Hi Anosha,
To solve the problem described in your textbook, we need to create a 1000x1000 matrix of random numbers, calculate the overall mean of the matrix, and then identify values greater than this mean using two methods:
- Using "for" and "if" statements (which is typically slower).
- Using logical indexing (referred to as "instant if-ing" in your book, which is much faster).
We will also measure the time it takes to perform each of these tasks using MATLAB's "tic" and "toc" functions.
Here is how you can do it in MATLAB:
% Create a 1000x1000 matrix of random numbers
M = rand(1000, 1000);
% Calculate the overall mean of the matrix
overallMean = mean(M(:));
% Method 1: Using for and if statements
tic; % Start timer
countForIf = 0; % Initialize counter for values greater than mean
for i = 1:numel(M)
if M(i) > overallMean
countForIf = countForIf + 1; % Increment counter
end
end
timeForIf = toc; % Measure elapsed time
% Display the time taken using for and if statements
fprintf('Time taken using for and if statements: %.6f seconds\n', timeForIf);
% Method 2: Using logical indexing (instant if-ing)
tic; % Start timer
countLogical = sum(M(:) > overallMean); % Count values greater than mean
timeLogical = toc; % Measure elapsed time
% Display the time taken using logical indexing
fprintf('Time taken using logical indexing: %.6f seconds\n', timeLogical);
In this script, we:
- Generate a 1000x1000 matrix "M" filled with random numbers using "rand".
- Compute the overall mean of "M" by using the "mean" function.
- Count the number of elements exceeding the mean with a "for" loop and "if" statements, and record the duration with "tic" and "toc" functions.
- Perform the same count more efficiently using logical indexing, and measure the time taken.
- Output the elapsed time for both methods.
For additional information on the "tic" and "toc" functions, refer these documentations:
I hope this helps!
