How to multiply matrices using for loops?

I have a problem in which I have to multiply two matrices, x (700x900) and y(900,1100), using a for loop. I'm not sure where to start, I've only been using MATLAB for about a month. Any advice/help/suggestions would be great!

Thank You

Answer 1

[Image Analyst]

Try this:

x = randi(9, 700, 900); % Sample data.
y = randi(9, 900, 1100);
[rowsx, colsx] = size(x);
[rowsy, colsy] = size(y);
theMatrixProduct = zeros(rowsx, colsy);
for row = 1 : rowsx
  row % Print progress to command window.
  for col = 1 : colsy
    theSum = 0;
    for k = 1 : colsx
      theSum = theSum + x(row, k) * y(k, col);
    end
    theMatrixProduct(row, col) = theSum;
  end
end

[Stefan]

Thank You!

[Michael Wood]

This solution does not work.

[Image Analyst]

Why do you say that it does not work? Of course it works. Now I guess I have to prove it, so add this code to the bottom so it will compare my code to the usual Mathworks matrix multiplication method and show that there is no difference:

% Do it the usual way, with matrix multiplication instead of for loops.
theMatrixProduct2 = x * y;
% Subtract to find the differences.
theDiff = theMatrixProduct2 - theMatrixProduct;
% If they're equal the max difference will be 0.
fprintf('Max difference = %f\n', max(theDiff(:)));
% It is zero, so the match.

[Sunil Kunjachan]

this wrong. please show resultant array

[Image Analyst]

It's NOT wrong. I don't know why people keep doubting it. Look, here is the full code (changed to be smaller matrices than the 700x900) with the arrays being printed to the command window so that you can see they match up perfectly:

x = randi(9, 7, 9); % Sample data.
y = randi(9, 9, 11);
[rowsx, colsx] = size(x);
[rowsy, colsy] = size(y);
theMatrixProduct = zeros(rowsx, colsy);
for row = 1 : rowsx
  row % Print progress to command window.
  for col = 1 : colsy
    theSum = 0;
    for k = 1 : colsx
      theSum = theSum + x(row, k) * y(k, col);
    end
    theMatrixProduct(row, col) = theSum;
  end
end

% Do it the usual way, with matrix multiplication instead of for loops.
theMatrixProduct2 = x * y;

% Print both to the command window
theMatrixProduct2
theMatrixProduct

% Subtract to find the differences.
theDiff = theMatrixProduct2 - theMatrixProduct;
% If they're equal the max difference will be 0.
fprintf('Max difference = %f\n', max(theDiff(:)));
% It is zero, so the match.

In the command window you'll see the proof:

theMatrixProduct2 =
   176   199   260   207   157   123   263   200   174   282   257
   161   155   166   124   115   110   165   143   154   204   209
   208   232   213   201   157   119   210   197   173   257   256
   181   243   267   206   144   138   262   199   241   296   295
   191   200   210   180   195   141   264   221   171   287   246
   297   305   315   305   203   155   315   290   250   333   358
   276   257   266   256   192   143   283   282   237   303   327
theMatrixProduct =
   176   199   260   207   157   123   263   200   174   282   257
   161   155   166   124   115   110   165   143   154   204   209
   208   232   213   201   157   119   210   197   173   257   256
   181   243   267   206   144   138   262   199   241   296   295
   191   200   210   180   195   141   264   221   171   287   246
   297   305   315   305   203   155   315   290   250   333   358
   276   257   266   256   192   143   283   282   237   303   327
Max difference = 0.000000

See, they're both the same and the differences are all zero.

Now it's your turn to show why the code is not correct by posting an example of where the matrices calculated the two different ways are different. Please provide your counter example so I can debug and correct my code (if needed).

Answer 2

[Kan Sun]

Suppose you have matrix1(N*M) and matrix2(M*L), then you can have the product using for loops as following:

product=zeros(N,L);

for i=1:N

for j=1:L

product(i,j)=matrix1(i,1)*matrix2(1,j);

for k=2:M

product(i,j)=product(i,j)+matrix1(i,k)*matrix2(k,j);

end

end

end

product1=product

At last you can compare this product1 to the result of matrix1*matrix2 to see if they are the same (yes they are).

[Aditya Sur]

I did'nt understand this statement: product(i,j)=matrix1(i,1)*matrix2(1,j);