def test_fft2D(dim1, dim2, d1, d2, dtype, op, fftw):
if fftw:
ift.fft.enable_fftw()
tol = _get_rtol(dtype)
a = ift.RGSpace([dim1, dim2], distances=[d1, d2])
b = ift.RGSpace([dim1, dim2],
distances=[1. / (dim1 * d1), 1. / (dim2 * d2)],
harmonic=True)
fft = op(domain=a, target=b)
inp = ift.Field.from_random(domain=a,
random_type='normal',
std=7,
mean=3,
dtype=dtype)
out = fft.inverse_times(fft.times(inp))
assert_allclose(inp.local_data, out.local_data, rtol=tol, atol=tol)
a, b = b, a
fft = ift.FFTOperator(domain=a, target=b)
inp = ift.Field.from_random(domain=a,
random_type='normal',
std=7,
mean=3,
dtype=dtype)
out = fft.inverse_times(fft.times(inp))
assert_allclose(inp.local_data, out.local_data, rtol=tol, atol=tol)
ift.fft.disable_fftw()
def test_fft1D(d, dtype, op, fftw):
if fftw:
ift.fft.enable_fftw()
dim1 = 16
tol = _get_rtol(dtype)
a = ift.RGSpace(dim1, distances=d)
b = ift.RGSpace(dim1, distances=1. / (dim1 * d), harmonic=True)
np.random.seed(16)
fft = op(domain=a, target=b)
inp = ift.Field.from_random(domain=a,
random_type='normal',
std=7,
mean=3,
dtype=dtype)
out = fft.inverse_times(fft.times(inp))
assert_allclose(inp.local_data, out.local_data, rtol=tol, atol=tol)
a, b = b, a
fft = ift.FFTOperator(domain=a, target=b)
inp = ift.Field.from_random(domain=a,
random_type='normal',
std=7,
mean=3,
dtype=dtype)
out = fft.inverse_times(fft.times(inp))
assert_allclose(inp.local_data, out.local_data, rtol=tol, atol=tol)
ift.fft.disable_fftw()
def test_simplification():
from nifty5.operators.operator import _ConstantOperator
f1 = ift.Field.full(ift.RGSpace(10), 2.)
op = ift.FFTOperator(f1.domain)
_, op2 = op.simplify_for_constant_input(f1)
assert_equal(isinstance(op2, _ConstantOperator), True)
assert_allclose(op(f1).local_data, op2(f1).local_data)
dom = {"a": ift.RGSpace(10)}
f1 = ift.full(dom, 2.)
op = ift.FFTOperator(f1.domain["a"]).ducktape("a")
_, op2 = op.simplify_for_constant_input(f1)
assert_equal(isinstance(op2, _ConstantOperator), True)
assert_allclose(op(f1).local_data, op2(f1).local_data)
dom = {"a": ift.RGSpace(10), "b": ift.RGSpace(5)}
f1 = ift.full(dom, 2.)
pdom = {"a": ift.RGSpace(10)}
f2 = ift.full(pdom, 2.)
o1 = ift.FFTOperator(f1.domain["a"])
o2 = ift.FFTOperator(f1.domain["b"])
op = (o1.ducktape("a").ducktape_left("a") +
o2.ducktape("b").ducktape_left("b"))
_, op2 = op.simplify_for_constant_input(f2)
assert_equal(isinstance(op2._op1, _ConstantOperator), True)
assert_allclose(op(f1)["a"].local_data, op2(f1)["a"].local_data)
assert_allclose(op(f1)["b"].local_data, op2(f1)["b"].local_data)
lin = ift.Linearization.make_var(ift.MultiField.full(op2.domain, 2.), True)
assert_allclose(op(lin).val["a"].local_data, op2(lin).val["a"].local_data)
assert_allclose(op(lin).val["b"].local_data, op2(lin).val["b"].local_data)
def test_outer():
x1 = ift.RGSpace((9, ))
x2 = ift.RGSpace((3, ))
m1 = ift.Field.full(x1, .5)
m2 = ift.Field.full(x2, 3.)
