def take_lagr(self, psi, phi, data, h, e, lamd, mu, alpha, rho, tau,
model):
lagr = cp.zeros(7, dtype="float32")
# Lagrangian ptycho part by angles partitions
for k in range(0, self.ptheta):
ids = np.arange(k * self.tomoshapep[0],
(k + 1) * self.tomoshapep[0])
self.cl_ptycho.setobj(self.scan[:, ids].data.ptr,
self.prb.data.ptr)
fpsi = self.fwd_ptycho(psi[ids])
datap = cp.array(data[ids])
if (model == 'poisson'):
lagr[0] += cp.sum(
cp.abs(fpsi)**2 - 2 * datap * self.mlog(cp.abs(fpsi)) -
(datap - 2 * datap * self.mlog(cp.sqrt(datap))))
if (model == 'gaussian'):
lagr[0] += cp.linalg.norm(cp.abs(fpsi) - cp.sqrt(datap))**2
lagr[1] = alpha * cp.sum(
np.sqrt(cp.real(cp.sum(phi * cp.conj(phi), 0))))
lagr[2] = 2 * cp.sum(cp.real(cp.conj(lamd) * (h - psi)))
lagr[3] = rho * cp.linalg.norm(h - psi)**2
lagr[4] = 2 * cp.sum(np.real(cp.conj(mu) * (e - phi)))
lagr[5] = tau * cp.linalg.norm(e - phi)**2
lagr[6] = cp.sum(lagr[0:5])
return lagr
def cupy_signal(signal):
amp = cp.sqrt(cp.real(signal * cp.conj(signal)))
phase = cp.angle(signal)
real = cp.real(signal)
imag = cp.imag(signal)
return amp, phase, real, imag
def besselj__n(n, z):
if n<0:
return -1**(-n) * besselj__n(-n, z)
if n==0:
return cupyx.scipy.special.j0(cp.real(z))
elif n==1:
return cupyx.scipy.special.j1(cp.real(z))
elif n>=2:
return 2*(n-1)*besselj__n(int(n)-1, z)/cp.real(z) - besselj__n(int(n)-2, z)
def julia_set_cp(zs, phase):
ns = cp.zeros_like(Z, dtype=cp.float32)
for i in range(n_iteration):
# cupy doesn't support complex in where, we need to decompose it to real and img parts
zs_real = cp.where(
cp.abs(zs) < R, cp.real(zs**2 + 0.7885 * cp.exp(phase)),
cp.real(zs))
zs_imag = cp.where(
cp.abs(zs) < R, cp.imag(zs**2 + 0.7885 * cp.exp(phase)),
cp.imag(zs))
zs = zs_real + 1j * zs_imag
not_diverged = cp.abs(zs) < R
ns = ns + not_diverged.astype(cp.float32)
return ns, zs
def test_extend_conv(self):
objsize = self.pf.shape
inisize = self.gaussff.shape
imxsize = objsize[0] + inisize[0]
imysize = objsize[1] + inisize[1]
cp.cuda.Device(0).use
objtmp = cp.ndarray([imxsize, imysize])
initmp = cp.ndarray([imxsize, imysize])
objtmp[0:objsize[0], 0:objsize[1]] = self.pf
initmp[0:inisize[0], 0:inisize[1]] = self.gaussff
objtmp = self.shift(objtmp, imxsize / 2 - objsize[0] / 2,
imysize / 2 - objsize[1] / 2)
initmp = self.shift(initmp, imxsize / 2 - inisize[0] / 2,
imysize / 2 - inisize[1] / 2)
objfft = self.shift(
cp.fft.fft2(objtmp) * cp.sqrt(imxsize * imysize), imxsize / 2,
imysize / 2)
inifft = self.shift(
cp.fft.fft2(initmp) * cp.sqrt(imxsize * imysize), imxsize / 2,
imysize / 2)
convfft = self.shift(
cp.fft.ifft2(self.shift(objfft * inifft, imxsize / 2,
imysize / 2)), imxsize / 2, imysize / 2)
self.conv = cp.real(convfft)
return float(self.conv)
def run(self):
max_shape = self._find_max_shape()
# compute FT, assuming they are the same size
fft1 = cp.asarray(self.image1, dtype=cp.complex64)
fft2 = cp.asarray(self.image2, dtype=cp.complex64)
plan = get_fft_plan(fft1, value_type="C2C")
fft1 = fftn(fft1, overwrite_x=True, plan=plan)
fft2 = fftn(fft2, overwrite_x=True, plan=plan)
print(f"shape: {fft1.shape}, dtype: {fft1.dtype}")
@cp.fuse
def normalize(fft_image):
re, im = cp.real(fft_image), cp.imag(fft_image)
length = cp.sqrt(re * re + im * im)
