Commit d0e343e0 authored by Martin Reinecke's avatar Martin Reinecke
Browse files

implement change; some things still need to be adjusted

parent 959bc62a
%% Cell type:markdown id: tags:
# A NIFTy demonstration
%% Cell type:markdown id: tags:
## IFT: Big Picture
IFT starting point:
$$d = Rs+n$$
Typically, $s$ is a continuous field, $d$ a discrete data vector. Particularly, $R$ is not invertible.
IFT aims at **inverting** the above uninvertible problem in the **best possible way** using Bayesian statistics.
## NIFTy
NIFTy (Numerical Information Field Theory) is a Python framework in which IFT problems can be tackled easily.
Main Interfaces:
- **Spaces**: Cartesian, 2-Spheres (Healpix, Gauss-Legendre) and their respective harmonic spaces.
- **Fields**: Defined on spaces.
- **Operators**: Acting on fields.
%% Cell type:markdown id: tags:
## Wiener Filter: Formulae
### Assumptions
- $d=Rs+n$, $R$ linear operator.
- $\mathcal P (s) = \mathcal G (s,S)$, $\mathcal P (n) = \mathcal G (n,N)$ where $S, N$ are positive definite matrices.
### Posterior
The Posterior is given by:
$$\mathcal P (s|d) \propto P(s,d) = \mathcal G(d-Rs,N) \,\mathcal G(s,S) \propto \mathcal G (s-m,D) $$
where
$$\begin{align}
m &= Dj \\
D^{-1}&= (S^{-1} +R^\dagger N^{-1} R )\\
j &= R^\dagger N^{-1} d
\end{align}$$
Let us implement this in NIFTy!
%% Cell type:markdown id: tags:
## Wiener Filter: Example
- We assume statistical homogeneity and isotropy. Therefore the signal covariance $S$ is diagonal in harmonic space, and is described by a one-dimensional power spectrum, assumed here as $$P(k) = P_0\,\left(1+\left(\frac{k}{k_0}\right)^2\right)^{-\gamma /2},$$
with $P_0 = 0.2, k_0 = 5, \gamma = 4$.
- $N = 0.2 \cdot \mathbb{1}$.
- Number of data points $N_{pix} = 512$.
- reconstruction in harmonic space.
- Response operator:
$$R = FFT_{\text{harmonic} \rightarrow \text{position}}$$
%% Cell type:code id: tags:
``` python
N_pixels = 512 # Number of pixels
def pow_spec(k):
P0, k0, gamma = [.2, 5, 4]
return P0 / ((1. + (k/k0)**2)**(gamma / 2))
```
%% Cell type:markdown id: tags:
## Wiener Filter: Implementation
%% Cell type:markdown id: tags:
### Import Modules
%% Cell type:code id: tags:
``` python
import numpy as np
import nifty6 as ift
import matplotlib.pyplot as plt
%matplotlib inline
```
%% Cell type:markdown id: tags:
### Implement Propagator
%% Cell type:code id: tags:
``` python
def Curvature(R, N, Sh):
IC = ift.GradientNormController(iteration_limit=50000,
tol_abs_gradnorm=0.1)
# WienerFilterCurvature is (R.adjoint*N.inverse*R + Sh.inverse) plus some handy
# helper methods.
return ift.WienerFilterCurvature(R,N,Sh,iteration_controller=IC,iteration_controller_sampling=IC)
```
%% Cell type:markdown id: tags:
### Conjugate Gradient Preconditioning
- $D$ is defined via:
$$D^{-1} = \mathcal S_h^{-1} + R^\dagger N^{-1} R.$$
In the end, we want to apply $D$ to $j$, i.e. we need the inverse action of $D^{-1}$. This is done numerically (algorithm: *Conjugate Gradient*).
<!--
- One can define the *condition number* of a non-singular and normal matrix $A$:
$$\kappa (A) := \frac{|\lambda_{\text{max}}|}{|\lambda_{\text{min}}|},$$
where $\lambda_{\text{max}}$ and $\lambda_{\text{min}}$ are the largest and smallest eigenvalue of $A$, respectively.
