` operation on.
Returns
-------
Union[COO, numpy.ndarray]
The result of the operation.
Raises
------
ValueError
If all arguments don't have zero fill-values.
See Also
--------
numpy.dot : NumPy equivalent function.
COO.dot : Equivalent function for COO objects.
"""
check_zero_fill_value(a, b)
if not hasattr(a, 'ndim') or not hasattr(b, 'ndim'):
raise TypeError(
"Cannot perform dot product on types %s, %s" %
(type(a), type(b)))
if a.ndim == 1 and b.ndim == 1:
return (a * b).sum()
a_axis = -1
b_axis = -2
if b.ndim == 1:
b_axis = -1
return tensordot(a, b, axes=(a_axis, b_axis))
def _dot(a, b):
from .core import COO
out_shape = (a.shape[0], b.shape[1])
if isinstance(a, COO) and isinstance(b, COO):
b = b.T
coords, data = _dot_coo_coo_type(a.dtype, b.dtype)(a.coords, a.data, b.coords, b.data)
return COO(coords, data, shape=out_shape, has_duplicates=False, sorted=True)
if isinstance(a, COO) and isinstance(b, np.ndarray):
b = b.view(type=np.ndarray).T
return _dot_coo_ndarray_type(a.dtype, b.dtype)(a.coords, a.data, b, out_shape)
if isinstance(a, np.ndarray) and isinstance(b, COO):
b = b.T
a = a.view(type=np.ndarray)
return _dot_ndarray_coo_type(a.dtype, b.dtype)(a, b.coords, b.data, out_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
--------
>>> 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 .core import COO
from .umath import _cartesian_product
check_zero_fill_value(a, b)
a_sparse = isinstance(a, (SparseArray, scipy.sparse.spmatrix))
b_sparse = isinstance(b, (SparseArray, scipy.sparse.spmatrix))
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))
return COO(o_coords, o_data, shape=o_shape, has_duplicates=False)
[docs]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)
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)
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)
[docs]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(set(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
dim = 0
new = np.empty(shape=(coords.shape[1],), dtype=np.intp)
for x in arrays:
new[nnz:x.nnz + nnz] = dim
dim += 1
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):
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)
[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):
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)
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
----------
x : 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 .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
else:
# 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.")
# shift elements
coords, data = np.copy(a.coords), np.copy(a.data)
for sh, ax in zip(shift, axis):
coords[ax] += sh
coords[ax] %= a.shape[ax]
return COO(coords, data=data, shape=a.shape, has_duplicates=False, fill_value=a.fill_value)
[docs]def eye(N, M=None, k=0, dtype=float):
"""Return a 2-D COO array with ones on the diagonal and zeros elsewhere.
Parameters
----------
N : int
Number of rows in the output.
M : int, optional
Number of columns in the output. If None, defaults to `N`.
k : int, optional
Index of the diagonal: 0 (the default) refers to the main diagonal,
a positive value refers to an upper diagonal, and a negative value
to a lower diagonal.
dtype : data-type, optional
Data-type of the returned array.
Returns
-------
I : COO array of shape (N, M)
An array where all elements are equal to zero, except for the `k`-th
diagonal, whose values are equal to one.
Examples
--------
>>> eye(2, dtype=int).todense() # doctest: +NORMALIZE_WHITESPACE
array([[1, 0],
[0, 1]])
>>> eye(3, k=1).todense() # doctest: +SKIP
array([[0., 1., 0.],
[0., 0., 1.],
[0., 0., 0.]])
"""
from .core import COO
if M is None:
M = N
N = int(N)
M = int(M)
k = int(k)
data_length = min(N, M)
if k > 0:
data_length = max(min(data_length, M - k), 0)
n_coords = np.arange(data_length, dtype=np.intp)
m_coords = n_coords + k
elif k < 0:
data_length = max(min(data_length, N + k), 0)
m_coords = np.arange(data_length, dtype=np.intp)
n_coords = m_coords - k
else:
n_coords = m_coords = np.arange(data_length, dtype=np.intp)
coords = np.stack([n_coords, m_coords])
data = np.array(1, dtype=dtype)
return COO(coords, data=data, shape=(N, M), has_duplicates=False,
sorted=True)
[docs]def full(shape, fill_value, dtype=None):
"""Return a COO array of given shape and type, filled with `fill_value`.
Parameters
----------
shape : int or tuple of ints
Shape of the new array, e.g., ``(2, 3)`` or ``2``.
fill_value : scalar
Fill value.
dtype : data-type, optional
The desired data-type for the array. The default, `None`, means
`np.array(fill_value).dtype`.