return fft_image / length
fft1 = normalize(fft1)
fft2 = cp.conj(normalize(fft2))
# phase correlation spectrum
pcm = fft1 * fft2
pcm = ifftn(pcm, overwrite_x=True, plan=plan)
pcm = cp.real(pcm)
from skimage.morphology import disk
from skimage.filters import median
pcm = cp.asnumpy(pcm)
pcm = median(pcm, disk(3))
pcm = cp.asarray(pcm)
peak_list = self._extract_correlation_peaks(pcm)
def Hpower(self, x):
x = np.fft.ifft2(self.H *
np.fft.fft2(np.expand_dims(x, -1), axes=(0, 1)),
axes=(0, 1))
x = np.sum(self.mask * self.crop(np.real(x)), 2)
x = self.pad(x)
return x
def test_wiener(dtype):
psf = np.ones((5, 5)) / 25
data = signal.convolve2d(cp.asnumpy(test_img), psf, "same")
np.random.seed(0)
data += 0.1 * data.std() * np.random.standard_normal(data.shape)
psf = cp.asarray(psf, dtype=dtype)
data = cp.asarray(data, dtype=dtype)
deconvolved = restoration.wiener(data, psf, 0.05)
assert deconvolved.dtype == dtype
path = fetch('restoration/tests/camera_wiener.npy')
rtol = 1e-5 if dtype == np.float32 else 1e-12
atol = rtol
cp.testing.assert_allclose(deconvolved,
np.load(path),
rtol=rtol,
atol=atol)
_, laplacian = uft.laplacian(2, data.shape)
otf = uft.ir2tf(psf, data.shape, is_real=False)
deconvolved = restoration.wiener(data,
otf,
0.05,
reg=laplacian,
is_real=False)
cp.testing.assert_allclose(cp.real(deconvolved),
np.load(path),
rtol=rtol,
atol=atol)
def log_likelihood_ratio(self):
""" Calculates the real part of log-likelihood value
Returns
-------
float: The real part of the log likelihood
"""
waveform_polarizations = self.waveform_generator.frequency_domain_strain(
self.parameters)
if waveform_polarizations is None:
return np.nan_to_num(-np.inf)
d_inner_h = 0
h_inner_h = 0
for interferometer in self.interferometers:
d_inner_h_ifo, h_inner_h_ifo = self.calculate_snrs(
interferometer=interferometer,
waveform_polarizations=waveform_polarizations,
)
d_inner_h += d_inner_h_ifo
h_inner_h += h_inner_h_ifo
if self.distance_marginalization:
log_l = self.distance_marglinalized_likelihood(d_inner_h=d_inner_h,
h_inner_h=h_inner_h)
else:
log_l = -2 / self.duration * (h_inner_h - 2 * xp.real(d_inner_h))
return float(log_l.real)
def grad_ptycho(self, data, psi, prb, scan, zlamd, rho, niter):
"""Gradient solver for the ptychography problem |||FQpsi|-sqrt(data)||^2_2 + rho||psi-zlamd||^2_2"""
# minimization functional
def minf(fpsi, psi):
f = cp.linalg.norm(cp.abs(fpsi) - cp.sqrt(data))**2
if(rho > 0):
f += rho*cp.linalg.norm(psi-zlamd)**2
return f
for i in range(niter):
# compute the gradient
fpsi = self.fwd_ptycho(psi, prb, scan)
gradpsi = self.adj_ptycho(
fpsi - cp.sqrt(data)*fpsi/(cp.abs(fpsi)+1e-32), prb, scan)
# normalization coefficient for skipping the line search procedure
afpsi = self.adj_ptycho(fpsi, prb, scan)
norm_coeff = cp.real(cp.sum(psi*cp.conj(afpsi)) /
(cp.sum(afpsi*cp.conj(afpsi))+1e-32))
if(rho > 0):
gradpsi += rho*(psi-zlamd)
gradpsi *= min(1/rho, norm_coeff)/2
else:
gradpsi *= norm_coeff/2
# update psi
psi = psi - 0.5*gradpsi
# check convergence
# print(f'{i}) {minf(fpsi, psi).get():.2e} ')
return psi
def quantize(self, voltages, custom_stds=None):
"""
Quantize input complex voltages. Cache voltage means and standard deviations, per
polarization and per antenna.
