Commit 609ba005 authored by Martin Reinecke's avatar Martin Reinecke
Browse files

Merge branch 'nifty7_new_zm_handling' into 'NIFTy_7'

Revamp zero-mode handling

See merge request !607
parents 77d9d3e0 be037fd2
Pipeline #100796 passed with stages
in 25 minutes and 56 seconds
......@@ -110,6 +110,14 @@ run_getting_started_mf:
paths:
- '*.png'
run_getting_density:
stage: demo_runs
script:
- python3 demos/getting_started_density.py
artifacts:
paths:
- '*.png'
run_bernoulli:
stage: demo_runs
script:
......
Changes since NIFTy 6
=====================
New parametric amplitude model
------------------------------
The `ift.CorrelatedFieldMaker` now features two amplitude models. In addition
to the non-parametric one, one may choose to use a Matern kernel instead. The
method is aptly named `add_fluctuations_matern`. The major advantage of the
parametric model is its more intuitive scaling with the size of the position
space.
CorrelatedFieldMaker interface change
-------------------------------------
The interface of `ift.CorrelatedFieldMaker.make` and
`ift.CorrelatedFieldMaker.add_fluctuations` changed; it now expects the mean
and the standard deviation of their various parameters not as separate
arguments but as a tuple.
The interface of `ift.CorrelatedFieldMaker` changed and instances of it may now
be instantiated directly without the previously required `make` method. Upon
initialization, no zero-mode must be specified as the normalization for the
different axes of the power respectively amplitude spectrum now only happens
once in the `finalize` method. There is now a new call named
`set_amplitude_total_offset` to set the zero-mode. The method accepts either an
instance of `ift.Operator` or a tuple parameterizing a log-normal parameter.
Methods which require the zero-mode to be set raise a `NotImplementedError` if
invoked prior to having specified a zero-mode.
Furthermore, the interface of `ift.CorrelatedFieldMaker.add_fluctuations`
changed; it now expects the mean and the standard deviation of their various
parameters not as separate arguments but as a tuple. The same applies to all
new and renamed methods of the `CorrelatedFieldMaker` class.
Furthermore, it is now possible to disable the asperity and the flexibility
together with the asperity in the correlated field model. Note that disabling
......
%% Cell type:markdown id: tags:
# Notebook showcasing the NIFTy 6 Correlated Field model
**Skip to `Parameter Showcases` for the meat/veggies ;)**
The field model roughly works like this:
`f = HT( A * zero_mode * xi ) + offset`
`A` is a spectral power field which is constructed from power spectra that hold on subdomains of the target domain.
It is scaled by a zero mode operator and then pointwise multiplied by a gaussian excitation field, yielding
a representation of the field in harmonic space.
It is then transformed into the target real space and a offset added.
The power spectra `A` is constructed of are in turn constructed as the sum of a power law component
and an integrated Wiener process whose amplitude and roughness can be set.
## Setup code
%% Cell type:code id: tags:
``` python
import nifty7 as ift
import matplotlib.pyplot as plt
import numpy as np
ift.random.push_sseq_from_seed(43)
n_pix = 256
x_space = ift.RGSpace(n_pix)
```
%% Cell type:code id: tags:
``` python
# Plotting routine
def plot(fields, spectra, title=None):
# Plotting preparation is normally handled by nifty7.Plot
# It is done manually here to be able to tweak details
# Fields are assumed to have identical domains
fig = plt.figure(tight_layout=True, figsize=(12, 3.5))
if title is not None:
fig.suptitle(title, fontsize=14)
# Field
ax1 = fig.add_subplot(1, 2, 1)
ax1.axhline(y=0., color='k', linestyle='--', alpha=0.25)
for field in fields:
dom = field.domain[0]
xcoord = np.arange(dom.shape[0]) * dom.distances[0]
ax1.plot(xcoord, field.val)
ax1.set_xlim(xcoord[0], xcoord[-1])
ax1.set_ylim(-5., 5.)
ax1.set_xlabel('x')
ax1.set_ylabel('f(x)')
ax1.set_title('Field realizations')
# Spectrum
ax2 = fig.add_subplot(1, 2, 2)
for spectrum in spectra:
xcoord = spectrum.domain[0].k_lengths
ycoord = spectrum.val_rw()
ycoord[0] = ycoord[1]
ax2.plot(xcoord, ycoord)
ax2.set_ylim(1e-6, 10.)