- The larger $\kappa$ the slower Conjugate Gradient.
- By default, conjugate gradient solves: $D^{-1} m = j$ for $m$, where $D^{-1}$ can be badly conditioned. If one knows a non-singular matrix $T$ for which $TD^{-1}$ is better conditioned, one can solve the equivalent problem:
$$\tilde A m = \tilde j,$$
where $\tilde A = T D^{-1}$ and $\tilde j = Tj$.
- In our case $S^{-1}$ is responsible for the bad conditioning of $D$ depending on the chosen power spectrum. Thus, we choose
$$T = \mathcal F^\dagger S_h^{-1} \mathcal F.$$
-->
%% Cell type:markdown id: tags:
### Generate Mock data
- Generate a field $s$ and $n$ with given covariances.
- Calculate $d$.
%% Cell type:code id: tags:
``` python
s_space = ift.RGSpace(N_pixels)
h_space = s_space.get_default_codomain()
HT = ift.HarmonicTransformOperator(h_space, target=s_space)
# Operators
Sh = ift.create_power_operator(h_space, power_spectrum=pow_spec)
R = HT #*ift.create_harmonic_smoothing_operator((h_space,), 0, 0.02)
# Fields and data
sh = Sh.draw_sample()
sh = Sh.draw_sample(dtype=np.float64)
noiseless_data=R(sh)
noise_amplitude = np.sqrt(0.2)
N = ift.ScalingOperator(s_space, noise_amplitude**2)
n = ift.Field.from_random(domain=s_space, random_type='normal',
std=noise_amplitude, mean=0)
d = noiseless_data + n
j = R.adjoint_times(N.inverse_times(d))
curv = Curvature(R=R, N=N, Sh=Sh)
D = curv.inverse
```
%% Cell type:markdown id: tags:
### Run Wiener Filter
%% Cell type:code id: tags:
``` python
m = D(j)
```
%% Cell type:markdown id: tags:
### Signal Reconstruction
%% Cell type:code id: tags:
``` python
# Get signal data and reconstruction data
s_data = HT(sh).val
m_data = HT(m).val
d_data = d.val
plt.figure(figsize=(15,10))
plt.plot(s_data, 'r', label="Signal", linewidth=3)
plt.plot(d_data, 'k.', label="Data")
plt.plot(m_data, 'k', label="Reconstruction",linewidth=3)
plt.title("Reconstruction")
plt.legend()
plt.show()
```
%% Cell type:code id: tags:
``` python
plt.figure(figsize=(15,10))
plt.plot(s_data - s_data, 'r', label="Signal", linewidth=3)
plt.plot(d_data - s_data, 'k.', label="Data")
plt.plot(m_data - s_data, 'k', label="Reconstruction",linewidth=3)
plt.axhspan(-noise_amplitude,noise_amplitude, facecolor='0.9', alpha=.5)
plt.title("Residuals")
plt.legend()
plt.show()
```
%% Cell type:markdown id: tags:
### Power Spectrum
%% Cell type:code id: tags:
``` python
s_power_data = ift.power_analyze(sh).val
m_power_data = ift.power_analyze(m).val
plt.figure(figsize=(15,10))
plt.loglog()
plt.xlim(1, int(N_pixels/2))
ymin = min(m_power_data)
plt.ylim(ymin, 1)
xs = np.arange(1,int(N_pixels/2),.1)
plt.plot(xs, pow_spec(xs), label="True Power Spectrum", color='k',alpha=0.5)
plt.plot(s_power_data, 'r', label="Signal")
plt.plot(m_power_data, 'k', label="Reconstruction")
plt.axhline(noise_amplitude**2 / N_pixels, color="k", linestyle='--', label="Noise level", alpha=.5)
plt.axhspan(noise_amplitude**2 / N_pixels, ymin, facecolor='0.9', alpha=.5)
plt.title("Power Spectrum")
plt.legend()
plt.show()
```
%% Cell type:markdown id: tags:
## Wiener Filter on Incomplete Data
%% Cell type:code id: tags:
``` python
# Operators
Sh = ift.create_power_operator(h_space, power_spectrum=pow_spec)
N = ift.ScalingOperator(s_space, noise_amplitude**2)
# R is defined below
# Fields
sh = Sh.draw_sample()
sh = Sh.draw_sample(dtype=np.float64)
s = HT(sh)
n = ift.Field.from_random(domain=s_space, random_type='normal',
std=noise_amplitude, mean=0)
```
%% Cell type:markdown id: tags:
### Partially Lose Data
%% Cell type:code id: tags:
``` python
l = int(N_pixels * 0.2)
h = int(N_pixels * 0.2 * 2)
mask = np.full(s_space.shape, 1.)
