"""List of Lists sparse matrix class
"""
__docformat__ = "restructuredtext en"
__all__ = ['lil_matrix', 'isspmatrix_lil']
from bisect import bisect_left
import numpy as np
from ._base import spmatrix, isspmatrix
from ._index import IndexMixin, INT_TYPES, _broadcast_arrays
from ._sputils import (getdtype, isshape, isscalarlike, upcast_scalar,
get_index_dtype, check_shape, check_reshape_kwargs)
from . import _csparsetools
[docs]class lil_matrix(spmatrix, IndexMixin):
"""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 a matrix efficiently, make sure the items are pre-sorted by
index, per row.
This can be instantiated in several ways:
lil_matrix(D)
with a dense matrix or rank-2 ndarray D
lil_matrix(S)
with another sparse 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
Number of stored values, including explicit zeros
data
LIL format data array of the matrix
rows
LIL format row index array of the matrix
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``.
"""
format = 'lil'
[docs] def __init__(self, arg1, shape=None, dtype=None, copy=False):
spmatrix.__init__(self)
self.dtype = getdtype(dtype, arg1, default=float)
# First get the shape
if isspmatrix(arg1):
if isspmatrix_lil(arg1) and copy:
A = arg1.copy()
else:
A = arg1.tolil()
if dtype is not None:
A = A.astype(dtype, copy=False)
self._shape = check_shape(A.shape)
self.dtype = A.dtype
self.rows = A.rows
self.data = A.data
elif isinstance(arg1,tuple):
if isshape(arg1):
if shape is not None:
raise ValueError('invalid use of shape parameter')
M, N = arg1
self._shape = check_shape((M, N))
self.rows = np.empty((M,), dtype=object)
self.data = np.empty((M,), dtype=object)
for i in range(M):
self.rows[i] = []
self.data[i] = []
else:
raise TypeError('unrecognized lil_matrix constructor usage')
else:
# assume A is dense
try:
A = self._ascontainer(arg1)
except TypeError as e:
raise TypeError('unsupported matrix type') from e
else:
A = self._csr_container(A, dtype=dtype).tolil()
self._shape = check_shape(A.shape)
self.dtype = A.dtype
self.rows = A.rows
self.data = A.data
[docs] def __iadd__(self,other):
self[:,:] = self + other
return self
[docs] def __isub__(self,other):
self[:,:] = self - other
return self
[docs] def __imul__(self,other):
if isscalarlike(other):
self[:,:] = self * other
return self
else:
return NotImplemented
[docs] def __itruediv__(self,other):
if isscalarlike(other):
self[:,:] = self / other
return self
else:
return NotImplemented
# Whenever the dimensions change, empty lists should be created for each
# row
[docs] def getnnz(self, axis=None):
if axis is None:
return sum([len(rowvals) for rowvals in self.data])
if axis < 0:
axis += 2
if axis == 0:
out = np.zeros(self.shape[1], dtype=np.intp)
for row in self.rows:
out[row] += 1
return out
elif axis == 1:
return np.array([len(rowvals) for rowvals in self.data], dtype=np.intp)
else:
raise ValueError('axis out of bounds')
[docs] def count_nonzero(self):
return sum(np.count_nonzero(rowvals) for rowvals in self.data)
getnnz.__doc__ = spmatrix.getnnz.__doc__
count_nonzero.__doc__ = spmatrix.count_nonzero.__doc__
[docs] def __str__(self):
val = ''
for i, row in enumerate(self.rows):
for pos, j in enumerate(row):
val += " %s\t%s\n" % (str((i, j)), str(self.data[i][pos]))
return val[:-1]
[docs] def getrowview(self, i):
"""Returns a view of the 'i'th row (without copying).
"""
new = self._lil_container((1, self.shape[1]), dtype=self.dtype)
new.rows[0] = self.rows[i]
new.data[0] = self.data[i]
return new
[docs] def getrow(self, i):
"""Returns a copy of the 'i'th row.
