620 lines
20 KiB
Python
620 lines
20 KiB
Python
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"""List of Lists sparse matrix class
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"""
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__docformat__ = "restructuredtext en"
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__all__ = ['lil_array', 'lil_matrix', 'isspmatrix_lil']
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from bisect import bisect_left
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import numpy as np
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from ._matrix import spmatrix
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from ._base import _spbase, sparray, issparse
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from ._index import IndexMixin, INT_TYPES, _broadcast_arrays
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from ._sputils import (getdtype, isshape, isscalarlike, upcast_scalar,
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check_shape, check_reshape_kwargs)
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from . import _csparsetools
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class _lil_base(_spbase, IndexMixin):
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_format = 'lil'
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def __init__(self, arg1, shape=None, dtype=None, copy=False):
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_spbase.__init__(self)
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self.dtype = getdtype(dtype, arg1, default=float)
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# First get the shape
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if issparse(arg1):
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if arg1.format == "lil" and copy:
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A = arg1.copy()
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else:
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A = arg1.tolil()
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if dtype is not None:
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A = A.astype(dtype, copy=False)
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self._shape = check_shape(A.shape)
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self.dtype = A.dtype
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self.rows = A.rows
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self.data = A.data
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elif isinstance(arg1,tuple):
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if isshape(arg1):
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if shape is not None:
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raise ValueError('invalid use of shape parameter')
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M, N = arg1
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self._shape = check_shape((M, N))
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self.rows = np.empty((M,), dtype=object)
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self.data = np.empty((M,), dtype=object)
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for i in range(M):
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self.rows[i] = []
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self.data[i] = []
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else:
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raise TypeError('unrecognized lil_array constructor usage')
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else:
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# assume A is dense
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try:
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A = self._ascontainer(arg1)
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except TypeError as e:
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raise TypeError('unsupported matrix type') from e
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if isinstance(self, sparray) and A.ndim != 2:
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raise ValueError(f"LIL arrays don't support {A.ndim}D input. Use 2D")
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A = self._csr_container(A, dtype=dtype).tolil()
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self._shape = check_shape(A.shape)
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self.dtype = A.dtype
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self.rows = A.rows
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self.data = A.data
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def __iadd__(self,other):
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self[:,:] = self + other
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return self
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def __isub__(self,other):
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self[:,:] = self - other
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return self
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def __imul__(self,other):
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if isscalarlike(other):
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self[:,:] = self * other
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return self
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else:
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return NotImplemented
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def __itruediv__(self,other):
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if isscalarlike(other):
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self[:,:] = self / other
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return self
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else:
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return NotImplemented
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# Whenever the dimensions change, empty lists should be created for each
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# row
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def _getnnz(self, axis=None):
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if axis is None:
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return sum([len(rowvals) for rowvals in self.data])
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if axis < 0:
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axis += 2
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if axis == 0:
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out = np.zeros(self.shape[1], dtype=np.intp)
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for row in self.rows:
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out[row] += 1
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return out
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elif axis == 1:
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return np.array([len(rowvals) for rowvals in self.data], dtype=np.intp)
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else:
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raise ValueError('axis out of bounds')
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def count_nonzero(self):
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return sum(np.count_nonzero(rowvals) for rowvals in self.data)
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_getnnz.__doc__ = _spbase._getnnz.__doc__
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count_nonzero.__doc__ = _spbase.count_nonzero.__doc__
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def __str__(self):
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val = ''
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for i, row in enumerate(self.rows):
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for pos, j in enumerate(row):
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val += f" {str((i, j))}\t{str(self.data[i][pos])}\n"
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return val[:-1]
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def getrowview(self, i):
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"""Returns a view of the 'i'th row (without copying).
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"""
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new = self._lil_container((1, self.shape[1]), dtype=self.dtype)
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new.rows[0] = self.rows[i]
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new.data[0] = self.data[i]
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return new
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def getrow(self, i):
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"""Returns a copy of the 'i'th row.
