Timing Experiment - Matrices

Question

Determine a matrix size that you can comfortably fit into your available RAM. For example, if you have a 4 GB machine, you should be able to comfortably store a matrix that occupies about 800MB. Store this value in a variable Mb. Use the following information to compute a maximum matrix dimension N that you can store in Mb megabytes of memory.

• A megabyte has 1024 kilobytes

• A kilobyte is 1024 bytes

• A floating point number is 8 bytes.

• An N × N matrix contains N^2 floating point numbers.

Call the N you compute nmax.

(b) Create two random matrices A and B each of size Nmax × Nmax. Using the MATLAB functions tic and toc, determine how much time (seconds) it takes to compute the product AB. Determine the number of floating point operations (additions and multiplications) it takes to compute the Nmax × Nmax matrix-matrix product (2/3)n^3. Use this number to estimate the number of floating point operations per second (’flops’) your computer can carry out. Call this flop rate flops.

% Part A
nmax = sqrt((1600*1024*1024)/8); % 8GB of RAM

% Part B
A = (nmax:nmax);
B = (nmax:nmax);

tic 
prod = A*B;
prod_time = toc

flops = (2/3)*(prod).^3

Everything runs fine but I feel like I am not creating a matrix for the values A and B. What am I doing wrong?

Answer 1

Two main things: you messed up your matrix assignment; c:c where c is a constant just returns the constant. The colon, :, creates arrays, such as

c = 5;
N = 1:c
    1  2  3  4  5

Feeding the colon operator the same start- and endpoint obviously just returns that point.

Second: the total number of operations was proportional to the number of elements, not the actual result of the matrix product (which is irrelevant actually, we're just interested in the time). So first calculate the total number of FLoating point Operations.

Remember that we used tic/toc? Well, perhaps we should find out what the total time was, which is stored in prod_time. This is the number of seconds it took to perform the matrix multiplication. Dividing Totflops by prod_time gives you the FLoating point Operations Per Second, i.e. FLOPS.

---

[~,systemview] = memory; % Get RAM info
tmp = systemview.PhysicalMemory;
% tmp.Total stores the total system RAM

Mb = 0.2*((tmp.Total/(1024^2))); % 20% of the total RAM

% floor your nmax to force it to be integer
nmax = floor(sqrt((Mb*1024^2/8))); % create your nmax

A = rand(nmax); % random nmax x nmax matrix
B = rand(nmax); % random nmax x nmax matrix

tic
prod = A*B;
prod_time = toc;

% Total flops
Totflops = (2/3)*(nmax).^3;

flops = Totflops/prod_time; % flops/sec

Which on my system (8GB RAM and an i5 750 2.66GHz) gives flops = 1.0617e+10