Is it possible to create a numpy.ndarray that holds complex integers?

Consider using matrices of the form [[a,-b],[b,a]] as a stand-in for the complex numbers.

Ordinary multiplication and addition of matrices corresponds to addition an multiplication of complex numbers (this subring of the collection of 2x2 matrices is isomorphic to the complex numbers).

I think Python can handle integer matrix algebra.

I also deal with lots of complex integer data, generally basebanded data.

I use

dtype = np.dtype([('re', np.int16), ('im', np.int16)])

It's not perfect, but it adequately describes the data. I use it for loading into memory without doubling the size of the data. It also has the advantage of being able to load and store transparently with HDF5.

DATATYPE  H5T_COMPOUND {
    H5T_STD_I16LE "re";
    H5T_STD_I16LE "im";
}

Using it is straightforward and is just different.

x = np.zeros((3,3),dtype)
x[0,0]['re'] = 1
x[0,0]['im'] = 2
x
>> array([[(1, 2), (0, 0), (0, 0)],
>>        [(0, 0), (0, 0), (0, 0)],
>>        [(0, 0), (0, 0), (0, 0)]],
>>  dtype=[('re', '<i2'), ('im', '<i2')])

To do math with it, I convert to a native complex float type. The obvious approach doesn't work, but it's also not that hard.

y = x.astype(np.complex64) # doesn't work, only gets the real part
y = x['re'] + 1.j*x['im']  # works, but slow and big
y = x.view(np.int16).astype(np.float32).view(np.complex64)
y
>> array([[ 1.+2.j,  0.+0.j,  0.+0.j],
>>        [ 0.+0.j,  0.+0.j,  0.+0.j],
>>        [ 0.+0.j,  0.+0.j,  0.+0.j]], dtype=complex64)

This last conversion approach was inspired by an answer to What's the fastest way to convert an interleaved NumPy integer array to complex64?