Commit 92e7fe7d authored by Martin Reinecke's avatar Martin Reinecke
Browse files

big simplifications; power_synthesize() -> draw_sample()

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%% 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:
$$\mathcal P (s|d) \propto P(s,d) = \mathcal G(d-Rs,N) \,\mathcal G(s,S) \propto \mathcal G (m,D) $$
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
np.random.seed(40)
import nifty4 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)
inverter = ift.ConjugateGradient(controller=IC)
# WienerFilterCurvature is (R.adjoint*N.inverse*R + Sh.inverse) plus some handy
# helper methods.
return ift.library.WienerFilterCurvature(R,N,Sh,inverter)
```
%% 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)
p_space = ift.PowerSpace(h_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 = ift.power_synthesize(ift.PS_field(p_space, pow_spec),real_signal=True)
sh = Sh.draw_sample()
noiseless_data=R(sh)
noise_amplitude = np.sqrt(0.2)
N = ift.ScalingOperator(noise_amplitude**2, s_space)
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).to_global_data()
m_data = HT(m).to_global_data()
d_data = d.to_global_data()
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).to_global_data()
m_power_data = ift.power_analyze(m).to_global_data()
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(noise_amplitude**2,s_space)
# R is defined below
# Fields
sh = ift.power_synthesize(ift.PS_field(p_space,pow_spec),real_signal=True)
sh = Sh.draw_sample()
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_global_data(s_space, mask)
R = ift.DiagonalOperator(mask)*HT
n = n.to_global_data()
n[l:h] = 0
n = ift.Field.from_global_data(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.to_global_data()
m_data = HT(m).to_global_data()
m_var_data = m_var.to_global_data()
uncertainty = np.sqrt(m_var_data)
d_data = d.to_global_data()
# 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)
p_space = ift.PowerSpace(h_space)
# Operators
Sh = ift.create_power_operator(h_space, power_spectrum=pow_spec)
N = ift.ScalingOperator(sigma2,s_space)
# Fields and data
sh = ift.power_synthesize(ift.PS_field(p_space,pow_spec),real_signal=True)
sh = Sh.draw_sample()
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_global_data(s_space, mask)
R = ift.DiagonalOperator(mask)*HT
n = n.to_global_data()
n[l:h, l:h] = 0
n = ift.Field.from_global_data(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).to_global_data()
m_data = HT(m).to_global_data()
m_var_data = m_var.to_global_data()
d_data = d.to_global_data()
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()+m).to_global_data()
post_mean = (m_mean + HT(m)).to_global_data()
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 v4 **more or less stable!**
......
......@@ -31,21 +31,21 @@ if __name__ == "__main__":
p_space = ift.PowerSpace(h_space,
binbounds=ift.PowerSpace.useful_binbounds(
h_space, logarithmic=True))
s_spec = ift.Field.full(p_space, 1e-5)
# Choosing the prior correlation structure and defining
# correlation operator
p = ift.PS_field(p_space, p_spec)
log_p = ift.log(p)
S = ift.create_power_operator(h_space, power_spectrum=s_spec)
S = ift.create_power_operator(h_space, power_spectrum=lambda k: 1e-5)
# Drawing a sample sh from the prior distribution in harmonic space
sh = ift.power_synthesize(s_spec)
sh = S.draw_sample()
# Choosing the measurement instrument
# Instrument = SmoothingOperator(s_space, sigma=0.01)
mask = np.ones(s_space.shape)
#mask[6000:8000] = 0.
mask[30:70,30:70] = 0.
