def __init__(self,
EnAxis,
EnOutput,
TAxis,
TOutput,
num_electrons1,
num_electrons2,
dE=0,
dT=0):
from streaking_cal.statistics import weighted_avg_and_std
centralE, dE = weighted_avg_and_std(EnAxis.get(),
cp.square(cp.abs(EnOutput)).get())
self.p0 = eV_in_au(centralE)
if dT == 0:
dT = weighted_avg_and_std(TAxis.get(),
cp.square(cp.abs(TOutput)).get())[1]
self.dE = dE
self.dT = dT
self.__spec = EnOutput
self.__eAxis = EnAxis
self.__temp = TOutput
self.__tAxis = TAxis
self.num_electrons1 = num_electrons1
self.num_electrons2 = num_electrons2
self.__is_low_res = False
self.__streakspeed = 0
del (EnAxis)
del (EnOutput)
del (TAxis)
del (TOutput)
def __init__(self, IT, K_dB, wavelength, tx, ty, tz, rx, ry, rz):
"""
Args:
IT (int): the number of parallel channel matrices.
K_dB (float): the rician K factor in dB.
wavelength (float): the wavelength.
tx (numpy.array): the x positions of transmit antenna elements.
ty (numpy.array): the y positions of transmit antenna elements.
tz (numpy.array): the z positions of transmit antenna elements.
rx (numpy.array): the x positions of receive antenna elements.
ry (numpy.array): the y positions of receive antenna elements.
rz (numpy.array): the z positions of receive antenna elements.
"""
self.IT = IT
self.K = 10**(K_dB / 10.0)
self.M = len(tx) # the number of transmit antenna elements
self.N = len(rx) # the number of receive antenna elements
r = xp.zeros((self.N, self.M), dtype=xp.complex)
for n in range(self.N):
for m in range(self.M):
r[n][m] = xp.sqrt(
xp.square(rx[n] - tx[m]) + xp.square(ry[n] - ty[m]) +
xp.square(rz[n] - tz[m]))
anHLoS = xp.exp(-1j * 2.0 * xp.pi / wavelength * r)
self.HLoS = xp.tile(anHLoS.T, IT).T # IT \cdot N \times M
def var(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False):
"""Returns the variance along an axis.
Args:
a (cupy.ndarray): Array to compute variance.
axis (int): Along which axis to compute variance. The flattened array
is used by default.
dtype: Data type specifier.
out (cupy.ndarray): Output array.
keepdims (bool): If True, the axis is remained as an axis of size one.
Returns:
cupy.ndarray: The variance of the input array along the axis.
.. seealso:: :func:`numpy.var`
"""
if axis is None:
axis = tuple(range(a.ndim))
if not isinstance(axis, tuple):
axis = (axis,)
if dtype is None and issubclass(a.dtype.type,
(numpy.integer, numpy.bool_)):
dtype = numpy.dtype(numpy.float64)
arrmean = mean(a, axis=axis, dtype=dtype, keepdims=True)
x = cupy.subtract(a, arrmean, dtype=dtype)
cupy.square(x, x)
ret = cupy.sum(x, axis=axis, dtype=dtype, out=out, keepdims=keepdims)
rcount = max(_count_reduce_items(a, axis) - ddof, 0)
return cupy.multiply(ret, ret.dtype.type(1.0 / rcount), out=ret)
def _update_wavefront(data, varying_probe, scan, psi, op):
# Compute the diffraction patterns for all of the probe modes at once.
# We need access to all of the modes of a position to solve the phase
# problem. The Ptycho operator doesn't do this natively, so it's messy.
patches = cp.zeros(data.shape, dtype='complex64')
patches = op.diffraction.patch.fwd(
patches=patches,
images=psi,
positions=scan,
patch_width=varying_probe.shape[-1],
)
patches = patches.reshape(*scan.shape[:-1], 1, 1, op.detector_shape,
op.detector_shape)
nearplane = cp.tile(patches, reps=(1, 1, 1, varying_probe.shape[-3], 1, 1))
pad, end = op.diffraction.pad, op.diffraction.end
nearplane[..., pad:end, pad:end] *= varying_probe
# Solve the farplane phase problem ----------------------------------------
farplane = op.propagation.fwd(nearplane, overwrite=True)
intensity = cp.sum(cp.square(cp.abs(farplane)), axis=(2, 3))
cost = op.propagation.cost(data, intensity)
logger.info('%10s cost is %+12.5e', 'farplane', cost)
farplane -= 0.5 * op.propagation.grad(data, farplane, intensity)
if __debug__:
intensity = cp.sum(cp.square(cp.abs(farplane)), axis=(2, 3))
cost = op.propagation.cost(data, intensity)
logger.info('%10s cost is %+12.5e', 'farplane', cost)