Parameters
----------
voltages : array
Array of complex voltages
custom_stds : float, list, or array
Custom standard deviation to use for scaling, instead of automatic calculation. Each quantizer will go
from custom_stds values to self.target_std. Can either be a single value or an array-like object of length
2, to set the custom standard deviation for real and imaginary parts.
Returns
-------
q_voltages : array
Array of complex quantized voltages
"""
try:
assert len(custom_stds) == 2
except TypeError:
custom_stds = [custom_stds] * 2
q_r = self.quantizer_r.quantize(xp.real(voltages),
custom_std=custom_stds[0])
q_i = self.quantizer_i.quantize(xp.imag(voltages),
custom_std=custom_stds[1])
self.stats_cache_r = self.quantizer_r.stats_cache
self.stats_cache_i = self.quantizer_i.stats_cache
return q_r + q_i * 1j
def test_masked_registration_random_masks_non_equal_sizes():
"""masked_register_translation should be able to register
translations between images that are not the same size even
with random masks."""
# See random number generator for reproducible results
np.random.seed(23)
reference_image = cp.asarray(camera())
shift = (-7, 12)
shifted = cp.real(
fft.ifft2(fourier_shift(fft.fft2(reference_image), shift)))
# Crop the shifted image
shifted = shifted[64:-64, 64:-64]
# Random masks with 75% of pixels being valid
ref_mask = np.random.choice([True, False],
reference_image.shape,
p=[3 / 4, 1 / 4])
shifted_mask = np.random.choice([True, False],
shifted.shape,
p=[3 / 4, 1 / 4])
reference_image = cp.asarray(reference_image)
shifted = cp.asarray(shifted)
measured_shift = masked_register_translation(
reference_image,
shifted,
cp.ones(ref_mask.shape, dtype=ref_mask.dtype),
cp.ones(shifted_mask.shape, dtype=shifted_mask.dtype),
)
cp.testing.assert_array_equal(measured_shift, -cp.asarray(shift))
def test_masked_registration_random_masks():
"""masked_register_translation should be able to register translations
between images even with random masks."""
