Commit 903e6bb7 authored by Martin Reinecke's avatar Martin Reinecke

merge

parents 54a560d8 9855fce6
Pipeline #75404 passed with stages
in 9 minutes and 5 seconds
......@@ -65,11 +65,16 @@ pages:
before_script:
- python3 setup.py install --user -f
run_ipynb:
run_ipynb0:
stage: demo_runs
script:
- jupyter nbconvert --execute --ExecutePreprocessor.timeout=None demos/getting_started_0.ipynb
run_ipynb1:
stage: demo_runs
script:
- jupyter nbconvert --execute --ExecutePreprocessor.timeout=None demos/getting_started_4_CorrelatedFields.ipynb
run_getting_started_1:
stage: demo_runs
script:
......@@ -99,7 +104,7 @@ run_getting_started_3:
run_getting_started_mf:
stage: demo_runs
script:
- python3 demos/getting_started_mf.py
- python3 demos/getting_started_5_mf.py
artifacts:
paths:
- '*.png'
......
......@@ -55,6 +55,10 @@ if __name__ == '__main__':
position_space = ift.RGSpace([128, 128])
# For a detailed showcase of the effects the parameters
# of the CorrelatedField model have on the generated fields,
# see 'getting_started_4_CorrelatedFields.ipynb'.
cfmaker = ift.CorrelatedFieldMaker.make(
offset_mean = 0.0, # 0.
offset_std_mean = 1e-3, # 1e-3
......@@ -62,22 +66,21 @@ if __name__ == '__main__':
prefix = '')
fluctuations_dict = {
# Amplitude of the fluctuations
# Amplitude of field fluctuations
'fluctuations_mean': 2.0, # 1.0
'fluctuations_stddev': 1.0, # 1e-2
# Smooth variation speed
# Exponent of power law power spectrum component
'loglogavgslope_mean': -2.0, # -3.0
'loglogavgslope_stddev': 0.5, # 0.5
# Amplitude of integrated Wiener process power spectrum component
'flexibility_mean': 2.5, # 1.0
'flexibility_stddev': 1.0, # 0.5
# How strong the ragged component of the spectrum is
# (Ratio of Wiener process and integrated Wiener process ?)
# How ragged the integrated Wiener process component is
'asperity_mean': 0.5, # 0.1
'asperity_stddev': 0.5, # 0.5
# Slope of linear spectrum component
'loglogavgslope_mean': -2.0, # -3.0
'loglogavgslope_stddev': 0.5 # 0.5
'asperity_stddev': 0.5 # 0.5
}
cfmaker.add_fluctuations(position_space, **fluctuations_dict)
......@@ -135,7 +138,7 @@ if __name__ == '__main__':
# Plot current reconstruction
plot = ift.Plot()
plot.add(signal(KL.position), title="reconstruction")
plot.add([A.force(KL.position), A.force(mock_position)], title="power")
plot.add([A.force(mock_position), A.force(KL.position)], title="power")
plot.output(ny=1, ysize=6, xsize=16,
name=filename.format("loop_{:02d}".format(i)))
......@@ -153,8 +156,8 @@ if __name__ == '__main__':
powers = [A.force(s + KL.position) for s in KL.samples]
plot.add(
powers + [A.force(KL.position),
A.force(mock_position)],
powers + [A.force(mock_position),
A.force(KL.position)],
title="Sampled Posterior Power Spectrum",
linewidth=[1.]*len(powers) + [3., 3.])
plot.output(ny=1, nx=3, xsize=24, ysize=6, name=filename_res)
......
