coo_matrix — SciPy v1.15.2 Manual (original) (raw)

scipy.sparse.

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

A sparse matrix in COOrdinate format.

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

This can be instantiated in several ways:

coo_matrix(D)

where D is a 2-D ndarray

coo_matrix(S)

with another sparse array or 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

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 COO 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)

Canonical format

• Entries and coordinates sorted by row, then column.
• There are no duplicate entries (i.e. duplicate (i,j) locations)
• Data arrays MAY have explicit zeros.

Examples

Constructing an empty matrix

import numpy as np 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 coordinates

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 coordinates 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]])

Attributes:

dtypedtype

Data type of the matrix

shape2-tuple

Shape of the matrix

ndimint

Number of dimensions (this is always 2)

nnz

Number of stored values, including explicit zeros.

size

Number of stored values.

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

has_canonical_formatbool

Whether the matrix has sorted indices and no duplicates

format

Format string for matrix.

T

Transpose.

Methods