Commit 0b7b4e88 authored by Martin Reinecke's avatar Martin Reinecke

Merge branch 'fix_complex_samples' into 'NIFTy_6'

Fix complex samples

See merge request !539
parents ccbf5012 a6bbaa1e
Pipeline #76971 passed with stages
in 13 minutes and 16 seconds
......@@ -58,6 +58,19 @@ print(met)
print(met.draw_sample())
```
New approach for sampling complex numbers
=========================================
When calling draw_sample_with_dtype with a complex dtype,
the variance is now used for the imaginary part and real part separately.
This is done in order to be consistent with the Hamiltonian.
Note that by this,
```
np.std(ift.from_random(domain, 'normal', dtype=np.complex128).val)
````
does not give 1, but sqrt(2) as a result.
MPI parallelisation over samples in MetricGaussianKL
====================================================
......@@ -73,6 +86,7 @@ the generation of reproducible random numbers in the presence of MPI parallelism
and leads to cleaner code overall. Please see the documentation of
`nifty6.random` for details.
Interface Change for from_random and OuterProduct
=================================================
......
......@@ -135,6 +135,8 @@ class Field(Operator):
The domain of the output random Field.
dtype : type
The datatype of the output random Field.
If the datatype is complex, each real and imaginary part
have variance 1
Returns
-------
......
......@@ -112,6 +112,8 @@ class MultiField(Operator):
The domain of the output random Field.
dtype : type
The datatype of the output random Field.
If the datatype is complex, each real an imaginary part have
variance 1.
Returns
-------
......
......@@ -27,7 +27,7 @@ from .linear_operator import LinearOperator
from .operator import Operator
from .sampling_enabler import SamplingDtypeSetter, SamplingEnabler
from .scaling_operator import ScalingOperator
from .simple_linear_operators import VdotOperator
from .simple_linear_operators import VdotOperator, FieldAdapter
def _check_sampling_dtype(domain, dtypes):
......@@ -187,6 +187,13 @@ class GaussianEnergy(EnergyOperator):
domain : Domain, DomainTuple, tuple of Domain or MultiDomain
Operator domain. By default it is inferred from `mean` or
`covariance` if specified
sampling_dtype : type
Here one can specify whether the distribution is a complex Gaussian or
not. Note that for a complex Gaussian the inverse_covariance is
.. math ::
(<ff^dagger>)^{-1}_P(f)/2,
where the additional factor of 2 is necessary because the
domain of s has double as many dimensions as in the real case.
Note
----
......
......@@ -238,8 +238,8 @@ class Random(object):
raise TypeError("mean must not be complex for a real result field")
if np.issubdtype(dtype, np.complexfloating):
x = np.empty(shape, dtype=dtype)
x.real = _rng[-1].normal(mean.real, std*np.sqrt(0.5), shape)
x.imag = _rng[-1].normal(mean.imag, std*np.sqrt(0.5), shape)
x.real = _rng[-1].normal(mean.real, std, shape)
x.imag = _rng[-1].normal(mean.imag, std, shape)
else:
x = _rng[-1].normal(mean, std, shape).astype(dtype, copy=False)
return x
......
......@@ -266,6 +266,8 @@ def from_random(domain, random_type='normal', dtype=np.float64, **kwargs):
The random distribution to use.
dtype : type
data type of the output field (e.g. numpy.float64)
If the datatype is complex, each real an imaginary part have
variance 1.
**kwargs : additional parameters for the random distribution
('mean' and 'std' for 'normal', 'low' and 'high' for 'uniform')
......
# 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) 2013-2020 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.
import numpy as np
import pytest
import nifty6 as ift
from ..common import list2fixture, setup_function, teardown_function
from scipy.stats import norm
Nsamp = 20000
np.random.seed(42)
def _to_array(d):
if isinstance(d, np.ndarray):
return d
assert isinstance(d, dict)
return np.concatenate(list(d.values()))
def test_GaussianEnergy():
sp = ift.UnstructuredDomain(Nsamp)
S = ift.ScalingOperator(sp, 1.)
samp = S.draw_sample_with_dtype(dtype=np.complex128)
real_std = np.std(samp.val.real)
imag_std = np.std(samp.val.imag)
np.testing.assert_allclose(real_std, imag_std,
atol=5./np.sqrt(Nsamp))
sp1 = ift.UnstructuredDomain(1)
mean = ift.full(sp1, 0.)
real_icov = ift.ScalingOperator(sp1, real_std**(-2))
