text: """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._version import NumpyVersion
  from scipy._lib.six import xrange, zip
  
  if NumpyVersion(np.__version__) >= '1.17.0':
      from scipy._lib._util import _broadcast_arrays
  else:
      from numpy import broadcast_arrays as _broadcast_arrays
  
  from .base import spmatrix, isspmatrix
  from .sputils import (getdtype, isshape, isscalarlike, IndexMixin,
                        upcast_scalar, get_index_dtype, isintlike, check_shape,
                        check_reshape_kwargs, asmatrix)
  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 = 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, _ = _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)
  