def __init__(
self,
N_pix=1024,
power_spectrum_beta=lambda k: 2 / (k**4 + 1),
noise_variance=0.01,
rho=1,
sigma_f=1,
minimizer=None,
controller=None,
beta_init=None,
tau_f_init=None,
):
super().__init__(N_pix=N_pix)
self.power_spectrum_beta = power_spectrum_beta
self.noise_variance = noise_variance
self.rho = rho
self.sigma_f = sigma_f
if controller is None:
controller = nifty5.GradientNormController(tol_rel_gradnorm=1e-2,
iteration_limit=500)
if minimizer is None:
minimizer = nifty5.VL_BFGS(controller=controller)
self.minimizer = minimizer
self.beta_init = beta_init
self.tau_f_init = tau_f_init
def curvature(self):
iteration_controller = nifty5.GradientNormController(
iteration_limit=300,
tol_abs_gradnorm=1e-3,
name=None)
return nifty5.InversionEnabler(
BetaCurvature(
domain=self.s_space,
beta=self.beta,
B=self.B,
rho=self.rho),
iteration_controller=iteration_controller)
def metric(self):
class RBCurv(ift.EndomorphicOperator):
def __init__(self, loc):
self._loc = loc.to_global_data_rw()
self._capability = self.TIMES
self._domain = space
def apply(self, x, mode):
self._check_input(x, mode)
inp = x.to_global_data_rw()
out = ift.Field.from_global_data(
space, rosen_hess_prod(self._loc.copy(), inp))
return out
t1 = ift.GradientNormController(
tol_abs_gradnorm=1e-5, iteration_limit=1000)
return ift.InversionEnabler(RBCurv(self._position), t1)
def wf_test(signal, noise, signal_boost, npix = 400):
pixel_space = ift.RGSpace([npix, npix])
fourier_space = pixel_space.get_default_codomain()
signal_field = ift.Field.from_global_data(pixel_space, signal.astype(float))
HT = ift.HartleyOperator(fourier_space, target=pixel_space)
power_field = ift.power_analyze(HT.inverse(signal_field), binbounds=ift.PowerSpace.useful_binbounds(fourier_space, True))
Sh = ift.create_power_operator(fourier_space, power_spectrum=power_field)
R = HT
noise_field = ift.Field.from_global_data(pixel_space, noise.astype(float))
noise_power_field = ift.power_analyze(HT.inverse(noise_field), binbounds=ift.PowerSpace.useful_binbounds(fourier_space, True))
N = ift.create_power_operator(HT.domain, noise_power_field)
N_inverse = HT@[email protected]
amplify = len(signal_boost)
s_data = np.zeros((amplify, npix, npix))
m_data = np.zeros((amplify, npix, npix))
d_data = np.zeros((amplify, npix, npix))
for i in np.arange(amplify):
data = noise_field
# Wiener filtering the data
j = (R.adjoint @N_inverse.inverse)(data)
D_inv = R.adjoint @ N_inverse.inverse @ R + Sh.inverse
IC = ift.GradientNormController(iteration_limit=500, tol_abs_gradnorm=1e-3)
D = ift.InversionEnabler(D_inv, IC, approximation=Sh.inverse).inverse
m = D(j)
s_data[i,:,:] = (signal_field * signal_boost[i]).to_global_data()
m_data[i,:,:] = HT(m).to_global_data()
d_data[i,:,:] = data.to_global_data()
return (s_data, m_data, d_data)
def __init__(
self,
N_pix=1024,
power_spectrum_f=lambda k: 1/(k**4+1),
power_spectrum_beta=lambda k: 1/(k**4+1),
noise_var=0.1,
rho=1,
minimization=None,
minimizer=None,
):
super().__init__(
N_pix=N_pix)
# because of how nifty implements the FFT, we have to multiply the
# amplitude by N_pix
self.power_spectrum_f = lambda q: power_spectrum_f(q)*N_pix
self.power_spectrum_beta = lambda q: power_spectrum_beta(q)*N_pix
self.noise_var = noise_var
self.rho = rho
if minimizer is None:
minimizer = nifty5.VL_BFGS(
controller=nifty5.GradientNormController(
tol_abs_gradnorm=1,
iteration_limit=100))
self.minimizer = minimizer
signal_response = R(correlated_field)
# Set up likelihood and load data
N = ift.ScalingOperator(0.1, data_space)
data, ground_truth = generate_mysterious_data(position_space)
data = ift.from_global_data(data_space, data)
likelihood = ift.GaussianEnergy(mean=data,
inverse_covariance=N.inverse)(signal_response)
#### SOLVING PROBLEM ####
ic_sampling = ift.GradientNormController(iteration_limit=100)
ic_newton = ift.GradInfNormController(
name='Newton', tol=1e-6, iteration_limit=30)
minimizer = ift.NewtonCG(ic_newton)
H = ift.StandardHamiltonian(likelihood, ic_sampling)
initial_mean = ift.MultiField.full(H.domain, 0.)
mean = initial_mean
# number of samples used to estimate the KL
N_samples = 10
# Draw new samples to approximate the KL ten times
for i in range(10):
# Draw new samples and minimize KL
data_space = GR.target
# Set the noise covariance N
noise = 5.
N = ift.ScalingOperator(noise, data_space)
# Create mock data
MOCK_SIGNAL = S.draw_sample()
MOCK_NOISE = N.draw_sample()
data = R(MOCK_SIGNAL) + MOCK_NOISE
# Build inverse propagator D and information source j
D_inv = R.adjoint @ N.inverse @ R + S.inverse
j = R.adjoint_times(N.inverse_times(data))
# Make D_inv invertible (via Conjugate Gradient)
IC = ift.GradientNormController(iteration_limit=500, tol_abs_gradnorm=1e-3)
D = ift.InversionEnabler(D_inv, IC, approximation=S.inverse).inverse
# Calculate WIENER FILTER solution
m = D(j)
# Plotting
rg = isinstance(position_space, ift.RGSpace)
plot = ift.Plot()
filename = "getting_started_1_mode_{}.png".format(mode)
if rg and len(position_space.shape) == 1:
plot.add([HT(MOCK_SIGNAL), GR.adjoint(data),
HT(m)],
label=['Mock signal', 'Data', 'Reconstruction'],
alpha=[1, .3, 1])
plot.add(mask_to_nan(mask, HT(m - MOCK_SIGNAL)), title='Residuals')
accuracy = 0
sum_of_weights = 0
weighted_correct = 0
for i in range(FIRST_ID-1, LAST_ID):
(x, y), true_direction, weight = get_pair(
i, BENCHMARK, subsample_size=SUBSAMPLE)
if true_direction == 0:
continue
scaler = MinMaxScaler(scale)
x, y = scaler.fit_transform(np.array((x, y)).T).T
minimizer = nifty5.RelaxedNewton(controller=nifty5.GradientNormController(
tol_rel_gradnorm=TOL_REL_GRADNORM,
iteration_limit=ITERATION_LIMIT,
convergence_level=5,
))
bcm = bayesian_causal_model_nifty.cause_model_shallow.CausalModelShallow(
N_bins=N_BINS,
noise_var=NOISE_VAR,
rho=RHO,
power_spectrum_beta=POWER_SPECTRUM_BETA,
power_spectrum_f=POWER_SPECTRUM_F,
minimizer=minimizer,
)
bcm.set_data(x, y)
H1 = bcm.get_evidence(direction=1, verbosity=VERBOSITY - 1)
def nifty_wf(signal, noise, y_map, npix = 400, pxsize = 1.5, kernel = 9.68, n = 10, smooth = False):
cmb_mocks = noise.shape[0]
A = (2*np.sqrt(2*np.log(2)))
if smooth is True:
signal_smooth = np.zeros((cmb_mocks, npix, npix))
noise_smooth = np.zeros((cmb_mocks, npix, npix))
for i in np.arange(cmb_mocks):
noise_data = ndimage.gaussian_filter(noise[i], sigma= kernel/A/pxsize, order=0, mode = "reflect", truncate = 10)
#signal_data = ndimage.gaussian_filter(signal[i], sigma= kernel/A/pxsize, order=0, mode = "reflect", truncate = 10)
signal_data = signal[i] #uncomment here if smoothing signal and noise
noise_smooth[i,:,:] = noise_data
signal_smooth[i,:,:] = signal_data
else:
noise_smooth = noise
signal_smooth = signal
pixel_space = ift.RGSpace([npix, npix])
fourier_space = pixel_space.get_default_codomain()
s_data = np.zeros((cmb_mocks, npix, npix))
m_data = np.zeros((cmb_mocks, npix, npix))
d_data = np.zeros((cmb_mocks, npix, npix))
for i in np.arange(cmb_mocks):
signal_field = ift.Field.from_global_data(pixel_space, signal_smooth.astype(float)) #[i] for mock_data
HT = ift.HartleyOperator(fourier_space, target=pixel_space)
power_field = ift.power_analyze(HT.inverse(signal_field), binbounds=ift.PowerSpace.useful_binbounds(fourier_space, True))
Sh = ift.create_power_operator(fourier_space, power_spectrum=power_field)
R = HT
noise_field = ift.Field.from_global_data(pixel_space, noise_smooth[i].astype(float))
noise_power_field = ift.power_analyze(HT.inverse(noise_field), binbounds=ift.PowerSpace.useful_binbounds(fourier_space, True))
N = ift.create_power_operator(HT.domain, noise_power_field)
N_inverse = HT@[email protected]
data = signal_field + noise_field # --->when using mock_data
# Wiener filtering the data
j = (R.adjoint @N_inverse.inverse)(data)
D_inv = R.adjoint @ N_inverse.inverse @ R + Sh.inverse
IC = ift.GradientNormController(iteration_limit=500, tol_abs_gradnorm=1e-3)
D = ift.InversionEnabler(D_inv, IC, approximation=Sh.inverse).inverse
m = D(j)
#s_data[i,:,:] = (signal_field).to_global_data()
m_data[i,:,:] = HT(m).to_global_data()
#d_data[i,:,:] = data.to_global_data()
#Squaring the filtered map and also taking the absoute val of filtered map
# uncomment here for no cross correlation
squared_m_data = np.zeros((cmb_mocks, npix, npix))
abs_m_data = np.zeros((cmb_mocks, npix, npix))
for i in np.arange(m_data.shape[0]):
squared_m_data[i,:,:] = m_data[i,:,:] * m_data[i,:,:]
abs_m_data[i,:,:] = np.abs(m_data[i,:,:])
#Stacking all filtered maps
stack1 = np.sum(squared_m_data, axis = 0)/m_data.shape[0]
stack2 = np.sum(abs_m_data, axis = 0)/m_data.shape[0]
return (m_data, squared_m_data, abs_m_data, stack1, stack2) #change here to return the right values ---->, stack_square, stack_abs
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
# Copyright(C) 2013-2019 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.
from unittest import SkipTest
import numpy as np
import pytest
from numpy.testing import assert_allclose, assert_equal
import nifty5 as ift
pmp = pytest.mark.parametrize
IC = ift.GradientNormController(tol_abs_gradnorm=1e-5, iteration_limit=1000)
spaces = [ift.RGSpace([1024], distances=0.123), ift.HPSpace(32)]
minimizers = [
'ift.VL_BFGS(IC)',
'ift.NonlinearCG(IC, "Polak-Ribiere")',
# 'ift.NonlinearCG(IC, "Hestenes-Stiefel"),
'ift.NonlinearCG(IC, "Fletcher-Reeves")',
'ift.NonlinearCG(IC, "5.49")',
'ift.L_BFGS_B(ftol=1e-10, gtol=1e-5, maxiter=1000)',
'ift.L_BFGS(IC)',
'ift.NewtonCG(IC)'
]
newton_minimizers = ['ift.RelaxedNewton(IC)']
N = ift.ScalingOperator(0.1, data_space)
data = ift.from_global_data(data_space, sheared_image) + N.draw_sample()
# Similar to the fourier transform, but we have real numbers as output
harmonic_space = position_space.get_default_codomain()
HT = ift.HartleyOperator(harmonic_space, target=position_space)
S_h = ift.create_power_operator(harmonic_space, prior_spectrum)
# @ is as if doing function composition
S = HT @ S_h @ HT.adjoint
D_inv = S.inverse + R.adjoint @ N.inverse @ R
j = (R.adjoint @ N.inverse)(data)
IC = ift.GradientNormController(name = 'CG', iteration_limit=100, tol_abs_gradnorm=1e-7)
D = ift.InversionEnabler(D_inv.inverse, IC, approximation=S)
# Conjugate gradiend applied here
m = D(j)
result_image = m.val
# Plot the images
f, axarr = plt.subplots(1,3)
axarr[0].imshow(image_original_arr)
axarr[1].imshow(data.val)
axarr[2].imshow(m.val)
plt.savefig('Original_data_mean.png', dpi = 150)