mask[l:h] = 0
mask = ift.Field.from_raw(s_space, mask)
R = ift.DiagonalOperator(mask)(HT)
n = n.val_rw()
n[l:h] = 0
n = ift.Field.from_raw(s_space, n)
d = R(sh) + n
```
%% Cell type:code id: tags:
``` python
curv = Curvature(R=R, N=N, Sh=Sh)
D = curv.inverse
j = R.adjoint_times(N.inverse_times(d))
m = D(j)
```
%% Cell type:markdown id: tags:
### Compute Uncertainty
%% Cell type:code id: tags:
``` python
m_mean, m_var = ift.probe_with_posterior_samples(curv, HT, 200)
```
%% Cell type:markdown id: tags:
### Get data
%% Cell type:code id: tags:
``` python
# Get signal data and reconstruction data
s_data = s.val
m_data = HT(m).val
m_var_data = m_var.val
uncertainty = np.sqrt(m_var_data)
d_data = d.val_rw()
# Set lost data to NaN for proper plotting
d_data[d_data == 0] = np.nan
```
%% Cell type:code id: tags:
``` python
fig = plt.figure(figsize=(15,10))
plt.axvspan(l, h, facecolor='0.8',alpha=0.5)
plt.fill_between(range(N_pixels), m_data - uncertainty, m_data + uncertainty, facecolor='0.5', alpha=0.5)
plt.plot(s_data, 'r', label="Signal", alpha=1, linewidth=3)
plt.plot(d_data, 'k.', label="Data")
plt.plot(m_data, 'k', label="Reconstruction", linewidth=3)
plt.title("Reconstruction of incomplete data")
plt.legend()
```
%% Cell type:markdown id: tags:
# 2d Example
%% Cell type:code id: tags:
``` python
N_pixels = 256 # Number of pixels
sigma2 = 2. # Noise variance
def pow_spec(k):
P0, k0, gamma = [.2, 2, 4]
return P0 * (1. + (k/k0)**2)**(-gamma/2)
s_space = ift.RGSpace([N_pixels, N_pixels])
```
%% Cell type:code id: tags:
``` python
h_space = s_space.get_default_codomain()
HT = ift.HarmonicTransformOperator(h_space,s_space)
# Operators
Sh = ift.create_power_operator(h_space, power_spectrum=pow_spec)
N = ift.ScalingOperator(s_space, sigma2)
# Fields and data
sh = Sh.draw_sample()
sh = Sh.draw_sample(dtype=np.float64)
n = ift.Field.from_random(domain=s_space, random_type='normal',
std=np.sqrt(sigma2), mean=0)
# Lose some data
l = int(N_pixels * 0.33)
h = int(N_pixels * 0.33 * 2)
mask = np.full(s_space.shape, 1.)
mask[l:h,l:h] = 0.
