Storage Schemes

Storage Schemes#

Sparse Array Classes#

  • There are seven sparse array types in scipy.sparse:

    1. csr_array: Compressed Sparse Row format

    2. csc_array: Compressed Sparse Column format

    3. bsr_array: Block Sparse Row format

    4. lil_array: List of Lists format

    5. dok_array: Dictionary of Keys format

    6. coo_array: COOrdinate format (aka IJV, triplet format)

    7. dia_array: DIAgonal format

  • each suitable for some tasks

  • many employ sparsetools C++ module by Nathan Bell

  • assume the following is imported:

import numpy as np
import scipy as sp
import matplotlib.pyplot as plt

  • warning for Numpy users:

    • passing a sparse array object to NumPy functions that expect ndarray/matrix does not work. Use sparse functions.

    • the older csr_matrix classes use ‘*’ for matrix multiplication (dot product) and ‘A.multiply(B)’ for elementwise multiplication.

    • the newer csr_array uses ‘@’ for dot product and ‘*’ for elementwise multiplication

    • sparse arrays can be 1D or 2D, but not nD for n > 2 (unlike Numpy arrays).

Common Methods#

  • all scipy.sparse array classes are subclasses of sparray

    • default implementation of arithmetic operations

      • always converts to CSR

      • subclasses override for efficiency

    • shape, data type, set/get

    • indices of nonzero values in the array

    • format conversion, interaction with NumPy (toarray())

    • …

  • attributes:

    • mtx.T - transpose (same as mtx.transpose())

    • mtx.real - real part of complex matrix

    • mtx.imag - imaginary part of complex matrix

    • mtx.size - the number of nonzeros (same as self.getnnz())

    • mtx.shape - the number of rows and columns (tuple)

  • data and indices usually stored in 1D NumPy arrays

Summary#

format

matrix * vector

get item

fancy get

set item

fancy set

solvers

note

CSR

sparsetools

yes

yes

slow

.

any

has data array, fast row-wise ops

CSC

sparsetools

yes

yes

slow

.

any

has data array, fast column-wise ops

BSR

sparsetools

.

.

.

.

specialized

has data array, specialized

COO

sparsetools

.

.

.

.

iterative

has data array, facilitates fast conversion

DIA

sparsetools

.

.

.

.

iterative

has data array, specialized

LIL

via CSR

yes

yes

yes

yes

iterative

arithmetic via CSR, incremental construction

DOK

Python

yes

one axis only

yes

yes

iterative

O(1) item access, incremental construction, slow arithmetic
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