I just started learning Matlab.
I follow the help and use the code shown below (Matlab Full) to calculate the Mandelbrot Set, z(n+1)=z(n)^2+C (30000 iterations). The code uses GPU.
It is compared to a program I make by using VB.net, which, I also don't know much and the code is not optimized. The code uses CPU because I don't know how to use GPU in VB.
The (Matlab Part) code is a modification of the Matlab code, in which I try to calculate part of the pixels instead of the full image. The code uses GPU, but only 84%~90% depending on the region calculating.
For each type of code, I calculate three regions (with same number of pixels):
(1) Divergent, small region around Creal=-2.7, Cimag=0.5, where all C values give divergent results. VB program takes only 0.14s to complete, since the VB program uses for loop to go through all pixels and at each pixel if the calculation diverges, the iteration will stop and it will move on to the next pixel. The matlab code, on the contrary, takes a lot of time since it needs to go through all the iterations.
(2) Full region, covering Creal from -2.8 to 1.5, Cimag centered at 0. This region shows the whole Mandelbrot Set structure and contains both divergent and convergent regions.
(3) Convergent, small region around Creal=0 and Cimag=0, where all C values give convergent results. Both VB and Matlab programs need to go through all pixels. But the Matlab Full code takes much less time to complete.
So my questions are:
(1) How can I speed up my (Matlab Full) code? Now, the code needs to calculate all pixels (the whole z matrix) even if some of them diverged. And the code needs to go through all iterations even if all pixels diverged. I try to calculate some of the pixels only, as shown in (Matlab Part) code. But the code takes much longer time, as shown in the figure.
(2) The (Matlab Part) code taks much longer time. It takes 84% to 90% of the GPU instead of 100% as in (Matlab Full) case. And (Matlab Part) code takes 100% of one of the CPU thread. Why is this?
(3) In each region, the (Matlab Full) code will need to go through all iterations. I expect it to take the same amount of time to complete. But no, it takes much less time to complete in the convergent region. Why is this difference?
(4) This is not a question. From the comparison of (Matlab Full) and VB results at convergent region, we see that Matlab code runs much faster than my (not optimized) VB code. I expect the Matlab code will be much faster at other regions if it doesn't need to go through all iterations.
Calculation Time Figure:
(Matlab Full) Code:
function ButtonGPUPushed(app, event)
X1=str2double(app.X1EditField.Value);
X2=str2double(app.X2EditField.Value);
Y1=str2double(app.Y1EditField.Value);
XX=gpuArray.linspace(X1,X2,XN);
YY=gpuArray.linspace(Y1,Y2,YN);
[ttt,vvv]=meshgrid(XX,YY);
count=zeros(size(CU),'gpuArray');
Cin=[0 0.15 0.25;0 0.6 1;1 0.6 0;0 1 0;0.6 0 1;1 0 0.6;0 0 0];
ooo=[(linspace(Cin(k,1),Cin(k+1,1),CStepSize))' (linspace(Cin(k,2),Cin(k+1,2),CStepSize))' (linspace(Cin(k,3),Cin(k+1,3),CStepSize))'];
for k=1:(size(Cblock,1)-1)
colormap(app.UIAxes, Cblock)
ii=image(app.UIAxes,[X1 X2],[Y1 Y2],count);
set(app.UIAxes,"YDir","normal")
(Matlab Part) Code, the 'For' iteration part is changed to:
for k=1:(size(Cblock,1)-1)
zz(inside)=zz(inside).*zz(inside)+CU(inside);
