PHAS0102: Techniques of 
High-Performance Computing 

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d 24hourmaths.com 
a @24hmaths 

Assignment 2 
● On Moodle and mscroggs.co.uk/phas0102 
● Deadline: 5pm on Thursday 3 November 

Example problem 
● Poisson problem 


Finite differences 

0 1 2 ... N 
N+1 N+2 N+3 … 2N+1 
2N+2 … 3N+2 
N2+N … (N+1)2 - 1 

[live code demo] 

Sparse matrix storage 
● We would like to not have to store all the 0s in the  
matrix in memory. 
● Ideas? 

COO (coordinate) format 
● Store two lists of integers and one list of data: 
– First integer list is rows 
– Second integer list is columns 
– Data list is values in (row, column) 
● eg 
– [0, 1] 
– [1,0] 
– [0.5, 0.7] 
● COO is the easiest format to use to create a sparse matrix 

CSR (compressed sparse rows) format 
● Store two lists of integers and one list of data: 
– First integer list is columns 
– Second integer list is when row changes 
– Data list is values in (row, column) 
● eg 
– [0, 1] 
– [1] 
– [0.5, 0.7] 
● CSR uses less storage space, and is used by many sparse solvers. 

CSC (compressed sparse columns) format 
● This is the same as CSR, but with the role of rows  
and columns swapped. 

[live code demo] 

Other formats 
● There are lots of other sparse matrix formats,  
including: 
– LIL (list of lists) 
– DOK (dictionary of keys) 
– DIA (diagonal storage) 
– BSR (block sparse rows)