2.5.2. Storage Schemes

• seven sparse matrix types in scipy.sparse:

  1. csc_matrix: Compressed Sparse Column format
  2. csr_matrix: Compressed Sparse Row format
  3. bsr_matrix: Block Sparse Row format
  4. lil_matrix: List of Lists format
  5. dok_matrix: Dictionary of Keys format
  6. coo_matrix: COOrdinate format (aka IJV, triplet format)
  7. dia_matrix: 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.sparse as sps
  >>> import matplotlib.pyplot as plt
  

• warning for NumPy users:

  • the multiplication with ‘*’ is the matrix multiplication (dot product)

  • not part of NumPy!

    • passing a sparse matrix object to NumPy functions expecting ndarray/matrix does not work

2.5.2.1. Common Methods

• all scipy.sparse classes are subclasses of spmatrix

  • default implementation of arithmetic operations

    • always converts to CSR
    • subclasses override for efficiency

  • shape, data type set/get

  • nonzero indices

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

  • ...

• attributes:

  • mtx.A - same as mtx.toarray()
  • mtx.T - transpose (same as mtx.transpose())
  • mtx.H - Hermitian (conjugate) 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 usually stored in NumPy arrays

2.5.2.2. Sparse Matrix Classes

• 2.5.2.2.1. Diagonal Format (DIA)
  • 2.5.2.2.1.1. Examples
• 2.5.2.2.2. List of Lists Format (LIL)
  • 2.5.2.2.2.1. Examples
• 2.5.2.2.3. Dictionary of Keys Format (DOK)
  • 2.5.2.2.3.1. Examples
• 2.5.2.2.4. Coordinate Format (COO)
  • 2.5.2.2.4.1. Examples
• 2.5.2.2.5. Compressed Sparse Row Format (CSR)
  • 2.5.2.2.5.1. Examples
• 2.5.2.2.6. Compressed Sparse Column Format (CSC)
  • 2.5.2.2.6.1. Examples
• 2.5.2.2.7. Block Compressed Row Format (BSR)
  • 2.5.2.2.7.1. Examples

2.5.2.3. Summary

Summary of storage schemes.

format	matrix * vector	get item	fancy get	set item	fancy set	solvers	note
DIA	sparsetools	.	.	.	.	iterative	has data array, specialized
LIL	via CSR	yes	yes	yes	yes	iterative	arithmetics via CSR, incremental construction
DOK	python	yes	one axis only	yes	yes	iterative	O(1) item access, incremental construction
COO	sparsetools	.	.	.	.	iterative	has data array, facilitates fast conversion
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