# mask[6000:8000] = 0.
mask[30:70, 30:70] = 0.
mask = ift.Field.from_global_data(s_space, mask)
MaskOperator = ift.DiagonalOperator(mask)
......@@ -69,7 +69,7 @@ if __name__ == "__main__":
# Creating the mock data
d = noiseless_data + n
m0 = ift.power_synthesize(ift.Field.full(p_space, 1e-7))
m0 = ift.Field.full(h_space, 1e-7)
t0 = ift.Field.full(p_space, -4.)
power0 = Distributor.times(ift.exp(0.5 * t0))
......@@ -120,5 +120,5 @@ if __name__ == "__main__":
ift.plot(nonlinearity(HT(power0*m0)), title="Reconstructed sky",
name="reconstructed_sky.png", zmin=zmin, zmax=zmax, **plotdict)
ymin = np.min(p.to_global_data())
ift.plot([ift.exp(t0),p], title="Power spectra",
ift.plot([ift.exp(t0), p], title="Power spectra",
name="ps.png", ymin=ymin, **plotdict)
......@@ -33,15 +33,14 @@ if __name__ == "__main__":
p_space = ift.PowerSpace(h_space,
binbounds=ift.PowerSpace.useful_binbounds(
h_space, logarithmic=True))
s_spec = ift.Field.full(p_space, 1.)
# Choosing the prior correlation structure and defining
# correlation operator
p = ift.PS_field(p_space, p_spec)
log_p = ift.log(p)
S = ift.create_power_operator(h_space, power_spectrum=s_spec)
S = ift.create_power_operator(h_space, lambda k: 1.)
# Drawing a sample sh from the prior distribution in harmonic space
sh = ift.power_synthesize(s_spec)
sh = S.draw_sample()
# Choosing the measurement instrument
# Instrument = SmoothingOperator(s_space, sigma=0.01)
......@@ -70,7 +69,7 @@ if __name__ == "__main__":
# Creating the mock data
d = noiseless_data + n
m0 = ift.power_synthesize(ift.Field.full(p_space, 1e-7))
m0 = ift.Field.full(h_space, 1e-7)
t0 = ift.Field.full(p_space, -4.)
power0 = Distributor.times(ift.exp(0.5 * t0))
......@@ -116,4 +115,4 @@ if __name__ == "__main__":
ift.plot(nonlinearity(HT(power0*m0)),
name="reconstructed_sky.png", **plotdict)
ift.plot(MeasurementOperator.adjoint_times(d), name="data.png", **plotdict)
ift.plot([ift.exp(t0),p], name="ps.png")
ift.plot([ift.exp(t0), p], name="ps.png")
......@@ -20,43 +20,28 @@ if __name__ == "__main__":
a = 4 * correlation_length_1 * field_variance_1**2
return a / (1 + k * correlation_length_1) ** 4.
def power_spectrum_2(k): # note: field_variance**2 = a*k_0/4.
a = 4 * correlation_length_2 * field_variance_2**2
return a / (1 + k * correlation_length_2) ** 2.5
signal_space_1 = ift.RGSpace([N_pixels_1], distances=L_1/N_pixels_1)
harmonic_space_1 = signal_space_1.get_default_codomain()
signal_space_2 = ift.RGSpace([N_pixels_2], distances=L_2/N_pixels_2)
harmonic_space_2 = signal_space_2.get_default_codomain()
signal_domain = ift.DomainTuple.make((signal_space_1, signal_space_2))
mid_domain = ift.DomainTuple.make((signal_space_1, harmonic_space_2))
harmonic_domain = ift.DomainTuple.make((harmonic_space_1,
harmonic_space_2))
ht_1 = ift.HarmonicTransformOperator(harmonic_domain, space=0)
power_space_1 = ift.PowerSpace(harmonic_space_1)
mock_power_1 = ift.PS_field(power_space_1, power_spectrum_1)
def power_spectrum_2(k): # note: field_variance**2 = a*k_0/4.
