I am using numpy in python along with the linalg package to solve for the eigenvalues and eigenvectors of a 2x2 matrix. I also did this by hand, and coded the brute-force algebra step by step to compare with the numpy outputs. While the diagonals between the two methods are the same, the off-diagonal values are slightly different. Here is what is odd: they are both effectively zero i.e. 10^-10 to 10^-13, but they are not the same. Does this have to do with how python rounds numbers between using numpy and just doing arithmetic??
For reference, I am using the NOCI-MP2 method along with ALMO states, combining the ALMO states into one multireference wavefunction. When attempting to block diagonalize, the new Fock matrices are different between the methods (only added last part in case someone wanted to know why I was doing this). We are testing a new way to obtain coupling values between states using QChem. Thanks so much for any and all help.
Check the dtype (default is float64) of your input numpy arrays and consider increasing the precision if you are not satisfied that 10e-13 is 0, which is close to the precision of the underlying data type.
You can check with:
np.finfo(np.float64).precision
Numpy also has the 'longdouble' type, which depending on the architecture and c compiler of your machine, may give you more precision, check with:
np.finfo(np.longdouble).precision
You can read more about the basic Numpy data types here https://docs.scipy.org/doc/numpy-1.13.0/user/basics.types.html
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