"""
M, N = self.shape
if i < 0:
i += M
if i < 0 or i >= M:
raise IndexError('row index out of bounds')
new = self._lil_container((1, N), dtype=self.dtype)
new.rows[0] = self.rows[i][:]
new.data[0] = self.data[i][:]
return new
[docs] def __getitem__(self, key):
# Fast path for simple (int, int) indexing.
if (isinstance(key, tuple) and len(key) == 2 and
isinstance(key[0], INT_TYPES) and
isinstance(key[1], INT_TYPES)):
# lil_get1 handles validation for us.
return self._get_intXint(*key)
# Everything else takes the normal path.
return IndexMixin.__getitem__(self, key)
def _asindices(self, idx, N):
# LIL routines handle bounds-checking for us, so don't do it here.
try:
x = np.asarray(idx)
except (ValueError, TypeError, MemoryError) as e:
raise IndexError('invalid index') from e
if x.ndim not in (1, 2):
raise IndexError('Index dimension must be <= 2')
return x
def _get_intXint(self, row, col):
v = _csparsetools.lil_get1(self.shape[0], self.shape[1], self.rows,
self.data, row, col)
return self.dtype.type(v)
def _get_sliceXint(self, row, col):
row = range(*row.indices(self.shape[0]))
return self._get_row_ranges(row, slice(col, col+1))
def _get_arrayXint(self, row, col):
row = row.squeeze()
return self._get_row_ranges(row, slice(col, col+1))
def _get_intXslice(self, row, col):
return self._get_row_ranges((row,), col)
def _get_sliceXslice(self, row, col):
row = range(*row.indices(self.shape[0]))
return self._get_row_ranges(row, col)
def _get_arrayXslice(self, row, col):
return self._get_row_ranges(row, col)
def _get_intXarray(self, row, col):
row = np.array(row, dtype=col.dtype, ndmin=1)
return self._get_columnXarray(row, col)
def _get_sliceXarray(self, row, col):
row = np.arange(*row.indices(self.shape[0]))
return self._get_columnXarray(row, col)
def _get_columnXarray(self, row, col):
# outer indexing
row, col = _broadcast_arrays(row[:,None], col)
return self._get_arrayXarray(row, col)
def _get_arrayXarray(self, row, col):
# inner indexing
i, j = map(np.atleast_2d, _prepare_index_for_memoryview(row, col))
new = self._lil_container(i.shape, dtype=self.dtype)
_csparsetools.lil_fancy_get(self.shape[0], self.shape[1],
self.rows, self.data,
new.rows, new.data,
i, j)
return new
def _get_row_ranges(self, rows, col_slice):
"""
Fast path for indexing in the case where column index is slice.
This gains performance improvement over brute force by more
efficient skipping of zeros, by accessing the elements
column-wise in order.
Parameters
----------
rows : sequence or range
Rows indexed. If range, must be within valid bounds.
col_slice : slice
Columns indexed
"""
j_start, j_stop, j_stride = col_slice.indices(self.shape[1])
col_range = range(j_start, j_stop, j_stride)
nj = len(col_range)
new = self._lil_container((len(rows), nj), dtype=self.dtype)
_csparsetools.lil_get_row_ranges(self.shape[0], self.shape[1],
self.rows, self.data,
new.rows, new.data,
rows,
j_start, j_stop, j_stride, nj)
return new
def _set_intXint(self, row, col, x):
_csparsetools.lil_insert(self.shape[0], self.shape[1], self.rows,
self.data, row, col, x)
def _set_arrayXarray(self, row, col, x):
i, j, x = map(np.atleast_2d, _prepare_index_for_memoryview(row, col, x))
_csparsetools.lil_fancy_set(self.shape[0], self.shape[1],
self.rows, self.data,
i, j, x)
def _set_arrayXarray_sparse(self, row, col, x):
# Special case: full matrix assignment
if (x.shape == self.shape and
isinstance(row, slice) and row == slice(None) and
isinstance(col, slice) and col == slice(None)):
x = self._lil_container(x, dtype=self.dtype)
self.rows = x.rows
self.data = x.data
return
# Fall back to densifying x
x = np.asarray(x.toarray(), dtype=self.dtype)
x, _ = _broadcast_arrays(x, row)
self._set_arrayXarray(row, col, x)
[docs] def __setitem__(self, key, x):
# Fast path for simple (int, int) indexing.
if (isinstance(key, tuple) and len(key) == 2 and
isinstance(key[0], INT_TYPES) and
isinstance(key[1], INT_TYPES)):
x = self.dtype.type(x)
if x.size > 1:
raise ValueError("Trying to assign a sequence to an item")
return self._set_intXint(key[0], key[1], x)