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"""
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M, N = self.shape
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if i < 0:
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i += M
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if i < 0 or i >= M:
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raise IndexError('row index out of bounds')
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new = self._lil_container((1, N), dtype=self.dtype)
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new.rows[0] = self.rows[i][:]
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new.data[0] = self.data[i][:]
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return new
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def __getitem__(self, key):
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# Fast path for simple (int, int) indexing.
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if (isinstance(key, tuple) and len(key) == 2 and
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isinstance(key[0], INT_TYPES) and
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isinstance(key[1], INT_TYPES)):
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# lil_get1 handles validation for us.
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return self._get_intXint(*key)
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# Everything else takes the normal path.
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return IndexMixin.__getitem__(self, key)
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def _asindices(self, idx, N):
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# LIL routines handle bounds-checking for us, so don't do it here.
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try:
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x = np.asarray(idx)
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except (ValueError, TypeError, MemoryError) as e:
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raise IndexError('invalid index') from e
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if x.ndim not in (1, 2):
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raise IndexError('Index dimension must be <= 2')
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return x
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def _get_intXint(self, row, col):
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v = _csparsetools.lil_get1(self.shape[0], self.shape[1], self.rows,
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self.data, row, col)
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return self.dtype.type(v)
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def _get_sliceXint(self, row, col):
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row = range(*row.indices(self.shape[0]))
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return self._get_row_ranges(row, slice(col, col+1))
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def _get_arrayXint(self, row, col):
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row = row.squeeze()
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return self._get_row_ranges(row, slice(col, col+1))
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def _get_intXslice(self, row, col):
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return self._get_row_ranges((row,), col)
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def _get_sliceXslice(self, row, col):
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row = range(*row.indices(self.shape[0]))
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return self._get_row_ranges(row, col)
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def _get_arrayXslice(self, row, col):
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return self._get_row_ranges(row, col)
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def _get_intXarray(self, row, col):
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row = np.array(row, dtype=col.dtype, ndmin=1)
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return self._get_columnXarray(row, col)
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def _get_sliceXarray(self, row, col):
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row = np.arange(*row.indices(self.shape[0]))
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return self._get_columnXarray(row, col)
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def _get_columnXarray(self, row, col):
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# outer indexing
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row, col = _broadcast_arrays(row[:,None], col)
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return self._get_arrayXarray(row, col)
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def _get_arrayXarray(self, row, col):
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# inner indexing
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i, j = map(np.atleast_2d, _prepare_index_for_memoryview(row, col))
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new = self._lil_container(i.shape, dtype=self.dtype)
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_csparsetools.lil_fancy_get(self.shape[0], self.shape[1],
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self.rows, self.data,
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new.rows, new.data,
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i, j)
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return new
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def _get_row_ranges(self, rows, col_slice):
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"""
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Fast path for indexing in the case where column index is slice.
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This gains performance improvement over brute force by more
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efficient skipping of zeros, by accessing the elements
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column-wise in order.
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Parameters
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----------
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rows : sequence or range
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Rows indexed. If range, must be within valid bounds.
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col_slice : slice
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Columns indexed
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"""
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j_start, j_stop, j_stride = col_slice.indices(self.shape[1])
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col_range = range(j_start, j_stop, j_stride)
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nj = len(col_range)
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new = self._lil_container((len(rows), nj), dtype=self.dtype)
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_csparsetools.lil_get_row_ranges(self.shape[0], self.shape[1],
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self.rows, self.data,
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new.rows, new.data,
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rows,
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j_start, j_stop, j_stride, nj)
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return new
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def _set_intXint(self, row, col, x):
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_csparsetools.lil_insert(self.shape[0], self.shape[1], self.rows,
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self.data, row, col, x)
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def _set_arrayXarray(self, row, col, x):
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i, j, x = map(np.atleast_2d, _prepare_index_for_memoryview(row, col, x))
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_csparsetools.lil_fancy_set(self.shape[0], self.shape[1],
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self.rows, self.data,
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i, j, x)
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def _set_arrayXarray_sparse(self, row, col, x):
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# Fall back to densifying x
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x = np.asarray(x.toarray(), dtype=self.dtype)
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x, _ = _broadcast_arrays(x, row)
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self._set_arrayXarray(row, col, x)
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def __setitem__(self, key, x):
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if isinstance(key, tuple) and len(key) == 2:
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row, col = key
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# Fast path for simple (int, int) indexing.