imag_icov = ift.ScalingOperator(sp1, imag_std**(-2))
real_energy = ift.GaussianEnergy(mean, inverse_covariance=real_icov)
imag_energy = ift.GaussianEnergy(mean, inverse_covariance=imag_icov)
icov = ift.ScalingOperator(sp1, 1.)
complex_energy = ift.GaussianEnergy(mean+0.j, inverse_covariance=icov)
for i in range(min(10, Nsamp)):
fld = ift.full(sp1, samp.val[i])
val1 = (real_energy(fld.real) + imag_energy(fld.imag)).val
val2 = complex_energy(fld).val
np.testing.assert_allclose(val1, val2, atol=10./np.sqrt(Nsamp))
def test_WienerFilter():
sp = ift.UnstructuredDomain(30)
S = ift.ScalingOperator(sp, 1.)
R = ift.ContractionOperator(sp, None)
N = ift.ScalingOperator(R.target, 1/5**2)
IC = ift.GradientNormController(iteration_limit=10, tol_abs_gradnorm=1e-7)
D = ift.WienerFilterCurvature(R, N, S, IC, IC).inverse
s = S.draw_sample_with_dtype(dtype=np.complex128)
d = R(s)+N.draw_sample_with_dtype(dtype=np.complex128)
j = R.adjoint_times(N.inverse_times(d))
m = D(j)
sr = s.real
jr = j.real
mr = D(jr)
si = s.imag
ji = j.imag
mi = D(ji)
np.testing.assert_allclose((mr+mi*1.j).val, m.val, rtol=1e-7)
# 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) 2013-2020 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.
import numpy as np
import pytest
import nifty6 as ift
from ..common import list2fixture, setup_function, teardown_function
spaces = [ift.GLSpace(5),
(ift.RGSpace(3, distances=.789), ift.UnstructuredDomain(2))]
pmp = pytest.mark.parametrize
field = list2fixture([ift.from_random(sp, 'normal') for sp in spaces] +
[ift.from_random(sp, 'normal', dtype=np.complex128) for sp in spaces])
Nsamp = 2000
np.random.seed(42)
def _to_array(d):
if isinstance(d, np.ndarray):
return d
assert isinstance(d, dict)
return np.concatenate(list(d.values()))
def _complex2real(sp):
tup = tuple([d for d in sp])
rsp = ift.DomainTuple.make((ift.UnstructuredDomain(2),) + tup)
rl = ift.DomainTupleFieldInserter(rsp, 0, (0,))
im = ift.DomainTupleFieldInserter(rsp, 0, (1,))
x = ift.ScalingOperator(sp, 1)
return rl(x.real)+im(x.imag)
def test_complex2real():
sp = ift.UnstructuredDomain(3)
op = _complex2real(ift.makeDomain(sp))
f = ift.from_random(op.domain, 'normal', dtype=np.complex128)
assert np.all((f == op.adjoint_times(op(f))).val)
assert op(f).dtype == np.float64
f = ift.from_random(op.target, 'normal')
assert np.all((f == op(op.adjoint_times(f))).val)
def energy_tester_complex(pos, get_noisy_data, energy_initializer):
op = _complex2real(pos.domain)
npos = op(pos)
nget_noisy_data = lambda mean : get_noisy_data(op.adjoint_times(mean))
nenergy_initializer = lambda mean : energy_initializer(mean) @ op.adjoint
energy_tester(npos, nget_noisy_data, nenergy_initializer)
def energy_tester(pos, get_noisy_data, energy_initializer):
if np.issubdtype(pos.dtype, np.complexfloating):
energy_tester_complex(pos, get_noisy_data, energy_initializer)
return
domain = pos.domain
test_vec = ift.from_random(domain, 'normal')
results = []
lin = ift.Linearization.make_var(pos)
for i in range(Nsamp):
data = get_noisy_data(pos)
energy = energy_initializer(data)
grad = energy(lin).jac.adjoint(ift.full(energy.target, 1.))
results.append(_to_array((grad*grad.s_vdot(test_vec)).val))
print(energy)
print(grad)
res = np.mean(np.array(results), axis=0)
std = np.std(np.array(results), axis=0)/np.sqrt(Nsamp)
energy = energy_initializer(data)
lin = ift.Linearization.make_var(pos, want_metric=True)
res2 = _to_array(energy(lin).metric(test_vec).val)
np.testing.assert_allclose(res/std, res2/std, atol=6)
def test_GaussianEnergy(field):
dtype = field.dtype
icov = ift.from_random(field.domain, 'normal')**2
icov = ift.makeOp(icov)
get_noisy_data = lambda mean : mean + icov.draw_sample_with_dtype(
from_inverse=True, dtype=dtype)
E_init = lambda mean : ift.GaussianEnergy(mean=mean,
inverse_covariance=icov)
energy_tester(field, get_noisy_data, E_init)
def test_PoissonEnergy(field):
if not isinstance(field, ift.Field):
return
if np.iscomplexobj(field.val):
return
def get_noisy_data(mean):
return ift.makeField(mean.domain, np.random.poisson(mean.val))
lam = 10*(field**2).clip(0.1,None) # make rate positive and high enough to avoid bad statistic
E_init = lambda mean : ift.PoissonianEnergy(mean)
energy_tester(lam, get_noisy_data, E_init)
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