a = 4 * correlation_length_2 * field_variance_2**2
return a / (1 + k * correlation_length_2) ** 2.5
ht_2 = ift.HarmonicTransformOperator(mid_domain, space=1)
power_space_2 = ift.PowerSpace(harmonic_space_2)
mock_power_2 = ift.PS_field(power_space_2, power_spectrum_2)
ht_2 = ift.HarmonicTransformOperator(ht_1.target, space=1)
ht = ht_2*ht_1
mock_power = ift.Field.from_global_data(
(power_space_1, power_space_2),
np.outer(mock_power_1.to_global_data(),
mock_power_2.to_global_data()))
diagonal = ift.power_synthesize_nonrandom(mock_power, spaces=(0, 1))**2
S = ift.DiagonalOperator(diagonal)
S = (ift.create_power_operator(harmonic_domain, power_spectrum_1, 0) *
ift.create_power_operator(harmonic_domain, power_spectrum_2, 1))
np.random.seed(10)
mock_signal = ift.power_synthesize(mock_power, real_signal=True)
mock_signal = S.draw_sample()
# Setting up a exemplary response
N1_10 = int(N_pixels_1/10)
......
......@@ -20,15 +20,11 @@ if __name__ == "__main__":
signal_space = ift.RGSpace([N_pixels, N_pixels], distances=L/N_pixels)
harmonic_space = signal_space.get_default_codomain()
ht = ift.HarmonicTransformOperator(harmonic_space, target=signal_space)
power_space = ift.PowerSpace(
harmonic_space, binbounds=ift.PowerSpace.useful_binbounds(
harmonic_space, logarithmic=True))
# Creating the mock signal
S = ift.create_power_operator(harmonic_space,
power_spectrum=power_spectrum)
mock_power = ift.PS_field(power_space, power_spectrum)
mock_signal = ift.power_synthesize(mock_power, real_signal=True)
mock_signal = S.draw_sample()
# Setting up an exemplary response
mask = np.ones(signal_space.shape)
......
......@@ -9,7 +9,7 @@ if __name__ == "__main__":
L = 2.
# Typical distance over which the field is correlated (in same unit as L)
correlation_length = 0.1
# Variance of field in position space sqrt(<|s_x|^2>) (in unit of s)
# Variance of field in position space sqrt(<|s_x|^2>) (in same unit as s)
field_variance = 2.
# Smoothing length of response (in same unit as L)
response_sigma = 0.01
......@@ -29,14 +29,11 @@ if __name__ == "__main__":
s_space = ift.RGSpace([N_pixels, N_pixels], distances=pixel_width)
h_space = s_space.get_default_codomain()
HT = ift.HarmonicTransformOperator(h_space, s_space)
p_space = ift.PowerSpace(h_space)
# Create mock data
Sh = ift.create_power_operator(h_space, power_spectrum=pow_spec)
sp = ift.PS_field(p_space, pow_spec)
sh = ift.power_synthesize(sp, real_signal=True)
sh = Sh.draw_sample()
R = HT*ift.create_harmonic_smoothing_operator((h_space,), 0,
response_sigma)
......
......@@ -52,15 +52,13 @@ if __name__ == "__main__":
signal_space = ift.RGSpace(shape, distances=L/N_pixels)
harmonic_space = signal_space.get_default_codomain()
HT = ift.HarmonicTransformOperator(harmonic_space, target=signal_space)
power_space = ift.PowerSpace(harmonic_space)
# Creating the mock data
S = ift.create_power_operator(harmonic_space,
power_spectrum=power_spectrum)
np.random.seed(43)
mock_power = ift.PS_field(power_space, power_spectrum)
mock_signal = ift.power_synthesize(mock_power, real_signal=True)
mock_signal = S.draw_sample()
sensitivity = (1./nu.m)**dimensionality/nu.K
R = ift.GeometryRemover(signal_space)
......
......@@ -13,17 +13,13 @@ if __name__ == "__main__":
h_space = s_space.get_default_codomain()
ht = ift.HarmonicTransformOperator(h_space, s_space)
# Set up power space
p_space = ift.PowerSpace(h_space)
# Choose prior correlation structure and define correlation operator
p_spec = (lambda k: (42/(k+1)**3))
S = ift.create_power_operator(h_space, power_spectrum=p_spec)
# Draw sample sh from the prior distribution in harmonic space
sp = ift.PS_field(p_space, p_spec)
sh = ift.power_synthesize(sp, real_signal=True)
sh = S.draw_sample()
# Choose measurement instrument
diag = np.ones(s_space.shape)
......