# TODO: Only compute cost every 20 iterations or on a log sampling?
farplane = op.propagation.adj(farplane, overwrite=True)
return farplane, cost
def update(self, layers):
if len(self._cache_s) == 0 or len(self._cache_v) == 0:
self._init_cache(layers)
for idx, layer in enumerate(layers):
weights, gradients = layer.get_weight(), layer.get_gradient()
if weights is None or gradients is None:
continue
(w, b), (dw, db) = weights, gradients
dw_key, db_key = Adam._get_cache_keys(idx)
self._cache_v[dw_key] = self._beta1 * self._cache_v[dw_key] + (
1 - self._beta1) * dw
self._cache_v[db_key] = self._beta1 * self._cache_v[db_key] + (
1 - self._beta1) * db
self._cache_s[dw_key] = self._beta2 * self._cache_s[dw_key] + (
1 - self._beta2) * np.square(dw)
self._cache_s[db_key] = self._beta2 * self._cache_s[db_key] + (
1 - self._beta2) * np.square(db)
dw = self._cache_v[dw_key] / (np.sqrt(self._cache_s[dw_key]) +
self._eps)
db = self._cache_v[db_key] / (np.sqrt(self._cache_s[db_key]) +
self._eps)
layer.set_weight(w - self._lr * dw, b - self._lr * db)
def __get_streaked_spectra(self, streakspeed):
if self.is_low_res == True:
return None
else:
from cupy.fft import fft
def fs_in_au(t):
return 41.3414 * t # from fs to a.u.
# def eV_in_au(e): return 0.271106*np.sqrt(e) # from eV to a.u.
# in V/m; shape of Vectorpotential determines: 232000 V/m = 1 meV/fs max streakspeed
E0 = 232000 * streakspeed
ff1 = cp.flip(
fft(self.__temp * cp.exp(-1j * fs_in_au(self.__tAxis) *
(1 / (2) *
(self.p0 * E0 * p_times_A_vals_up +
1 * E0**2 * A_square_vals_up)))))
ff2 = cp.flip(
fft(self.__temp * cp.exp(-1j * fs_in_au(self.__tAxis) *
(1 / (2) *
(self.p0 * E0 * p_times_A_vals_down +
1 * E0**2 * A_square_vals_down)))))
spectrum1 = cp.square(cp.abs(ff1))
spectrum2 = cp.square(cp.abs(ff2))
# ff1=ff1/(cp.sum(cp.square(cp.abs(ff1))))
# ff1=ff2/(cp.sum(cp.square(cp.abs(ff2))))
return spectrum1, spectrum2
def calc_loss(embeddings, target_embeddings):
norm = cp.linalg.norm(embeddings, axis=1).reshape(
(embeddings.shape[0], 1))
norm_loss = float(cp.sum(cp.square(1 - norm) / norm))
target_loss = float(
cp.sum(cp.square(embeddings - target_embeddings) / 2))
loss = norm_loss + target_loss
return loss
def cp_trans_formula(self,
freqs: cp.ndarray,
freq: float = 1.) -> cp.ndarray:
freqs = freqs / freq * self.peak_freq(freq)
result = (self.c * cp.pi**(-1 / 4) *
(cp.exp(-cp.square(self.sigma - freqs) / 2) -
self.k * cp.exp(-cp.square(freqs) / 2)))
return result
def get_spectra(self,
streakspeed_in_meV_per_fs,
keep_originals=False,
discretized=True):
'''returns streaked spectra, measured with "number_electronsx" simulated electrons or nondiscretized as a tuple'''
from streaking_cal.statistics import weighted_avg_and_std
if not (self.is_low_res()):
(streaked1, streaked2
) = self.__get_streaked_spectra(streakspeed_in_meV_per_fs)
streaked1 = interp(tof_ens_gpu, self.__eAxis, streaked1)
streaked2 = interp(tof_ens_gpu, self.__eAxis, streaked2)
xuvonly = interp(tof_ens_gpu, self.__eAxis,
cp.square(cp.abs(self.__spec)))
if not (keep_originals):