ax2.set_xscale('log')
ax2.set_yscale('log')
ax2.set_xlabel('k')
ax2.set_ylabel('p(k)')
ax2.set_title('Power Spectrum')
fig.align_labels()
plt.show()
# Helper: draw main sample
main_sample = None
def init_model(m_pars, fl_pars):
global main_sample
cf = ift.CorrelatedFieldMaker.make(**m_pars)
cf = ift.CorrelatedFieldMaker(m_pars["prefix"])
cf.set_amplitude_total_offset(m_pars["offset_mean"], m_pars["offset_std"])
cf.add_fluctuations(**fl_pars)
field = cf.finalize(prior_info=0)
main_sample = ift.from_random(field.domain)
print("model domain keys:", field.domain.keys())
# Helper: field and spectrum from parameter dictionaries + plotting
def eval_model(m_pars, fl_pars, title=None, samples=None):
cf = ift.CorrelatedFieldMaker.make(**m_pars)
cf = ift.CorrelatedFieldMaker(m_pars["prefix"])
cf.set_amplitude_total_offset(m_pars["offset_mean"], m_pars["offset_std"])
cf.add_fluctuations(**fl_pars)
field = cf.finalize(prior_info=0)
spectrum = cf.amplitude
if samples is None:
samples = [main_sample]
field_realizations = [field(s) for s in samples]
spectrum_realizations = [spectrum.force(s) for s in samples]
plot(field_realizations, spectrum_realizations, title)
def gen_samples(key_to_vary):
if key_to_vary is None:
return [main_sample]
dct = main_sample.to_dict()
subdom_to_vary = dct.pop(key_to_vary).domain
samples = []
for i in range(8):
d = dct.copy()
d[key_to_vary] = ift.from_random(subdom_to_vary)
samples.append(ift.MultiField.from_dict(d))
return samples
def vary_parameter(parameter_key, values, samples_vary_in=None):
s = gen_samples(samples_vary_in)
for v in values:
if parameter_key in cf_make_pars.keys():
m_pars = {**cf_make_pars, parameter_key: v}
eval_model(m_pars, cf_x_fluct_pars, f"{parameter_key} = {v}", s)
else:
fl_pars = {**cf_x_fluct_pars, parameter_key: v}
eval_model(cf_make_pars, fl_pars, f"{parameter_key} = {v}", s)
```
%% Cell type:markdown id: tags:
## Before the Action: The Moment-Matched Log-Normal Distribution
Many properties of the correlated field are modelled as being lognormally distributed.
The distribution models are parametrized via their means and standard-deviations (first and second position in tuple).
To get a feeling of how the ratio of the `mean` and `stddev` parameters influences the distribution shape,
here are a few example histograms: (observe the x-axis!)
%% Cell type:code id: tags:
``` python
fig = plt.figure(figsize=(13, 3.5))
mean = 1.0
sigmas = [1.0, 0.5, 0.1]
for i in range(3):
op = ift.LognormalTransform(mean=mean, sigma=sigmas[i],
key='foo', N_copies=0)
op_samples = np.array(
[op(s).val for s in [ift.from_random(op.domain) for i in range(10000)]])
ax = fig.add_subplot(1, 3, i + 1)
ax.hist(op_samples, bins=50)
ax.set_title(f"mean = {mean}, sigma = {sigmas[i]}")
ax.set_xlabel('x')
del op_samples
plt.show()
```
%% Cell type:markdown id: tags:
## The Neutral Field
To demonstrate the effect of all parameters, first a 'neutral' set of parameters
is defined which then are varied one by one, showing the effect of the variation
on the generated field realizations and the underlying power spectrum from which
they were drawn.
As a neutral field, a model with a white power spectrum and vanishing spectral power was chosen.
