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c++matlabdouble-precision

matlab and c++ precision

Hi I'm rewriting a script from MATLAB to C++ using armadillo library for linear algebra and matrix.

for getting more or less the same output i called cout method:

cout.precision(4);
cout.setf(ios::fixed);

but i'm getting different result:

Matlab result:

0.0000    0.0000    0.0000    0.0000    0.0000   
0.0012    0.0014    0.0016    0.0020    0.0281  
0.0396    0.0297    0.0297    0.0495    0.0976

Armadillo c++ result:

0.0000    0.0000    0.0000    0.0000    0.0000 
0.0012    0.0014    0.0016    0.0020    0.0282 
0.0416    0.0312    0.0312    0.0520    0.1027

now, i don't know if thoose little imprecision (0.039 is near to 0.041) are caused by some errors in my C++ code translated or they should be considered normal differences between double precision in g++ and MATLAB

In my code I'm using a lot of cycle like this:

xi_summed = xi_summed + normalise((trans % (alpha.col(t) * b.t())));

where xi_summed, trans, alpha, b are arma::mat and % is a element-wise multiplication and mat::t() is transpose and normalise are a function that make the entries of matrix A array sum to 1.

Solution

  • This is certainly not a normal difference!

    The machine epsilon will be orders of magnitude smaller than the errors you are getting (i.e. 2.22e-016 vs. 2.0e-3).

    You can confirm your machine epsilon with the following C++ code:

    #include <limits>

cout << "Machine Epsilon is: " << numeric_limits<double>::epsilon() << endl;

    Your Matlab script will be bound to the same limitations; you can confirm this by entering the following into Matlab command window:

    eps

    If the computations you are performing in Matlab and C++ are mathematically equivalent then you should obtain the same result - especially with 4 d.p. precision!