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Notebook showcasing the NIFTy 6 Correlated Field model\n",
"\n",
"**Skip to `Parameter Showcases` for the meat/veggies ;)**\n",
"\n",
"The field model roughly works like this:\n",
"\n",
"`f = HT( A * zero_mode * xi ) + offset`\n",
"\n",
"`A` is a spectral power field which is constructed from power spectra that hold on subdomains of the target domain.\n",
"It is scaled by a zero mode operator and then pointwise multiplied by a gaussian excitation field, yielding\n",
"a representation of the field in harmonic space.\n",
"It is then transformed into the target real space and a offset added.\n",
"\n",
"The power spectra `A` is constructed of are in turn constructed as the sum of a power law component\n",
"and an integrated Wiener process whose amplitude and roughness can be set.\n",
"\n",
"## Setup code"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import nifty7 as ift\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"ift.random.push_sseq_from_seed(43)\n",
"\n",
"n_pix = 256\n",
"x_space = ift.RGSpace(n_pix)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Plotting routine\n",
"def plot(fields, spectra, title=None):\n",
" # Plotting preparation is normally handled by nifty7.Plot\n",
" # It is done manually here to be able to tweak details\n",
" # Fields are assumed to have identical domains\n",
" fig = plt.figure(tight_layout=True, figsize=(12, 3.5))\n",
" if title is not None:\n",
" fig.suptitle(title, fontsize=14)\n",
" \n",
" # Field\n",
" ax1 = fig.add_subplot(1, 2, 1)\n",
" ax1.axhline(y=0., color='k', linestyle='--', alpha=0.25)\n",
" for field in fields:\n",
" dom = field.domain[0]\n",
" xcoord = np.arange(dom.shape[0]) * dom.distances[0]\n",
" ax1.plot(xcoord, field.val)\n",
" ax1.set_xlim(xcoord[0], xcoord[-1])\n",
" ax1.set_ylim(-5., 5.)\n",
" ax1.set_xlabel('x')\n",
" ax1.set_ylabel('f(x)')\n",
" ax1.set_title('Field realizations')\n",
" \n",
" # Spectrum\n",
" ax2 = fig.add_subplot(1, 2, 2)\n",
" for spectrum in spectra:\n",
" xcoord = spectrum.domain[0].k_lengths\n",
" ycoord = spectrum.val_rw()\n",
" ycoord[0] = ycoord[1]\n",
" ax2.plot(xcoord, ycoord)\n",
" ax2.set_ylim(1e-6, 10.)\n",
" ax2.set_xscale('log')\n",
" ax2.set_yscale('log')\n",
" ax2.set_xlabel('k')\n",
" ax2.set_ylabel('p(k)')\n",
" ax2.set_title('Power Spectrum')\n",
" \n",
" fig.align_labels()\n",
" plt.show()\n",
"\n",
"# Helper: draw main sample\n",
"main_sample = None\n",
"def init_model(m_pars, fl_pars):\n",
" global main_sample\n",
" cf = ift.CorrelatedFieldMaker.make(**m_pars)\n",
" cf.add_fluctuations(**fl_pars)\n",
" field = cf.finalize(prior_info=0)\n",
" main_sample = ift.from_random(field.domain)\n",
" print(\"model domain keys:\", field.domain.keys())\n",
" \n",
"# Helper: field and spectrum from parameter dictionaries + plotting\n",
"def eval_model(m_pars, fl_pars, title=None, samples=None):\n",
" cf = ift.CorrelatedFieldMaker.make(**m_pars)\n",
" cf.add_fluctuations(**fl_pars)\n",
" field = cf.finalize(prior_info=0)\n",
" spectrum = cf.amplitude\n",
" if samples is None:\n",
" samples = [main_sample]\n",
" field_realizations = [field(s) for s in samples]\n",
" spectrum_realizations = [spectrum.force(s) for s in samples]\n",
" plot(field_realizations, spectrum_realizations, title)\n",
"\n",
"def gen_samples(key_to_vary):\n",
" if key_to_vary is None:\n",
" return [main_sample]\n",
" dct = main_sample.to_dict()\n",
" subdom_to_vary = dct.pop(key_to_vary).domain\n",
" samples = []\n",
" for i in range(8):\n",
" d = dct.copy()\n",
" d[key_to_vary] = ift.from_random(subdom_to_vary)\n",
" samples.append(ift.MultiField.from_dict(d))\n",
" return samples\n",
" \n",
"def vary_parameter(parameter_key, values, samples_vary_in=None):\n",
" s = gen_samples(samples_vary_in)\n",
" for v in values:\n",
" if parameter_key in cf_make_pars.keys():\n",
" m_pars = {**cf_make_pars, parameter_key: v}\n",
" eval_model(m_pars, cf_x_fluct_pars, f\"{parameter_key} = {v}\", s)\n",
" else:\n",
" fl_pars = {**cf_x_fluct_pars, parameter_key: v}\n",
" eval_model(cf_make_pars, fl_pars, f\"{parameter_key} = {v}\", s)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Before the Action: The Moment-Matched Log-Normal Distribution\n",
"Many properties of the correlated field are modelled as being lognormally distributed.\n",
"\n",
"The distribution models are parametrized via their means `_mean` and standard-deviations `_stddev`.\n",
"\n",
"To get a feeling of how the ratio of the `mean` and `stddev` parameters influences the distribution shape,\n",
"here are a few example histograms: (observe the x-axis!)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"fig = plt.figure(figsize=(13, 3.5))\n",
