scipy.sparse.

coo_matrix#

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

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

__len__()

__mul__(other)

arcsin()

Element-wise arcsin.

arcsinh()

Element-wise arcsinh.

arctan()

Element-wise arctan.

arctanh()

Element-wise arctanh.

argmax([axis, out, explicit])

Return indices of maximum elements along an axis.

argmin([axis, out, explicit])

Return indices of minimum elements along an axis.

asformat(format[, copy])

Return this array/matrix in the passed format.

asfptype()

Upcast matrix to a floating point format (if necessary)

astype(dtype[, casting, copy])

Cast the array/matrix elements to a specified type.

ceil()

Element-wise ceil.

conj([copy])

Element-wise complex conjugation.

conjugate([copy])

Element-wise complex conjugation.

copy()

Returns a copy of this array/matrix.

count_nonzero([axis])

Number of non-zero entries, equivalent to

deg2rad()

Element-wise deg2rad.

diagonal([k])

Returns the kth diagonal of the array/matrix.

dot(other)

Return the dot product of two arrays.

eliminate_zeros()

Remove zero entries from the array/matrix

expm1()

Element-wise expm1.

floor()

Element-wise floor.

getH()

Return the Hermitian transpose of this matrix.

get_shape()

Get the shape of the matrix

getcol(j)

Returns a copy of column j of the matrix, as an (m x 1) sparse matrix (column vector).

getformat()

Matrix storage format

getmaxprint()

Maximum number of elements to display when printed.

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, explicit])

Return the maximum of the array/matrix or maximum along an axis.

maximum(other)

Element-wise maximum between this and another array/matrix.

mean([axis, dtype, out])

Compute the arithmetic mean along the specified axis.

min([axis, out, explicit])

Return the minimum of the array/matrix or maximum along an axis.

minimum(other)

Element-wise minimum between this and another array/matrix.

multiply(other)

Point-wise multiplication by another array/matrix.

nanmax([axis, out, explicit])

Return the maximum, ignoring any Nans, along an axis.

nanmin([axis, out, explicit])

Return the minimum, ignoring any Nans, along an axis.

nonzero()

Nonzero indices of the array/matrix.

power(n[, dtype])

This function performs element-wise power.

rad2deg()

Element-wise rad2deg.

reshape(self, shape[, order, copy])

Gives a new shape to a sparse array/matrix without changing its data.

resize(*shape)

Resize the array/matrix in-place to dimensions given by shape

rint()

Element-wise rint.

set_shape(shape)

Set the shape of the matrix in-place

setdiag(values[, k])

Set diagonal or off-diagonal elements of the array/matrix.

sign()

Element-wise sign.

sin()

Element-wise sin.

sinh()

Element-wise sinh.

sqrt()

Element-wise sqrt.

sum([axis, dtype, out])

Sum the array/matrix elements over a given axis.

sum_duplicates()

Eliminate duplicate entries by adding them together

tan()

Element-wise tan.

tanh()

Element-wise tanh.

tensordot(other[, axes])

Return the tensordot product with another array along the given axes.

toarray([order, out])

Return a dense ndarray representation of this sparse array/matrix.

tobsr([blocksize, copy])

Convert this array/matrix to Block Sparse Row format.

tocoo([copy])

Convert this array/matrix to COOrdinate format.

tocsc([copy])

Convert this array/matrix to Compressed Sparse Column format

tocsr([copy])

Convert this array/matrix to Compressed Sparse Row format

todense([order, out])

Return a dense representation of this sparse matrix.

todia([copy])

Convert this array/matrix to sparse DIAgonal format.

todok([copy])

Convert this array/matrix to Dictionary Of Keys format.

tolil([copy])

Convert this array/matrix to List of Lists format.

trace([offset])

Returns the sum along diagonals of the sparse array/matrix.

transpose([axes, copy])

Reverses the dimensions of the sparse array/matrix.

trunc()

Element-wise trunc.

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]])
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