Different results when running the same MATLAB program on different version of MATLAB

Hello, I would like to ask a question. Please use the following MATLAB program,

N   = 256;
L = 50;
F = dftmtx(N);

RowsLeft = sort(setdiff(1:N, 20));  % to delete the 20th component from 1:N

B = F(RowsLeft,1:L);
C_matrix = abs(B'*B); 
C_matrix = triu(C_matrix,1); 
CDSValue = max(max(C_matrix)); When I run it on MATLAB R2011a, I get 1.000000000000009; however, when I run it on MATLAB R2009b, I get 1.000000000000011.

Now I would like to decide which component to delete so that the resulting matrix has the smallest CDSValue. Running on MATLAB R2011a, I will choose the 20th component, but on MATLAB R2009b, I will choose the 22th component. How can I avoid the difference?

Many thanks.

[Friedrich]

If you need that amount of precision consider writing a mex file (so C/C++ code) which does all the computation. And in that mex file you use some special library for the precision , e.g.

http://www.ginac.de/CLN/

Answer 1

[Sean de Wolski]

Are they on the same computer?

I would recommend not relying on something on the order of EPS. ( doc eps for more info).

[Daniel Shub]

Yeah what you said ...

[C. Qi]

For different computer, with the same version of MATLAB installed, the results are the same. However, for different version of MATLAB, the results are different.

Answer 2

[Daniel Shub]

That is pretty dang close. In fact, if I counted the zeros correctly, the difference is on the order of

eps(1)

Basically as close as you can get with double precision floating point numbers.

Answer 3

[Daniel Shub]

Looking at dftmtx in r2011a

type dftmtx

reveals that it has been changed on 2010/11/08. There is no change log and I do not have access to r2009b to do the comparison, but a slight change in the algorithm could easily result in a change in the output on the order of eps.

The bigger problem is that your algorithm is "broken". The problem is essentially FAQ 6.1. Basically you have at least 2 components that have the same magnitude (the 20th and 22nd). You need to look at all the components that have values "near the maximum" and then come up with a rule for throwing one out. Maybe what you want is

C_max = max(max(C_matrix));
tol = 5*eps(C_max);
thres = C_max-tol;
CDSValue = C_matrix(find(C_matrix > thres, 1, 'first'));

[C. Qi]

When I run the program,

N = 256;

L = 50;

F = dftmtx(N);

RowsLeft = sort(setdiff(1:N, 20)); % delelte the 20th component

B = F(RowsLeft,1:L);

C_matrix = abs(B'*B);

C_matrix = triu(C_matrix,1);

C_max = max(max(C_matrix));

tol = 5*eps(C_max);

thres = C_max-tol;

CDSValue = C_matrix(find(C_matrix > thres, 1, 'first'));

On MATLAB R2011a,

CDSValue = 1.000000000000009 if delete the 20th component

CDSValue = 1.000000000000012 if delete the 22th component

But on MATLAB R2009b,

CDSValue = 1.000000000000011 if delete the 20th component

CDSValue = 1.000000000000008 if delete the 22th component

Thanks