vectors equality test failure - decimals and sign issue on zeros

I shall test two vectors of same dimension for their equality: namely, x0 and xhat as defined below (they belong to different functions, xhat is return value of inner called function).

--- x0 ---

support = randsample(n,k);
x0 = zeros(n,1);
x0(support) = randn(k,1);

--- xhat ---

b = A*x0;
cvx_quiet(true);
cvx_begin 
variable x(n)
minimize( norm(x,1) ) 
subject to
A*x == b
cvx_end
xhat = x;

To test equality I use:

if isequal(xhat, x0, 1e-6)
or

if isequal(xhat, x0)

condition which never verifies because x0 contains '0' or other (4 decimals, signed), while xhat contains '0.0000', '-0.0000', or other (4 decimals, signed). The algorithm works properly as values (real) in magnitude are the same in both vectors, and at the same indexes, therefore the condition for 'equality' is satisfied in facts, but I miss the way to code it in matlab.

How can I 'turn' xhat into x0, so to get isequal() function answering TRUE ?

Many thanks!

[VMat]

Thank you very much Geoff: problem solved.

[Stephen23]

According to the isequal documentation, this syntax

 isequal(xhat, x0, 1e-6)

simply tests that all three arrays are equal, i.e. that xhat is the same as x0, and x0 is the same as 1e-6. Is that what you want to test for? Did you read the documentation ?

Answer 1

[Geoff Hayes]

VMat - see http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F for some details on comparing two floating-point numbers. When doing so, you shouldn't be using equality. Instead, compare the absolute difference to a tolerance. For example,

 tol = 1.0e-6;
 areEqual = all(abs(xhat-x0) < tol);

will return true if the pairwise absolute difference between each element of the two arrays is less than the tolerance.

[Guillaume]

@Vmat,

I guess that this tolerance comparison is what you were trying to do with your isequal(xhat, x0, 1e-6) but that is not how isequal works at all. There is no tolerance argument for isequal. As per the doc, the above simply checks that both xhat and x0 are equal to 1e-6.