# See random number generator for reproducible results
np.random.seed(23)
reference_image = cp.array(camera())
shift = (-7, 12)
shifted = cp.real(fft.ifft2(fourier_shift(
fft.fft2(reference_image), shift)))
# Random masks with 75% of pixels being valid
ref_mask = np.random.choice(
[True, False], reference_image.shape, p=[3 / 4, 1 / 4])
shifted_mask = np.random.choice(
[True, False], shifted.shape, p=[3 / 4, 1 / 4])
ref_mask = cp.asarray(ref_mask)
shifted_mask = cp.asarray(shifted_mask)
measured_shift = masked_register_translation(reference_image,
shifted,
reference_mask=ref_mask,
moving_mask=shifted_mask)
cp.testing.assert_array_equal(measured_shift, -cp.asarray(shift))
def test_wiener():
psf = np.ones((5, 5)) / 25
data = convolve2d(test_img.get(), psf, "same")
np.random.seed(0)
data += 0.1 * data.std() * np.random.standard_normal(data.shape)
psf = cp.asarray(psf)
data = cp.asarray(data)
deconvolved = restoration.wiener(data, psf, 0.05)
if have_fetch:
path = fetch("restoration/tests/camera_wiener.npy")
else:
path = pjoin(dirname(abspath(__file__)), "camera_wiener.npy")
cp.testing.assert_allclose(deconvolved, np.load(path), rtol=1e-3)
_, laplacian = uft.laplacian(2, data.shape)
otf = uft.ir2tf(psf, data.shape, is_real=False)
deconvolved = restoration.wiener(data,
otf,
0.05,
reg=laplacian,
is_real=False)
cp.testing.assert_allclose(cp.real(deconvolved), np.load(path), rtol=1e-3)
def solve_reg(self, u, mu, tau, alpha):
z = self.fwd_reg(u) + mu / tau
# Soft-thresholding
za = cp.sqrt(cp.real(cp.sum(z * cp.conj(z), 0)))
z[:, za <= alpha / tau] = 0
z[:, za > alpha/tau] -= alpha/tau * \
z[:, za > alpha/tau]/(za[za > alpha/tau])
return z
def positive_constrain(self,dn_3D,dF_3D_2):
n_med = 1.334
wavelength = 532
k2 = (2*np.pi*n_med/wavelength)**2
n_med2 = n_med**2
# dF_3D = cupy.multiply(cupy.subtract(cupy.divide(cupy.multiply(dn_3D,dn_3D),n_med2),1),-k2)
# dF_3D = cupy.fft.fftn(dF_3D)
# dF_3D[cupy.not_equal(dF_3D_2,0)] = dF_3D_2[cupy.not_equal(dF_3D_2,0)]
# dF_3D = cupy.fft.ifftn(dF_3D)
# dn_3D = cupy.multiply(cupy.sqrt(cupy.add(cupy.divide(dF_3D,-k2), 1)), n_med)
# dn_3D = cupy.fft.fftshift(dn_3D);
dn_3D[cupy.less(cupy.real(dn_3D),n_med)] = n_med+1j*cupy.imag(dn_3D[cupy.less(cupy.real(dn_3D),n_med)])
dn_3D[cupy.less(cupy.imag(dn_3D),0)] = cupy.real(dn_3D[cupy.less(cupy.imag(dn_3D), 0)])
return dn_3D
def compensate_dispersion_3D(spectra: np.ndarray,
calibration: dict) -> cp.array:
calib = cp.asarray(calibration['dispersion'])
Pdispersion = cp.asarray(calib * complex(0, 1) * Arguments.dispersion)
return cp.real(hilbert_3D(spectra) * cp.exp(Pdispersion))
def spectrum_shift_2D(Volume_spectra: cp.ndarray) -> cp.ndarray:
Volume_spectra = hilbert_2D(Volume_spectra)
spectrum_shift = cp.exp(complex(0,1) * cp.arange( start=0, stop=Arguments.dimension[2], dtype=cp.float ) * Arguments.shift)
Volume_spectra = cp.multiply(Volume_spectra, spectrum_shift)
return cp.real(Volume_spectra)
def compensate_dispersion_2D(Volume_spectra: cp.ndarray, dispersion) -> cp.ndarray:
Pdispersion = cp.asarray( dispersion * complex(0,1) * Arguments.dispersion )
compensated_spectra = hilbert_2D(Volume_spectra) * cp.exp( Pdispersion )
compensated_spectra = cp.real(compensated_spectra)
return compensated_spectra
def inner_with_domain(sub_loads, ignore_domain=False):
full_loads = cp.zeros(shape, dtype=dtype)
full_loads[domain] = sub_loads
fft_loads = forward_trans(full_loads, s=input_shape)
full = norm_inv * cp.real(backward_trans(fft_loads * fft_im))
full = full[:full_loads.shape[0], :full_loads.shape[1]]
if ignore_domain:
