memory - Are single loops or dense loops more computationlly efficent in matlab? -


im writing code implement numerical approximation 3d steady state heat equation using finite difference matrix methods. involves discritising 2nd order pde matrix , solving ax=b. x temperature @ each of specified grid points. further information on type of question can found here:

http://people.nas.nasa.gov/~pulliam/classes/new_notes/matrix_ode.pdf

to complete problem, have represented 3d matrix 2d array calling values in 1d array b using indexing function of form:

i+(j-1)*nx+nx*ny*(k-1)

for (i,j,k)th element of 3d matrix nx, ny, nz number of points in x,y,z coordinates. there ends being lot of loop computation in order create matrix , b , wondering computationally efficient , less memory exhaustive way run these loops, i.e. better use like

for j=1:ny     i=2:nx-1         b(i+(j-1)*nx)=d4;         end end   j=1:ny     i=2:nx-1         b(i+(j-1)*nx+nx*ny*(nz-1))=d3;        end end

or should condense these single loop like:

for j=1:ny     i=2:nx-1         b(i+(j-1)*nx)=d4;         b(i+(j-1)*nx+nx*ny*(nz-1))=d3;         end end

i have preallocated both arrays , b. there vectorised way also?

the second method should faster since performs same number of calculations fewer increments of loop variables. can matlab's built-in stopwatch commands tic , toc time code. http://www.mathworks.com/help/matlab/ref/tic.html

something more vectorized might possible need know more format of arrays contain d3 , d4. reshape() function might able help.


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