Core_EDA

# What is gather and scatter

gather and scattergather and scatter

First ref Algorithm 11.2 from Saad(page 379-380).

![](clipboard-202503230113-vz3yb.png)

![](clipboard-202503230114-sgipb.png)

When conducting CSC stored matrix vector multiplication, first we get the i-th column. Since the matrix is sparse, this operation is called 'gather'. The column is then added to the full vector y, which is called "scatter".

In addition, the stop condition of iterative loop in line 2 of the pseudocode illustrates the advantage of the last element in column pointer 'Ap' from another aspect. The access of each column of the matrix has the same code.

In other open software like INTEL MKL, this format is called 'Three array variation of CSC format', a variation of four array representation. 'pointerB' indicates the Beginning of the column and 'pointerE' indicates the End. It needs some cautions that various software may take the input with a little of difference.

![](clipboard-202503230114-pejt2.png)

By the way, the function by Y. Saad is called 'SAXPY' which is synonym of 'Sparse A times X Plus Y', while a more common one is 'cs_gaxpy' by Davis, 'Generalized (scaler) A times X Plus Y'. Some software may also use the name 'mvp' which is shortened for 'Matrix-Vector Product'. It is hoped that when calling all kinds of software no matter open or inner, the colleagues may find the relevant function.

http://10.30.200.21:8088/attachments/download/2807/Saad2003Iterative_Iterative_Methods_for_Sparse_Linear_Systems.pdf