self.__eAxis = None
self.__spec = None
t_square = cp.square(cp.abs(self.__temp))
t_mean, _ = weighted_avg_and_std(self.__tAxis.get(),
t_square.get())
self.__temp = interp(cp.asarray(standard_full_time),
self.__tAxis - t_mean, t_square).get()
self.__temp = self.__temp / cp.sum(self.__temp)
self.__tAxis = standard_full_time
self.__is_low_res = True
self.__streakedspectra = np.asarray(
(xuvonly.get(), streaked1.get(), streaked2.get()))
self.__streakspeed = streakspeed_in_meV_per_fs
self.__tAxis = standard_full_time
if discretized:
streaked1 = self.discretized_spectrum(streaked1,
self.num_electrons1)
streaked2 = self.discretized_spectrum(streaked2,
self.num_electrons2)
self.__streakspeed = streakspeed_in_meV_per_fs
return cp.asnumpy(xuvonly), cp.asnumpy(streaked1), cp.asnumpy(
streaked2)
elif discretized:
(xuvonly, streaked1, streaked2) = self.__streakedspectra
streaked1 = self.discretized_spectrum(streaked1,
self.num_electrons1)
streaked2 = self.discretized_spectrum(streaked2,
self.num_electrons2)
return cp.asnumpy(xuvonly), cp.asnumpy(streaked1), cp.asnumpy(
streaked2)
else:
return self.__streakedspectra.copy()
def _conv_syst(self, inputs, h_ij=None):
'''
Convolves the bandwidths with the resolutions scaled by the scale
systematics. Resolutions are in the units of the scaled dimension.
'''
if h_ij is None:
h_ij = self.h_ij
scales = inputs[0:3 * len(self.observables.scales):3]
resolutions = inputs[2:3 * len(self.observables.shifts):3]
return cp.sqrt(cp.square(scales * h_ij) + cp.square(resolutions))
def _computenorm(self):
"""Compute norm of probability distribution
Returns
-------
norm : float
"""
w2 = cp.reshape(self.w,(self.n_features,self.d,self.D,self.D))
tmp = cp.sum(cp.square(w2[0,:,0,:]),0) #First tensor
for i in range(1,self.n_features-1):
tmp = cp.dot(tmp,cp.sum(cp.square(w2[i,:,:,:]),0)) #MPS contraction
norm = cp.inner(tmp,cp.sum(cp.square(w2[self.n_features-1,:,:,0]),0))
return norm
def sobel(image):
width_array, height_array = generate_arrays(3, 3)
vertical_filter = np.array(([-1, 0, 1], [-2, 0, 2], [-1, 0, 1]))
horizontal_filter = np.flip(vertical_filter.T, axis=0)
new_image_x = convolution_sobel(image, vertical_filter)
new_image_y = convolution_sobel(image, horizontal_filter)
#magnitud_gradiente = np.sqrt(np.square(new_image_x) + np.square(new_image_y))
magnitud_gradiente = cp.sqrt(
cp.square(new_image_x) + cp.square(new_image_y))
magnitud_gradiente *= 255 / magnitud_gradiente.max()
return cp.asnumpy(magnitud_gradiente)
def __call__(self, params, g_params):
new_params, new_v = zip(
*[(cp.subtract(
param,
cp.multiply(
cp.divide(
self.rate,
cp.sqrt(
cp.add(cp.add(v, cp.square(g_param)),
self.eps).astype(cp.float32))), g_param)),
cp.add(v, cp.square(g_param)))
for param, g_param, v in zip(params, g_params, self.v)])
self.v = new_v
return new_params
def do_rmsprop(self, X, Y, update, learning_rate, **kwargs):
layers = len(self.structure) - 1
grads = self.calculate_grads(X, Y, kwargs["l2_reg_param"])
for ii in cp.arange(1, layers + 1):
