How to vectorize the MATLAB code?

This is the code that I have written and I saw articles about vectorization.

N = length(a);
b = zeros(1,N - 1);
for i = 1:N-1
    b(i) = a(i) + a (i + 1);
end

How should I vectorize my code in this circumstance? Any suggestions? Thank you.

Answer 1

[Jan]

a = rand(1, 11);

N = length(a);
b = zeros(1,N - 1);
for i = 1:N-1
    b(i) = a(i) + a (i + 1);
end

% Vectorized 1:
b2 = a(1:end-1) + a(2:end);

% Vectorized 2:
b3 = conv(a, [1,1], 'valid')

% [EDITED] % Vectorized 3:  Working only for even length of a!
% [EDITED] b4 = sum(reshape(a, 2, []));  % Not the same result!
% Thanks John D'Errico.

isequal(b, b2, b3)

ans = logical
   1

For a = rand(1,1e6) and 100 repetitions, Matlab 2018b needs:

% Elapsed time is 0.683647 seconds.   loop
% Elapsed time is 0.874940 seconds.   1:end-1 + 2:end
% Elapsed time is 0.477227 seconds.   conv

You see, that vectorization is not a standard trick for accelerating code. The memory access can take more time than the loop.

[Sam Yeoh]

Fully understood with thanks, @Jan

[John D'Errico]

While I gave a +1 to @Jan for the answer, b4 is incorrect.

a = rand(1, 10);

b3 = conv(a, [1,1], 'valid')

b3 = 1×9

1.0363 1.0664 0.8794 0.4572 0.8286 1.0839 0.8633 0.9137 0.8310

% Vectorized 3:  Working only for even length of a!
b4 = sum(reshape(a, 2, []));

b3

b3 = 1×9

1.0363 1.0664 0.8794 0.4572 0.8286 1.0839 0.8633 0.9137 0.8310

b4

b4 = 1×5

1.0363 0.8794 0.8286 0.8633 0.8310

b4 sums the 1st and second, but NOT the 2nd and 3rd elements.

[Jan]

Thanks, John.