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if isinstance(row, INT_TYPES) and isinstance(col, INT_TYPES):
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x = self.dtype.type(x)
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if x.size > 1:
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raise ValueError("Trying to assign a sequence to an item")
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return self._set_intXint(row, col, x)
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# Fast path for full-matrix sparse assignment.
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if (isinstance(row, slice) and isinstance(col, slice) and
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row == slice(None) and col == slice(None) and
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issparse(x) and x.shape == self.shape):
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x = self._lil_container(x, dtype=self.dtype)
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self.rows = x.rows
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self.data = x.data
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return
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# Everything else takes the normal path.
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IndexMixin.__setitem__(self, key, x)
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def _mul_scalar(self, other):
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if other == 0:
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# Multiply by zero: return the zero matrix
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new = self._lil_container(self.shape, dtype=self.dtype)
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else:
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res_dtype = upcast_scalar(self.dtype, other)
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new = self.copy()
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new = new.astype(res_dtype)
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# Multiply this scalar by every element.
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for j, rowvals in enumerate(new.data):
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new.data[j] = [val*other for val in rowvals]
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return new
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def __truediv__(self, other): # self / other
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if isscalarlike(other):
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new = self.copy()
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new.dtype = np.result_type(self, other)
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# Divide every element by this scalar
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for j, rowvals in enumerate(new.data):
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new.data[j] = [val/other for val in rowvals]
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return new
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else:
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return self.tocsr() / other
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def copy(self):
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M, N = self.shape
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new = self._lil_container(self.shape, dtype=self.dtype)
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# This is ~14x faster than calling deepcopy() on rows and data.
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_csparsetools.lil_get_row_ranges(M, N, self.rows, self.data,
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new.rows, new.data, range(M),
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0, N, 1, N)
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return new
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copy.__doc__ = _spbase.copy.__doc__
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def reshape(self, *args, **kwargs):
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shape = check_shape(args, self.shape)
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order, copy = check_reshape_kwargs(kwargs)
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# Return early if reshape is not required
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if shape == self.shape:
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if copy:
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return self.copy()
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else:
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return self
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new = self._lil_container(shape, dtype=self.dtype)
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if order == 'C':
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ncols = self.shape[1]
