"""`stuff` from https://github.com/OverLordGoldDragon/stuff"""
import numpy as np
import matplotlib.pyplot as plt
from numpy.fft import fft, fftshift
from stuff import plot, scat, cos_f


def show_basis(k, odd=False):
    if odd:
        scat(cos_f([k], Ne), show=1, title=f"cos, k={k}, N={Ne}")
    scat(cos_f([k], No), show=1, title=f"cos, k={k}, N={No}")

kwr = dict(show=1, dx1=1)
kwc = dict(show=1, dx1=1, complex=1, c_annot=1)
#%%
N = 6
Ne = 2 * N      # odd  symmetry len
No = 2 * N - 1  # even symmetry len
s = np.array([.4, -.4, -.2, .1, -.9, .2])
#%%# Symmetric ###############################################################
xe = np.hstack([s, s[::-1]])
xo = np.hstack([s, s[::-1][1:]])

plot(xe, title="Symmetric even-len x -- [s, s[::-1]]",     **kwr)
plot(xo, title="Symmetric odd-len x  -- [s, s[::-1][1:]]", **kwr)
#%%
xef = fft(xe)
xof = fft(xo)

plot(xef, title="DFT(x_even)", **kwc)
plot(xof, title="DFT(x_odd)",  **kwc)

#%%# DFT-symmetric ###########################################################
xde = np.hstack([s, s[::-1][1:-1]])
xdo = np.hstack([s, s[::-1][:-1] ])

plot(xde, title="DFT-symmetric even-len x -- [s, s[::-1][1:-1]]", **kwr)
plot(xdo, title="DFT-symmetric odd-len x  -- [s, s[::-1][:-1]]",  **kwr)
#%%
xdef = fft(xde)
xdof = fft(xdo)

plot(xdef, title="DFT(xd_even)", **kwc)
plot(xdof, title="DFT(xd_odd)",  **kwc)
#%%# Cosine basis, even vs odd ##############################################
show_basis(1, odd=1)
#%%# Even case for higher k #################################################
show_basis(2)
show_basis(3)
#%%# Pretend left-most sample isn't there
scat(cos_f([1], Ne), show=0, title=f"cos, k=1, N={Ne}")
plt.axvline(Ne / 2, color='tab:red'); plt.show()

scat(cos_f([1], No), show=0, title=f"cos, k=1, N={No}")
plt.axvline(No / 2, color='tab:red'); plt.show()
#%%# n=0 case ###############################################################
plot(xde,           title="DFT-symmetric even-len x", **kwr)
plot(fftshift(xde), title="DFT-symmetric even-len x, centered about n=0", **kwr)

plot(xdo,           title="DFT-symmetric odd-len x", **kwr)
plot(fftshift(xdo), title="DFT-symmetric odd-len x, centered about n=0", **kwr)