# Everything else takes the normal path.
IndexMixin.__setitem__(self, key, x)
def _mul_scalar(self, other):
if other == 0:
# Multiply by zero: return the zero matrix
new = self._lil_container(self.shape, dtype=self.dtype)
else:
res_dtype = upcast_scalar(self.dtype, other)
new = self.copy()
new = new.astype(res_dtype)
# Multiply this scalar by every element.
for j, rowvals in enumerate(new.data):
new.data[j] = [val*other for val in rowvals]
return new
[docs] def __truediv__(self, other): # self / other
if isscalarlike(other):
new = self.copy()
# Divide every element by this scalar
for j, rowvals in enumerate(new.data):
new.data[j] = [val/other for val in rowvals]
return new
else:
return self.tocsr() / other
[docs] def copy(self):
M, N = self.shape
new = self._lil_container(self.shape, dtype=self.dtype)
# This is ~14x faster than calling deepcopy() on rows and data.
_csparsetools.lil_get_row_ranges(M, N, self.rows, self.data,
new.rows, new.data, range(M),
0, N, 1, N)
return new
copy.__doc__ = spmatrix.copy.__doc__
[docs] def reshape(self, *args, **kwargs):
shape = check_shape(args, self.shape)
order, copy = check_reshape_kwargs(kwargs)
# Return early if reshape is not required
if shape == self.shape:
if copy:
return self.copy()
else:
return self
new = self._lil_container(shape, dtype=self.dtype)
if order == 'C':
ncols = self.shape[1]
for i, row in enumerate(self.rows):
for col, j in enumerate(row):
new_r, new_c = np.unravel_index(i * ncols + j, shape)
new[new_r, new_c] = self[i, j]
elif order == 'F':
nrows = self.shape[0]
for i, row in enumerate(self.rows):
for col, j in enumerate(row):
new_r, new_c = np.unravel_index(i + j * nrows, shape, order)
new[new_r, new_c] = self[i, j]
else:
raise ValueError("'order' must be 'C' or 'F'")
return new
reshape.__doc__ = spmatrix.reshape.__doc__
[docs] def resize(self, *shape):
shape = check_shape(shape)
new_M, new_N = shape
M, N = self.shape
if new_M < M:
self.rows = self.rows[:new_M]
self.data = self.data[:new_M]
elif new_M > M:
self.rows = np.resize(self.rows, new_M)
self.data = np.resize(self.data, new_M)
for i in range(M, new_M):
self.rows[i] = []
self.data[i] = []
if new_N < N:
for row, data in zip(self.rows, self.data):
trunc = bisect_left(row, new_N)
del row[trunc:]
del data[trunc:]
self._shape = shape
resize.__doc__ = spmatrix.resize.__doc__
[docs] 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__ = spmatrix.toarray.__doc__
[docs] def transpose(self, axes=None, copy=False):
return self.tocsr(copy=copy).transpose(axes=axes, copy=False).tolil(copy=False)
transpose.__doc__ = spmatrix.transpose.__doc__
[docs] def tolil(self, copy=False):
if copy:
return self.copy()
else:
return self
tolil.__doc__ = spmatrix.tolil.__doc__
[docs] 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 = 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 = 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__ = spmatrix.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_matrix, isspmatrix_lil
>>> isspmatrix_lil(lil_matrix([[5]]))
True
>>> from scipy.sparse import lil_matrix, csr_matrix, isspmatrix_lil
>>> isspmatrix_lil(csr_matrix([[5]]))
False
"""
from ._arrays import lil_array
return isinstance(x, lil_matrix) or isinstance(x, lil_array)