Source code for sparse.coo.umath

import itertools

import numba
import numpy as np
import scipy.sparse

from itertools import zip_longest

from ..utils import isscalar, equivalent, _zero_of_dtype


[docs]def elemwise(func, *args, **kwargs): """ Apply a function to any number of arguments. Parameters ---------- func : Callable The function to apply. Must support broadcasting. args : tuple, optional The arguments to the function. Can be :obj:`SparseArray` objects or :obj:`scipy.sparse.spmatrix` objects. kwargs : dict, optional Any additional arguments to pass to the function. Returns ------- COO The result of applying the function. Raises ------ ValueError If the operation would result in a dense matrix, or if the operands don't have broadcastable shapes. See Also -------- :obj:`numpy.ufunc` : A similar Numpy construct. Note that any :code:`ufunc` can be used as the :code:`func` input to this function. Notes ----- Previously, operations with Numpy arrays were sometimes supported. Now, it is necessary to convert Numpy arrays to :obj:`COO` objects. """ return _Elemwise(func, *args, **kwargs).get_result()
@numba.jit(nopython=True, nogil=True) def _match_arrays(a, b): # pragma: no cover """ Finds all indexes into a and b such that a[i] = b[j]. The outputs are sorted in lexographical order. Parameters ---------- a, b : np.ndarray The input 1-D arrays to match. If matching of multiple fields is needed, use np.recarrays. These two arrays must be sorted. Returns ------- a_idx, b_idx : np.ndarray The output indices of every possible pair of matching elements. """ if len(a) == 0 or len(b) == 0: return np.empty(0, dtype=np.uintp), np.empty(0, dtype=np.uintp) a_ind, b_ind = [], [] nb = len(b) ib = 0 match = 0 for ia, j in enumerate(a): if j == b[match]: ib = match while ib < nb and j >= b[ib]: if j == b[ib]: a_ind.append(ia) b_ind.append(ib) if b[match] < b[ib]: match = ib ib += 1 return np.array(a_ind, dtype=np.uintp), np.array(b_ind, dtype=np.uintp) def _get_nary_broadcast_shape(*shapes): """ Broadcast any number of shapes to a result shape. Parameters ---------- shapes : tuple[tuple[int]] The shapes to broadcast. Returns ------- tuple[int] The output shape. Raises ------ ValueError If the input shapes cannot be broadcast to a single shape. """ result_shape = () for shape in shapes: try: result_shape = _get_broadcast_shape(shape, result_shape) except ValueError: shapes_str = ', '.join(str(shape) for shape in shapes) raise ValueError('operands could not be broadcast together with shapes %s' % shapes_str) return result_shape def _get_broadcast_shape(shape1, shape2, is_result=False): """ Get the overall broadcasted shape. Parameters ---------- shape1, shape2 : tuple[int] The input shapes to broadcast together. is_result : bool Whether or not shape2 is also the result shape. Returns ------- result_shape : tuple[int] The overall shape of the result. Raises ------ ValueError If the two shapes cannot be broadcast together. """ # https://stackoverflow.com/a/47244284/774273 if not all((l1 == l2) or (l1 == 1) or ((l2 == 1) and not is_result) for l1, l2 in zip(shape1[::-1], shape2[::-1])): raise ValueError('operands could not be broadcast together with shapes %s, %s' % (shape1, shape2)) result_shape = tuple(l1 if l1 != 1 else l2 for l1, l2 in zip_longest(shape1[::-1], shape2[::-1], fillvalue=1))[::-1] return result_shape def _get_broadcast_parameters(shape, broadcast_shape): """ Get the broadcast parameters. Parameters ---------- shape : tuple[int] The input shape. broadcast_shape The shape to broadcast to. Returns ------- params : list A list containing None if the dimension isn't in the original array, False if it needs to be broadcast, and True if it doesn't. """ params = [None if l1 is None else l1 == l2 for l1, l2 in zip_longest(shape[::-1], broadcast_shape[::-1], fillvalue=None)][::-1] return params def _get_reduced_coords(coords, params): """ Gets only those dimensions of the coordinates that don't need to be broadcast. Parameters ---------- coords : np.ndarray The coordinates to reduce. params : list The params from which to check which dimensions to get. Returns ------- reduced_coords : np.ndarray The reduced coordinates. """ reduced_params = [bool(param) for param in params] return coords[reduced_params] def _get_reduced_shape(shape, params): """ Gets only those dimensions of the coordinates that don't need to be broadcast. Parameters ---------- coords : np.ndarray The coordinates to reduce. params : list The params from which to check which dimensions to get. Returns ------- reduced_coords : np.ndarray The reduced coordinates. """ reduced_shape = tuple(l for l, p in zip(shape, params) if p) return reduced_shape def _get_expanded_coords_data(coords, data, params, broadcast_shape): """ Expand coordinates/data to broadcast_shape. Does most of the heavy lifting for broadcast_to. Produces sorted output for sorted inputs. Parameters ---------- coords : np.ndarray The coordinates to expand. data : np.ndarray The data corresponding to the coordinates. params : list The broadcast parameters. broadcast_shape : tuple[int] The shape to broadcast to. Returns ------- expanded_coords : np.ndarray List of 1-D arrays. Each item in the list has one dimension of coordinates. expanded_data : np.ndarray The data corresponding to expanded_coords. """ first_dim = -1 expand_shapes = [] for d, p, l in zip(range(len(broadcast_shape)), params, broadcast_shape): if p and first_dim == -1: expand_shapes.append(coords.shape[1]) first_dim = d if not p: expand_shapes.append(l) all_idx = _cartesian_product(*(np.arange(d, dtype=np.intp) for d in expand_shapes)) false_dim = 0 dim = 0 expanded_coords = np.empty((len(broadcast_shape), all_idx.shape[1]), dtype=np.intp) if first_dim != -1: expanded_data = data[all_idx[first_dim]] else: expanded_coords = all_idx expanded_data = np.repeat(data, np.prod(broadcast_shape, dtype=np.int64)) return np.asarray(expanded_coords), np.asarray(expanded_data) for d, p, l in zip(range(len(broadcast_shape)), params, broadcast_shape): if p: expanded_coords[d] = coords[dim, all_idx[first_dim]] else: expanded_coords[d] = all_idx[false_dim + (d > first_dim)] false_dim += 1 if p is not None: dim += 1 return np.asarray(expanded_coords), np.asarray(expanded_data) # (c) senderle # Taken from https://stackoverflow.com/a/11146645/774273 # License: https://creativecommons.org/licenses/by-sa/3.0/ def _cartesian_product(*arrays): """ Get the cartesian product of a number of arrays. Parameters ---------- arrays : Tuple[np.ndarray] The arrays to get a cartesian product of. Always sorted with respect to the original array. Returns ------- out : np.ndarray The overall cartesian product of all the input arrays. """ broadcastable = np.ix_(*arrays) broadcasted = np.broadcast_arrays(*broadcastable) rows, cols = np.prod(broadcasted[0].shape), len(broadcasted) dtype = np.result_type(*arrays) out = np.empty(rows * cols, dtype=dtype) start, end = 0, rows for a in broadcasted: out[start:end] = a.reshape(-1) start, end = end, end + rows return out.reshape(cols, rows) def _get_matching_coords(coords, params): """ Get the matching coords across a number of broadcast operands. Parameters ---------- coords : list[numpy.ndarray] The input coordinates. params : list[Union[bool, none]] The broadcast parameters. Returns ------- numpy.ndarray The broacasted coordinates """ matching_coords = [] dims = np.zeros(len(coords), dtype=np.uint8) for p_all in zip(*params): for i, p in enumerate(p_all): if p: matching_coords.append(coords[i][dims[i]]) break else: matching_coords.append(coords[dims[0]]) for i, p in enumerate(p_all): if p is not None: dims[i] += 1 return np.asarray(matching_coords, dtype=np.intp) def broadcast_to(x, shape): """ Performs the equivalent of :obj:`numpy.broadcast_to` for :obj:`COO`. Note that this function returns a new array instead of a view. Parameters ---------- shape : tuple[int] The shape to broadcast the data to. Returns ------- COO The broadcasted sparse array. Raises ------ ValueError If the operand cannot be broadcast to the given shape. See also -------- :obj:`numpy.broadcast_to` : NumPy equivalent function """ from .core import COO if shape == x.shape: return x result_shape = _get_broadcast_shape(x.shape, shape, is_result=True) params = _get_broadcast_parameters(x.shape, result_shape) coords, data = _get_expanded_coords_data(x.coords, x.data, params, result_shape) # Check if all the non-broadcast axes are next to each other nonbroadcast_idx = [idx for idx, p in enumerate(params) if p] diff_nonbroadcast_idx = [a - b for a, b in zip(nonbroadcast_idx[1:], nonbroadcast_idx[:-1])] sorted = all(d == 1 for d in diff_nonbroadcast_idx) return COO(coords, data, shape=result_shape, has_duplicates=False, sorted=sorted, fill_value=x.fill_value) class _Elemwise: def __init__(self, func, *args, **kwargs): """ Initialize the element-wise function calculator. Parameters ---------- func : types.Callable The