mask = ift.Field.from_raw(s_space, mask)
R = ift.DiagonalOperator(mask)(HT)
n = n.val_rw()
n[l:h, l:h] = 0
n = ift.Field.from_raw(s_space, n)
curv = Curvature(R=R, N=N, Sh=Sh)
D = curv.inverse
d = R(sh) + n
j = R.adjoint_times(N.inverse_times(d))
# Run Wiener filter
m = D(j)
# Uncertainty
m_mean, m_var = ift.probe_with_posterior_samples(curv, HT, 20)
# Get data
s_data = HT(sh).val
m_data = HT(m).val
m_var_data = m_var.val
d_data = d.val
uncertainty = np.sqrt(np.abs(m_var_data))
```
%% Cell type:code id: tags:
``` python
cm = ['magma', 'inferno', 'plasma', 'viridis'][1]
mi = np.min(s_data)
ma = np.max(s_data)
fig, axes = plt.subplots(1, 2, figsize=(15, 7))
data = [s_data, d_data]
caption = ["Signal", "Data"]
for ax in axes.flat:
im = ax.imshow(data.pop(0), interpolation='nearest', cmap=cm, vmin=mi,
vmax=ma)
ax.set_title(caption.pop(0))
fig.subplots_adjust(right=0.8)
cbar_ax = fig.add_axes([0.85, 0.15, 0.05, 0.7])
fig.colorbar(im, cax=cbar_ax)
```
%% Cell type:code id: tags:
``` python
mi = np.min(s_data)
ma = np.max(s_data)
fig, axes = plt.subplots(3, 2, figsize=(15, 22.5))
sample = HT(curv.draw_sample(from_inverse=True)+m).val
sample = HT(curv.draw_sample(dtype=np.float64, from_inverse=True)+m).val
post_mean = (m_mean + HT(m)).val
data = [s_data, m_data, post_mean, sample, s_data - m_data, uncertainty]
caption = ["Signal", "Reconstruction", "Posterior mean", "Sample", "Residuals", "Uncertainty Map"]
for ax in axes.flat:
im = ax.imshow(data.pop(0), interpolation='nearest', cmap=cm, vmin=mi, vmax=ma)
ax.set_title(caption.pop(0))
fig.subplots_adjust(right=0.8)
cbar_ax = fig.add_axes([.85, 0.15, 0.05, 0.7])
fig.colorbar(im, cax=cbar_ax)
```
%% Cell type:markdown id: tags:
### Is the uncertainty map reliable?
%% Cell type:code id: tags:
``` python
precise = (np.abs(s_data-m_data) < uncertainty)
print("Error within uncertainty map bounds: " + str(np.sum(precise) * 100 / N_pixels**2) + "%")
plt.figure(figsize=(15,10))
plt.imshow(precise.astype(float), cmap="brg")
plt.colorbar()
```
%% Cell type:markdown id: tags:
# Start Coding
## NIFTy Repository + Installation guide
https://gitlab.mpcdf.mpg.de/ift/NIFTy
NIFTy v5 **more or less stable!**
......
......@@ -114,8 +114,8 @@ if __name__ == '__main__':
N = ift.ScalingOperator(data_space, noise)
# Create mock data
MOCK_SIGNAL = S.draw_sample()
MOCK_NOISE = N.draw_sample()
MOCK_SIGNAL = S.draw_sample(dtype=np.float64)
MOCK_NOISE = N.draw_sample(dtype=np.float64)
data = R(MOCK_SIGNAL) + MOCK_NOISE
# Build inverse propagator D and information source j
......
......@@ -99,7 +99,7 @@ if __name__ == '__main__':
# Generate mock signal and data
mock_position = ift.from_random('normal', signal_response.domain)
data = signal_response(mock_position) + N.draw_sample()
data = signal_response(mock_position) + N.draw_sample(dtype=np.float64)
# Minimization parameters
ic_sampling = ift.AbsDeltaEnergyController(
......
......@@ -98,7 +98,7 @@ if __name__ == '__main__':
# Generate mock signal and data
mock_position = ift.from_random('normal', signal_response.domain)
data = signal_response(mock_position) + N.draw_sample()
data = signal_response(mock_position) + N.draw_sample(dtype=np.float64)
plot = ift.Plot()
plot.add(signal(mock_position), title='Ground Truth')
......
......@@ -113,7 +113,7 @@ if __name__ == '__main__':
# Draw posterior samples
metric = Ham(ift.Linearization.make_var(H.position, want_metric=True)).metric
samples = [metric.draw_sample(from_inverse=True) + H.position
samples = [metric.draw_sample(dtype=np.float64, from_inverse=True) + H.position
for _ in range(N_samples)]
# Plotting
......
