add complex support

[v923z]

This PR adds rudimentary complex support to ulab. Detailed discussion can be found in #364.

At the moment, complex arrays can be initialised from complex iterables. E.g.,

from ulab import numpy as np
a = np.array([1, 2+2j, 3, 4], dtype=np.complex)
print(a)

behaves as expected. In addition, the PR also implements the real and imaginary functions for ndarrays, i.e., the following works:

from ulab import numpy as np

a = np.array([1, 2+2j, 3, 4], dtype=np.complex)
b = np.array([1, 2, 3, 4], dtype=np.uint8)

print(a)
print(np.real(a))
print(np.imag(a))
print(np.real(b))
print(np.imag(b))

[wired8]

Thanks for this. I've tried running on an ESP32 with MicroPython v1.17 but get kernel panics when doing any operations.
Sample stack trace:
ndarray_make_new_core
ndarray.c:?
ndarray_array_constructor

Any ideas what I may have done wrong?

[v923z]

@wired8 This draft is based on an older version of ulab, so I am pretty sure that it's not going to fly. Do you need complex support? If so, what would you need it for? This whole issue came up in the context of eigenvalues and eigenvectors, but your requirements could be different, I don't know.

[wired8]

@v923z thanks for the quick response.

Specifically I'm trying to port some filters from scipy.

The buttap function uses complex numbers.

def buttap(N):
    """Return (z,p,k) for analog prototype of Nth-order Butterworth filter.

    The filter will have an angular (e.g., rad/s) cutoff frequency of 1.

    See Also
    --------
    butter : Filter design function using this prototype

    """
    if abs(int(N)) != N:
        raise ValueError("Filter order must be a nonnegative integer")
    z = numpy.array([])
    m = numpy.arange(-N+1, N, 2)
    # Middle value is 0 to ensure an exactly real pole
    p = -numpy.exp(1j * np.pi * m / (2 * N))
    k = 1
    return z, p, k

[v923z]

The exp function could be solved as cos() + 1j * sin(), somewhat similar to how the FFT is handled now. But I assume that, after you generate the filter coefficients, you want to pipe your data into lfilter, or something similar. Is that correct?
What I am trying to say is that complex is most probably only the first stage of what you need.

[wired8]

Correct, data is then piped through one of low/high/band or bandstop filter.

[v923z]

@wired8 I think I can relatively easily fix the complex code, but if you want to use it, we have to implement the filter functions in question. In order to not invest effort, where it is not needed, could you, please, point out which are the most important functions that you would need. Preferably, in order of importance.

EDIT: could you, please, open a new ticket for each function, with a link to the scipy documentation? Thanks!

[wired8]

#447
#448
#449

Thanks @v923z

[v923z]

Closing this now, on-going work is in #456