res = m1.outer(m2)
assert_allclose(res.to_global_data(), np.full((9, 3), 1.5))
def test_integrate():
x1 = ift.RGSpace((9, ), distances=2.)
x2 = ift.RGSpace((2, 12), distances=(0.3, ))
m1 = ift.Field.from_global_data(ift.makeDomain(x1), np.arange(9))
m2 = ift.Field.full(ift.makeDomain((x1, x2)), 0.45)
res1 = m1.integrate()
res2 = m2.integrate(spaces=1)
assert_allclose(res1, 36 * 2)
assert_allclose(res2.to_global_data(), np.full(9, 2 * 12 * 0.45 * 0.3**2))
def test_get_signal_variance():
space = ift.RGSpace(3)
hspace = space.get_default_codomain()
spec1 = lambda x: np.ones_like(x)
assert_equal(ift.get_signal_variance(spec1, hspace), 3.)
space = ift.RGSpace(3, distances=1.)
hspace = space.get_default_codomain()
def spec2(k):
t = np.zeros_like(k)
t[k == 0] = 1.
return t
assert_equal(ift.get_signal_variance(spec2, hspace), 1 / 9.)
def test_stdfunc():
s = ift.RGSpace((200, ))
f = ift.Field.full(s, 27)
assert_equal(f.local_data, 27)
assert_equal(f.shape, (200, ))
assert_equal(f.dtype, np.int)
fx = ift.full(f.domain, 0)
assert_equal(f.dtype, fx.dtype)
assert_equal(f.shape, fx.shape)
assert_equal(fx.local_data, 0)
fx = ift.full(f.domain, 1)
assert_equal(f.dtype, fx.dtype)
assert_equal(f.shape, fx.shape)
assert_equal(fx.local_data, 1)
fx = ift.full(f.domain, 67.)
assert_equal(f.shape, fx.shape)
assert_equal(fx.local_data, 67.)
f = ift.Field.from_random("normal", s)
f2 = ift.Field.from_random("normal", s)
assert_equal((f > f2).local_data, f.local_data > f2.local_data)
assert_equal((f >= f2).local_data, f.local_data >= f2.local_data)
assert_equal((f < f2).local_data, f.local_data < f2.local_data)
assert_equal((f <= f2).local_data, f.local_data <= f2.local_data)
assert_equal((f != f2).local_data, f.local_data != f2.local_data)
assert_equal((f == f2).local_data, f.local_data == f2.local_data)
assert_equal((f + f2).local_data, f.local_data + f2.local_data)
assert_equal((f - f2).local_data, f.local_data - f2.local_data)
assert_equal((f * f2).local_data, f.local_data * f2.local_data)
assert_equal((f / f2).local_data, f.local_data / f2.local_data)
assert_equal((-f).local_data, -(f.local_data))
assert_equal(abs(f).local_data, abs(f.local_data))
def testLinearInterpolator():
sp = ift.RGSpace((10, 8), distances=(0.1, 3.5))
pos = np.random.rand(2, 23)
pos[0, :] *= 0.9
pos[1, :] *= 7 * 3.5
op = ift.LinearInterpolator(sp, pos)
ift.extra.consistency_check(op)
def test_dvol():
hp = ift.RGSpace(10, harmonic=True)
p = ift.PowerSpace(harmonic_partner=hp)
v1 = hp.dvol
v1 = hp.size*v1 if np.isscalar(v1) else np.sum(v1)
v2 = p.dvol
v2 = p.size*v2 if np.isscalar(v2) else np.sum(v2)
assert_allclose(v1, v2)
def test_composed_fft(index, dtype, op, fftw):
if fftw:
ift.fft.enable_fftw()
tol = _get_rtol(dtype)
a = [a1, a2,
a3] = [ift.RGSpace((32, )),
ift.RGSpace((4, 4)),
ift.RGSpace((5, 6))]
fft = op(domain=a, space=index)
inp = ift.Field.from_random(domain=(a1, a2, a3),
random_type='normal',
std=7,
mean=3,
dtype=dtype)
out = fft.inverse_times(fft.times(inp))
assert_allclose(inp.local_data, out.local_data, rtol=tol, atol=tol)
ift.fft.disable_fftw()
def test_smooth_regular2(sz1, sz2, d1, d2, sigma, tp):
tol = _get_rtol(tp)
sp = ift.RGSpace([sz1, sz2], distances=[d1, d2])