......@@ -50,7 +50,7 @@ class Field(Operator):
raise TypeError("domain must be of type DomainTuple")
if not isinstance(val, np.ndarray):
if np.isscalar(val):
val = np.full(domain.shape, val)
val = np.broadcast_to(val, domain.shape)
else:
raise TypeError("val must be of type numpy.ndarray")
if domain.shape != val.shape:
......
......@@ -67,8 +67,8 @@ class _KLMetric(EndomorphicOperator):
self._check_input(x, mode)
return self._KL.apply_metric(x)
def draw_sample(self, from_inverse=False, dtype=np.float64):
return self._KL._metric_sample(from_inverse, dtype)
def draw_sample(self, dtype, from_inverse=False):
return self._KL._metric_sample(dtype, from_inverse)
class MetricGaussianKL(Energy):
......@@ -180,7 +180,7 @@ class MetricGaussianKL(Energy):
for i in range(self._lo, self._hi):
with random.Context(sseq[i]):
_local_samples.append(met.draw_sample(
from_inverse=True, dtype=lh_sampling_dtype))
dtype=lh_sampling_dtype, from_inverse=True))
_local_samples = tuple(_local_samples)
else:
if len(_local_samples) != self._hi-self._lo:
......@@ -264,7 +264,7 @@ class MetricGaussianKL(Energy):
if self._mirror_samples:
yield -s
def _metric_sample(self, from_inverse=False, dtype=np.float64):
def _metric_sample(self, dtype, from_inverse=False):
if from_inverse:
raise NotImplementedError()
lin = self._lin.with_want_metric()
......@@ -272,7 +272,7 @@ class MetricGaussianKL(Energy):
sseq = random.spawn_sseq(self._n_samples)
for i, v in enumerate(self._local_samples):
with random.Context(sseq[self._lo+i]):
samp = samp + self._hamiltonian(lin+v).metric.draw_sample(from_inverse=False, dtype=dtype)
samp = samp + self._hamiltonian(lin+v).metric.draw_sample(dtype=dtype, from_inverse=False)
if self._mirror_samples:
samp = samp + self._hamiltonian(lin-v).metric.draw_sample(from_inverse=False, dtype=dtype)
samp = samp + self._hamiltonian(lin-v).metric.draw_sample(dtype=dtype, from_inverse=False)
return _allreduce_sum_field(self._comm, samp)/self._n_eff_samples
......@@ -48,10 +48,10 @@ class BlockDiagonalOperator(EndomorphicOperator):
for op, v in zip(self._ops, x.values()))
return MultiField(self._domain, val)
def draw_sample(self, from_inverse=False, dtype=np.float64):
def draw_sample(self, dtype, from_inverse=False):
from ..sugar import from_random
val = tuple(
op.draw_sample(from_inverse, dtype)
op.draw_sample(dtype, from_inverse)
if op is not None
else from_random('normal', self._domain[key], dtype=dtype)
for op, key in zip(self._ops, self._domain.keys()))
......
......@@ -160,7 +160,7 @@ class DiagonalOperator(EndomorphicOperator):
res = samp.val*np.sqrt(self._ldiag)
return Field(self._domain, res)
def draw_sample(self, from_inverse=False, dtype=np.float64):
def draw_sample(self, dtype, from_inverse=False):
res = Field.from_random(random_type="normal", domain=self._domain,
dtype=dtype)
return self.process_sample(res, from_inverse)
......
......@@ -32,7 +32,7 @@ class EndomorphicOperator(LinearOperator):
for endomorphic operators."""
return self._domain
def draw_sample(self, from_inverse=False, dtype=np.float64):
def draw_sample(self, dtype, from_inverse=False):
"""Generate a zero-mean sample
Generates a sample from a Gaussian distribution with zero mean and
......@@ -42,7 +42,7 @@ class EndomorphicOperator(LinearOperator):
----------
from_inverse : bool (default : False)
if True, the sample is drawn from the inverse of the operator
dtype : numpy datatype (default : numpy.float64)
dtype : numpy datatype
the data type to be used for the sample
Returns
......