......@@ -10,7 +10,8 @@ from .operators import *
from .field import Field, sqrt, exp, log
from .probing.utils import probe_with_posterior_samples, probe_diagonal
from .probing.utils import probe_with_posterior_samples, probe_diagonal, \
StatCalculator
from .minimization import *
......
......@@ -18,8 +18,6 @@
from ..operators.endomorphic_operator import EndomorphicOperator
from ..operators.inversion_enabler import InversionEnabler
from ..field import Field, sqrt
from ..sugar import power_analyze, power_synthesize
import numpy as np
......
......@@ -17,6 +17,7 @@
# and financially supported by the Studienstiftung des deutschen Volkes.
from .linear_operator import LinearOperator
import numpy as np
class ChainOperator(LinearOperator):
......@@ -119,3 +120,9 @@ class ChainOperator(LinearOperator):
for op in t_ops:
x = op.apply(x, mode)
return x
def draw_sample(self, dtype=np.float64):
sample = self._ops[-1].draw_sample(dtype)
for op in reversed(self._ops[:-1]):
sample = op.process_sample(sample)
return sample
......@@ -133,6 +133,14 @@ class DiagonalOperator(EndomorphicOperator):
return DiagonalOperator(self._diagonal.conjugate(), self._domain,
self._spaces)
def process_sample(self, sample):
if np.issubdtype(self._ldiag.dtype, np.complexfloating):
raise ValueError("cannot draw sample from complex-valued operator")
res = Field.empty_like(sample)
res.local_data[()] = sample.local_data * np.sqrt(self._ldiag)
return res
def draw_sample(self, dtype=np.float64):
if np.issubdtype(self._ldiag.dtype, np.complexfloating):
raise ValueError("cannot draw sample from complex-valued operator")
......
......@@ -83,6 +83,11 @@ class ScalingOperator(EndomorphicOperator):
return self.TIMES | self.ADJOINT_TIMES
return self._all_ops
def process_sample(self, sample):
if self._factor.imag != 0. or self._factor.real <= 0.:
raise ValueError("Operator not positive definite")
return sample * np.sqrt(self._factor)
def draw_sample(self, dtype=np.float64):
if self._factor.imag != 0. or self._factor.real <= 0.:
raise ValueError("Operator not positive definite")
......
......@@ -28,18 +28,16 @@ from . import dobj, utilities
__all__ = ['PS_field',
'power_analyze',
'power_synthesize',
'power_synthesize_nonrandom',
'create_power_field',
'create_power_operator',
'create_harmonic_smoothing_operator']
def PS_field(pspace, func, dtype=None):
def PS_field(pspace, func):
if not isinstance(pspace, PowerSpace):
raise TypeError
data = dobj.from_global_data(func(pspace.k_lengths))
return Field(pspace, val=data, dtype=dtype)
return Field(pspace, val=data)
def _single_power_analyze(field, idx, binbounds):
......@@ -119,21 +117,21 @@ def power_analyze(field, spaces=None, binbounds=None,
return parts[0] + 1j*parts[1] if keep_phase_information else parts[0]
def power_synthesize_nonrandom(field, spaces=None):
def _power_synthesize_nonrandom(field, spaces=None):
spaces = utilities.parse_spaces(spaces, len(field.domain))
result_domain = list(field.domain)
spec = sqrt(field)
amplitude = sqrt(field)
for i in spaces:
result_domain[i] = field.domain[i].harmonic_partner
pd = PowerDistributor(result_domain, field.domain[i], i)
spec = pd(spec)
amplitude = pd(amplitude)
return spec
return amplitude
def power_synthesize(field, spaces=None, real_power=True, real_signal=True):
"""Returns a sampled field with `field`\**2 as its power spectrum.
def _power_synthesize(field, spaces=None, real_power=True, real_signal=True):
"""Returns a sampled field with `field` as its power spectrum.
