scipy.sparse.coo_matrix

class scipy.sparse.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, ij), [shape=(M, N)])

The arguments ‘data’ and ‘ij’ represent three arrays:

1. data[:] the entries of the matrix, in any order
2. ij[0][:] the row indices of the matrix entries
3. ij[1][:] the column indices of the matrix entries

Where A[ij[0][k], ij[1][k] = data[k]. When shape is not specified, it is inferred from the index arrays

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

>>> from scipy.sparse import *
>>> from scipy import *
>>> coo_matrix( (3,4), dtype=int8 ).todense()
matrix([[0, 0, 0, 0],
        [0, 0, 0, 0],
        [0, 0, 0, 0]], dtype=int8)

>>> row  = array([0,3,1,0])
>>> col  = array([0,3,1,2])
>>> data = 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  = 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])
>>> 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]])

Attributes

dtype
shape
ndim	int(x[, base]) -> integer
nnz

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

Methods

asformat(format)	Return this matrix in a given sparse format
asfptype()	Upcast matrix to a floating point format (if necessary)
astype(t)
conj()
conjugate()
copy()
diagonal()	Returns the main diagonal of the matrix
dot(other)
getH()
get_shape()
getcol(j)	Returns a copy of column j of the matrix, as an (m x 1) sparse
getformat()
getmaxprint()
getnnz()
getrow(i)	Returns a copy of row i of the matrix, as a (1 x n) sparse
mean([axis])	Average the matrix over the given axis.
multiply(other)	Point-wise multiplication by another matrix
nonzero()	nonzero indices
reshape(shape)
set_shape(shape)
setdiag(values[, k])	Fills the diagonal elements {a_ii} with the values from the given sequence.
sum([axis])	Sum the matrix over the given axis.
toarray()
tobsr([blocksize])
tocoo([copy])
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()
todia()
todok()
tolil()
transpose([copy])