smo = ift.HarmonicSmoothingOperator(sp, sigma=sigma)
inp = ift.Field.from_random(domain=sp,
random_type='normal',
std=1,
mean=4,
dtype=tp)
out = smo(inp)
assert_allclose(inp.sum(), out.sum(), rtol=tol, atol=tol)
def test_err():
s1 = ift.RGSpace((10, ))
s2 = ift.RGSpace((11, ))
f1 = ift.Field.full(s1, 27)
with assert_raises(ValueError):
f2 = ift.Field(ift.DomainTuple.make(s2), f1.val)
with assert_raises(TypeError):
f2 = ift.Field.full(s2, "xyz")
with assert_raises(TypeError):
if f1:
pass
with assert_raises(TypeError):
f1.full((2, 4, 6))
with assert_raises(TypeError):
f2 = ift.Field(None, None)
with assert_raises(TypeError):
f2 = ift.Field(s1, None)
with assert_raises(ValueError):
f1.imag
with assert_raises(TypeError):
f1.vdot(42)
with assert_raises(ValueError):
f1.vdot(ift.Field.full(s2, 1.))
with assert_raises(TypeError):
ift.full(s1, [2, 3])
with assert_raises(TypeError):
ift.Field(s2, [0, 1])
with assert_raises(TypeError):
f1.outer([0, 1])
with assert_raises(ValueError):
f1.extract(s2)
with assert_raises(TypeError):
f1 += f1
f2 = ift.Field.full(s2, 27)
with assert_raises(ValueError):
f1 + f2
def test_weight():
s1 = ift.RGSpace((10, ))
f = ift.Field.full(s1, 10.)
f2 = f.weight(1)
assert_equal(f.weight(1).local_data, f2.local_data)
assert_equal(f.total_volume(), 1)
assert_equal(f.total_volume(0), 1)
assert_equal(f.total_volume((0, )), 1)
assert_equal(f.scalar_weight(), 0.1)
assert_equal(f.scalar_weight(0), 0.1)
assert_equal(f.scalar_weight((0, )), 0.1)
s1 = ift.GLSpace(10)
f = ift.Field.full(s1, 10.)
assert_equal(f.scalar_weight(), None)
assert_equal(f.scalar_weight(0), None)
assert_equal(f.scalar_weight((0, )), None)
def __init__(
self,
N_bins=1024,
power_spectrum_beta=lambda q: 1 / (q**4 + 1),
power_spectrum_f=lambda q: 1 / (q**4 + 1),
noise_var=0.1,
):
"""
N_bins : int
number of bins for the sample spaces
p_spec_beta : function
power spectrum for beta
p_spec_f : function
power spectrum for f
noise_var : scalar
the variance of the noise variable
"""
self.N_bins = N_bins
self.s_space = nifty5.RGSpace([N_bins], )
self.h_space = self.s_space.get_default_codomain()
self.p_space = nifty5.PowerSpace(self.h_space)
# covariance operator for the beta distribution
self.power_spectrum_beta = power_spectrum_beta
B_h = nifty5.create_power_operator(
self.h_space, power_spectrum=self.power_spectrum_beta)
fft = nifty5.FFTOperator(self.s_space)
self.B = nifty5.SandwichOperator.make(fft, B_h)
self.beta = self.B.draw_sample()
# numerical values for p(x|beta) = exp(beta(x)) / sum_z exp(beta(z))
self.p_x_val = np.exp(np.array(self.beta.to_global_data()))
self.p_x_val = (1 / np.sum(self.p_x_val)) * self.p_x_val
# get the covariance operator for the f distribution
self.power_spectrum_f = power_spectrum_f
F_h = nifty5.create_power_operator(
self.h_space, power_spectrum=self.power_spectrum_f)
self.F = nifty5.SandwichOperator.make(fft, F_h)
# sample the transformation function f
self.f = self.F.draw_sample()
self.f_val = np.array(self.f.to_global_data())
# set the noise variance
self.noise_var = noise_var
def test_trivialities():
s1 = ift.RGSpace((10, ))
f1 = ift.Field.full(s1, 27)
assert_equal(f1.clip(min=29).local_data, 29.)
