How to avoid using 'for' loop

'u' and 'v' are 401*401 matrices and 'R' is a 401*1 matrix. I have a function which gets 'u' and 'v' vectors and one value of 'R' per iteration and calculates the value of the function. Then after that, I have to sum all these values to get the final result. I wish to achieve my goal without using 'for' loop. Is it possible?

Example:

      % Initialize 'u', 'v', and 'R' matrices
      u = ...; % 401x401 matrix
      v = ...; % 401x401 matrix
      R = ...; % 401x1 matrix

      functionValues =zeros(401,401);
      % Calculate the values of the function for each element
      for i=1:numel(R)،
      functionValues = functionValues + calculateValue(u, v, R(i)); % 401x401 matrix
      end

In fact I wish to avoid using 'for' loop to increase running speed.

[moh mor]

Note: 'functionValues' has the same dimension as 'u' and 'v'. In fact I wish to sum up values of 'functionValues' for different 'R' at each position of 'functionValues'.

Answer 1

[Image Analyst]

Just modify youir calculateValue() so that it takes multiple values of R (can handle R being a vector) and returns a vector instead of a single scalar number. Then just call the function -- no for loop needed.

[moh mor]

Sorry, I think sth is misunderstood. 'functionValues' has the same dimension as 'u' and 'v'. In fact I wish to sum up values of 'functionValues' for different 'R' at each position.

[Image Analyst]

Then why not

theSum = 0;
for k = 1 : numel(R)،
    theSum = theSum + calculateValue(u, v, R(k)); % 401x401 matrix
end

And I agree with @Dyuman Joshi with only a few iterations (401*401) you'd most likely not notice any difference at all. It might be a different story if you had hundreds of millions of elements.

Answer 2

[Dyuman Joshi]

Vectorize the function calculateValue() and use sum for calculateValue(u, v, R).

However, this assumes that calculateValue() can be vectorized.

And if it can be, I doubt if you will see any noticeable speed increase by using vectorization instead of using a for loop.

[moh mor]

Sorry, I think sth is misunderstood. 'functionValues' has the same dimension as 'u' and 'v'. In fact I wish to sum up values of 'functionValues' for different 'R' at each position.

[moh mor]

I have heard that deploying 'for' loop decrease the speed by a huge amount.

[Dyuman Joshi]

"I have heard that deploying 'for' loop decrease the speed by a huge amount."

No, that is not generally true. If utilized properly, for loops can be faster.

However, Vectorization is faster because MATLAB is optimized for it. But that does not mean for loop are very slow.

On the other hand, if someone writes an inefficient for loop, then it might be slower, but that is because the way the code was written, not due to the nature of the for loop.

"'Sorry, I think sth is misunderstood. functionValues' has the same dimension as 'u' and 'v'. In fact I wish to sum up values of 'functionValues' for different 'R' at each position."

I understood your query perfectly and yes, I know that.

Using a for loop, the sum has to be updated in each iteration, whereas in the case of vectorization, the values are calculated together.

Check out this link to know more about vectorization - Vectorization.

Did you try to vectorize the function calculateValue()?

[moh mor]

As much as I could, I've Vectorized my problem.

[Dyuman Joshi]

@moh mor, is there still a problem?

Does it work properly? And did you check the speed of the two methods for comparison?