%% Cell type:code id: tags:
``` python
# Neutral model parameters yielding a quasi-constant field
cf_make_pars = {
'offset_mean': 0.,
'offset_std': (1e-3, 1e-16),
'prefix': ''
}
cf_x_fluct_pars = {
'target_subdomain': x_space,
'fluctuations': (1e-3, 1e-16),
'flexibility': (1e-3, 1e-16),
'asperity': (1e-3, 1e-16),
'loglogavgslope': (0., 1e-16)
}
init_model(cf_make_pars, cf_x_fluct_pars)
```
%% Cell type:code id: tags:
``` python
# Show neutral field
eval_model(cf_make_pars, cf_x_fluct_pars, "Neutral Field")
```
%% Cell type:markdown id: tags:
# Parameter Showcases
## The `fluctuations` parameters of `add_fluctuations()`
determine the **amplitude of variations along the field dimension**
for which `add_fluctuations` is called.
`fluctuations[0]` set the _average_ amplitude of the fields fluctuations along the given dimension,\
`fluctuations[1]` sets the width and shape of the amplitude distribution.
The amplitude is modelled as being log-normally distributed,
see `The Moment-Matched Log-Normal Distribution` above for details.
#### `fluctuations` mean:
%% Cell type:code id: tags:
``` python
vary_parameter('fluctuations', [(0.05, 1e-16), (0.5, 1e-16), (2., 1e-16)], samples_vary_in='xi')
```
%% Cell type:markdown id: tags:
#### `fluctuations` std:
%% Cell type:code id: tags:
``` python
vary_parameter('fluctuations', [(1., 0.01), (1., 0.1), (1., 1.)], samples_vary_in='fluctuations')
cf_x_fluct_pars['fluctuations'] = (1., 1e-16)
```
%% Cell type:markdown id: tags:
## The `loglogavgslope` parameters of `add_fluctuations()`
determine **the slope of the loglog-linear (power law) component of the power spectrum**.
The slope is modelled to be normally distributed.
#### `loglogavgslope` mean:
%% Cell type:code id: tags:
``` python
vary_parameter('loglogavgslope', [(-6., 1e-16), (-2., 1e-16), (2., 1e-16)], samples_vary_in='xi')
```
%% Cell type:markdown id: tags:
#### `loglogavgslope` std:
%% Cell type:code id: tags:
``` python
vary_parameter('loglogavgslope', [(-2., 0.02), (-2., 0.2), (-2., 2.0)], samples_vary_in='loglogavgslope')
cf_x_fluct_pars['loglogavgslope'] = (-2., 1e-16)
```
%% Cell type:markdown id: tags:
## The `flexibility` parameters of `add_fluctuations()`
determine **the amplitude of the integrated Wiener process component of the power spectrum**
(how strong the power spectrum varies besides the power-law).
`flexibility[0]` sets the _average_ amplitude of the i.g.p. component,\
`flexibility[1]` sets how much the amplitude can vary.\
These two parameters feed into a moment-matched log-normal distribution model,
see above for a demo of its behavior.
#### `flexibility` mean:
%% Cell type:code id: tags:
``` python
vary_parameter('flexibility', [(0.4, 1e-16), (4.0, 1e-16), (12.0, 1e-16)], samples_vary_in='spectrum')
```
%% Cell type:markdown id: tags:
#### `flexibility` std:
%% Cell type:code id: tags:
``` python
vary_parameter('flexibility', [(4., 0.02), (4., 0.2), (4., 2.)], samples_vary_in='flexibility')
cf_x_fluct_pars['flexibility'] = (4., 1e-16)
```
%% Cell type:markdown id: tags:
## The `asperity` parameters of `add_fluctuations()`
`asperity` determines **how rough the integrated Wiener process component of the power spectrum is**.
`asperity[0]` sets the average roughness, `asperity[1]` sets how much the roughness can vary.\
These two parameters feed into a moment-matched log-normal distribution model,
see above for a demo of its behavior.
#### `asperity` mean:
%% Cell type:code id: tags:
``` python
vary_parameter('asperity', [(0.001, 1e-16), (1.0, 1e-16), (5., 1e-16)], samples_vary_in='spectrum')
```
%% Cell type:markdown id: tags:
#### `asperity` std:
%% Cell type:code id: tags:
``` python
vary_parameter('asperity', [(1., 0.01), (1., 0.1), (1., 1.)], samples_vary_in='asperity')
cf_x_fluct_pars['asperity'] = (1., 1e-16)
```
%% Cell type:markdown id: tags:
## The `offset_mean` parameter of `CorrelatedFieldMaker.make()`
The `offset_mean` parameter defines a global additive offset on the field realizations.