update["w" + str(ii)] = kwargs["beta"] * update.get(
"w" + str(ii), 0) + (1 - kwargs["beta"]) * cp.square(
cp.sum(grads["w" + str(ii)], axis=0))
update["b" + str(ii)] = kwargs["beta"] * update.get(
"b" + str(ii), 0) + (1 - kwargs["beta"]) * cp.square(
cp.sum(grads["b" + str(ii)], axis=1).reshape(-1, 1))
self.params["w"+str(ii)] -= cp.multiply((learning_rate/ cp.sqrt(kwargs["epsilon"] + update["w"+str(ii)])),\
cp.sum(grads["w"+str(ii)],axis=0))
self.params["b"+str(ii)] -= cp.multiply((learning_rate / cp.sqrt(kwargs["epsilon"] + update["b"+str(ii)])),\
cp.sum(grads["b"+str(ii)],axis=1).reshape(-1,1))
return update
def spherical_cosmask(n,mask_radius, edge_width, origin=None):
"""mask = spherical_cosmask(n, mask_radius, edge_width, origin)
"""
if type(n) is int:
n = np.array([n])
sz = np.array([1, 1, 1])
sz[0:np.size(n)] = n[:]
szl = -np.floor(sz/2)
szh = szl + sz
x,y,z = np.meshgrid( np.arange(szl[0],szh[0]),
np.arange(szl[1],szh[1]),
np.arange(szl[2],szh[2]), indexing='ij', sparse=True)
r = np.sqrt(x*x + y*y + z*z)
m = np.zeros(sz.tolist())
# edgezone = np.where( (x*x + y*y + z*z >= mask_radius) & (x*x + y*y + z*z <= np.square(mask_radius + edge_width)))
edgezone = np.all( [ (x*x + y*y + z*z >= mask_radius), (x*x + y*y + z*z <= np.square(mask_radius + edge_width))], axis=0)
m[edgezone] = 0.5 + 0.5*np.cos( 2*np.pi*(r[edgezone] - mask_radius) / (2*edge_width))
m[ np.all( [ (x*x + y*y + z*z <= mask_radius*mask_radius) ], axis=0 ) ] = 1
# m[ np.where(x*x + y*y + z*z <= mask_radius*mask_radius)] = 1
return m
def save_evaluations(user, population, optim):
# define pearson correlation coefficient vector
pearsons = cupy.zeros(population.shape[0], dtype=cupy.float64)
# define mse vector
mse = cupy.zeros(population.shape[0], dtype=cupy.float64)
# define common gene counter vector
common_genes = cupy.zeros(population.shape[0], dtype=cupy.int64)
# define cosine similarity vector
cosines = cupy.zeros(population.shape[0], dtype=cupy.float64)
# compute vectors
for i in range(population.shape[0]):
pearsons[i] = cupy.corrcoef(population[i], optim)[0, 1]
mse[i] = (cupy.square(optim - population[i])).mean(axis=None)
common_genes[i] = evaluate_chromosome(population[i], optim)
cosines[i] = 1 - scipy.spatial.distance.cosine(optim, population[i])
# save vectors to txt files using as prefix the user id
cupy.savetxt("user_" + str(user) + "-pearsons.txt",
pearsons,
delimiter="\t")
cupy.savetxt("user_" + str(user) + "-mse.txt", mse, delimiter="\t")
cupy.savetxt("user_" + str(user) + "-common_genes.txt",
common_genes.astype(int),
fmt='%i',
delimiter="\t")
cupy.savetxt("user_" + str(user) + "-cosines.txt", cosines, delimiter="\t")
return
def row_norms(X, squared=False):
"""Row-wise (squared) Euclidean norm of X.
Equivalent to np.sqrt((X * X).sum(axis=1)), but also supports sparse
matrices.
Performs no input validation.
Parameters
----------
X : array_like
The input array
squared : bool, optional (default = False)
If True, return squared norms.
Returns
-------
array_like
The row-wise (squared) Euclidean norm of X.