function to compute args : tuple[Union[SparseArray, ndarray, scipy.sparse.spmatrix]] The arguments to compute the function on. kwargs : dict Extra arguments to pass to the function. """ from .core import COO from ..sparse_array import SparseArray processed_args = [] for arg in args: if isinstance(arg, scipy.sparse.spmatrix): processed_args.append(COO.from_scipy_sparse(arg)) elif isscalar(arg) or isinstance(arg, np.ndarray): # Faster and more reliable to pass ()-shaped ndarrays as scalars. processed_args.append(np.asarray(arg)) elif isinstance(arg, SparseArray) and not isinstance(arg, COO): processed_args.append(COO(arg)) elif not isinstance(arg, COO): self.args = None return else: processed_args.append(arg) self.args = tuple(processed_args) self.func = func self.dtype = kwargs.pop('dtype', None) self.kwargs = kwargs self.cache = {} self._get_fill_value() self._check_broadcast() def get_result(self): from .core import COO if self.args is None: return NotImplemented if any(s == 0 for s in self.shape): data = np.empty((0,), dtype=self.fill_value.dtype) coords = np.empty((0, len(self.shape)), dtype=np.intp) return COO(coords, data, shape=self.shape, has_duplicates=False, fill_value=self.fill_value) data_list = [] coords_list = [] for mask in itertools.product(*[[True, False] if isinstance(arg, COO) else [None] for arg in self.args]): if not any(mask): continue r = self._get_func_coords_data(mask) if r is not None: coords_list.append(r[0]) data_list.append(r[1]) # Concatenate matches and mismatches data = np.concatenate(data_list) if len(data_list) else np.empty((0,), dtype=self.fill_value.dtype) coords = np.concatenate(coords_list, axis=1) if len(coords_list) else \ np.empty((0, len(self.shape)), dtype=np.intp) return COO(coords, data, shape=self.shape, has_duplicates=False, fill_value=self.fill_value) def _get_fill_value(self): """ A function that finds and returns the fill-value. Raises ------ ValueError If the fill-value is inconsistent. """ from .core import COO zero_args = tuple(arg.fill_value[...] if isinstance(arg, COO) else arg for arg in self.args) # Some elemwise functions require a dtype argument, some abhorr it. try: fill_value_array = self.func(*zero_args, dtype=self.dtype, **self.kwargs) self.dtype = None except TypeError: fill_value_array = self.func(*zero_args, **self.kwargs) try: fill_value = fill_value_array[(0,) * fill_value_array.ndim] except IndexError: zero_args = tuple( arg.fill_value if isinstance(arg, COO) else _zero_of_dtype(arg.dtype) for arg in self.args) fill_value = self.func(*zero_args, **self.kwargs)[()] if not equivalent(fill_value, fill_value_array).all(): raise ValueError('Performing a mixed sparse-dense operation that would result in a dense array. ' 'Please make sure that func(sparse_fill_values, ndarrays) is a constant array.') # Store dtype separately if needed. if self.dtype is not None: fill_value = fill_value.astype(self.dtype) self.fill_value = fill_value self.dtype = self.fill_value.dtype def _check_broadcast(self): """ Checks if adding the ndarrays changes the broadcast shape. Raises ------ ValueError If the check fails. """ from .core import COO full_shape = _get_nary_broadcast_shape(*tuple(arg.shape for arg in self.args)) non_ndarray_shape = _get_nary_broadcast_shape( *tuple(arg.shape for arg in self.args if isinstance(arg, COO)) ) if full_shape != non_ndarray_shape: raise ValueError('Please make sure that the broadcast shape of just the sparse arrays is ' 'the same as the broadcast shape of all the operands.') self.shape = full_shape def _get_func_coords_data(self, mask): """ Gets the coords/data for a certain mask Parameters ---------- mask : tuple[Union[bool, NoneType]] The mask determining whether to match or unmatch. Returns ------- None or tuple The coords/data tuple for the given mask. """ from .core import COO matched_args = [arg for arg, m in zip(self.args, mask) if m is not None and m] unmatched_args = [arg for arg, m in zip(self.args, mask) if m is not None and not m] ndarray_args = [arg for arg, m in zip(self.args, mask) if m is None] matched_broadcast_shape = _get_nary_broadcast_shape( *tuple(arg.shape for arg in itertools.chain(matched_args, ndarray_args)) ) matched_arrays = self._match_coo(*matched_args, cache=self.cache, broadcast_shape=matched_broadcast_shape) func_args = [] m_arg = 0 for arg, m in zip(self.args, mask): if m is None: func_args.append(np.broadcast_to(arg, matched_broadcast_shape)[tuple(matched_arrays[0].coords)]) continue