from __future__ import print_function, division
import functools
import itertools
from sympy.core.sympify import _sympify
from sympy import S, Dict, flatten, SparseMatrix, Basic, Tuple
from sympy.tensor.array.mutable_ndim_array import MutableNDimArray
from sympy.tensor.array.ndim_array import NDimArray, ImmutableNDimArray
class SparseNDimArray(NDimArray):
def __new__(self, *args, **kwargs):
return ImmutableSparseNDimArray(*args, **kwargs)
def __getitem__(self, index):
"""
Get an element from a sparse N-dim array.
Examples
========
>>> from sympy.tensor.array import MutableSparseNDimArray
>>> a = MutableSparseNDimArray(range(4), (2, 2))
>>> a
[[0, 1], [2, 3]]
>>> a[0, 0]
0
>>> a[1, 1]
3
>>> a[0]
0
>>> a[2]
2
"""
# `index` is a tuple with one or more slices:
if isinstance(index, tuple) and any([isinstance(i, slice) for i in index]):
def slice_expand(s, dim):
if not isinstance(s, slice):
return (s,)
start, stop, step = s.indices(dim)
return [start + i*step for i in range((stop-start)//step)]
sl_factors = [slice_expand(i, dim) for (i, dim) in zip(index, self.shape)]
eindices = itertools.product(*sl_factors)
array = [self._sparse_array.get(self._parse_index(i), S.Zero) for i in eindices]
nshape = [len(el) for i, el in enumerate(sl_factors) if isinstance(index[i], slice)]
return type(self)(array, nshape)
else:
# `index` is a single slice:
if isinstance(index, slice):
start, stop, step = index.indices(self._loop_size)
retvec = [self._sparse_array.get(ind, S.Zero) for ind in range(start, stop, step)]
return retvec
# `index` is a number or a tuple without any slice:
else:
index = self._parse_index(index)
return self._sparse_array.get(index, S.Zero)
@classmethod
def zeros(cls, *shape):
"""
Return a sparse N-dim array of zeros.
"""
return cls({}, shape)
def tomatrix(self):
"""
Converts MutableDenseNDimArray to Matrix. Can convert only 2-dim array, else will raise error.
Examples
========
>>> from sympy.tensor.array import MutableSparseNDimArray
>>> a = MutableSparseNDimArray([1 for i in range(9)], (3, 3))
>>> b = a.tomatrix()
>>> b
Matrix([
[1, 1, 1],
[1, 1, 1],
[1, 1, 1]])
"""
if self.rank() != 2:
raise ValueError('Dimensions must be of size of 2')
mat_sparse = {}
for key, value in self._sparse_array.items():
mat_sparse[self._get_tuple_index(key)] = value
return SparseMatrix(self.shape[0], self.shape[1], mat_sparse)
def __iter__(self):
def iterator():
for i in range(self._loop_size):
yield self[i]
return iterator()
def reshape(self, *newshape):
new_total_size = functools.reduce(lambda x,y: x*y, newshape)
if new_total_size != self._loop_size:
raise ValueError("Invalid reshape parameters " + newshape)
return type(self)(*(newshape + (self._array,)))
[docs]class ImmutableSparseNDimArray(SparseNDimArray, ImmutableNDimArray):
def __new__(cls, *args, **kwargs):
shape, flat_list = cls._handle_ndarray_creation_inputs(*args, **kwargs)
shape = Tuple(*map(_sympify, shape))
loop_size = functools.reduce(lambda x,y: x*y, shape) if shape else 0
# Sparse array:
if isinstance(flat_list, (dict, Dict)):
sparse_array = Dict(flat_list)
else:
sparse_array = {}
for i, el in enumerate(flatten(flat_list)):
if el != 0:
sparse_array[i] = _sympify(el)
sparse_array = Dict(sparse_array)
self = Basic.__new__(cls, sparse_array, shape, **kwargs)
self._shape = shape
self._rank = len(shape)
self._loop_size = loop_size
self._sparse_array = sparse_array
return self
def __setitem__(self, index, value):
raise TypeError("immutable N-dim array")
[docs]class MutableSparseNDimArray(MutableNDimArray, SparseNDimArray):
def __new__(cls, *args, **kwargs):
shape, flat_list = cls._handle_ndarray_creation_inputs(*args, **kwargs)
self = object.__new__(cls)
self._shape = shape
self._rank = len(shape)
self._loop_size = functools.reduce(lambda x,y: x*y, shape) if shape else 0
# Sparse array:
if isinstance(flat_list, (dict, Dict)):
self._sparse_array = dict(flat_list)
return self
self._sparse_array = {}
for i, el in enumerate(flatten(flat_list)):
if el != 0:
self._sparse_array[i] = _sympify(el)
return self
def __setitem__(self, index, value):
"""Allows to set items to MutableDenseNDimArray.
Examples
========
>>> from sympy.tensor.array import MutableSparseNDimArray
>>> a = MutableSparseNDimArray.zeros(2, 2)
>>> a[0, 0] = 1
>>> a[1, 1] = 1
>>> a
[[1, 0], [0, 1]]
"""
index = self._parse_index(index)
if not isinstance(value, MutableNDimArray):
value = _sympify(value)
if isinstance(value, NDimArray):
return NotImplementedError
if value == 0 and index in self._sparse_array:
self._sparse_array.pop(index)
else:
self._sparse_array[index] = value
