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 __init__(
self,
domain,
beta,
k,
grid,
power_spectrum=lambda q: 2/(q**4 + 1),
rho=1,
verbosity=0):
super().__init__()
self.beta = beta
self._domain = (domain, )
self.fft = nifty5.FFTOperator(self._domain)
self.h_space = self.fft.target[0]
self.grid = grid
self.k = k
self.rho = rho
B_h = nifty5.create_power_operator(
domain=self.h_space, power_spectrum=power_spectrum)
self.B = nifty5.SandwichOperator.make(self.fft, B_h)
# the diagonal operator rho*e^beta
rho_e_beta = np.zeros(domain.shape[0])
for i, pos in enumerate(self.grid):
rho_e_beta[pos] = (
self.rho*np.exp(self.beta.val[pos]))
rho_e_beta_field = nifty5.Field(domain=domain, val=rho_e_beta)
self.rho_e_beta_diag = nifty5.DiagonalOperator(
domain=self._domain,
diagonal=rho_e_beta_field)
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 __init__(
self,
position,
k,
x,
y,
x_indices,
s_space,
h_space,
p_space,
grid,
sigma_f=1,
noise_variance=0.01,
Lambda_modes_list=None,
term_factors=[1] * 11,
):
super().__init__(position=position)
self.domain = position.domain
self.k, self.x, self.y = k, x, y
self.x_indices = x_indices
self.N = len(self.x)
self.sigma_f = sigma_f
self.noise_variance = noise_variance
self.tau_f = position
self.s_space = s_space
self.h_space = h_space
self.p_space = p_space
self.len_p_space = self.p_space.shape[0]
self.grid = grid
self.fft = nifty5.FFTOperator(domain=self.s_space, target=self.h_space)
self.F_h = nifty5.create_power_operator(domain=self.h_space,
power_spectrum=nifty5.exp(
self.tau_f))
self.F = nifty5.SandwichOperator.make(self.fft, self.F_h)
self.F_matrix = probe_operator(self.F)
self.F_tilde = np.zeros((self.N, self.N))
for i in range(self.N):
for j in range(i + 1):
self.F_tilde[i, j] = self.F_matrix[x_indices[i], x_indices[j]]
if i != j:
self.F_tilde[j, i] = self.F_matrix[x_indices[i],
x_indices[j]]
self.noise_covariance = np.diag(
[self.noise_variance for i in range(self.N)])
self.G = np.linalg.inv(self.F_tilde + self.noise_covariance)
self.smoothness_operator_f = nifty5.SmoothnessOperator(
domain=self.p_space, logarithmic=True, strength=1 / self.sigma_f)
if Lambda_modes_list is None:
self.get_Lambda_modes(speedup=True)
else:
self.Lambda_modes_list = Lambda_modes_list
self.term_factors = term_factors
self.get_Lambdas()
def __init__(
self,
position,
k,
grid,
sigma_beta=1,
rho=1,
mode='multifield',
single_fields=None,
term_factors=[1]*5,
):
super().__init__(position=position)
self.domain = position.domain
self.k = k
self.sigma_beta = sigma_beta
self.rho = rho
self.mode = mode
self.fields = single_fields
self.term_factors = term_factors
if mode == 'multifield':
self.beta = position.val['beta']
self.tau_beta = position.val['tau_beta']
else:
self.fields[mode] = position
self.beta = self.fields['beta']
self.tau_beta = self.fields['tau_beta']
self.s_space = self.beta.domain[0]
self.h_space = self.s_space.get_default_codomain()
self.p_space = self.tau_beta.domain
self.len_p_space = self.p_space.shape[0]
self.len_s_space = self.s_space.shape[0]
self.grid = grid
self.grid_coordinates = [i*self.s_space.distances[0] for i in range(
self.s_space.shape[0])]
# beta_vector is the R^N_bins vector with beta field values at the grid
# positions
self.beta_vector = np.array([self.beta.val[i] for i in self.grid])
self.fft = nifty5.FFTOperator(domain=self.s_space, target=self.h_space)
self.B_inv_h = nifty5.create_power_operator(
domain=self.h_space,
power_spectrum=nifty5.exp(-self.tau_beta))
self.B_inv = nifty5.SandwichOperator.make(self.fft, self.B_inv_h)
self.smoothness_operator_beta = nifty5.SmoothnessOperator(
domain=self.p_space,
strength=1/self.sigma_beta)
self.get_del_B()
def __init__(
self,
domain,
beta,
B,
rho=1,
verbosity=0,
):
super().__init__()
self.beta = beta
self._domain = (domain, )
self.fft = nifty5.FFTOperator(self._domain)
self.h_space = self.fft.target[0]
self.rho = rho
self.B = B
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 testBinary(type1, type2, space, seed):
dom1 = ift.MultiDomain.make({'s1': space})
dom2 = ift.MultiDomain.make({'s2': space})
# FIXME Remove this?
_make_linearization(type1, dom1, seed)
_make_linearization(type2, dom2, seed)
dom = ift.MultiDomain.union((dom1, dom2))
select_s1 = ift.ducktape(None, dom1, "s1")
select_s2 = ift.ducktape(None, dom2, "s2")
model = select_s1 * select_s2
pos = ift.from_random("normal", dom)
ift.extra.check_jacobian_consistency(model, pos, ntries=20)
model = select_s1 + select_s2
pos = ift.from_random("normal", dom)
ift.extra.check_jacobian_consistency(model, pos, ntries=20)
model = select_s1.scale(3.)