if m: func_args.append(matched_arrays[m_arg].data) m_arg += 1 else: func_args.append(arg.fill_value) # Try our best to preserve the output dtype. try: func_data = self.func(*func_args, dtype=self.dtype, **self.kwargs) except TypeError: try: func_args = np.broadcast_arrays(*func_args) out = np.empty(func_args[0].shape, dtype=self.dtype) func_data = self.func(*func_args, out=out, **self.kwargs) except TypeError: func_data = self.func(*func_args, **self.kwargs).astype(self.dtype) unmatched_mask = ~equivalent(func_data, self.fill_value) if not unmatched_mask.any(): return None func_coords = matched_arrays[0].coords[:, unmatched_mask] func_data = func_data[unmatched_mask] if matched_arrays[0].shape != self.shape: params = _get_broadcast_parameters(matched_arrays[0].shape, self.shape) func_coords, func_data = _get_expanded_coords_data(func_coords, func_data, params, self.shape) if all(m is None or m for m in mask): return func_coords, func_data # Not really sorted but we need the sortedness. func_array = COO(func_coords, func_data, self.shape, has_duplicates=False, sorted=True) unmatched_mask = np.ones(func_array.nnz, dtype=np.bool) for arg in unmatched_args: matched_idx = self._match_coo(func_array, arg, return_midx=True)[0] unmatched_mask[matched_idx] = False coords = np.asarray(func_array.coords[:, unmatched_mask], order='C') data = np.asarray(func_array.data[unmatched_mask], order='C') return coords, data @staticmethod def _match_coo(*args, **kwargs): """ Matches the coordinates for any number of input :obj:`COO` arrays. Equivalent to "sparse" broadcasting for all arrays. Parameters ---------- args : Tuple[COO] The input :obj:`COO` arrays. return_midx : bool Whether to return matched indices or matched arrays. Matching only supported for two arrays. ``False`` by default. cache : dict Cache of things already matched. No cache by default. Returns ------- matched_idx : List[ndarray] The indices of matched elements in the original arrays. Only returned if ``return_midx`` is ``True``. matched_arrays : List[COO] The expanded, matched :obj:`COO` objects. Only returned if ``return_midx`` is ``False``. """ from .core import COO from .common import linear_loc cache = kwargs.pop('cache', None) return_midx = kwargs.pop('return_midx', False) broadcast_shape = kwargs.pop('broadcast_shape', None) if kwargs: raise ValueError('Unknown kwargs: {}'.format(kwargs.keys())) if return_midx and (len(args) != 2 or cache is not None): raise NotImplementedError('Matching indices only supported for two args, and no cache.') matched_arrays = [args[0]] cache_key = [id(args[0])] for arg2 in args[1:]: cache_key.append(id(arg2)) key = tuple(cache_key) if cache is not None and key in cache: matched_arrays = cache[key] continue cargs = [matched_arrays[0], arg2] current_shape = _get_broadcast_shape(matched_arrays[0].shape, arg2.shape) params = [_get_broadcast_parameters(arg.shape, current_shape) for arg in cargs] reduced_params = [all(p) for p in zip(*params)] reduced_shape = _get_reduced_shape(arg2.shape, reduced_params[-arg2.ndim:]) reduced_coords = [_get_reduced_coords(arg.coords, reduced_params[-arg.ndim:]) for arg in cargs] linear = [linear_loc(rc, reduced_shape) for rc in reduced_coords] sorted_idx = [np.argsort(idx) for idx in linear] linear = [idx[s] for idx, s in zip(linear, sorted_idx)] matched_idx = _match_arrays(*linear) if return_midx: matched_idx = [sidx[midx] for sidx, midx in zip(sorted_idx, matched_idx)] return matched_idx coords = [arg.coords[:, s] for arg, s in zip(cargs, sorted_idx)] mcoords = [c[:, idx] for c, idx in zip(coords, matched_idx)] mcoords = _get_matching_coords(mcoords, params) mdata = [arg.data[sorted_idx[0]][matched_idx[0]] for arg in matched_arrays] mdata.append(arg2.data[sorted_idx[1]][matched_idx[1]]) # The coords aren't truly sorted, but we don't need them, so it's # best to avoid the extra cost. matched_arrays = [ COO(mcoords, md, shape=current_shape, sorted=True, has_duplicates=False) for md in mdata] if cache is not None: cache[key] = matched_arrays if broadcast_shape is not None and matched_arrays[0].shape != broadcast_shape: params = _get_broadcast_parameters(matched_arrays[0].shape, broadcast_shape) coords, idx = _get_expanded_coords_data( matched_arrays[0].coords, np.arange(matched_arrays[0].nnz), params, broadcast_shape ) matched_arrays = [ COO(coords, arr.data[idx], shape=broadcast_shape, sorted=True, has_duplicates=False) for arr in matched_arrays ] return matched_arrays