import functools
import operator
from collections.abc import Iterable
from functools import reduce
from numbers import Integral
import numba
import numpy as np
def assert_eq(x, y, check_nnz=True, compare_dtype=True, **kwargs):
from ._coo import COO
assert x.shape == y.shape
if compare_dtype:
assert x.dtype == y.dtype
check_equal = (
np.array_equal
if (np.issubdtype(x.dtype, np.integer) and np.issubdtype(y.dtype, np.integer))
or (np.issubdtype(x.dtype, np.flexible) and np.issubdtype(y.dtype, np.flexible))
else functools.partial(np.allclose, equal_nan=True)
)
if isinstance(x, COO):
assert is_canonical(x)
if isinstance(y, COO):
assert is_canonical(y)
if isinstance(x, COO) and isinstance(y, COO) and check_nnz:
assert np.array_equal(x.coords, y.coords)
assert check_equal(x.data, y.data, **kwargs)
assert x.fill_value == y.fill_value
return
if hasattr(x, "todense"):
xx = x.todense()
if check_nnz:
assert_nnz(x, xx)
else:
xx = x
if hasattr(y, "todense"):
yy = y.todense()
if check_nnz:
assert_nnz(y, yy)
else:
yy = y
assert check_equal(xx, yy, **kwargs)
def assert_gcxs_slicing(s, x):
"""
Util function to test slicing of GCXS matrices after product multiplication.
For simplicity, it tests only tensors with number of dimension = 3.
Parameters
----------
s: sparse product matrix
x: dense product matrix
"""
rng = np.random.default_rng()
row = rng.integers(s.shape[s.ndim - 2])
assert np.allclose(s[0][row].data, [num for num in x[0][row] if num != 0])
# regression test
col = s.shape[s.ndim - 1]
for i in range(len(s.indices) // col):
j = col * i
k = col * (1 + i)
s.data[j:k] = s.data[j:k][::-1]
s.indices[j:k] = s.indices[j:k][::-1]
assert np.array_equal(s[0][row].data, np.array([]))
def assert_nnz(s, x):
fill_value = s.fill_value if hasattr(s, "fill_value") else _zero_of_dtype(s.dtype)
assert np.sum(~equivalent(x, fill_value)) == s.nnz
def is_canonical(x):
return not x.shape or ((np.diff(x.linear_loc()) > 0).all() and not equivalent(x.data, x.fill_value).any())
def _zero_of_dtype(dtype):
"""
Creates a ()-shaped 0-dimensional zero array of a given dtype.
Parameters
----------
dtype : numpy.dtype
The dtype for the array.
Returns
-------
np.ndarray
The zero array.
"""
return np.zeros((), dtype=dtype)[()]
@numba.jit(nopython=True, nogil=True)
def algD(n, N, random_state):
"""
Random Sampling without Replacement
Alg D proposed by J.S. Vitter in Faster Methods for Random Sampling
Parameters:
n = sample size (nnz)
N = size of system (elements)
random_state = seed for random number generation
"""
n = np.int64(n + 1)
N = np.int64(N)
qu1 = N - n + 1
Vprime = np.exp(np.log(random_state.random()) / n)
i = 0
arr = np.zeros(n - 1, dtype=np.int64)
arr[-1] = -1
while n > 1:
nmin1inv = 1 / (n - 1)
while True:
while True:
X = N * (1 - Vprime)
S = np.int64(X)
if qu1 > S:
break
Vprime = np.exp(np.log(random_state.random()) / n)
y1 = np.exp(np.log(random_state.random() * N / qu1) * nmin1inv)
Vprime = y1 * (1 - X / N) * (qu1 / (qu1 - S))
if Vprime <= 1:
break
y2 = 1
top = N - 1
if n - 1 > S:
bottom = N - n
limit = N - S
else:
bottom = N - S - 1
limit = qu1
t = N - 1
while t >= limit:
y2 *= top / bottom
top -= 1
bottom -= 1
t -= 1
if y1 * np.exp(np.log(y2) / nmin1inv) <= N / (N - X):
Vprime = np.exp(np.log(random_state.random()) * nmin1inv)
break
Vprime = np.exp(np.log(random_state.random()) / n)
arr[i] = arr[i - 1] + S + 1
i += 1
N = N - S - 1
n -= 1
qu1 = qu1 - S
return arr
@numba.jit(nopython=True, nogil=True)
def algA(n, N, random_state):
"""
Random Sampling without Replacement
Alg A proposed by J.S. Vitter in Faster Methods for Random Sampling
Parameters:
n = sample size (nnz)
N = size of system (elements)
random_state = seed for random number generation
"""
n = np.int64(n)
N = np.int64(N)
arr = np.zeros(n, dtype=np.int64)
arr[-1] = -1
i = 0
top = N - n
while n >= 2:
V = random_state.random()
S = 0
quot = top / N
while quot > V:
S += 1
top -= 1
N -= 1
quot *= top / N
arr[i] = arr[i - 1] + S + 1
i += 1
N -= 1
n -= 1
