Using vectorization instead of a 'for Loop' in Matlab - matlab

Question

I have a set of 32 bits binary values incoming from a sensor. I have to form all the possible combinations of these values and then convert them into a decimal value.
The code slows down terribly if the incoming rows are more that 80000 - 90000. It takes 120 minutes to run.
I want to optimize this code, since 3 For loops and a function within the innermost loop is slowing down my algorithm. Is there any chance that I can eliminate some For loops and substitute them with vectorizing to speed up the process.
b1 = [0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 1];
b2 = [0 1 0 1 0 1 1 1 1 1 1 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 1];
b3 = [0 1 0 1 0 1 0 1 1 1 0 1 1 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 0 1];
b4 = [0 1 0 1 0 1 1 1 1 1 0 1 1 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 1];
b5 = [0 1 0 1 1 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 0 1 0 1 0 0 1 0 0 1];
FullVector = [b1;b2;b3;b4;b5];
for Idx = 1:size(FullVector,1)
k = 1;
MinLength = 4;
MaxLength = 8;
StepSize = 2;
for StartByte = 1:8
for StartBit = 1:8
for SignalLength = MinLength:StepSize:MaxLength
DecimalVals.s(Idx,k) = BitCombinations(FullVector,StartByte,StartBit,SignalLength);
k = k+1;
end
end
end
end
The function:
function decimal = BitCombinations(ByteArray,Sbyte,Sbit,lengthSignal)
%function extracts the required bits from a byte array and
%returns the decimal equivalent of the bits.
%Inputs:
%Sbyte - Starting byte
%Sbit - Starting bit in the given byte
%length - length of bits to be extracted
%Output:
%dec - Returns the dec
startbit_pos = ((Sbyte-1)*8+Sbit);
endbit_pos = ((Sbyte-1)*8+Sbit+lengthSignal-1);
if endbit_pos <= 64
extractedbits = ByteArray(startbit_pos:endbit_pos);
extractedbits = fliplr(extractedbits);
decimal = bi2de(extractedbits);
else
decimal = NaN;
end
end

Answer 1

you should preallocate your result matrix DecimalVals by using the following code example:
b1 = repmat([0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 1],10000,1);
b2 = repmat([0 1 0 1 0 1 1 1 1 1 1 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 1],10000,1);
b3 = repmat([0 1 0 1 0 1 0 1 1 1 0 1 1 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 0 1],10000,1);
b4 = repmat([0 1 0 1 0 1 1 1 1 1 0 1 1 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 1],10000,1);
b5 = repmat([0 1 0 1 1 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 0 1 0 1 0 0 1 0 0 1],10000,1);
FullVector = [b1;b2;b3;b4;b5];
MinLength = 4;
MaxLength = 8;
StepSize = 2;
% Preallocation of the result struct
noOfValues = (((MaxLength - MinLength) / 2) + 1) * MaxLength * MaxLength;
DecimalVals = zeros(size(FullVector,1),noOfValues);
for Idx = 1:size(FullVector,1)
k = 1;
for StartByte = 1:MaxLength
for StartBit = 1:MaxLength
for SignalLength = MinLength:StepSize:MaxLength
DecimalVals(Idx,k) = BitCombinations(FullVector,StartByte,StartBit,SignalLength);
k = k+1;
end
end
end
end
result (on my machine):
time consumption without preallocation: 560 seconds
time consumption WITH preallocation: 300 seconds
Furthermore, please use the MATLAB Profiler (Starting the script by using "Run and Time") to identify the bottleneck, respectively which function takes most time and add the function/line to your question.
Unfortunately, I've got no access to the functions of the Communication System Toolbox, so I used the function bi2de from the File Exchange. In this version, there is one sort of error checking, which takes a lot of time: ~230 seconds

Answer 2

Another thing you could do, besides pre-allocating your array, is to not use fliplr. Take a look at this code snippet
tic
N = 10000;
A = [1:N];
for i = 1:N/2
b = A(N-i+1:-1:i);
end
toc
b = [];
tic
for i = 1:N/2
b = fliplr(A(i:N-i+1));
end
toc
Elapsed time is 0.060007 seconds.
Elapsed time is 0.118267 seconds.
So fliplr is around 2x slower to use, rather than simply use "backwards" indexing. I'm pretty sure you would have something to gain also by making your own bi2de function that is specific to your problem.
I made an attempt on this, haven't checked it for efficiency though, but maybe you can use it for your purposes
function values = myBi2Dec(byte,signalLengths)
persistent indexes
if isempty(indexes)
% Find the matrix indexes for this
indexes = [];
for iBit = 1:8
for iSL = signalLengths
if iBit+iSL-1<=8
indexes = [indexes;sub2ind([8,8],iBit,iBit+iSL-1)];
end
end
end
end
% Lets get the cumulative value
cumB2D = cumBi2Dec(byte);
% We already calculated their position, so simply return them
values = cumB2D(indexes);
function cumB2D = cumBi2Dec(byte)
persistent B2D
if isempty(B2D)
B2D = zeros(8,8);
tmp = 2.^[0:7];
for i = 1:8
B2D(i,i:8) = tmp(1:8-(i-1));
end
end
cumB2D = cumsum(repmat(fliplr(byte),8,1).*B2D,2);
Then try, for example, myBi2Dec([0,0,0,0,1,1,1,1],[4:2:8])