This method draws a Gaussian random field in the harmonic partner
domain of this field's domains, using this field as power spectrum.
......@@ -141,7 +139,7 @@ def power_synthesize(field, spaces=None, real_power=True, real_signal=True):
Parameters
----------
field : Field
The input field containing the square root of the power spectrum
The input field containing the power spectrum
spaces : None, int, or tuple of int, optional
Specifies the subdomains containing all the PowerSpaces which
should be converted (default : None).
......@@ -161,16 +159,16 @@ def power_synthesize(field, spaces=None, real_power=True, real_signal=True):
Notes
-----
For this the spaces specified by `spaces` must be a PowerSpace.
This expects this field to be the square root of a power spectrum, i.e.
to have the unit of the field to be sampled.
For this the spaces specified by `spaces` must be of type PowerSpace.
This expects this field to be a power spectrum, i.e.
to have the unit of "field to be sampled"**2.
Raises
------
ValueError : If a domain specified by `spaces` is not a PowerSpace.
"""
spec = power_synthesize_nonrandom(field, spaces)
spec = _power_synthesize_nonrandom(field, spaces)
self_real = not np.issubdtype(spec.dtype, np.complexfloating)
if (not real_power) and self_real:
raise ValueError("can't draw complex realizations from real spectrum")
......@@ -190,7 +188,7 @@ def power_synthesize(field, spaces=None, real_power=True, real_signal=True):
return result[0] if real_power else result[0] + 1j*result[1]
def create_power_field(domain, power_spectrum, dtype=None):
def create_power_field(domain, power_spectrum):
if not callable(power_spectrum): # we have a Field living on a PowerSpace
if not isinstance(power_spectrum, Field):
raise TypeError("Field object expected")
......@@ -199,15 +197,15 @@ def create_power_field(domain, power_spectrum, dtype=None):
if not isinstance(power_spectrum.domain[0], PowerSpace):
raise TypeError("PowerSpace required")
power_domain = power_spectrum.domain[0]
fp = Field(power_domain, val=power_spectrum.val, dtype=dtype)
fp = Field(power_domain, val=power_spectrum.val)
else:
power_domain = PowerSpace(domain)
fp = PS_field(power_domain, power_spectrum, dtype)
fp = PS_field(power_domain, power_spectrum)
return PowerDistributor(domain, power_domain)(fp)
def create_power_operator(domain, power_spectrum, space=None, dtype=None):
def create_power_operator(domain, power_spectrum, space=None):
""" Creates a diagonal operator with the given power spectrum.
Constructs a diagonal operator that lives over the specified domain.
......@@ -220,10 +218,6 @@ def create_power_operator(domain, power_spectrum, space=None, dtype=None):
An object that contains the power spectrum as a function of k.
space : int
the domain index on which the power operator will work
dtype : None or type, optional
dtype that the field holding the power spectrum shall use
(default : None).
if dtype is None: the dtype of `power_spectrum` will be used.
Returns
-------
......@@ -233,7 +227,7 @@ def create_power_operator(domain, power_spectrum, space=None, dtype=None):
domain = DomainTuple.make(domain)
space = utilities.infer_space(domain, space)
return DiagonalOperator(
create_power_field(domain[space], power_spectrum, dtype),
create_power_field(domain[space], power_spectrum),
domain=domain, spaces=space)
......
......@@ -22,10 +22,10 @@ from itertools import product
import abc
from future.utils import with_metaclass
__all__ = ["get_slice_list", "safe_cast", "parse_spaces", "infer_space",
"memo", "NiftyMetaBase", "hartley", "my_fftn_r2c"]
def get_slice_list(shape, axes):
"""
Helper function which generates slice list(s) to traverse over all
......
......@@ -58,66 +58,57 @@ class Test_Functionality(unittest.TestCase):
np.random.seed(11)