S = np.int64(N * random_state.random())
arr[i] = arr[i - 1] + S + 1
i += 1
return arr
@numba.jit(nopython=True, nogil=True)
def reverse(inv, N):
"""
If density of random matrix is greater than .5, it is faster to sample states not included
Parameters:
arr = np.array(np.int64) of indices to be excluded from sample
N = size of the system (elements)
"""
N = np.int64(N)
a = np.zeros(np.int64(N - len(inv)), dtype=np.int64)
j = 0
k = 0
for i in range(N):
if j == len(inv):
a[k:] = np.arange(i, N)
break
if i == inv[j]:
j += 1
else:
a[k] = i
k += 1
return a
default_rng = np.random.default_rng()
[docs]
def random(
shape,
density=None,
nnz=None,
random_state=None,
data_rvs=None,
format="coo",
fill_value=None,
idx_dtype=None,
**kwargs,
):
"""Generate a random sparse multidimensional array
Parameters
----------
shape : Tuple[int]
Shape of the array
density : float, optional
Density of the generated array; default is 0.01.
Mutually exclusive with `nnz`.
nnz : int, optional
Number of nonzero elements in the generated array.
Mutually exclusive with `density`.
random_state : Union[numpy.random.Generator, int], optional
Random number generator or random seed. If not given, the
singleton numpy.random will be used. This random state will be used
for sampling the sparsity structure, but not necessarily for sampling
the values of the structurally nonzero entries of the matrix.
data_rvs : Callable
Data generation callback. Must accept one single parameter: number of
:code:`nnz` elements, and return one single NumPy array of exactly
that length.
format : str
The format to return the output array in.
fill_value : scalar
The fill value of the output array.
Returns
-------
SparseArray
The generated random matrix.
See Also
--------
:obj:`scipy.sparse.rand` : Equivalent Scipy function.
:obj:`numpy.random.rand` : Similar Numpy function.
Examples
--------
>>> from sparse import random
>>> from scipy import stats
>>> rvs = lambda x: stats.poisson(25, loc=10).rvs(x, random_state=np.random.RandomState(1))
>>> s = random((2, 3, 4), density=0.25, random_state=np.random.RandomState(1), data_rvs=rvs)
>>> s.todense() # doctest: +NORMALIZE_WHITESPACE
array([[[ 0, 0, 0, 0],
[34, 0, 29, 30],
[ 0, 0, 0, 0]],
<BLANKLINE>
[[33, 0, 0, 34],
[34, 0, 0, 0],
[ 0, 0, 0, 0]]])
"""
# Copied, in large part, from scipy.sparse.random
# See https://github.com/scipy/scipy/blob/main/LICENSE.txt
from ._coo import COO
if density is not None and nnz is not None:
raise ValueError("'density' and 'nnz' are mutually exclusive")
if density is None:
density = 0.01
if not (0 <= density <= 1):
raise ValueError(f"density {density} is not in the unit interval")
elements = np.prod(shape, dtype=np.intp)
if nnz is None:
nnz = int(elements * density)
if not (0 <= nnz <= elements):
raise ValueError(f"cannot generate {nnz} nonzero elements for an array with {elements} total elements")
if random_state is None:
random_state = default_rng
elif isinstance(random_state, Integral):
random_state = np.random.default_rng(random_state)
if data_rvs is None:
data_rvs = random_state.random
if nnz == elements or density >= 1:
ind = np.arange(elements)
elif nnz < 2:
ind = random_state.choice(elements, nnz)
# Faster to find non-sampled indices and remove them for dens > .5
elif elements - nnz < 2:
ind = reverse(random_state.choice(elements, elements - nnz), elements)
elif nnz > elements / 2:
nnztemp = elements - nnz
# Using algorithm A for dens > .1
if elements > 10 * nnztemp:
ind = reverse(
algD(nnztemp, elements, random_state),
elements,
)
else:
ind = reverse(
algA(nnztemp, elements, random_state),
elements,
)
else:
ind = algD(nnz, elements, random_state) if elements > 10 * nnz else algA(nnz, elements, random_state)
data = data_rvs(nnz)
ar = COO(
ind[None, :],
data,
shape=elements,
fill_value=fill_value,
).reshape(shape)
if idx_dtype:
if can_store(idx_dtype, max(shape)):
ar.coords = ar.coords.astype(idx_dtype)
else:
raise ValueError(f"cannot cast array with shape {shape} to dtype {idx_dtype}.")