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for i, row in enumerate(self.rows):
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for col, j in enumerate(row):
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new_r, new_c = np.unravel_index(i * ncols + j, shape)
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new[new_r, new_c] = self[i, j]
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elif order == 'F':
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nrows = self.shape[0]
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for i, row in enumerate(self.rows):
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for col, j in enumerate(row):
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new_r, new_c = np.unravel_index(i + j * nrows, shape, order)
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new[new_r, new_c] = self[i, j]
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else:
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raise ValueError("'order' must be 'C' or 'F'")
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return new
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reshape.__doc__ = _spbase.reshape.__doc__
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def resize(self, *shape):
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shape = check_shape(shape)
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new_M, new_N = shape
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M, N = self.shape
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if new_M < M:
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self.rows = self.rows[:new_M]
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self.data = self.data[:new_M]
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elif new_M > M:
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self.rows = np.resize(self.rows, new_M)
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self.data = np.resize(self.data, new_M)
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for i in range(M, new_M):
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self.rows[i] = []
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self.data[i] = []
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if new_N < N:
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for row, data in zip(self.rows, self.data):
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trunc = bisect_left(row, new_N)
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del row[trunc:]
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del data[trunc:]
|
||
|
|
|
||
|
|
self._shape = shape
|
||
|
|
|
||
|
|
resize.__doc__ = _spbase.resize.__doc__
|
||
|
|
|
||
|
|
def toarray(self, order=None, out=None):
|
||
|
|
d = self._process_toarray_args(order, out)
|
||
|
|
for i, row in enumerate(self.rows):
|
||
|
|
for pos, j in enumerate(row):
|
||
|
|
d[i, j] = self.data[i][pos]
|
||
|
|
return d
|
||
|
|
|
||
|
|
toarray.__doc__ = _spbase.toarray.__doc__
|
||
|
|
|
||
|
|
def transpose(self, axes=None, copy=False):
|
||
|
|
return self.tocsr(copy=copy).transpose(axes=axes, copy=False).tolil(copy=False)
|
||
|
|
|
||
|
|
transpose.__doc__ = _spbase.transpose.__doc__
|
||
|
|
|
||
|
|
def tolil(self, copy=False):
|
||
|
|
if copy:
|
||
|
|
return self.copy()
|
||
|
|
else:
|
||
|
|
return self
|
||
|
|
|
||
|
|
tolil.__doc__ = _spbase.tolil.__doc__
|
||
|
|
|
||
|
|
def tocsr(self, copy=False):
|
||
|
|
M, N = self.shape
|
||
|
|
if M == 0 or N == 0:
|
||
|
|
return self._csr_container((M, N), dtype=self.dtype)
|
||
|
|
|
||
|
|
# construct indptr array
|
||
|
|
if M*N <= np.iinfo(np.int32).max:
|
||
|
|
# fast path: it is known that 64-bit indexing will not be needed.
|
||
|
|
idx_dtype = np.int32
|
||
|
|
indptr = np.empty(M + 1, dtype=idx_dtype)
|
||
|
|
indptr[0] = 0
|
||
|
|
_csparsetools.lil_get_lengths(self.rows, indptr[1:])
|
||
|
|
np.cumsum(indptr, out=indptr)
|
||
|
|
nnz = indptr[-1]
|
||
|
|
else:
|
||
|
|
idx_dtype = self._get_index_dtype(maxval=N)
|
||
|
|
lengths = np.empty(M, dtype=idx_dtype)
|
||
|
|
_csparsetools.lil_get_lengths(self.rows, lengths)
|
||
|
|
nnz = lengths.sum(dtype=np.int64)
|
||
|
|
idx_dtype = self._get_index_dtype(maxval=max(N, nnz))
|
||
|
|
indptr = np.empty(M + 1, dtype=idx_dtype)
|
||
|
|
indptr[0] = 0
|
||
|
|
np.cumsum(lengths, dtype=idx_dtype, out=indptr[1:])
|
||
|
|
|
||
|
|
indices = np.empty(nnz, dtype=idx_dtype)
|
||
|
|
data = np.empty(nnz, dtype=self.dtype)
|
||
|
|
_csparsetools.lil_flatten_to_array(self.rows, indices)
|
||
|
|
_csparsetools.lil_flatten_to_array(self.data, data)
|
||
|
|
|
||
|
|
# init csr matrix
|
||
|
|
return self._csr_container((data, indices, indptr), shape=self.shape)
|
||
|
|
|
||
|
|
tocsr.__doc__ = _spbase.tocsr.__doc__
|
||
|
|
|
||
|
|
|
||
|
|
def _prepare_index_for_memoryview(i, j, x=None):
|
||
|
|
"""
|
||
|
|
Convert index and data arrays to form suitable for passing to the
|
||
|
|
Cython fancy getset routines.
