Matlab multiplication of two matrices in max-plus algebra?

In max-plus algebra

x+y=max(x,y)
x*y=x+y

where x , y denote the entries.

How two multiply two matrices in MATLAB such that addition implies maximum value and multiplication imply sum .

Thanks

Answer 1

[John D'Errico]

You will need to write the code, overloading + and * (thus the functions plus and mtimes) for inputs of class double. Then you need to learn how to overload operators in MATLAB.

This is a VERY bad idea, because that will completely disable addition or multiplication of matrices when next you use MATLAB for some other project. Worse, other functions in MATLAB will now fail, if they use addition or multiplication. Even scalar multiplies or adds will now fail to work properly.

As I said, that is just an insanely bad idea.

Instead, just write two functions myplus and mytimes (call them what you want, as long as they are not plus and times) that operate exactly as you wish. Then use them to compute the desired results, wherever you want those operations.

[Ammy]

How to write two functions myplus and mytimes ? If I have two matrices

A=[1 2 3;4 5 6;7 8 9];

B=[2 3 5; 1 2 3;6 4 2];

How can I multiply these two matrices such that addition implies maximum value and multiplication imply sum .

[Walter Roberson]

You could define a maxplus class and define mtimes and plus operators for it.

[Ammy]

How can I define these? would you please help me for these matlab codes .

[John D'Errico]

That will indeed work as long as you have created the matrices A and B as members of the maxplus class. But it will not apply to any general double precision matrices.

[Steven Lord]

Write myplus:

function result = myplus(input1, input2)
% You need to fill in the body of the function
% so it does what you want

Now you would need to call this function on your arrays.

% Define A and B then call the function
C = myplus(A, B)