return full
return full[domain]
def spectrum_shift_3D(temp: cp.ndarray):
spectrum_shift = cp.exp(
complex(0, 1) * cp.arange(start=0, stop=Arguments.dimension[2]) *
shift)
temp = cp.multiply(temp, spectrum_shift)
temp = cp.real(temp)
def distance_marglinalized_likelihood(self, d_inner_h, h_inner_h):
log_l = (
-2 / self.duration *
xp.real(h_inner_h * self.parameters["luminosity_distance"]**2 /
self.distance_array**2 -
2 * d_inner_h * self.parameters["luminosity_distance"] /
self.distance_array))
log_l = xp.log(xp.sum(xp.exp(log_l) * self.distance_prior_array))
return log_l
def Hadj(self, x):
x = np.expand_dims(x, -1)
x = x * self.mask
x = self.pad(x)
x = np.fft.fft2(x, axes=(0, 1))
x = np.fft.ifft2(self.Hconj * x, axes=(0, 1))
x = np.real(x)
return x
def Compute_fiedler_vector(G):
nrom_laplacian_matrics = nx.normalized_laplacian_matrix(G,weight='weight')
nrom_laplacian_matrics_cupy=cp.asarray(nrom_laplacian_matrics.toarray())
w,v=cp.linalg.eigh(nrom_laplacian_matrics_cupy)
#algebraic_connectivity,fiedler_vector=power_iteration(nrom_laplacian_matrics.)
algebraic_connectivity = w[1] # Neat measure of how tight the graph is
fiedler_vector = v[:,1].T
fiedler_vector=torch.Tensor(cp.asarray(cp.real(fiedler_vector)))
algebraic_connectivity=torch.Tensor(cp.asarray(algebraic_connectivity))
return algebraic_connectivity, fiedler_vector
def magnetization(s, B, d):
sz = cp.diag([Sz(conf, 0) for conf in range(0, d)])
# sz=cp.array([[0,1],[1,0]])
mag = cp.array(0., dtype=np.float32)
for i_bond in range(2):
sB = cp.tensordot(cp.diag(s[np.mod(i_bond - 1, 2)]),
B[i_bond],
axes=(1, 1))
C = cp.tensordot(sB, cp.conj(sB), axes=([0, 2], [0, 2]))
mag += cp.real(cp.tensordot(C, sz, axes=([0, 1], [0, 1])).get())
return mag * 0.5
def take_lagr(self, data, psi, prb, scan, z, lamd, rho):
"""Compute Lagrangian"""
lagr = np.zeros(4, dtype='float32')
for k in range(self.nnodes):
ids = cp.arange(k*self.nscan, (k+1)*self.nscan)
lagr[0] += cp.linalg.norm(cp.abs(self.fwd_ptycho(psi[k],
prb, scan[:, ids]))-cp.sqrt(data[ids]))**2
lagr[1] = 2*cp.sum(cp.real(cp.conj(lamd)*(psi-z)))
lagr[2] = rho*cp.linalg.norm(psi-z)**2
lagr[3] = cp.sum(lagr[:3])
return lagr
def inner_no_domain(full_loads):
full_loads = cp.asarray(full_loads)
if full_loads.shape == shape:
flat = False
else:
full_loads = cp.reshape(full_loads, loads.shape)
flat = True
fft_loads = forward_trans(full_loads, s=input_shape)
full = norm_inv * cp.real(backward_trans(fft_loads * fft_im))
full = full[:full_loads.shape[0], :full_loads.shape[1]]
if flat:
full = full.flatten()
return full
def dftUpsample(imageCorr, upsampleFactor, xyShift):
"""
This performs a matrix multiply DFT around a small neighboring region of the inital
correlation peak. By using the matrix multiply DFT to do the Fourier upsampling, the
efficiency is greatly improved. This is adapted from the subfuction dftups found in
the dftregistration function on the Matlab File Exchange.
https://www.mathworks.com/matlabcentral/fileexchange/18401-efficient-subpixel-image-registration-by-cross-correlation
The matrix multiplication DFT is from:
Manuel Guizar-Sicairos, Samuel T. Thurman, and James R. Fienup, "Efficient subpixel
image registration algorithms," Opt. Lett. 33, 156-158 (2008).
http://www.sciencedirect.com/science/article/pii/S0045790612000778
Args:
imageCorr (complex valued ndarray):
Correlation image between two images in Fourier space.
upsampleFactor (int):
Scalar integer of how much to upsample.
xyShift (list of 2 floats):
Coordinates in the UPSAMPLED GRID around which to upsample.