assert_equal(f1.clip(max=25).local_data, 25.)
assert_equal(f1.local_data, f1.real.local_data)
assert_equal(f1.local_data, (+f1).local_data)
f1 = ift.Field.full(s1, 27. + 3j)
assert_equal(f1.one_over().local_data, (1. / f1).local_data)
assert_equal(f1.real.local_data, 27.)
assert_equal(f1.imag.local_data, 3.)
assert_equal(f1.sum(), f1.sum(0))
assert_equal(f1.conjugate().local_data,
ift.Field.full(s1, 27. - 3j).local_data)
f1 = ift.from_global_data(s1, np.arange(10))
# assert_equal(f1.min(), 0)
# assert_equal(f1.max(), 9)
assert_equal(f1.prod(), 0)
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 test_dvol(shape, distances, harmonic, power):
r = ift.RGSpace(shape=shape, distances=distances, harmonic=harmonic)
assert_allclose(r.dvol, np.prod(r.distances)**power)
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.
import numpy as np
import pytest
import nifty5 as ift
from itertools import product
# Currently it is not possible to parametrize fixtures. But this will
# hopefully be fixed in the future.
# https://docs.pytest.org/en/latest/proposals/parametrize_with_fixtures.html
SPACES = [
ift.GLSpace(15),
ift.RGSpace(64, distances=.789),
ift.RGSpace([32, 32], distances=.789)
]
SEEDS = [4, 78, 23]
PARAMS = product(SEEDS, SPACES)
@pytest.fixture(params=PARAMS)
def field(request):
np.random.seed(request.param[0])
S = ift.ScalingOperator(1., request.param[1])
s = S.draw_sample()
return ift.MultiField.from_dict({'s1': s})['s1']
def test_gaussian(field):
def testLinearInterpolator():
sp = ift.RGSpace((10, 8), distances=(0.1, 3.5))
pos = np.random.rand(2, 23)
pos[0, :] *= 0.9
pos[1, :] *= 7 * 3.5
_check_repr(ift.LinearInterpolator(sp, pos))
def testZeroPadder(space, factor, dtype, central):
dom = (ift.RGSpace(10), ift.UnstructuredDomain(13), ift.RGSpace(7, 12),
ift.HPSpace(4))
newshape = [int(factor * l) for l in dom[space].shape]
_check_repr(ift.FieldZeroPadder(dom, newshape, space, central))
def testDomainTupleFieldInserter():
target = ift.DomainTuple.make(
(ift.UnstructuredDomain([3, 2]), ift.UnstructuredDomain(7),
ift.RGSpace([4, 22])))
_check_repr(ift.DomainTupleFieldInserter(target, 1, (5, )))
def testContractionOperator(spaces, wgt, dtype):
dom = (ift.RGSpace(10), ift.RGSpace(13), ift.GLSpace(5), ift.HPSpace(4))
_check_repr(ift.ContractionOperator(dom, spaces, wgt))
# 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) 2013-2019 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.