|
||
|
|
|
||
|
|
The conversions are necessary since to (i) ensure the integer
|
||
|
|
index arrays are in one of the accepted types, and (ii) to ensure
|
||
|
|
the arrays are writable so that Cython memoryview support doesn't
|
||
|
|
choke on them.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
i, j
|
||
|
|
Index arrays
|
||
|
|
x : optional
|
||
|
|
Data arrays
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
i, j, x
|
||
|
|
Re-formatted arrays (x is omitted, if input was None)
|
||
|
|
|
||
|
|
"""
|
||
|
|
if i.dtype > j.dtype:
|
||
|
|
j = j.astype(i.dtype)
|
||
|
|
elif i.dtype < j.dtype:
|
||
|
|
i = i.astype(j.dtype)
|
||
|
|
|
||
|
|
if not i.flags.writeable or i.dtype not in (np.int32, np.int64):
|
||
|
|
i = i.astype(np.intp)
|
||
|
|
if not j.flags.writeable or j.dtype not in (np.int32, np.int64):
|
||
|
|
j = j.astype(np.intp)
|
||
|
|
|
||
|
|
if x is not None:
|
||
|
|
if not x.flags.writeable:
|
||
|
|
x = x.copy()
|
||
|
|
return i, j, x
|
||
|
|
else:
|
||
|
|
return i, j
|
||
|
|
|
||
|
|
|
||
|
|
def isspmatrix_lil(x):
|
||
|
|
"""Is `x` of lil_matrix type?
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
x
|
||
|
|
object to check for being a lil matrix
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
bool
|
||
|
|
True if `x` is a lil matrix, False otherwise
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> from scipy.sparse import lil_array, lil_matrix, coo_matrix, isspmatrix_lil
|
||
|
|
>>> isspmatrix_lil(lil_matrix([[5]]))
|
||
|
|
True
|
||
|
|
>>> isspmatrix_lil(lil_array([[5]]))
|
||
|
|
False
|
||
|
|
>>> isspmatrix_lil(coo_matrix([[5]]))
|
||
|
|
False
|
||
|
|
"""
|
||
|
|
return isinstance(x, lil_matrix)
|
||
|
|
|
||
|
|
|
||
|
|
# This namespace class separates array from matrix with isinstance
|
||
|
|
class lil_array(_lil_base, sparray):
|
||
|
|
"""
|
||
|
|
Row-based LIst of Lists sparse array.
|
||
|
|
|
||
|
|
This is a structure for constructing sparse arrays incrementally.
|
||
|
|
Note that inserting a single item can take linear time in the worst case;
|
||
|
|
to construct the array efficiently, make sure the items are pre-sorted by
|
||
|
|
index, per row.
|
||
|
|
|
||
|
|
This can be instantiated in several ways:
|
||
|
|
lil_array(D)
|
||
|
|
where D is a 2-D ndarray
|
||
|
|
|
||
|
|
lil_array(S)
|
||
|
|
with another sparse array or matrix S (equivalent to S.tolil())
|
||
|
|
|
||
|
|
lil_array((M, N), [dtype])
|
||
|
|
to construct an empty array with shape (M, N)
|
||
|
|
dtype is optional, defaulting to dtype='d'.
|
||
|
|
|
||
|
|
Attributes
|
||
|
|
----------
|
||
|
|
dtype : dtype
|
||
|
|
Data type of the array
|
||
|
|
shape : 2-tuple
|
||
|
|
Shape of the array
|
||
|
|
ndim : int
|
||
|
|
Number of dimensions (this is always 2)
|
||
|
|
nnz
|
||
|
|
size
|
||
|
|
data
|
||
|
|
LIL format data array of the array
|
||
|
|
rows
|
||
|
|
LIL format row index array of the array
|
||
|
|
T
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
Sparse arrays can be used in arithmetic operations: they support
|
||
|
|
addition, subtraction, multiplication, division, and matrix power.
