2.5.2. Storage Schemes

• 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).

2.5.2.1. 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

2.5.2.2. Sparse Array Classes

• Diagonal Format (DIA)
  • Examples
• List of Lists Format (LIL)
  • Examples
• Dictionary of Keys Format (DOK)
  • Examples
• Coordinate Format (COO)
  • Examples
• Compressed Sparse Row Format (CSR)
  • Examples
• Compressed Sparse Column Format (CSC)
  • Examples
• Block Compressed Row Format (BSR)
  • Examples

2.5.2.3. Summary

Summary of storage schemes.

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