sparse.coo

A sparse matrix in COOrdinate or ‘triplet’ format

Module Contents

Classes

coo_matrix(self,arg1,shape=None,dtype=None,copy=False) A sparse matrix in COOrdinate format.

Functions

isspmatrix_coo(x) Is x of coo_matrix type?
class coo_matrix(arg1, shape=None, dtype=None, copy=False)

A sparse matrix in COOrdinate format.

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

This can be instantiated in several ways:
coo_matrix(D)
with a dense matrix D
coo_matrix(S)
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

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

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)
>>> # Constructing an empty matrix
>>> 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)
>>> # Constructing a matrix using ijv format
>>> 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]])
>>> # Constructing a matrix with duplicate indices
>>> 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 = coo_matrix((data, (row, col)), shape=(4, 4))
>>> # Duplicate indices are maintained until implicitly or explicitly summed
>>> np.max(coo.data)
1
>>> coo.toarray()
array([[3, 0, 1, 0],
       [0, 2, 0, 0],
       [0, 0, 0, 0],
       [0, 0, 0, 1]])
__init__(arg1, shape=None, dtype=None, copy=False)
getnnz(axis=None)
_check()

Checks data structure for consistency

transpose(axes=None, copy=False)
toarray(order=None, out=None)

See the docstring for spmatrix.toarray.

tocsc(copy=False)

Convert this matrix to Compressed Sparse Column format

Duplicate entries will be summed together.

>>> from numpy import array
>>> from scipy.sparse import coo_matrix
>>> row  = array([0, 0, 1, 3, 1, 0, 0])
>>> col  = array([0, 2, 1, 3, 1, 0, 0])
>>> data = array([1, 1, 1, 1, 1, 1, 1])
>>> A = coo_matrix((data, (row, col)), shape=(4, 4)).tocsc()
>>> A.toarray()
array([[3, 0, 1, 0],
       [0, 2, 0, 0],
       [0, 0, 0, 0],
       [0, 0, 0, 1]])
tocsr(copy=False)

Convert this matrix to Compressed Sparse Row format

Duplicate entries will be summed together.

>>> from numpy import array
>>> from scipy.sparse import coo_matrix
>>> row  = array([0, 0, 1, 3, 1, 0, 0])
>>> col  = array([0, 2, 1, 3, 1, 0, 0])
>>> data = array([1, 1, 1, 1, 1, 1, 1])
>>> A = coo_matrix((data, (row, col)), shape=(4, 4)).tocsr()
>>> A.toarray()
array([[3, 0, 1, 0],
       [0, 2, 0, 0],
       [0, 0, 0, 0],
       [0, 0, 0, 1]])
tocoo(copy=False)
todia(copy=False)
todok(copy=False)
diagonal(k=0)
_setdiag(values, k)
_with_data(data, copy=True)

Returns a matrix with the same sparsity structure as self, but with different data. By default the index arrays (i.e. .row and .col) are copied.

sum_duplicates()

Eliminate duplicate matrix entries by adding them together

This is an in place operation

_sum_duplicates(row, col, data)
eliminate_zeros()

Remove zero entries from the matrix

This is an in place operation

_add_dense(other)
_mul_vector(other)
_mul_multivector(other)
isspmatrix_coo(x)

Is x of coo_matrix type?

x
object to check for being a coo matrix
bool
True if x is a coo matrix, False otherwise
>>> from scipy.sparse import coo_matrix, isspmatrix_coo
>>> isspmatrix_coo(coo_matrix([[5]]))
True
>>> from scipy.sparse import coo_matrix, csr_matrix, isspmatrix_coo
>>> isspmatrix_coo(csr_matrix([[5]]))
False