import numpy as np
import pytest
import nifty5 as ift
from ..common import list2fixture
_h_RG_spaces = [
ift.RGSpace(7, distances=0.2, harmonic=True),
ift.RGSpace((12, 46), distances=(.2, .3), harmonic=True)
]
_h_spaces = _h_RG_spaces + [ift.LMSpace(17)]
_p_RG_spaces = [
ift.RGSpace(19, distances=0.7),
ift.RGSpace((1, 2, 3, 6), distances=(0.2, 0.25, 0.34, .8))
]
_p_spaces = _p_RG_spaces + [ift.HPSpace(17), ift.GLSpace(8, 13)]
_pow_spaces = [ift.PowerSpace(ift.RGSpace((17, 38), harmonic=True))]
pmp = pytest.mark.parametrize
dtype = list2fixture([np.float64, np.complex128])
def _check_repr(op):
#
# 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) 2013-2019 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.
from numpy.testing import assert_allclose, assert_equal
import nifty5 as ift
from ..common import list2fixture
space1 = list2fixture([
ift.RGSpace(4),
ift.PowerSpace(ift.RGSpace((4, 4), harmonic=True)),
ift.LMSpace(5),
ift.HPSpace(4),
ift.GLSpace(4)
])
space2 = space1
def test_times_adjoint_times(space1, space2):
cspace = (space1, space2)
diag1 = ift.Field.from_random('normal', domain=space1)
diag2 = ift.Field.from_random('normal', domain=space2)
op1 = ift.DiagonalOperator(diag1, cspace, spaces=(0, ))
op2 = ift.DiagonalOperator(diag2, cspace, spaces=(1, ))
# 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) 2013-2019 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.
import numpy as np
import nifty5 as ift
from helpers import (checkerboard_response, generate_gaussian_data,
plot_prior_samples_2d, plot_reconstruction_2d)
np.random.seed(42)
position_space = ift.RGSpace(2*(256,))
harmonic_space = position_space.get_default_codomain()
HT = ift.HarmonicTransformOperator(harmonic_space, target=position_space)
power_space = ift.PowerSpace(harmonic_space)
# Set up generative model
A = ift.SLAmplitude(
**{
'target': power_space,
'n_pix': 64, # 64 spectral bins
# Smoothness of spectrum
'a': 10, # relatively high variance of spectral curvature
'k0': .2, # quefrency mode below which cepstrum flattens
# Power-law part of spectrum
'sm': -4, # preferred power-law slope
'sv': .6, # low variance of power-law slope
def test_k_length_array(shape, distances, expected):
r = ift.RGSpace(shape=shape, distances=distances, harmonic=True)
assert_allclose(r.get_k_length_array().to_global_data(), expected)
def test_constructor(shape, distances, harmonic, expected):
x = ift.RGSpace(shape, distances, harmonic)
for key, value in expected.items():
assert_equal(getattr(x, key), value)
#
# 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) 2013-2019 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.
import numpy as np
import nifty5 as ift
from helpers import plot_WF, power_plot, generate_mysterious_data
np.random.seed(42)
position_space = ift.RGSpace(256)
harmonic_space = position_space.get_default_codomain()
HT = ift.HarmonicTransformOperator(harmonic_space, target=position_space)
power_space = ift.PowerSpace(harmonic_space)
# Set up an amplitude operator for the field
# We want to set up a model for the amplitude spectrum with some magic numbers
dct = {
'target': power_space,
'n_pix': 64, # 64 spectral bins
# Spectral smoothness (affects Gaussian process part)
'a': 10, # relatively high variance of spectral curvature
'k0': .2, # quefrency mode below which cepstrum flattens
# Power-law part of spectrum:
#
# 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) 2013-2019 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.
from numpy.testing import assert_allclose
import nifty5 as ift
from ..common import list2fixture
s = list2fixture([
ift.RGSpace(8, distances=12.9),
ift.RGSpace(59, distances=.24, harmonic=True),
ift.RGSpace([12, 3])
])
def test_value(s):
Regrid = ift.RegriddingOperator(s, s.shape)
f = ift.from_random('normal', Regrid.domain)
assert_allclose(f.to_global_data(), Regrid(f).to_global_data())
def test_property_ret_type(attribute, expected_type):
x = ift.RGSpace(1)
assert_(isinstance(getattr(x, attribute), expected_type))