pos = ift.from_random("normal", dom1)
ift.extra.check_jacobian_consistency(model, pos, ntries=20)
model = ift.ScalingOperator(2.456, space)(select_s1 * select_s2)
pos = ift.from_random("normal", dom)
ift.extra.check_jacobian_consistency(model, pos, ntries=20)
model = ift.sigmoid(2.456 * (select_s1 * select_s2))
pos = ift.from_random("normal", dom)
ift.extra.check_jacobian_consistency(model, pos, ntries=20)
pos = ift.from_random("normal", dom)
model = ift.OuterProduct(pos['s1'], ift.makeDomain(space))
ift.extra.check_jacobian_consistency(model, pos['s2'], ntries=20)
model = select_s1**2
pos = ift.from_random("normal", dom1)
ift.extra.check_jacobian_consistency(model, pos, ntries=20)
model = select_s1.clip(-1, 1)
pos = ift.from_random("normal", dom1)
ift.extra.check_jacobian_consistency(model, pos, ntries=20)
f = ift.from_random("normal", space)
model = select_s1.clip(f - 0.1, f + 1.)
pos = ift.from_random("normal", dom1)
ift.extra.check_jacobian_consistency(model, pos, ntries=20)
if isinstance(space, ift.RGSpace):
model = ift.FFTOperator(space)(select_s1 * select_s2)
pos = ift.from_random("normal", dom)
ift.extra.check_jacobian_consistency(model, pos, ntries=20)
def __init__(
self,
position,
k,
s_space,
power_spectrum_beta,
rho,
):
super().__init__(position=position)
self.k = k
self.rho = rho
self.power_spectrum_beta = power_spectrum_beta
self.N = k.sum()
self.beta = position
self.beta_arr = position.to_global_data()
self.s_space = s_space
self.fft = nifty5.FFTOperator(self.s_space)
self.h_space = self.fft.target[0]
# B in Fourier space:
self.B_h = nifty5.create_power_operator(
domain=self.h_space,
power_spectrum=power_spectrum_beta)
self.B = nifty5.SandwichOperator.make(self.fft, self.B_h)
def testFFT(sp, dtype):
_check_repr(ift.FFTOperator(sp))
_check_repr(ift.FFTOperator(sp.get_default_codomain()))
def testFFT(sp, dtype):
op = ift.FFTOperator(sp)
ift.extra.consistency_check(op, dtype, dtype)
op = ift.FFTOperator(sp.get_default_codomain())
ift.extra.consistency_check(op, dtype, dtype)
def __init__(
self,
position,
k,
x,
y,
grid,
sigma_f=1,
sigma_beta=1,
sigma_eta=1,
rho=1,
mode='multifield',
single_fields=None,
Lambda_modes_list=None,
term_factors=[1]*11,
):
super().__init__(position=position)
self.domain = position.domain
self.k, self.x, self.y = k, x, y
self.N = len(self.x)
self.sigma_beta = sigma_beta
self.sigma_f = sigma_f
self.sigma_eta = sigma_eta
self.rho = rho
self.mode = mode
self.fields = single_fields
if mode == 'multifield':
self.beta = position.val['beta']
self.tau_beta = position.val['tau_beta']
self.tau_f = position.val['tau_f']
self.eta = position.val['eta']
else:
self.fields[mode] = position
self.beta = self.fields['beta']
self.tau_beta = self.fields['tau_beta']
self.tau_f = self.fields['tau_f']
self.eta = self.fields['eta']
self.s_space = self.beta.domain[0]
self.h_space = self.s_space.get_default_codomain()
self.p_space = self.tau_f.domain
self.len_p_space = self.p_space.shape[0]
self.len_s_space = self.s_space.shape[0]
self.grid = grid
self.grid_coordinates = [i*self.s_space.distances[0] for i in range(
self.s_space.shape[0])]
# beta_vector is the R^N_bins vector with beta field values at the grid
# positions
self.beta_vector = np.array([self.beta.val[i] for i in self.grid])
self.fft = nifty5.FFTOperator(domain=self.s_space, target=self.h_space)
self.F_h = nifty5.create_power_operator(
domain=self.h_space,
power_spectrum=nifty5.exp(self.tau_f))
self.B_inv_h = nifty5.create_power_operator(
domain=self.h_space,
power_spectrum=nifty5.exp(-self.tau_beta))
self.B_inv = nifty5.SandwichOperator.make(self.fft, self.B_inv_h)
self.F = nifty5.SandwichOperator.make(self.fft, self.F_h)
self.F_matrix = probe_operator(self.F)
self.F_tilde = np.zeros((self.N, self.N))
for i in range(self.N):
for j in range(i+1):
self.F_tilde[i, j] = self.F_matrix[
self.x_indices[i], self.x_indices[j]]
if i != j:
self.F_tilde[j, i] = self.F_matrix[
self.x_indices[i], self.x_indices[j]]
self.exp_hat_eta_x = np.diag([np.exp(
self.eta.val[self.x_indices[i]]) for i in range(self.N)])
self.G = np.linalg.inv(self.F_tilde + self.exp_hat_eta_x)
self.smoothness_operator_f = nifty5.SmoothnessOperator(
domain=self.p_space,
strength=1/self.sigma_f)
self.smoothness_operator_beta = nifty5.SmoothnessOperator(
domain=self.p_space,
strength=1/self.sigma_beta)
# second derivative of eta
nabla_nabla_eta = np.zeros(self.eta.val.shape)
scipy.ndimage.laplace(
input=self.eta.val,
output=nabla_nabla_eta)
self.nabla_nabla_eta_field = nifty5.Field(
domain=self.s_space,
val=nabla_nabla_eta)
if Lambda_modes_list is None:
self.get_Lambda_modes(speedup=True)
else:
self.Lambda_modes_list = Lambda_modes_list
self.term_factors = term_factors
self.get_Lambdas()
self.get_del_B()
self.get_del_exp_eta_x()