# 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 as sp
>>> 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

## 2.5.2.3. 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

arithmetic 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