Returns
-------
out : COO
Array of `fill_value` with the given shape and dtype.
Examples
--------
>>> full(5, 9).todense() # doctest: +NORMALIZE_WHITESPACE
array([9, 9, 9, 9, 9])
>>> full((2, 2), 9, dtype=float).todense() # doctest: +SKIP
array([[9., 9.],
[9., 9.]])
"""
from .core import COO
if dtype is None:
dtype = np.array(fill_value).dtype
if not isinstance(shape, tuple):
shape = (shape,)
data = np.empty(0, dtype=dtype)
coords = np.empty((len(shape), 0), dtype=np.intp)
return COO(coords, data=data, shape=shape,
fill_value=fill_value, has_duplicates=False,
sorted=True)
[docs]def full_like(a, fill_value, dtype=None):
"""Return a full array with the same shape and type as a given array.
Parameters
----------
a : array_like
The shape and data-type of the result will match those of `a`.
dtype : data-type, optional
Overrides the data type of the result.
Returns
-------
out : COO
Array of `fill_value` with the same shape and type as `a`.
Examples
--------
>>> x = np.ones((2, 3), dtype='i8')
>>> full_like(x, 9.0).todense() # doctest: +NORMALIZE_WHITESPACE
array([[9, 9, 9],
[9, 9, 9]])
"""
return full(a.shape, fill_value, dtype=(a.dtype if dtype is None else dtype))
[docs]def zeros(shape, dtype=float):
"""Return a COO array of given shape and type, filled with zeros.
Parameters
----------
shape : int or tuple of ints
Shape of the new array, e.g., ``(2, 3)`` or ``2``.
dtype : data-type, optional
The desired data-type for the array, e.g., `numpy.int8`. Default is
`numpy.float64`.
Returns
-------
out : COO
Array of zeros with the given shape and dtype.
Examples
--------
>>> zeros(5).todense() # doctest: +SKIP
array([0., 0., 0., 0., 0.])
>>> zeros((2, 2), dtype=int).todense() # doctest: +NORMALIZE_WHITESPACE
array([[0, 0],
[0, 0]])
"""
return full(shape, 0, np.dtype(dtype))
[docs]def zeros_like(a, dtype=None):
"""Return a COO array of zeros with the same shape and type as ``a``.
Parameters
----------
a : array_like
The shape and data-type of the result will match those of `a`.
dtype : data-type, optional
Overrides the data type of the result.
Returns
-------
out : COO
Array of zeros with the same shape and type as `a`.
Examples
--------
>>> x = np.ones((2, 3), dtype='i8')
>>> zeros_like(x).todense() # doctest: +NORMALIZE_WHITESPACE
array([[0, 0, 0],
[0, 0, 0]])
"""
return zeros(a.shape, dtype=(a.dtype if dtype is None else dtype))
[docs]def ones(shape, dtype=float):
"""Return a COO array of given shape and type, filled with ones.
Parameters
----------
shape : int or tuple of ints
Shape of the new array, e.g., ``(2, 3)`` or ``2``.
dtype : data-type, optional
The desired data-type for the array, e.g., `numpy.int8`. Default is
`numpy.float64`.
Returns
-------
out : COO
Array of ones with the given shape and dtype.
Examples
--------
>>> ones(5).todense() # doctest: +SKIP
array([1., 1., 1., 1., 1.])
>>> ones((2, 2), dtype=int).todense() # doctest: +NORMALIZE_WHITESPACE
array([[1, 1],
[1, 1]])
"""
return full(shape, 1, np.dtype(dtype))
[docs]def ones_like(a, dtype=None):
"""Return a COO array of ones with the same shape and type as ``a``.
Parameters
----------
a : array_like
The shape and data-type of the result will match those of `a`.
dtype : data-type, optional
Overrides the data type of the result.
Returns
-------
out : COO
Array of ones with the same shape and type as `a`.
Examples
--------
>>> x = np.ones((2, 3), dtype='i8')
>>> ones_like(x).todense() # doctest: +NORMALIZE_WHITESPACE
array([[1, 1, 1],
[1, 1, 1]])
"""
return ones(a.shape, dtype=(a.dtype if dtype is None else dtype))
def _memoize_dtype(f):
"""
Memoizes a function taking in NumPy dtypes.
