class scipy.sparse.lil_matrix(arg1, shape=None, dtype=None, copy=False)[source]

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:
with a dense matrix or rank-2 ndarray D
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’.


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


shape Get shape of a matrix.
nnz Number of stored values, including explicit zeros.
dtype (dtype) Data type of the matrix
ndim (int) Number of dimensions (this is always 2)
data LIL format data array of the matrix
rows LIL format row index array of the matrix


asformat(format) Return this matrix in a given sparse format
asfptype() Upcast matrix to a floating point format (if necessary)
astype(t) Cast the matrix elements to a specified type.
conj() Element-wise complex conjugation.
conjugate() Element-wise complex conjugation.
copy() Returns a copy of this matrix.
count_nonzero() Number of non-zero entries, equivalent to
diagonal() Returns the main diagonal of the matrix
dot(other) Ordinary dot product
getH() Return the Hermitian transpose of this matrix.
get_shape() Get shape of a matrix.
getcol(j) Returns a copy of column j of the matrix, as an (m x 1) sparse matrix (column vector).
getformat() Format of a matrix representation as a string.
getmaxprint() Maximum number of elements to display when printed.
getnnz([axis]) Number of stored values, including explicit zeros.
getrow(i) Returns a copy of the ‘i’th row.
getrowview(i) Returns a view of the ‘i’th row (without copying).
maximum(other) Element-wise maximum between this and another matrix.
mean([axis, dtype, out]) Compute the arithmetic mean along the specified axis.
minimum(other) Element-wise minimum between this and another matrix.
multiply(other) Point-wise multiplication by another matrix
nonzero() nonzero indices
power(n[, dtype]) Element-wise power.
reshape(shape[, order]) Gives a new shape to a sparse matrix without changing its data.
set_shape(shape) See reshape.
setdiag(values[, k]) Set diagonal or off-diagonal elements of the array.
sum([axis, dtype, out]) Sum the matrix elements over a given axis.
toarray([order, out]) Return a dense ndarray representation of this matrix.
tobsr([blocksize, copy]) Convert this matrix to Block Sparse Row format.
tocoo([copy]) Convert this matrix to COOrdinate format.
tocsc([copy]) Convert this matrix to Compressed Sparse Column format.
tocsr([copy]) Convert this matrix to Compressed Sparse Row format.
todense([order, out]) Return a dense matrix representation of this matrix.
todia([copy]) Convert this matrix to sparse DIAgonal format.
todok([copy]) Convert this matrix to Dictionary Of Keys format.
tolil([copy]) Convert this matrix to LInked List format.
transpose([axes, copy]) Reverses the dimensions of the sparse matrix.