|
||
|
|
|
||
|
|
Advantages of the LIL format
|
||
|
|
- supports flexible slicing
|
||
|
|
- changes to the array sparsity structure are efficient
|
||
|
|
|
||
|
|
Disadvantages of the LIL format
|
||
|
|
- arithmetic operations LIL + LIL are slow (consider CSR or CSC)
|
||
|
|
- slow column slicing (consider CSC)
|
||
|
|
- slow matrix vector products (consider CSR or CSC)
|
||
|
|
|
||
|
|
Intended Usage
|
||
|
|
- LIL is a convenient format for constructing sparse arrays
|
||
|
|
- once an array has been constructed, convert to CSR or
|
||
|
|
CSC format for fast arithmetic and matrix vector operations
|
||
|
|
- consider using the COO format when constructing large arrays
|
||
|
|
|
||
|
|
Data Structure
|
||
|
|
- An array (``self.rows``) of rows, each of which is a sorted
|
||
|
|
list of column indices of non-zero elements.
|
||
|
|
- The corresponding nonzero values are stored in similar
|
||
|
|
fashion in ``self.data``.
|
||
|
|
|
||
|
|
"""
|
||
|
|
|
||
|
|
|
||
|
|
class lil_matrix(spmatrix, _lil_base):
|
||
|
|
"""
|
||
|
|
Row-based LIst of Lists sparse matrix.
|
||
|
|
|
||
|
|
This is a structure for constructing sparse matrices incrementally.
|
||
|
|
Note that inserting a single item can take linear time in the worst case;
|
||
|
|
to construct the matrix efficiently, make sure the items are pre-sorted by
|
||
|
|
index, per row.
|
||
|
|
|
||
|
|
This can be instantiated in several ways:
|
||
|
|
lil_matrix(D)
|
||
|
|
where D is a 2-D ndarray
|
||
|
|
|
||
|
|
lil_matrix(S)
|
||
|
|
with another sparse array or matrix S (equivalent to S.tolil())
|
||
|
|
|
||
|
|
lil_matrix((M, N), [dtype])
|
||
|
|
to construct an empty matrix with shape (M, N)
|
||
|
|
dtype is optional, defaulting to dtype='d'.
|
||
|
|
|
||
|
|
Attributes
|
||
|
|
----------
|
||
|
|
dtype : dtype
|
||
|
|
Data type of the matrix
|
||
|
|
shape : 2-tuple
|
||
|
|
Shape of the matrix
|
||
|
|
ndim : int
|
||
|
|
Number of dimensions (this is always 2)
|
||
|
|
nnz
|
||
|
|
size
|
||
|
|
data
|
||
|
|
LIL format data array of the matrix
|
||
|
|
rows
|
||
|
|
LIL format row index array of the matrix
|
||
|
|
T
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
Sparse matrices can be used in arithmetic operations: they support
|
||
|
|
addition, subtraction, multiplication, division, and matrix power.
|
||
|
|
|
||
|
|
Advantages of the LIL format
|
||
|
|
- supports flexible slicing
|
||
|
|
- changes to the matrix sparsity structure are efficient
|
||
|
|
|
||
|
|
Disadvantages of the LIL format
|
||
|
|
- arithmetic operations LIL + LIL are slow (consider CSR or CSC)
|
||
|
|
- slow column slicing (consider CSC)
|
||
|
|
- slow matrix vector products (consider CSR or CSC)
|
||
|
|
|
||
|
|
Intended Usage
|
||
|
|
- LIL is a convenient format for constructing sparse matrices
|
||
|
|
- once a matrix has been constructed, convert to CSR or
|
||
|
|
CSC format for fast arithmetic and matrix vector operations
|
||
|
|
- consider using the COO format when constructing large matrices
|
||
|
|
|
||
|
|
Data Structure
|
||
|
|
- An array (``self.rows``) of rows, each of which is a sorted
|
||
|
|
list of column indices of non-zero elements.
|
||
|
|
- The corresponding nonzero values are stored in similar
|
||
|
|
fashion in ``self.data``.
|
||
|
|
|
||
|
|
"""
|