return ar.asformat(format, **kwargs)
def isscalar(x):
from ._sparse_array import SparseArray
return not isinstance(x, SparseArray) and np.isscalar(x)
def random_value_array(value, fraction):
def replace_values(n):
i = int(n * fraction)
ar = np.empty((n,), dtype=np.float_)
ar[:i] = value
ar[i:] = default_rng.random(n - i)
return ar
return replace_values
def normalize_axis(axis, ndim):
"""
Normalize negative axis indices to their positive counterpart for a given
number of dimensions.
Parameters
----------
axis : Union[int, Iterable[int], None]
The axis indices.
ndim : int
Number of dimensions to normalize axis indices against.
Returns
-------
axis
The normalized axis indices.
"""
if axis is None:
return None
if isinstance(axis, Integral):
axis = int(axis)
if axis < 0:
axis += ndim
if axis >= ndim or axis < 0:
raise ValueError(f"Invalid axis index {axis} for ndim={ndim}")
return axis
if isinstance(axis, Iterable):
if not all(isinstance(a, Integral) for a in axis):
raise ValueError(f"axis {axis} not understood")
return tuple(normalize_axis(a, ndim) for a in axis)
raise ValueError(f"axis {axis} not understood")
def equivalent(x, y):
"""
Checks the equivalence of two scalars or arrays with broadcasting. Assumes
a consistent dtype.
Parameters
----------
x : scalar or numpy.ndarray
y : scalar or numpy.ndarray
Returns
-------
equivalent : scalar or numpy.ndarray
The element-wise comparison of where two arrays are equivalent.
Examples
--------
>>> equivalent(1, 1)
True
>>> equivalent(np.nan, np.nan + 1)
True
>>> equivalent(1, 2)
False
>>> equivalent(np.inf, np.inf)
True
>>> equivalent(np.PZERO, np.NZERO)
True
"""
x = np.asarray(x)
y = np.asarray(y)
# Can't contain NaNs
if any(np.issubdtype(x.dtype, t) for t in [np.integer, np.bool_, np.character]):
return x == y
# Can contain NaNs
# FIXME: Complex floats and np.void with multiple values can't be compared properly.
return (x == y) | ((x != x) & (y != y)) # noqa: PLR0124
# copied from zarr
# See https://github.com/zarr-developers/zarr-python/blob/main/zarr/util.py
def human_readable_size(size):
if size < 2**10:
return str(size)
if size < 2**20:
return f"{size / 2**10:.1f}K"
if size < 2**30:
return f"{size / 2**20:.1f}M"
if size < 2**40:
return f"{size / 2**30:.1f}G"
if size < 2**50:
return f"{size / 2**40:.1f}T"
return f"{size / 2**50:.1f}P"
def html_table(arr):
table = ["<table><tbody>"]
headings = ["Format", "Data Type", "Shape", "nnz", "Density", "Read-only"]
density = np.float_(arr.nnz) / np.float_(arr.size)
info = [
type(arr).__name__.lower(),
str(arr.dtype),
str(arr.shape),
str(arr.nnz),
str(density),
]
# read-only
info.append(str(not hasattr(arr, "__setitem__")))
if hasattr(arr, "nbytes"):
headings.append("Size")
info.append(human_readable_size(arr.nbytes))
headings.append("Storage ratio")
info.append(f"{np.float_(arr.nbytes) / np.float_(reduce(operator.mul, arr.shape, 1) * arr.dtype.itemsize):.2f}")
# compressed_axes
if type(arr).__name__ == "GCXS":
headings.append("Compressed Axes")
info.append(str(arr.compressed_axes))
for h, i in zip(headings, info):
table.append(f'<tr><th style="text-align: left">{h}</th><td style="text-align: left">{i}</td></tr>')
table.append("</tbody></table>")
return "".join(table)
def check_compressed_axes(ndim, compressed_axes):
"""
Checks if the given compressed_axes are compatible with the shape of the array.
