Optomize a vectorized code

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Christopher
Christopher 2014-11-10
编辑： Christopher 2014-11-10
I have a vectorized code. It runs fast (I think), but I would benefit enormously from reducing its computational cost. I have attached a picture of the result of the MATLAB profiler and the text of the code is appended:
This is a small part of a much larger code but it is a huge bottleneck.
Some matrix sizes: brdzeros: 4x4 CLa_wbrd: 128x128 CLa: 120x120 Qx_La, CPLa_t, etc.: 120x120
As you can see, the steps of the code are:
1. [ln. 978-986] Pad a matrix with periodic borders.
2. [ln. 990-1006] create matrices which are offset by 1 or -1 columns or 1 or -1 rows
3. [ln. 1009-1025] divide matrices by another preallocated matrix
4. [ln. 1029-1042] solve a finite difference equation using the above preallocated matrices
5. [ln. 1044-1045] get a ratio of some results.
Are there faster ways of doing the same computations? Could I use GPU acceleration?
Any ideas or strategies are much appreciated.
Code:
for d=1:dstep
% new concentrations mapped to wbrd grid
CLa_wbrd = [brdzeros CLa(end-brd+1:end,:) brdzeros;
CLa(:,end-brd+1:end) CLa CLa(:,1:brd);
brdzeros CLa(1:brd,:) brdzeros];
CSm_wbrd = [brdzeros CSm(end-brd+1:end,:) brdzeros;
CSm(:,end-brd+1:end) CSm CSm(:,1:brd);
brdzeros CSm(1:brd,:) brdzeros];
CYb_wbrd = [brdzeros CYb(end-brd+1:end,:) brdzeros;
CYb(:,end-brd+1:end) CYb CYb(:,1:brd);
brdzeros CYb(1:brd,:) brdzeros];
% create offset matrices of size(O): concentrations
CLa_t = CLa_wbrd(5-1:end-4-1,5:end-4);
CLa_r = CLa_wbrd(5:end-4,5+1:end-4+1);
CLa_b = CLa_wbrd(5+1:end-4+1,5:end-4);
CLa_l = CLa_wbrd(5:end-4,5-1:end-4-1);
CLa_i = CLa_wbrd(5:end-4,5:end-4);
CSm_t = CSm_wbrd(5-1:end-4-1,5:end-4);
CSm_r = CSm_wbrd(5:end-4,5+1:end-4+1);
CSm_b = CSm_wbrd(5+1:end-4+1,5:end-4);
CSm_l = CSm_wbrd(5:end-4,5-1:end-4-1);
CSm_i = CSm_wbrd(5:end-4,5:end-4);
CYb_t = CYb_wbrd(5-1:end-4-1,5:end-4);
CYb_r = CYb_wbrd(5:end-4,5+1:end-4+1);
CYb_b = CYb_wbrd(5+1:end-4+1,5:end-4);
CYb_l = CYb_wbrd(5:end-4,5-1:end-4-1);
CYb_i = CYb_wbrd(5:end-4,5:end-4);
% preallocated C/P's
CPLa_t = CLa_t./PmatLa_t;
CPLa_r = CLa_r./PmatLa_r;
CPLa_b = CLa_b./PmatLa_b;
CPLa_l = CLa_l./PmatLa_l;
CPLa_i = CLa_i./PmatLa_i;
CPSm_t = CSm_t./PmatSm_t;
CPSm_r = CSm_r./PmatSm_r;
CPSm_b = CSm_b./PmatSm_b;
CPSm_l = CSm_l./PmatSm_l;
CPSm_i = CSm_i./PmatSm_i;
CPYb_t = CYb_t./PmatYb_t;
CPYb_r = CYb_r./PmatYb_r;
CPYb_b = CYb_b./PmatYb_b;
CPYb_l = CYb_l./PmatYb_l;
CPYb_i = CYb_i./PmatYb_i;
% FLUXES, dC's, and new C's
Qx_La = ((DmatLa_l+DmatLa_i).*(CPLa_l-CPLa_i)+(DmatLa_r+DmatLa_i).*(CPLa_r-CPLa_i));
Qy_La = ((DmatLa_t+DmatLa_i).*(CPLa_t-CPLa_i)+(DmatLa_b+DmatLa_i).*(CPLa_b-CPLa_i));
dCLa = (Qx_La/twoxstp2+Qy_La/twoystp2)*dtimestep; % CHANGE IN HEAT CONTENT FROM HEAT FLUX
CLa = CLa+dCLa;
Qx_Sm = ((DmatSm_l+DmatSm_i).*(CPSm_l-CPSm_i)+(DmatSm_r+DmatSm_i).*(CPSm_r-CPSm_i));
Qy_Sm = ((DmatSm_t+DmatSm_i).*(CPSm_t-CPSm_i)+(DmatSm_b+DmatSm_i).*(CPSm_b-CPSm_i));
dCSm = (Qx_Sm/twoxstp2+Qy_Sm/twoystp2)*dtimestep; % CHANGE IN HEAT CONTENT FROM HEAT FLUX
CSm = CSm+dCSm;
Qx_Yb = ((DmatYb_l+DmatYb_i).*(CPYb_l-CPYb_i)+(DmatYb_r+DmatYb_i).*(CPYb_r-CPYb_i));
Qy_Yb = ((DmatYb_t+DmatYb_i).*(CPYb_t-CPYb_i)+(DmatYb_b+DmatYb_i).*(CPYb_b-CPYb_i));
dCYb = (Qx_Yb/twoxstp2+Qy_Yb/twoystp2)*dtimestep; % CHANGE IN HEAT CONTENT FROM HEAT FLUX
CYb = CYb+dCYb;
CLaSm = CLa./CSm;
CSmYb = CSm./CYb;
end

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