How to solve linear equation for 3 unkowns using SOR in GPU

Question

Seereen 2019-9-18

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/481014-how-to-solve-linear-equation-for-3-unkowns-using-sor-in-gpu

回答： Matt J 2019-9-19

在 MATLAB Online 中打开

I am trying to find the motion (u,v,w) for each pixel in my frame by solving the linear system Ax=b

A is a 3 by 3 ... each element for example A (1,1) is equivalent to the frame size ... let's say ( 512 X 512)

A = [ A B C ; D E F ; G H I]

x is unknown need to be estimated ( u,v,w) ... u , v and w should be ( 512 X 512)

b is a 3 by 1 matrix and each element is equivalent to the frame size as well

b= [ J K L]

I am trying to solve this system using the SOR iteration method so I have this provided function

problems:

-In this code I have to use omega = 1 otherwise I got the wrong answer totaly !

-How can I solve this system using the SOR iteration method?

-How can I improve it to use GPU to speed up?

Any assistance will be so appreciated

function [u,v,w,error]=SORstep(A,B,C,D,E,F,G,H,I,J,K,L,omega,du_temp,dv_temp,dw_temp) % du_temp, dv_temp, dw_temp previouse estimation 
u=((1.0-omega).*du_temp)+(omega./A).*(J-(B.*dv_temp+C.*dw_temp));
v=((1.0-omega).*dv_temp)+(omega./E).*(K-(D.*u+F.*dw_temp));
w=((1.0-omega).*dw_temp)+(omega./I).*(L-(G.*u+H.*v));
error = norm([u;v;w]-[du_temp;dv_temp;dw_temp])./norm([u;v;w]);
end 

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Answer 1

Matt J 2019-9-18

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/481014-how-to-solve-linear-equation-for-3-unkowns-using-sor-in-gpu#answer_392494

在 MATLAB Online 中打开

Not sure why you would be using an iterative method when an analytical solution is available.

A=gpuArray.rand(3,3,512^2);
b=gpuArray.rand(3,1,512^2);
x=pagefun(@mldivide, A,b);
u=reshape(x(1,:),512,512);
v=reshape(x(2,:),512,512);
w=reshape(x(3,:),512,512);