# 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

## 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

## 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