Parameters
----------
ndim : int
compressed_axes : Iterable
Raises
------
ValueError
If the compressed_axes are incompatible with the number of dimensions
"""
if compressed_axes is None:
return
if isinstance(ndim, Iterable):
ndim = len(ndim)
if not isinstance(compressed_axes, Iterable):
raise ValueError("compressed_axes must be an iterable")
if len(compressed_axes) == ndim:
raise ValueError("cannot compress all axes")
if not np.array_equal(list(set(compressed_axes)), compressed_axes):
raise ValueError("axes must be sorted without repeats")
if not all(isinstance(a, Integral) for a in compressed_axes):
raise ValueError("axes must be represented with integers")
if min(compressed_axes) < 0 or max(compressed_axes) >= ndim:
raise ValueError("axis out of range")
def check_zero_fill_value(*args):
"""
Checks if all the arguments have zero fill-values.
Parameters
----------
*args : Iterable[SparseArray]
Raises
------
ValueError
If all arguments don't have zero fill-values.
Examples
--------
>>> import sparse
>>> s1 = sparse.random((10,), density=0.5)
>>> s2 = sparse.random((10,), density=0.5, fill_value=0.5)
>>> check_zero_fill_value(s1)
>>> check_zero_fill_value(s2)
Traceback (most recent call last):
...
ValueError: This operation requires zero fill values, but argument 0 had a fill value of 0.5.
>>> check_zero_fill_value(s1, s2)
Traceback (most recent call last):
...
ValueError: This operation requires zero fill values, but argument 1 had a fill value of 0.5.
"""
for i, arg in enumerate(args):
if hasattr(arg, "fill_value") and not equivalent(arg.fill_value, _zero_of_dtype(arg.dtype)):
raise ValueError(
"This operation requires zero fill values, "
f"but argument {i:d} had a fill value of {arg.fill_value!s}."
)
def check_consistent_fill_value(arrays):
"""
Checks if all the arguments have consistent fill-values.
Parameters
----------
args : Iterable[SparseArray]
Raises
------
ValueError
If all elements of :code:`arrays` don't have the same fill-value.
Examples
--------
>>> import sparse
>>> s1 = sparse.random((10,), density=0.5, fill_value=0.1)
>>> s2 = sparse.random((10,), density=0.5, fill_value=0.5)
>>> check_consistent_fill_value([s1, s1])
>>> check_consistent_fill_value([s1, s2]) # doctest: +NORMALIZE_WHITESPACE
Traceback (most recent call last):
...
ValueError: This operation requires consistent fill-values, but argument 1 had a fill value of 0.5,\
which is different from a fill_value of 0.1 in the first argument.
"""
arrays = list(arrays)
from ._sparse_array import SparseArray
if not all(isinstance(s, SparseArray) for s in arrays):
raise ValueError("All arrays must be instances of SparseArray.")
if len(arrays) == 0:
raise ValueError("At least one array required.")
fv = arrays[0].fill_value
for i, arg in enumerate(arrays):
if not equivalent(fv, arg.fill_value):
raise ValueError(
"This operation requires consistent fill-values, "
f"but argument {i:d} had a fill value of {arg.fill_value!s}, which "
f"is different from a fill_value of {fv!s} in the first "
"argument."
)
def get_out_dtype(arr, scalar):
out_type = arr.dtype
if not can_store(out_type, scalar):
out_type = np.min_scalar_type(scalar)
return out_type
def can_store(dtype, scalar):
return np.array(scalar, dtype=dtype) == np.array(scalar)
def is_unsigned_dtype(dtype):
return np.array(-1, dtype=dtype) != np.array(-1)
def convert_format(format):
from ._sparse_array import SparseArray
if isinstance(format, type):
if not issubclass(format, SparseArray):
raise ValueError(f"Invalid format: {format}")
return format.__name__.lower()
if isinstance(format, str):
return format
raise ValueError(f"Invalid format: {format}")