Parameters
----------
f : Callable
Returns
-------
wrapped : Callable
Examples
--------
>>> def func(dt1):
... return object()
>>> func = _memoize_dtype(func)
>>> func(np.dtype('i8')) is func(np.dtype('int64'))
True
>>> func(np.dtype('i8')) is func(np.dtype('i4'))
False
"""
cache = {}
@wraps(f)
def wrapped(*args):
key = tuple(arg.name for arg in args)
if key in cache:
return cache[key]
result = f(*args)
cache[key] = result
return result
return wrapped
@_memoize_dtype
def _dot_coo_coo_type(dt1, dt2):
dtr = np.result_type(dt1, dt2)
@numba.jit(nopython=True, nogil=True,
locals={'data_curr': numba.numpy_support.from_dtype(dtr)})
def _dot_coo_coo(coords1, data1, coords2, data2): # pragma: no cover
"""
Utility function taking in two ``COO`` objects and calculating a "sense"
of their dot product. Acually computes ``s1 @ s2.T``.
Parameters
----------
data1, coords1 : np.ndarray
The data and coordinates of ``s1``.
data2, coords2 : np.ndarray
The data and coordinates of ``s2``.
"""
coords_out = []
data_out = []
didx1 = 0
while didx1 < len(data1):
oidx1 = coords1[0, didx1]
didx2 = 0
didx1_curr = didx1
while didx2 < len(data2) and didx1 < len(data1) and coords1[0, didx1] == oidx1:
oidx2 = coords2[0, didx2]
data_curr = 0
while didx2 < len(data2) and didx1 < len(data1) and \
coords2[0, didx2] == oidx2 and coords1[0, didx1] == oidx1:
if coords1[1, didx1] < coords2[1, didx2]:
didx1 += 1
elif coords1[1, didx1] > coords2[1, didx2]:
didx2 += 1
else:
data_curr += data1[didx1] * data2[didx2]
didx1 += 1
didx2 += 1
while didx2 < len(data2) and coords2[0, didx2] == oidx2:
didx2 += 1
if didx2 < len(data2):
didx1 = didx1_curr
if data_curr != 0:
coords_out.append((oidx1, oidx2))
data_out.append(data_curr)
while didx1 < len(data1) and coords1[0, didx1] == oidx1:
didx1 += 1
if len(data_out) == 0:
return np.empty((2, 0), dtype=np.intp), np.empty((0,), dtype=dtr)
return np.array(coords_out).T, np.array(data_out)
return _dot_coo_coo
@_memoize_dtype
def _dot_coo_ndarray_type(dt1, dt2):
dtr = np.result_type(dt1, dt2)
@numba.jit(nopython=True, nogil=True)
def _dot_coo_ndarray(coords1, data1, array2, out_shape): # pragma: no cover
"""
Utility function taking in one `COO` and one ``ndarray`` and
calculating a "sense" of their dot product. Acually computes
``s1 @ x2.T``.
Parameters
----------
data1, coords1 : np.ndarray
The data and coordinates of ``s1``.
array2 : np.ndarray
The second input array ``x2``.
out_shape : Tuple[int]
The output shape.
"""
out = np.zeros(out_shape, dtype=dtr)
didx1 = 0
while didx1 < len(data1):
oidx1 = coords1[0, didx1]
didx1_curr = didx1
for oidx2 in range(out_shape[1]):
didx1 = didx1_curr
while didx1 < len(data1) and coords1[0, didx1] == oidx1:
out[oidx1, oidx2] += data1[didx1] * array2[oidx2, coords1[1, didx1]]
didx1 += 1
return out
return _dot_coo_ndarray
@_memoize_dtype
def _dot_ndarray_coo_type(dt1, dt2):
dtr = np.result_type(dt1, dt2)
@numba.jit(nopython=True, nogil=True)
def _dot_ndarray_coo(array1, coords2, data2, out_shape): # pragma: no cover
"""
Utility function taking in two one ``ndarray`` and one ``COO`` and
calculating a "sense" of their dot product. Acually computes ``x1 @ s2.T``.
Parameters
----------
array1 : np.ndarray
The input array ``x1``.
data2, coords2 : np.ndarray
The data and coordinates of ``s2``.
out_shape : Tuple[int]
The output shape.
"""
out = np.zeros(out_shape, dtype=dtr)
for oidx1 in range(out_shape[0]):
for didx2 in range(len(data2)):
oidx2 = coords2[0, didx2]
out[oidx1, oidx2] += array1[oidx1, coords2[1, didx2]] * data2[didx2]
return out
return _dot_ndarray_coo