Comparing two matrix in Matlab

I have two matrices x and y, both are results from different algorithms/routines that are supposed to calculate the same result. While I know that the isequal() would check if x and y are the same matrix, the entries in those matrices would not be exactly the same (i.e. some entries may be with 5% off in worst case scenario). In this scenario, what would be the best method of comparing them to see if they are close enough to be considered the same result? Thanks in advance for the advices.

[Anuj Kumar]

you can try this,assumming x and y has same dimensions

len=lenght(x);

tolerance=x-y;

check=tolerance<0.001;

sum_Check=sum(check)

if sum_Check==len %then results can be accepted

Answer 1

[Titus Edelhofer]

Hi,

this question is rather tricky to answer in general. A simple approach is to compute the relative error. That works fine as long as there are no zeros in it, i.e.,

absError = abs(A-B);
relError = max(absError(:) ./ abs(A(:)));

This also assumes, that A and B are at least comparable in size, so it does not make a difference if you devide by A or B.

Taking care of all eventualities (NaN, inf, zeros ...) makes it more difficult to answer.

Titus

[john vattic]

i got inf as result of relError

Answer 2

[Anastasios]

I assume you have some floating point variables, in order to have this 5% error. Try to define a function to check if they are relatively equal, such as

function test = isequalRel(x,y,tol);
test = ( abs(x-y) <= ( tol*max(abs(x),abs(y)) + eps) );
if (!  test)
    printf("fail x=%e y=%e tol=%e\n", x, y, tol);
end

So basically you do the following :

|a-b| < tol*max(|a|,|b|) + tol_floor

[john vattic]

sorry, i did not understand your idea.I want to test if they are equal at least by 5% of changing

[Anastasios]

Use the following command

 abs(A-B) <= ( tol*max(abs(A),abs(B)) + eps)

where the tol = 0.005 (5%) You will get a logical answer if they are within this error of 5% the answer would be 1 otherwise 0.

Hope it helps

[vanita]

how to decide tolerance ? is their is any standard?