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 ``Ai[k], j[k] = datak``. When shape is not specified, it is inferred from the index arrays
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 stored values, including explicit zeros 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
Notes -----
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)
Examples --------
>>> # 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])