"""
if sparse.issparse(X):
if isinstance(
X, (sparse.csr_matrix, sparse.csc_matrix, sparse.coo_matrix)):
X_copy = X.copy()
X_copy.data = np.square(X_copy.data)
norms = X_copy.sum(axis=1).squeeze()
else:
raise ValueError('Sparse matrix not compatible')
else:
norms = np.einsum('ij,ij->i', X, X)
if not squared:
np.sqrt(norms, norms)
return norms
def update(self, trainable_variables):
self.iterations += 1
if self.ms is None:
#initialize
self.ms = [
cp.zeros_like(p.output_tensor) for p in trainable_variables
]
if self.vs is None:
#initialize
self.vs = [
cp.zeros_like(p.output_tensor) for p in trainable_variables
]
for i, (v, m,
var) in enumerate(zip(self.vs, self.ms, trainable_variables)):
v = self.beta1 * v + (1 - self.beta1) * var.grads
m = self.beta2 * m + (1 - self.beta2) * cp.square(var.grads)
v_correct = v / (1 - pow(self.beta1, self.iterations))
m_correct = m / (1 - pow(self.beta2, self.iterations))
var.output_tensor -= self.lr * (
v_correct / (cp.sqrt(m_correct) + self.epsilon))
self.ms[i] = m
self.vs[i] = v
super(Adam, self).update(trainable_variables)
def sub_routine(vector_u, matrix_V, vector_train, bias, measure, topK=500, gpu=True):
train_index = vector_train.nonzero()[1]
if measure == "Cosine":
vector_predict = matrix_V.dot(vector_u)
else:
if gpu:
import cupy as cp
vector_predict = -cp.sum(cp.square(matrix_V - vector_u), axis=1)
else:
vector_predict = -np.sum(np.square(matrix_V - vector_u), axis=1)
if bias is not None:
if gpu:
import cupy as cp
vector_predict = vector_predict + cp.array(bias)
else:
vector_predict = vector_predict + bias
if gpu:
import cupy as cp
candidate_index = cp.argpartition(-vector_predict, topK+len(train_index))[:topK+len(train_index)]
vector_predict = candidate_index[vector_predict[candidate_index].argsort()[::-1]]
vector_predict = cp.asnumpy(vector_predict).astype(np.float32)
else:
candidate_index = np.argpartition(-vector_predict, topK+len(train_index))[:topK+len(train_index)]
vector_predict = candidate_index[vector_predict[candidate_index].argsort()[::-1]]
vector_predict = np.delete(vector_predict, np.isin(vector_predict, train_index).nonzero()[0])
return vector_predict[:topK]
def __call__(self, x):
regularization = 0.
if self.l1:
regularization += cp.sum(self.l1 * cp.abs(x)) / x.shape[0]
if self.l2:
regularization += cp.sum(self.l1 * cp.square(x)) / (2 * x.shape[0])
return regularization
def _lossA(self, A, P):
inum = cupy.array(1.0j, cupy.complex64)
loss = cupy.square(A['y'] - A['x']).mean()
grad = self._overlapadd(
cupy.fft.irfft(
(A['x'] - A['y']) * cupy.exp(inum * P['x'])) * self.norm)
return loss, grad
def test_score(nrows, ncols, nclusters, random_state):
X, y = make_blobs(int(nrows),
ncols,
nclusters,
cluster_std=1.0,
shuffle=False,
random_state=0)
cuml_kmeans = cuml.KMeans(init="k-means||",
n_clusters=nclusters,
random_state=random_state,
output_type='numpy')
cuml_kmeans.fit(X)
actual_score = cuml_kmeans.score(X)
predictions = cuml_kmeans.predict(X)
centers = cuml_kmeans.cluster_centers_
expected_score = 0.0
for idx, label in enumerate(predictions):
x = X[idx, :]
y = cp.array(centers[label, :], dtype=cp.float32)
sq_euc_dist = cp.sum(cp.square((x - y)))
expected_score += sq_euc_dist
expected_score *= -1
cp.testing.assert_allclose(actual_score,
expected_score,
atol=0.1,
rtol=1e-5)
def phase_optimization(filename_psf_target,scale=1,step=1.0,iterations=100,filename_phi="phases/foo.npy"):
psf_target = np.load(filename_psf_target)
print("Performing phase optimization...")