"mean = 1.0\n",
"sigmas = [1.0, 0.5, 0.1]\n",
"\n",
"for i in range(3):\n",
" op = ift.library.correlated_fields._LognormalMomentMatching(mean=mean,\n",
" sig=sigmas[i],\n",
" key='foo',\n",
" N_copies=0)\n",
" op_samples = np.array(\n",
" [op(s).val for s in [ift.from_random(op.domain) for i in range(10000)]])\n",
"\n",
" ax = fig.add_subplot(1, 3, i + 1)\n",
" ax.hist(op_samples, bins=50)\n",
" ax.set_title(f\"mean = {mean}, sigma = {sigmas[i]}\")\n",
" ax.set_xlabel('x')\n",
" del op_samples\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The Neutral Field\n",
"\n",
"To demonstrate the effect of all parameters, first a 'neutral' set of parameters\n",
"is defined which then are varied one by one, showing the effect of the variation\n",
"on the generated field realizations and the underlying power spectrum from which\n",
"they were drawn.\n",
"\n",
"As a neutral field, a model with a white power spectrum and vanishing spectral power was chosen."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Neutral model parameters yielding a quasi-constant field\n",
"cf_make_pars = {\n",
" 'offset_mean': 0.,\n",
" 'offset_std_mean': 1e-3,\n",
" 'offset_std_std': 1e-16,\n",
" 'prefix': ''\n",
"}\n",
"\n",
"cf_x_fluct_pars = {\n",
" 'target_subdomain': x_space,\n",
" 'fluctuations_mean': 1e-3,\n",
" 'fluctuations_stddev': 1e-16,\n",
" 'flexibility_mean': 1e-3,\n",
" 'flexibility_stddev': 1e-16,\n",
" 'asperity_mean': 1e-3,\n",
" 'asperity_stddev': 1e-16,\n",
" 'loglogavgslope_mean': 0.,\n",
" 'loglogavgslope_stddev': 1e-16\n",
"}\n",
"\n",
"init_model(cf_make_pars, cf_x_fluct_pars)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Show neutral field\n",
"eval_model(cf_make_pars, cf_x_fluct_pars, \"Neutral Field\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Parameter Showcases\n",
"\n",
"## The `fluctuations_` parameters of `add_fluctuations()`\n",
"\n",
"determine the **amplitude of variations along the field dimension**\n",
"for which `add_fluctuations` is called.\n",
"\n",
"`fluctuations_mean` set the _average_ amplitude of the fields fluctuations along the given dimension,\\\n",
"`fluctuations_stddev` sets the width and shape of the amplitude distribution.\n",
"\n",
"The amplitude is modelled as being log-normally distributed,\n",
"see `The Moment-Matched Log-Normal Distribution` above for details.\n",
"\n",
"#### `fluctuations_mean`:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"vary_parameter('fluctuations_mean', [0.05, 0.5, 2.], samples_vary_in='xi')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### `fluctuations_stddev`:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"cf_x_fluct_pars['fluctuations_mean'] = 1.0\n",
"vary_parameter('fluctuations_stddev', [0.01, 0.1, 1.0], samples_vary_in='fluctuations')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The `loglogavgslope_` parameters of `add_fluctuations()`\n",
"\n",
"determine **the slope of the loglog-linear (power law) component of the power spectrum**.\n",
"\n",
"The slope is modelled to be normally distributed.\n",
"\n",
"#### `loglogavgslope_mean`:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"vary_parameter('loglogavgslope_mean', [-3., -1., 1.], samples_vary_in='xi')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### `loglogavgslope_stddev`:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"cf_x_fluct_pars['loglogavgslope_mean'] = -1.0\n",
"vary_parameter('loglogavgslope_stddev', [0.01, 0.1, 1.0], samples_vary_in='loglogavgslope')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The `flexibility_` parameters of `add_fluctuations()`\n",
"\n",
"determine **the amplitude of the integrated Wiener process component of the power spectrum**\n",
"(how strong the power spectrum varies besides the power-law).\n",
"\n",
"`flexibility_mean` sets the _average_ amplitude of the i.g.p. component,\n",
"`flexibility_stddev` sets how much the amplitude can vary.\\\n",
"These two parameters feed into a moment-matched log-normal distribution model,\n",
"see above for a demo of its behavior.\n",
"\n",
"#### `flexibility_mean`:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"vary_parameter('flexibility_mean', [0.1, 1.0, 3.0], samples_vary_in='spectrum')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### `flexibility_stddev`:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"cf_x_fluct_pars['flexibility_mean'] = 2.0\n",
"vary_parameter('flexibility_stddev', [0.01, 0.1, 1.0], samples_vary_in='flexibility')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The `asperity_` parameters of `add_fluctuations()`\n",
