# 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 .
#
# 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.
from numpy import sqrt
from numpy.random import randn
def generate_krylov_samples(D_inv, S, j=None, N_samps=1, N_iter=10,
name=None):
"""
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, optional
How many samples to generate. Default: 1
N_iter : Int, optional
How many iterations of the conjugate gradient to run. Default: 10
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
"""
j = S.draw_sample(from_inverse=True) if j is None else j
x = j*0
r = j.copy()
p = r.copy()
d = p.vdot(D_inv(p))
y = [S.draw_sample() for _ in range(N_samps)]
for k in range(1, 1+N_iter):
gamma = r.vdot(r)/d
if gamma == 0.:
break
x += gamma*p
for i in range(N_samps):
y[i] -= p.vdot(D_inv(y[i])) * p / d
y[i] += randn() / sqrt(d) * p
r_new = r - gamma * D_inv(p)
beta = r_new.vdot(r_new) / r.vdot(r)
r = r_new
p = r + beta * p
d = p.vdot(D_inv(p))
if d == 0.:
break
if name is not None:
print('{}: Iteration #{}'.format(name, k))
return x, y