def _make_quaternion(self, data):
if data.ndim % 2 != 0:
raise ValueError(
"An array of data to be transformed to quaternion must be 2D.")
if data.dtype not in TYPE_COMPLEX:
if data.shape[1] % 2 != 0:
raise ValueError(
"An array of real data to be transformed to quaternion must have even number of columns!."
)
# convert to double precision complex
data = self._make_complex(data)
if data.shape[0] % 2 != 0:
raise ValueError(
"An array data to be transformed to quaternion must have even number of rows!."
)
r = data[::2]
i = data[1::2]
# _data = as_quat_array(list(zip(r.real.flatten(), r.imag.flatten(), i.real.flatten(), i.imag.flatten())))
# _data = _data.reshape(r.shape)
self._dtype = None # reset dtyep
return as_quaternion(r, i)
def _ifft(data):
if data.dtype == typequaternion:
fr = get_component(data, "R")
dr = np.fft.ifft(np.fft.ifftshift(fr, -1))
fi = get_component(data, "I")
di = np.fft.ifft(np.fft.ifftshift(fi, -1))
# rebuild the quaternion
data = as_quaternion(dr, di)
else:
data = np.fft.ifft(np.fft.ifftshift(data, -1))
return data
def _ifft_positive(data):
if data.dtype == typequaternion:
fr = get_component(data, "R")
dr = np.fft.fft(np.fft.ifftshift(fr, -1)) * data.shape[-1]
fi = get_component(data, "I")
di = np.fft.fft(np.fft.ifftshift(fi, -1)) * data.shape[-1]
# rebuild the quaternion
data = as_quaternion(dr, di)
else:
data = np.fft.fft(np.fft.ifftshift(data, -1)) * data.shape[-1]
return data
def _fft(data):
if data.dtype == typequaternion:
dr = get_component(data, "R")
fr = np.fft.fftshift(np.fft.fft(dr), -1)
di = get_component(data, "I")
fi = np.fft.fftshift(np.fft.fft(di), -1)
# rebuild the quaternion
data = as_quaternion(fr, fi)
else:
data = np.fft.fftshift(np.fft.fft(data), -1)
return data
def _echoanti_fft(data):
# FFT transform according to ECHO-ANTIECHO encoding
# warning: at this point, data must have been swapped so the last dimension is the one used for FFT
wt, yt, xt, zt = as_float_array(
data).T # x and y are exchanged due to swapping of dims
w, y, x, z = wt.T, xt.T, yt.T, zt.T
c = (w + y) + 1j * (w - y)
s = (x + z) - 1j * (x - z)
fc = np.fft.fftshift(np.fft.fft(c / 2.0), -1)
fs = np.fft.fftshift(np.fft.fft(s / 2.0), -1)
data = as_quaternion(fc, fs)
return data
def _fft_positive(data):
if data.dtype == typequaternion:
dr = get_component(data, "R")
fr = np.fft.fftshift(np.fft.ifft(dr).astype(
data.dtype)) * data.shape[-1]
di = get_component(data, "I")
fi = np.fft.fftshift(np.fft.ifft(di).astype(
data.dtype)) * data.shape[-1]
# rebuild the quaternion
data = as_quaternion(fr, fi)
else:
data = np.fft.fftshift(np.fft.ifft(data).astype(
data.dtype)) * data.shape[-1]
return data
def _tppi_fft(data):
# FFT transform according to TPPI encoding
# warning: at this point, data must have been swapped so the last dimension is the one used for FFT
wt, yt, xt, zt = as_float_array(
data).T # x and y are exchanged due to swapping of dims
w, y, x, z = wt.T, xt.T, yt.T, zt.T
sx = w + 1j * y
sy = x + 1j * z
sx[..., 1::2] = -sx[..., 1::2]
sy[..., 1::2] = -sy[..., 1::2]
fx = np.fft.fftshift(np.fft.fft(sx), -1) # reverse
fy = np.fft.fftshift(np.fft.fft(sy), -1)
# rebuild the quaternion
data = as_quaternion(fx, fy)
return data
def _states_fft(data, tppi=False):
# FFT transform according to STATES encoding
# warning: at this point, data must have been swapped so the last dimension is the one used for FFT
wt, yt, xt, zt = as_float_array(
data).T # x and y are exchanged due to swapping of dims
w, y, x, z = wt.T, yt.T, xt.T, zt.T
sr = (w - 1j * y) / 2.0
si = (x - 1j * z) / 2.0
if tppi:
sr[..., 1::2] = -sr[..., 1::2]
si[..., 1::2] = -si[..., 1::2]
fr = np.fft.fftshift(np.fft.fft(sr), -1)
fi = np.fft.fftshift(np.fft.fft(si), -1)
# rebuild the quaternion
data = as_quaternion(fr, fi)
return data