......@@ -78,5 +78,5 @@ class InversionEnabler(EndomorphicOperator):
logger.warning("Error detected during operator inversion")
return r.position
def draw_sample(self, from_inverse=False, dtype=np.float64):
return self._op.draw_sample(from_inverse, dtype)
def draw_sample(self, dtype, from_inverse=False):
return self._op.draw_sample(dtype, from_inverse)
......@@ -58,10 +58,10 @@ class OperatorAdapter(LinearOperator):
return self._op.apply(x,
self._modeTable[self._trafo][self._ilog[mode]])
def draw_sample(self, from_inverse=False, dtype=np.float64):
def draw_sample(self, dtype, from_inverse=False):
if self._trafo & self.INVERSE_BIT:
return self._op.draw_sample(not from_inverse, dtype)
return self._op.draw_sample(from_inverse, dtype)
return self._op.draw_sample(dtype, not from_inverse)
return self._op.draw_sample(dtype, from_inverse)
def __repr__(self):
from ..utilities import indent
......
......@@ -62,19 +62,19 @@ class SamplingEnabler(EndomorphicOperator):
self._domain = self._op.domain
self._capability = self._op.capability
def draw_sample(self, from_inverse=False, dtype=np.float64):
def draw_sample(self, dtype, from_inverse=False):
try:
return self._op.draw_sample(from_inverse, dtype)
return self._op.draw_sample(dtype, from_inverse)
except NotImplementedError:
if not from_inverse:
raise ValueError("from_inverse must be True here")
if self._start_from_zero:
b = self._op.draw_sample()
b = self._op.draw_sample(dtype)
energy = QuadraticEnergy(0*b, self._op, b)
else:
s = self._prior.draw_sample(from_inverse=True)
s = self._prior.draw_sample(dtype, from_inverse=True)
sp = self._prior(s)
nj = self._likelihood.draw_sample(dtype=dtype)
nj = self._likelihood.draw_sample(dtype)
energy = QuadraticEnergy(s, self._op, sp + nj,
_grad=self._likelihood(s) - nj)
inverter = ConjugateGradient(self._ic)
......
......@@ -74,12 +74,12 @@ class SandwichOperator(EndomorphicOperator):
def apply(self, x, mode):
return self._op.apply(x, mode)
def draw_sample(self, from_inverse=False, dtype=np.float64):
def draw_sample(self, dtype, from_inverse=False):
# Inverse samples from general sandwiches are not possible
if from_inverse:
if self._bun.capability & self._bun.INVERSE_TIMES:
try:
s = self._cheese.draw_sample(from_inverse, dtype)
s = self._cheese.draw_sample(dtype, from_inverse)
return self._bun.inverse_times(s)
except NotImplementedError:
pass
......@@ -88,7 +88,7 @@ class SandwichOperator(EndomorphicOperator):
# Samples from general sandwiches
return self._bun.adjoint_times(
self._cheese.draw_sample(from_inverse, dtype))
self._cheese.draw_sample(dtype, from_inverse))
def __repr__(self):
from ..utilities import indent
......
......@@ -91,7 +91,7 @@ class ScalingOperator(EndomorphicOperator):
raise ValueError("operator not positive definite")
return 1./np.sqrt(fct) if from_inverse else np.sqrt(fct)
def draw_sample(self, from_inverse=False, dtype=np.float64):
def draw_sample(self, dtype, from_inverse=False):
from ..sugar import from_random
return from_random(random_type="normal", domain=self._domain,
std=self._get_fct(from_inverse), dtype=dtype)
......
......@@ -190,7 +190,7 @@ class SumOperator(LinearOperator):
res = res.flexible_addsub(tmp, neg)
return res
def draw_sample(self, from_inverse=False, dtype=np.float64):
def draw_sample(self, dtype, from_inverse=False):
if from_inverse:
raise NotImplementedError(
"cannot draw from inverse of this operator")
......@@ -199,7 +199,7 @@ class SumOperator(LinearOperator):
from .simple_linear_operators import NullOperator
if isinstance(op, NullOperator):
continue
tmp = op.draw_sample(from_inverse, dtype)
tmp = op.draw_sample(dtype, from_inverse)
res = tmp if res is None else res.unite(tmp)
return res
......