"\n",
"`asperity_` determines **how rough the integrated Wiener process component of the power spectrum is**.\n",
"\n",
"`asperity_mean` sets the average roughness, `asperity_stddev` sets how much the roughness can vary.\\\n",
"These two parameters feed into a moment-matched log-normal distribution model,\n",
"see above for a demo of its behavior.\n",
"\n",
"#### `asperity_mean`:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"vary_parameter('asperity_mean', [0.001, 1.0, 5.0], samples_vary_in='spectrum')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### `asperity_stddev`:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"cf_x_fluct_pars['asperity_mean'] = 1.0\n",
"vary_parameter('asperity_stddev', [0.01, 0.1, 1.0], samples_vary_in='asperity')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The `offset_mean` parameter of `CorrelatedFieldMaker.make()`\n",
"\n",
"The `offset_mean` parameter defines a global additive offset on the field realizations.\n",
"\n",
"If the field is used for a lognormal model `f = field.exp()`, this acts as a global signal magnitude offset."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Reset model to neutral\n",
"cf_x_fluct_pars['fluctuations_mean'] = 1e-3\n",
"cf_x_fluct_pars['flexibility_mean'] = 1e-3\n",
"cf_x_fluct_pars['asperity_mean'] = 1e-3\n",
"cf_x_fluct_pars['loglogavgslope_mean'] = 1e-3"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"vary_parameter('offset_mean', [3., 0., -2.])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The `offset_std_` parameters of `CorrelatedFieldMaker.make()`\n",
"\n",
"Variation of the global offset of the field are modelled as being log-normally distributed.\n",
"See `The Moment-Matched Log-Normal Distribution` above for details.\n",
"\n",
"The `offset_std_mean` parameter sets how much NIFTy will vary the offset *on average*.\\\n",
"The `offset_std_std` parameters defines the with and shape of the offset variation distribution.\n",
"\n",
"#### `offset_std_mean`:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"vary_parameter('offset_std_mean', [1e-16, 0.5, 2.], samples_vary_in='xi')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### `offset_std_std`:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"cf_make_pars['offset_std_mean'] = 1.0\n",
"vary_parameter('offset_std_std', [0.01, 0.1, 1.0], samples_vary_in='zeromode')"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.2"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
......@@ -356,24 +356,23 @@ class CorrelatedFieldMaker:
"""Constrution helper for hirarchical correlated field models.
The correlated field models are parametrized by creating
power spectrum operators ("amplitudes")
acting on their target subdomains
via calls to :func:`add_fluctuations`.
power spectrum operators ("amplitudes") via calls to
:func:`add_fluctuations` that act on the targeted field subdomains.
During creation of the :class:`CorrelatedFieldMaker` via
:func:`make`, a global offset from zero can be added to the
field to be created and an operator applying gaussian fluctuations
around this offset needs to be parametrized.
:func:`make`, a global offset from zero of the field model
can be defined and an operator applying fluctuations
around this offset is parametrized.
The resulting correlated field model operator has a
:class:`~nifty7.multi_domain.MultiDomain` as its domain and
expects its input values to be univariately gaussian.
The target of the constructed operator will be a
:class:`~nifty7.domain_tuple.DomainTuple`
containing the `target_subdomains` of the added fluctuations in the
order of the `add_fluctuations` calls.
:class:`~nifty7.domain_tuple.DomainTuple` containing the
`target_subdomains` of the added fluctuations in the order of
the `add_fluctuations` calls.
Creation of the model operator is finished by calling the method
Creation of the model operator is completed by calling the method
:func:`finalize`, which returns the configured operator.
An operator representing an array of correlated field models
......@@ -482,9 +481,9 @@ class CorrelatedFieldMaker:
fluctuations_{mean,stddev} : float
Total spectral energy -> Amplitude of the fluctuations
flexibility_{mean,stddev} : float
Smooth variation speed of the power spectrum
Amplitude of the non-power-law power spectrum component
asperity_{mean,stddev} : float
Strength of unsmoothed power spectrum variations
Roughness of the non-power-law power spectrum component
Used to accomodate single frequency peaks
loglogavgslope_{mean,stddev} : float
Power law component exponent
......
Markdown is supported
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment