Commit 208763a9 authored by Philipp Arras's avatar Philipp Arras

Remove Krylov sampling

parent 03823a8d
import nifty4 as ift
import numpy as np
import matplotlib.pyplot as plt
from nifty4.sugar import create_power_operator
np.random.seed(42)
x_space = ift.RGSpace(1024)
h_space = x_space.get_default_codomain()
d_space = x_space
N_hat = np.full(d_space.shape, 10.)
N_hat[400:450] = 0.0001
N_hat = ift.Field.from_global_data(d_space, N_hat)
N = ift.DiagonalOperator(N_hat)
FFT = ift.HarmonicTransformOperator(h_space, x_space)
R = ift.ScalingOperator(1., x_space)
def ampspec(k): return 1. / (1. + k**2.)
S = ift.ScalingOperator(1., h_space)
A = create_power_operator(h_space, ampspec)
s_h = S.draw_sample()
sky = FFT * A
s_x = sky(s_h)
n = N.draw_sample()
d = R(s_x) + n
R_p = R * FFT * A
j = R_p.adjoint(N.inverse(d))
D_inv = ift.SandwichOperator.make(R_p, N.inverse) + S.inverse
N_samps = 200
N_iter = 100
IC = ift.GradientNormController(tol_abs_gradnorm=1e-3, iteration_limit=N_iter)
m, samps = ift.library.generate_krylov_samples(D_inv, S, j, N_samps, IC)
m_x = sky(m)
inverter = ift.ConjugateGradient(IC)
curv = ift.library.WienerFilterCurvature(S=S, N=N, R=R_p, inverter=inverter,
sampling_inverter=inverter)
samps_old = [curv.draw_sample(from_inverse=True) for i in range(N_samps)]
plt.plot(d.to_global_data(), '+', label="data", alpha=.5)
plt.plot(s_x.to_global_data(), label="original")
plt.plot(m_x.to_global_data(), label="reconstruction")
plt.legend()
plt.savefig('Krylov_reconstruction.png')
plt.close()
pltdict = {'alpha': .3, 'linewidth': .2}
for i in range(N_samps):
if i == 0:
plt.plot(sky(samps_old[i]).to_global_data(), color='b',
label='Traditional samples (residuals)',
**pltdict)
plt.plot(sky(samps[i]).to_global_data(), color='r',
label='Krylov samples (residuals)',
**pltdict)
else:
plt.plot(sky(samps_old[i]).to_global_data(), color='b', **pltdict)
plt.plot(sky(samps[i]).to_global_data(), color='r', **pltdict)
plt.plot((s_x - m_x).to_global_data(), color='k', label='signal - mean')
plt.legend()
plt.savefig('Krylov_samples_residuals.png')
plt.close()
D_hat_old = ift.full(x_space, 0.).to_global_data()
D_hat_new = ift.full(x_space, 0.).to_global_data()
for i in range(N_samps):
D_hat_old += sky(samps_old[i]).to_global_data()**2
D_hat_new += sky(samps[i]).to_global_data()**2
plt.plot(np.sqrt(D_hat_old / N_samps), 'r--', label='Traditional uncertainty')
plt.plot(-np.sqrt(D_hat_old / N_samps), 'r--')
plt.fill_between(range(len(D_hat_new)), -np.sqrt(D_hat_new / N_samps), np.sqrt(
D_hat_new / N_samps), facecolor='0.5', alpha=0.5,
label='Krylov uncertainty')
plt.plot((s_x - m_x).to_global_data(), color='k', label='signal - mean')
plt.legend()
plt.savefig('Krylov_uncertainty.png')
plt.close()
......@@ -5,5 +5,4 @@ from .nonlinear_power_energy import NonlinearPowerEnergy
from .nonlinear_wiener_filter_energy import NonlinearWienerFilterEnergy
from .poisson_energy import PoissonEnergy
from .nonlinearities import Exponential, Linear, Tanh, PositiveTanh
from .krylov_sampling import generate_krylov_samples
from .los_response import LOSResponse
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
# Copyright(C) 2013-2018 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik
# and financially supported by the Studienstiftung des deutschen Volkes.
import numpy as np
from ..minimization.quadratic_energy import QuadraticEnergy
def generate_krylov_samples(D_inv, S, j, N_samps, controller):
"""
Generates inverse samples from a curvature D.
This algorithm iteratively generates samples from
a curvature D by applying conjugate gradient steps
and resampling the curvature in search direction.
Parameters
----------
D_inv : EndomorphicOperator
The curvature which will be the inverse of the covarianc
of the generated samples
S : EndomorphicOperator (from which one can sample)
A prior covariance operator which is used to generate prior
samples that are then iteratively updated
j : Field, optional
A Field to which the inverse of D_inv is applied. The solution
of this matrix inversion problem is a side product of generating
the samples.
If not supplied, it is sampled from the inverse prior.
N_samps : Int
How many samples to generate.
controller : IterationController
convergence controller for the conjugate gradient iteration
Returns
-------
(solution, samples) : A tuple of a field 'solution' and a list of fields
'samples'. The first entry of the tuple is the solution x to
D_inv(x) = j
and the second entry are a list of samples from D_inv.inverse
"""
# RL FIXME: make consistent with complex numbers
j = S.draw_sample(from_inverse=True) if j is None else j
energy = QuadraticEnergy(j.empty_copy().fill(0.), D_inv, j)
y = [S.draw_sample() for _ in range(N_samps)]
status = controller.start(energy)
if status != controller.CONTINUE:
return energy.position, y
r = energy.gradient
d = r.copy()
previous_gamma = r.vdot(r).real
if previous_gamma == 0:
return energy.position, y
while True:
q = energy.curvature(d)
ddotq = d.vdot(q).real
if ddotq == 0.:
logger.error("Error: ConjugateGradient: ddotq==0.")
return energy.position, y
alpha = previous_gamma/ddotq
if alpha < 0:
logger.error("Error: ConjugateGradient: alpha<0.")
return energy.position, y
for i in range(len(y)):
y[i] += (np.random.randn()*np.sqrt(ddotq) - y[i].vdot(q))/ddotq * d
q *= -alpha
r = r + q
energy = energy.at_with_grad(energy.position - alpha*d, r)
gamma = r.vdot(r).real
if gamma == 0:
return energy.position, y
status = controller.check(energy)
if status != controller.CONTINUE:
return energy.position, y
d *= max(0, gamma/previous_gamma)
d += r
previous_gamma = gamma
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