if scale==1:
Y = psf_target
Y= cp.asarray(Y)
else:
dim_0 = scale*psf_target.shape[0]
dim_1 = scale*psf_target.shape[1]
dim = (dim_0,dim_1)
Y= cv.resize(psf_target, dim, interpolation=cv.INTER_NEAREST)
Y= cp.asarray(Y)
if len(Y.shape)==2:
Y = Y/cp.sum(Y)
else:
Y = Y/cp.reshape(cp.sum(Y,axis=(0,1)),(1,1)+Y.shape[2:])
phi = cp.random.random_sample(Y.shape)*2.0*np.pi
#phi = cp.fft.fftshift(cp.angle(cp.fft.fft2(cp.sqrt(Y),axes=(0, 1))),axes=(0,1))+2.0*np.pi
losses = []
#grads = []
mempool.free_all_blocks()
for i in range(iterations):
h = cp.fft.ifft2(cp.fft.ifftshift(cp.exp(1.0j*phi),axes=(0, 1)),axes=(0, 1))
psf_new = cp.square(cp.abs(h))
if len(psf_new.shape)==2:
norm = cp.sum(psf_new)
else:
norm = cp.reshape(cp.sum(psf_new,axis=(0,1)),(1,1)+psf_new.shape[2:])
psf_new = psf_new/norm
h = h/cp.sqrt(norm)
D = (Y-psf_new)
loss = cp.sum(cp.square(D))
losses.append(loss)
if i%100==0:
print("Iteration {} of {}, Loss: {}".format(i,iterations,loss))
gradient = -4.0*cp.imag(cp.exp(-1.0j*phi)*cp.fft.fftshift(cp.fft.fft2((D*h),axes=(0, 1)),axes=(0,1)))
phi = phi - step*gradient
#grads.append(cp.sum(gradient**2))
mempool.free_all_blocks()
print("Phase Optimization process completed!")
phi_np = cp.asnumpy(phi)
np.save(filename_phi,phi_np)
def get_loss(self, X, Y, l2_reg_param=0, Y_pred=None):
weight_sum = 0
for ii in range(1, len(self.structure)):
weight_sum += cp.sum(cp.square(self.params["w" + str(ii)]))
if Y_pred is None:
Y_pred = self.predict(X)
return cp.asnumpy((cp.sum(-cp.log(cp.choose(Y, Y_pred))) +
(l2_reg_param / 2) * weight_sum) / len(Y))
def mse(predictions, targets, cuda=False):
if cuda:
res = cp.square(cp.subtract(predictions, targets)).mean()
cp.cuda.Stream.null.synchronize()
return res
else:
return np.square(np.subtract(predictions,
targets)).sum() / len(predictions)
def square(x: Array, /) -> Array:
"""
Array API compatible wrapper for :py:func:`np.square <numpy.square>`.
See its docstring for more information.
"""
if x.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in square")
return Array._new(np.square(x._array))
def f(n):
tot = 0
num_range = np.arange(0, n, dtype=cp.uint32)
for p in ittr.product(num_range, repeat=6):
k = cp.square(cp.array(p, dtype=cp.uint32))
nn = cp.power(p, 2)
if gcd(k.sum(), nn) == 1:
tot += 1
return tot
def __stopping_rule(self) -> bool:
"""
Implementation of Morozov discrepancy stopping rule. If the distance between solution and observations is smaller
than estimated noise level, then the algorithm will stop.
:return: boolean representing whether the stop condition is reached (False) or not (True).
"""
residual = cp.matmul(self.KHK, self.solution) - self.q_estimator
residual = cp.sqrt(cp.sum(cp.square(residual)) / self.grid_size)
return residual > (cp.sqrt(self.tau) * self.delta)
def rand(self, snr=1.):
"""Fill vector with random number (~U[1,-1]) with a given SNR"""
rms = cp.sqrt(cp.mean(cp.square(self.getNdArray())))
amp_noise = 1.0
if rms != 0.:
amp_noise = cp.sqrt(3. / snr) * rms # sqrt(3*Power_signal/SNR)
self.getNdArray()[:] = amp_noise * (
2. * cp.random.random(self.getNdArray().shape) - 1.)
return self
def log_prior(self, par,**args):
for k,v in args.items():
if k=='y_train':
y=v
K=0
for var in par.keys():
dim=(cp.asarray(par[var])).size
K+=dim*0.5*cp.log(self.hyper['alpha']/(2*np.pi))
K-=0.5*self.hyper['alpha']*cp.sum(cp.square(par[var]))
return K
def sample_function(x, y, z):
return cupy.square(cupy.add(x, y))