If the field is used for a lognormal model `f = field.exp()`, this acts as a global signal magnitude offset.
%% Cell type:code id: tags:
``` python
# Reset model to neutral
cf_x_fluct_pars['fluctuations'] = (1e-3, 1e-16)
cf_x_fluct_pars['flexibility'] = (1e-3, 1e-16)
cf_x_fluct_pars['asperity'] = (1e-3, 1e-16)
cf_x_fluct_pars['loglogavgslope'] = (1e-3, 1e-16)
```
%% Cell type:code id: tags:
``` python
vary_parameter('offset_mean', [3., 0., -2.])
```
%% Cell type:markdown id: tags:
## The `offset_std` parameters of `CorrelatedFieldMaker.make()`
Variation of the global offset of the field are modelled as being log-normally distributed.
See `The Moment-Matched Log-Normal Distribution` above for details.
The `offset_std[0]` parameter sets how much NIFTy will vary the offset *on average*.\
The `offset_std[1]` parameters defines the with and shape of the offset variation distribution.
#### `offset_std` mean:
%% Cell type:code id: tags:
``` python
vary_parameter('offset_std', [(1e-16, 1e-16), (0.5, 1e-16), (2., 1e-16)], samples_vary_in='xi')
```
%% Cell type:markdown id: tags:
#### `offset_std` std:
%% Cell type:code id: tags:
``` python
vary_parameter('offset_std', [(1., 0.01), (1., 0.1), (1., 1.)], samples_vary_in='zeromode')
```
......
......@@ -11,7 +11,7 @@
# 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
# Copyright(C) 2013-2021 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.
......@@ -73,14 +73,17 @@ def main():
sp2 = ift.RGSpace(npix2)
# Set up signal model
cfmaker = ift.CorrelatedFieldMaker.make(0., (1e-2, 1e-6), '')
cfmaker.add_fluctuations(sp1, (0.1, 1e-2), (2, .2), (.01, .5), (-4, 2.), 'amp1')
cfmaker.add_fluctuations(sp2, (0.1, 1e-2), (2, .2), (.01, .5),
(-3, 1), 'amp2')
cfmaker = ift.CorrelatedFieldMaker('')
cfmaker.add_fluctuations(sp1, (0.1, 1e-2), (2, .2), (.01, .5), (-4, 2.),
'amp1')
cfmaker.add_fluctuations(sp2, (0.1, 1e-2), (2, .2), (.01, .5), (-3, 1),
'amp2')
cfmaker.set_amplitude_total_offset(0., (1e-2, 1e-6))
correlated_field = cfmaker.finalize()
pspec1 = cfmaker.normalized_amplitudes[0]**2
pspec2 = cfmaker.normalized_amplitudes[1]**2
normalized_amp = cfmaker.get_normalized_amplitudes()
pspec1 = normalized_amp[0]**2
pspec2 = normalized_amp[1]**2
DC = SingleDomain(correlated_field.target, position_space)
# Apply a nonlinearity
......
#!/usr/bin/env python3
# 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) 2013-2021 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.
