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

A sparse matrix in COOrdinate format.

Also known as the ‘ijv’ or ‘triplet’ format.

This can be instantiated in several ways:
with a dense matrix D
with another sparse matrix S (equivalent to S.tocoo())
coo_matrix((M, N), [dtype])
to construct an empty matrix with shape (M, N) dtype is optional, defaulting to dtype=’d’.
coo_matrix((data, (i, j)), [shape=(M, N)])
to construct from three arrays:
  1. data[:] the entries of the matrix, in any order
  2. i[:] the row indices of the matrix entries
  3. j[:] the column indices of the matrix entries

Where A[i[k], j[k]] = data[k]. When shape is not specified, it is inferred from the index arrays


Sparse matrices can be used in arithmetic operations: they support addition, subtraction, multiplication, division, and matrix power.

Advantages of the COO format
  • facilitates fast conversion among sparse formats
  • permits duplicate entries (see example)
  • very fast conversion to and from CSR/CSC formats
Disadvantages of the COO format
  • does not directly support:
    • arithmetic operations
    • slicing
Intended Usage
  • COO is a fast format for constructing sparse matrices
  • Once a matrix has been constructed, convert to CSR or CSC format for fast arithmetic and matrix vector operations
  • By default when converting to CSR or CSC format, duplicate (i,j) entries will be summed together. This facilitates efficient construction of finite element matrices and the like. (see example)


>>> from scipy.sparse import coo_matrix
>>> coo_matrix((3,4), dtype=np.int8).todense()
matrix([[0, 0, 0, 0],
        [0, 0, 0, 0],
        [0, 0, 0, 0]], dtype=int8)
>>> row  = np.array([0,3,1,0])
>>> col  = np.array([0,3,1,2])
>>> data = np.array([4,5,7,9])
>>> coo_matrix((data,(row,col)), shape=(4,4)).todense()
matrix([[4, 0, 9, 0],
        [0, 7, 0, 0],
        [0, 0, 0, 0],
        [0, 0, 0, 5]])
>>> # example with duplicates
>>> row  = np.array([0,0,1,3,1,0,0])
>>> col  = np.array([0,2,1,3,1,0,0])
>>> data = np.array([1,1,1,1,1,1,1])
>>> coo_matrix((data, (row,col)), shape=(4,4)).todense()
matrix([[3, 0, 1, 0],
        [0, 2, 0, 0],
        [0, 0, 0, 0],
        [0, 0, 0, 1]])


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 COO format data array of the matrix
row COO format row index array of the matrix
col COO format column index array of the matrix


arcsin() Element-wise arcsin.
arcsinh() Element-wise arcsinh.
arctan() Element-wise arctan.
arctanh() Element-wise arctanh.
asformat(format) Return this matrix in a given sparse format
asfptype() Upcast matrix to a floating point format (if necessary)
ceil() Element-wise ceil.
deg2rad() Element-wise deg2rad.
diagonal() Returns the main diagonal of the matrix
dot(other) Ordinary dot product ..
expm1() Element-wise expm1.
floor() Element-wise floor.
getcol(j) Returns a copy of column j of the matrix, as an (m x 1) sparse
getrow(i) Returns a copy of row i of the matrix, as a (1 x n) sparse
log1p() Element-wise log1p.
max() Maximum of the elements of this matrix.
mean([axis]) Average the matrix over the given axis.
min() Minimum of the elements of this matrix.
multiply(other) Point-wise multiplication by another matrix
nonzero() nonzero indices
rad2deg() Element-wise rad2deg.
rint() Element-wise rint.
setdiag(values[, k]) Fills the diagonal elements {a_ii} with the values from the given sequence.
sign() Element-wise sign.
sin() Element-wise sin.
sinh() Element-wise sinh.
sqrt() Element-wise sqrt.
sum([axis]) Sum the matrix over the given axis.
tan() Element-wise tan.
tanh() Element-wise tanh.
toarray([order, out]) See the docstring for spmatrix.toarray.
tocsc() Return a copy of this matrix in Compressed Sparse Column format
tocsr() Return a copy of this matrix in Compressed Sparse Row format
todense([order, out]) Return a dense matrix representation of this matrix.
trunc() Element-wise trunc.