These must be single-pixel IN THE UPSAMPLED GRID
Returns:
(ndarray):
Upsampled image from region around correlation peak.
"""
imageSize = imageCorr.shape
pixelRadius = 1.5
numRow = np.ceil(pixelRadius * upsampleFactor)
numCol = numRow
colKern = cp.exp(
(-1j * 2 * cp.pi / (imageSize[1] * upsampleFactor))
* cp.outer(
(cp.fft.ifftshift((cp.arange(imageSize[1]))) - cp.floor(imageSize[1] / 2)),
(cp.arange(numCol) - xyShift[1]),
)
)
rowKern = cp.exp(
(-1j * 2 * cp.pi / (imageSize[0] * upsampleFactor))
* cp.outer(
(cp.arange(numRow) - xyShift[0]),
(cp.fft.ifftshift(cp.arange(imageSize[0])) - cp.floor(imageSize[0] / 2)),
)
)
imageUpsample = cp.real(rowKern @ imageCorr @ colKern)
return imageUpsample
def corrszsz(dist, s, B, d):
sz = cp.diag([Sz(conf, 0) for conf in range(0, d)])
corr = cp.array(0., dtype=np.float32)
if dist == 0:
sz2 = cp.tensordot(sz, sz, axes=(1, 0))
for i_bond in range(2):
sB = cp.tensordot(cp.diag(s[np.mod(i_bond - 1, 2)]),
B[i_bond],
axes=(1, 1))
C = cp.tensordot(sB, cp.conj(sB), axes=([0, 2], [0, 2]))
corr += cp.real(
cp.tensordot(C, sz2, axes=([0, 1], [0, 1])) -
cp.tensordot(C, sz, axes=([0, 1], [0, 1])) *
cp.tensordot(C, sz, axes=([0, 1], [0, 1])))
return 0.5 * corr
if dist != 0:
dist = cp.abs(dist)
for i_bond in range(2):
sB = cp.tensordot(cp.diag(s[np.mod(i_bond - 1, 2)]),
B[i_bond],
axes=(1, 1))
C = cp.tensordot(sB, cp.conj(sB), axes=(0, 0))
R = cp.tensordot(C, sz, axes=([0, 2], [0, 1]))
mean1 = cp.trace(R)
for i in range(dist - 1):
T = cp.tensordot(R, B[np.mod(i_bond + 1 + i, 2)], axes=(0, 1))
T = cp.tensordot(T,
cp.conj(B[np.mod(i_bond + 1 + i, 2)]),
axes=(0, 1))
R = cp.trace(T, axis1=0, axis2=2)
C = cp.tensordot(B[cp.mod(i_bond + dist, 2)],
cp.conj(B[cp.mod(i_bond + dist, 2)]),
axes=(2, 2))
L = cp.tensordot(R, C, axes=([0, 1], [1, 3]))
corr += cp.real(
cp.tensordot(L, sz, axes=([0, 1], [0, 1])) - mean1 * mean1)
return 0.5 * corr
def besselFirstKindOnGPU(order, arg):
import cupy as cp
from cupyx.scipy import special
if order == 0:
bess = special.j0(arg)
elif order == 1:
bess = special.j1(arg)
elif order >= 2:
bess = 2 * (float(order) - 1) * besselFirstKindOnGPU(
int(order) - 1, arg) / cp.real(arg) - besselFirstKindOnGPU(
int(order) - 2, arg)
if not cp.all(arg):
zero_idx = cp.where(arg == 0)
bess[zero_idx] = 0
return bess