scipy.sparse.

coo_array#

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

A sparse array in COOrdinate format.

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

This can be instantiated in several ways:
coo_array(D)

where D is an ndarray

coo_array(S)

with another sparse array or matrix S (equivalent to S.tocoo())

coo_array(shape, [dtype])

to construct an empty sparse array with shape shape dtype is optional, defaulting to dtype=’d’.

coo_array((data, coords), [shape])
to construct from existing data and index arrays:

  1. data[:] the entries of the sparse array, in any order

  2. coords[i][:] the axis-i coordinates of the data entries

Where A[coords] = data, and coords is a tuple of index arrays. When shape is not specified, it is inferred from the index arrays.

Attributes:
dtypedtype

Data type of the sparse array

shapetuple of integers

Shape of the sparse array

ndimint

Number of dimensions of the sparse array

nnz

Number of stored values, including explicit zeros.

size

Number of stored values.

data

COO format data array of the sparse array

coords

COO format tuple of index arrays

has_canonical_formatbool

Whether the matrix has sorted coordinates and no duplicates

format

Format string for matrix.

T

Transpose.

Methods

__len__()

arcsin()

Element-wise arcsin.

arcsinh()

Element-wise arcsinh.

arctan()

Element-wise arctan.

arctanh()

Element-wise arctanh.

argmax([axis, out])

Return indices of maximum elements along an axis.

argmin([axis, out])

Return indices of minimum elements along an axis.

asformat(format[, copy])

Return this array/matrix in the passed format.

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()

Number of non-zero entries, equivalent to

deg2rad()

Element-wise deg2rad.

diagonal([k])

Returns the kth diagonal of the array/matrix.

dot(other)

Ordinary dot product

eliminate_zeros()

Remove zero entries from the array/matrix

expm1()

Element-wise expm1.

floor()

Element-wise floor.

log1p()

Element-wise log1p.

max([axis, out])

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])

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])

Return the maximum of the array/matrix or maximum along an axis, ignoring any NaNs.

nanmin([axis, out])

Return the minimum of the array/matrix or minimum along an axis, ignoring any NaNs.

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.

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.

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 array/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.

__mul__

Notes

Sparse arrays 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 arrays

  • Once a COO array 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 sparse array
>>> import numpy as np
>>> from scipy.sparse import coo_array
>>> coo_array((3, 4), dtype=np.int8).toarray()
array([[0, 0, 0, 0],
       [0, 0, 0, 0],
       [0, 0, 0, 0]], dtype=int8)

>>> # Constructing a sparse array 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_array((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 sparse array 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_array((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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