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).toarray()
array([[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)).toarray()
array([[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)).toarray()
array([[3, 0, 1, 0],
       [0, 2, 0, 0],
       [0, 0, 0, 0],
       [0, 0, 0, 1]])


nnz Number of stored values, including explicit zeros.
dtype (dtype) Data type of the matrix
shape (2-tuple) Shape of the matrix
ndim (int) Number of dimensions (this is always 2)
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.
count_nonzero() Number of non-zero entries, equivalent to
deg2rad() Element-wise deg2rad.
diagonal() Returns the main diagonal of the matrix
dot(other) Ordinary dot product
eliminate_zeros() Remove zero entries from the matrix
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 matrix (column vector).
getnnz([axis]) Number of stored values, including explicit zeros.
getrow(i) Returns a copy of row i of the matrix, as a (1 x n) sparse matrix (row vector).
log1p() Element-wise log1p.
max([axis, out]) Return the maximum of the matrix or maximum along an axis.
mean([axis, dtype, out]) Compute the arithmetic mean along the specified axis.
min([axis, out]) Return the minimum of the matrix or maximum along an axis.
multiply(other) Point-wise multiplication by another matrix
nonzero() nonzero indices
power(n[, dtype]) This function performs element-wise power.
rad2deg() Element-wise rad2deg.
reshape(shape[, order]) Gives a new shape to a sparse matrix without changing its data.
rint() Element-wise rint.
setdiag(values[, k]) Set diagonal or off-diagonal elements of the array.
sign() Element-wise sign.
sin() Element-wise sin.
sinh() Element-wise sinh.
sqrt() Element-wise sqrt.
sum([axis, dtype, out]) Sum the matrix elements over a given axis.
sum_duplicates() Eliminate duplicate matrix entries by adding them together
tan() Element-wise tan.
tanh() Element-wise tanh.
toarray([order, out]) See the docstring for spmatrix.toarray.
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.
trunc() Element-wise trunc.