############################################################
# Density estimation
#
# Compute a density estimate for a log-normal process measured by a
# Poissonian likelihood.
#
# Demo takes a while to compute
#############################################################
import numpy as np
import nifty7 as ift
def density_estimator(domain, pad=1.0, cf_fluctuations=None, cf_azm_uniform=None):
cf_azm_uniform_sane_default = (1e-4, 1.0)
cf_fluctuations_sane_default = {
"scale": (0.5, 0.3),
"cutoff": (4.0, 3.0),
"loglogslope": (-6.0, 3.0)
}
domain = ift.DomainTuple.make(domain)
dom_scaling = 1. + np.broadcast_to(pad, (len(domain.axes), ))
if cf_fluctuations is None:
cf_fluctuations = cf_fluctuations_sane_default
if cf_azm_uniform is None:
cf_azm_uni = cf_azm_uniform_sane_default
domain_padded = []
for d_scl, d in zip(dom_scaling, domain):
if not isinstance(d, ift.RGSpace) or d.harmonic:
te = [f"unexpected domain encountered in `domain`: {domain}"]
te += "expected a non-harmonic `ift.RGSpace`"
raise TypeError("\n".join(te))
shape_padded = tuple((d_scl * np.array(d.shape)).astype(int))
domain_padded.append(ift.RGSpace(shape_padded, distances=d.distances))
domain_padded = ift.DomainTuple.make(domain_padded)
# Set up the signal model
azm_offset_mean = 0.0 # The zero-mode should be inferred only from the data
cfmaker = ift.CorrelatedFieldMaker("")
for i, d in enumerate(domain_padded):
if isinstance(cf_fluctuations, (list, tuple)):
cf_fl = cf_fluctuations[i]
else:
cf_fl = cf_fluctuations
cfmaker.add_fluctuations_matern(d, **cf_fl, prefix=f"ax{i}")
scalar_domain = ift.DomainTuple.scalar_domain()
uniform = ift.UniformOperator(scalar_domain, *cf_azm_uni)
azm = uniform.ducktape("zeromode")
cfmaker.set_amplitude_total_offset(azm_offset_mean, azm)
correlated_field = cfmaker.finalize(0).clip(-10., 10.)
normalized_amplitudes = cfmaker.get_normalized_amplitudes()
domain_shape = tuple(d.shape for d in domain)
slc = ift.SliceOperator(correlated_field.target, domain_shape)
signal = ift.exp(slc @ correlated_field)
model_operators = {
"correlated_field": correlated_field,
"select_subset": slc,
"amplitude_total_offset": azm,
"normalized_amplitudes": normalized_amplitudes
}
return signal, model_operators
if __name__ == "__main__":
filename = "getting_started_density_{}.png"
ift.random.push_sseq_from_seed(42)
# Set up signal domain
npix1 = 128
npix2 = 128
sp1 = ift.RGSpace(npix1)
sp2 = ift.RGSpace(npix2)
position_space = ift.DomainTuple.make((sp1, sp2))
signal, ops = density_estimator(position_space)
correlated_field = ops["correlated_field"]
data_space = signal.target
# Generate mock signal and data
rng = ift.random.current_rng()
mock_position = ift.from_random(signal.domain, "normal")
data = ift.Field.from_raw(data_space, rng.poisson(signal(mock_position).val))
# Rejoin domains for plotting
plotting_domain = ift.DomainTuple.make(ift.RGSpace((npix1, npix2)))
plotting_domain_expanded = ift.DomainTuple.make(ift.RGSpace((2 * npix1, 2 * npix2)))
plot = ift.Plot()
plot.add(
ift.Field.from_raw(
plotting_domain_expanded, ift.exp(correlated_field(mock_position)).val
),
title="Pre-Slicing Truth",
)
plot.add(
ift.Field.from_raw(plotting_domain, signal(mock_position).val),
title="Ground Truth",
)
plot.add(ift.Field.from_raw(plotting_domain, data.val), title="Data")
plot.output(ny=1, nx=3, xsize=10, ysize=3, name=filename.format("setup"))
print("Setup saved as", filename.format("setup"))
# Minimization parameters
ic_sampling = ift.AbsDeltaEnergyController(
name="Sampling", deltaE=0.01, iteration_limit=100
)
ic_newton = ift.AbsDeltaEnergyController(
name="Newton", deltaE=0.01, iteration_limit=35
)
ic_sampling.enable_logging()
ic_newton.enable_logging()
minimizer = ift.NewtonCG(ic_newton, enable_logging=True)
# Number of samples used to estimate the KL
n_samples = 5
# Set up likelihood and information Hamiltonian
likelihood = ift.PoissonianEnergy(data) @ signal
ham = ift.StandardHamiltonian(likelihood, ic_sampling)
# Start minimization
initial_mean = ift.MultiField.full(ham.domain, 0.)
mean = initial_mean
for i in range(5):
# Draw new samples and minimize KL
kl = ift.MetricGaussianKL.make(mean, ham, n_samples, True)
kl, convergence = minimizer(kl)
mean = kl.position
# Plot current reconstruction
plot = ift.Plot()
plot.add(