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"""LInked List sparse matrix class
"""
from __future__ import division, print_function, absolute_import
__docformat__ = "restructuredtext en"
__all__ = ['lil_matrix','isspmatrix_lil']
from bisect import bisect_left
import numpy as np
from scipy._lib.six import xrange, zip
from .base import spmatrix, isspmatrix
from .sputils import (getdtype, isshape, isscalarlike, IndexMixin,
upcast_scalar, get_index_dtype, isintlike, check_shape,
check_reshape_kwargs)
from . import _csparsetools
class lil_matrix(spmatrix, IndexMixin):
"""Row-based linked list 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 nonzero elements
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'
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)
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 = np.asmatrix(arg1)
except TypeError:
raise TypeError('unsupported matrix type')
else:
from .csr import csr_matrix
A = csr_matrix(A, dtype=dtype).tolil()
self._shape = check_shape(A.shape)
self.dtype = A.dtype
self.rows = A.rows
self.data = A.data
def __iadd__(self,other):
self[:,:] = self + other
return self
def __isub__(self,other):
self[:,:] = self - other
return self
def __imul__(self,other):
if isscalarlike(other):
self[:,:] = self * other
return self
else:
return NotImplemented
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
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')
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__
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]
def getrowview(self, i):
"""Returns a view of the 'i'th row (without copying).
"""
new = lil_matrix((1, self.shape[1]), dtype=self.dtype)
new.rows[0] = self.rows[i]
new.data[0] = self.data[i]
return new
def getrow(self, i):
"""Returns a copy of the 'i'th row.
"""
i = self._check_row_bounds(i)
new = lil_matrix((1, self.shape[1]), dtype=self.dtype)
new.rows[0] = self.rows[i][:]
new.data[0] = self.data[i][:]
return new
def _check_row_bounds(self, i):
if i < 0:
i += self.shape[0]
if i < 0 or i >= self.shape[0]:
raise IndexError('row index out of bounds')
return i
def _check_col_bounds(self, j):
if j < 0:
j += self.shape[1]
if j < 0 or j >= self.shape[1]:
raise IndexError('column index out of bounds')
return j
def __getitem__(self, index):
"""Return the element(s) index=(i, j), where j may be a slice.
This always returns a copy for consistency, since slices into
Python lists return copies.
"""
# Scalar fast path first
if isinstance(index, tuple) and len(index) == 2:
i, j = index
# Use isinstance checks for common index types; this is
# ~25-50% faster than isscalarlike. Other types are
# handled below.
if ((isinstance(i, int) or isinstance(i, np.integer)) and
(isinstance(j, int) or isinstance(j, np.integer))):
v = _csparsetools.lil_get1(self.shape[0], self.shape[1],
self.rows, self.data,
i, j)
return self.dtype.type(v)
# Utilities found in IndexMixin
i, j = self._unpack_index(index)
# Proper check for other scalar index types
i_intlike = isintlike(i)
j_intlike = isintlike(j)
if i_intlike and j_intlike:
v = _csparsetools.lil_get1(self.shape[0], self.shape[1],
self.rows, self.data,
i, j)
return self.dtype.type(v)
elif j_intlike or isinstance(j, slice):
# column slicing fast path
if j_intlike:
j = self._check_col_bounds(j)
j = slice(j, j+1)
if i_intlike:
i = self._check_row_bounds(i)
i = xrange(i, i+1)
i_shape = None
elif isinstance(i, slice):
i = xrange(*i.indices(self.shape[0]))
i_shape = None
else:
i = np.atleast_1d(i)
i_shape = i.shape
if i_shape is None or len(i_shape) == 1:
return self._get_row_ranges(i, j)
i, j = self._index_to_arrays(i, j)
if i.size == 0:
return lil_matrix(i.shape, dtype=self.dtype)
new = lil_matrix(i.shape, dtype=self.dtype)
i, j = _prepare_index_for_memoryview(i, j)
_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 xrange
Rows indexed. If xrange, must be within valid bounds.
col_slice : slice
Columns indexed
"""
j_start, j_stop, j_stride = col_slice.indices(self.shape[1])
col_range = xrange(j_start, j_stop, j_stride)
nj = len(col_range)
new = lil_matrix((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 __setitem__(self, index, x):
# Scalar fast path first
if isinstance(index, tuple) and len(index) == 2:
i, j = index
# Use isinstance checks for common index types; this is
# ~25-50% faster than isscalarlike. Scalar index
# assignment for other types is handled below together
# with fancy indexing.
if ((isinstance(i, int) or isinstance(i, np.integer)) and
(isinstance(j, int) or isinstance(j, np.integer))):
x = self.dtype.type(x)
if x.size > 1:
# Triggered if input was an ndarray
raise ValueError("Trying to assign a sequence to an item")
_csparsetools.lil_insert(self.shape[0], self.shape[1],
self.rows, self.data, i, j, x)
return
# General indexing
i, j = self._unpack_index(index)
# shortcut for common case of full matrix assign:
if (isspmatrix(x) and isinstance(i, slice) and i == slice(None) and
isinstance(j, slice) and j == slice(None)
and x.shape == self.shape):
x = lil_matrix(x, dtype=self.dtype)
self.rows = x.rows
self.data = x.data
return
i, j = self._index_to_arrays(i, j)
if isspmatrix(x):
x = x.toarray()
# Make x and i into the same shape
x = np.asarray(x, dtype=self.dtype)
x, _ = np.broadcast_arrays(x, i)
if x.shape != i.shape:
raise ValueError("shape mismatch in assignment")
# Set values
i, j, x = _prepare_index_for_memoryview(i, j, x)
_csparsetools.lil_fancy_set(self.shape[0], self.shape[1],
self.rows, self.data,
i, j, x)
def _mul_scalar(self, other):
if other == 0:
# Multiply by zero: return the zero matrix
new = lil_matrix(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
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
def copy(self):
from copy import deepcopy
new = lil_matrix(self.shape, dtype=self.dtype)
new.data = deepcopy(self.data)
new.rows = deepcopy(self.rows)
return new
copy.__doc__ = spmatrix.copy.__doc__
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 = lil_matrix(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__
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__
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__
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__
def tolil(self, copy=False):
if copy:
return self.copy()
else:
return self
tolil.__doc__ = spmatrix.tolil.__doc__
def tocsr(self, copy=False):
lst = [len(x) for x in self.rows]
idx_dtype = get_index_dtype(maxval=max(self.shape[1], sum(lst)))
indptr = np.cumsum([0] + lst, dtype=idx_dtype)
indices = np.array([x for y in self.rows for x in y], dtype=idx_dtype)
data = np.array([x for y in self.data for x in y], dtype=self.dtype)
from .csr import csr_matrix
return csr_matrix((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
"""
return isinstance(x, lil_matrix)