The Notes

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====== Matlab Tips ======
===== General tips =====
  - If you plan to use parallel for-loop, put the parfor statement in the outermost loop to reduce inter-process communication.
===== Simple text progress bar =====
<code matlab>
disp('     ');
for i = 1:x
    fprintf('\b\b\b\b\b\b%05.2f%%', i/x*100);
    %%%%% Do your biddings here %%%%%
end
disp(' ');
</code>

===== Highly unscientific benchmark of prod() =====
==== Sparse vs Dense ====
<code matlab>
>> a = rand(1000);
>> b = eye(1000);
>> c = sparse(a);
>> d = sparse(b);
>> tic; for i = 1:10000; prod(a); end; toc
Elapsed time is 7.212577 seconds.
>> tic; for i = 1:10000; prod(b); end; toc
Elapsed time is 3.566560 seconds.
>> tic; for i = 1:10000; prod(c); end; toc
Elapsed time is 27.455137 seconds.
>> tic; for i = 1:10000; prod(d); end; toc
Elapsed time is 0.030041 seconds.
>> tic; for i = 1:10000; prod(a); end; toc
Elapsed time is 7.250969 seconds.
>> tic; for i = 1:10000; prod(b); end; toc
Elapsed time is 3.645549 seconds.
>> tic; for i = 1:10000; prod(c); end; toc
Elapsed time is 27.538796 seconds.
>> tic; for i = 1:10000; prod(d); end; toc
Elapsed time is 0.029214 seconds.
>>

>> n = 100000;
>> a = rand(n,1);
>> b = 1;
>> tic; for i = 1:n; prod(a); end; toc;
Elapsed time is 4.849304 seconds.
>> tic; for i = 1:n; b = b * prod(a(i)); end; toc
Elapsed time is 0.004573 seconds.
>> 
</code>

==== Prod vs repeated multiplication ====
=== Script ===
<code matlab>
clear;
n = 10000;
a = rand(n,1) * exp(1);
b = 1;

tic; 
for i = 1:n; 
    c = prod(a); 
end; 
toc;

tic; 
for j = 1:n
    for i = 1:n; 
        b = b * a(i); 
    end; 
end
toc;
</code>
=== Results ===
<code matlab>
>> test
Elapsed time is 0.168450 seconds.
Elapsed time is 1.003991 seconds.
</code>
Note that with repeated multiplication your numerical accuracy will suffer too!