......@@ -40,7 +40,7 @@ pmp = pytest.mark.parametrize
def field(request):
with ift.random.Context(request.param[0]):
S = ift.ScalingOperator(request.param[1], 1.)
return S.draw_sample()
return S.draw_sample(dtype=np.float64)
def test_gaussian(field):
......@@ -59,12 +59,12 @@ def test_ScaledEnergy(field):
res1 = met1(field)
res2 = met2(field)/0.3
ift.extra.assert_allclose(res1, res2, 0, 1e-12)
met2.draw_sample()
met2.draw_sample(dtype=np.float64)
def test_QuadraticFormOperator(field):
op = ift.ScalingOperator(field.domain, 1.2)
endo = ift.makeOp(op.draw_sample())
endo = ift.makeOp(op.draw_sample(dtype=np.float64))
energy = ift.QuadraticFormOperator(endo)
ift.extra.check_jacobian_consistency(energy, field)
......@@ -83,7 +83,7 @@ def test_hamiltonian_and_KL(field):
hamiltonian = ift.StandardHamiltonian(lh)
ift.extra.check_jacobian_consistency(hamiltonian, field)
S = ift.ScalingOperator(space, 1.)
samps = [S.draw_sample() for i in range(3)]
samps = [S.draw_sample(dtype=np.float64) for i in range(3)]
kl = ift.AveragedEnergy(hamiltonian, samps)
ift.extra.check_jacobian_consistency(kl, field)
......@@ -95,7 +95,7 @@ def test_variablecovariancegaussian(field):
mf = ift.MultiField.from_dict(dc)
energy = ift.VariableCovarianceGaussianEnergy(field.domain, 'a', 'b')
ift.extra.check_jacobian_consistency(energy, mf, tol=1e-6)
energy(ift.Linearization.make_var(mf, want_metric=True)).metric.draw_sample()
energy(ift.Linearization.make_var(mf, want_metric=True)).metric.draw_sample(dtype=np.float64)
def test_inverse_gamma(field):
......
......@@ -65,7 +65,7 @@ def test_power_synthesize_analyze(space1, space2):
sc1 = ift.StatCalculator()
sc2 = ift.StatCalculator()
for ii in range(samples):
sk = opfull.draw_sample()
sk = opfull.draw_sample(dtype=np.float64)
sp = ift.power_analyze(sk, spaces=(0, 1), keep_phase_information=False)
sc1.add(sp.sum(spaces=1)/fp2.s_sum())
......@@ -93,7 +93,7 @@ def test_DiagonalOperator_power_analyze2(space1, space2):
sc2 = ift.StatCalculator()
for ii in range(samples):
sk = S_full.draw_sample()
sk = S_full.draw_sample(dtype=np.float64)
sp = ift.power_analyze(sk, spaces=(0, 1), keep_phase_information=False)
sc1.add(sp.sum(spaces=1)/fp2.s_sum())
sc2.add(sp.sum(spaces=0)/fp1.s_sum())
......
......@@ -53,7 +53,7 @@ def test_gaussian_energy(space, nonlinearity, noise, seed):
pspec = ift.PS_field(pspace, pspec)
A = Dist(pspec.ptw("sqrt"))
N = ift.ScalingOperator(space, noise)
n = N.draw_sample()
n = N.draw_sample(dtype=np.float64)
R = ift.ScalingOperator(space, 10.)
def d_model():
......
......@@ -93,8 +93,8 @@ def test_WF_curvature(space):
1./all_diag.val,
rtol=1e-3,
atol=1e-3)
curv.draw_sample()
curv.draw_sample(from_inverse=True)
curv.draw_sample(dtype=np.float64)
curv.draw_sample(dtype=np.float64, from_inverse=True)
if len(space.shape) == 1:
R = ift.ValueInserter(space, [0])
......@@ -110,8 +110,8 @@ def test_WF_curvature(space):
1./all_diag.val,
rtol=1e-3,
atol=1e-3)
curv.draw_sample()
curv.draw_sample(from_inverse=True)
curv.draw_sample(dtype=np.float64)
curv.draw_sample(dtype=np.float64, from_inverse=True)
@pmp('minimizer', minimizers + newton_minimizers)
......
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