From 35e632b032eec6cdb1ad04f2effd052cbb29b441 Mon Sep 17 00:00:00 2001
From: Martin Reinecke <martin@mpa-garching.mpg.de>
Date: Sun, 4 Feb 2018 16:10:59 +0100
Subject: [PATCH] make the 1D part (sort of) work with NIFTy4
---
demos/Wiener Filter.ipynb | 187 ++++++++++++++++----------------------
1 file changed, 80 insertions(+), 107 deletions(-)
diff --git a/demos/Wiener Filter.ipynb b/demos/Wiener Filter.ipynb
index eddcb03db..0ad954caa 100644
--- a/demos/Wiener Filter.ipynb
+++ b/demos/Wiener Filter.ipynb
@@ -93,7 +93,6 @@
"cell_type": "code",
"execution_count": null,
"metadata": {
- "collapsed": true,
"slideshow": {
"slide_type": "-"
}
@@ -101,7 +100,6 @@
"outputs": [],
"source": [
"N_pixels = 512 # Number of pixels\n",
- "sigma2 = .5 # Noise variance\n",
"\n",
"def pow_spec(k):\n",
" P0, k0, gamma = [.2, 5, 6]\n",
@@ -140,11 +138,11 @@
},
"outputs": [],
"source": [
- "import matplotlib.pyplot as plt\n",
"import numpy as np\n",
- "from nifty import (DiagonalOperator, EndomorphicOperator, FFTOperator, Field,\n",
- " InvertibleOperatorMixin, PowerSpace, RGSpace,\n",
- " create_power_operator, SmoothingOperator, DiagonalProberMixin, Prober)"
+ "np.random.seed(42)\n",
+ "import nifty4 as ift\n",
+ "import matplotlib.pyplot as plt\n",
+ "%matplotlib inline"
]
},
{
@@ -162,43 +160,20 @@
"cell_type": "code",
"execution_count": null,
"metadata": {
- "collapsed": true,
"slideshow": {
"slide_type": "-"
}
},
"outputs": [],
"source": [
- "class PropagatorOperator(InvertibleOperatorMixin, EndomorphicOperator):\n",
- " def __init__(self, R, N, Sh, default_spaces=None):\n",
- " super(PropagatorOperator, self).__init__(default_spaces=default_spaces,\n",
- " preconditioner=lambda x : fft.adjoint_times(Sh.times(fft.times(x))))\n",
- "\n",
- " self.R = R\n",
- " self.N = N\n",
- " self.Sh = Sh\n",
- " self._domain = R.domain\n",
- " self.fft = FFTOperator(domain=R.domain, target=Sh.domain)\n",
- "\n",
- " def _inverse_times(self, x, spaces, x0=None):\n",
- " return self.R.adjoint_times(self.N.inverse_times(self.R(x))) \\\n",
- " + self.fft.adjoint_times(self.Sh.inverse_times(self.fft(x)))\n",
- "\n",
- " @property\n",
- " def domain(self):\n",
- " return self._domain\n",
- "\n",
- " @property\n",
- " def unitary(self):\n",
- " return False\n",
- "\n",
- " @property\n",
- " def symmetric(self):\n",
- " return False\n",
- "\n",
- " @property\n",
- " def self_adjoint(self):\n",
- " return True"
+ "def PropagatorOperator(R, N, Sh):\n",
+ " IC = ift.GradientNormController(name=\"inverter\", iteration_limit=50000,\n",
+ " tol_abs_gradnorm=0.1)\n",
+ " inverter = ift.ConjugateGradient(controller=IC)\n",
+ " D = (R.adjoint*N.inverse*R + Sh.inverse).inverse\n",
+ " # MR FIXME: we can/should provide a preconditioner here as well!\n",
+ " return ift.InversionEnabler(D, inverter)\n",
+ " #return ift.library.wiener_filter_curvature.WienerFilterCurvature(R,N,Sh,inverter).inverse\n"
]
},
{
@@ -247,30 +222,33 @@
{
"cell_type": "code",
"execution_count": null,
- "metadata": {
- "collapsed": true
- },
+ "metadata": {},
"outputs": [],
"source": [
- "s_space = RGSpace(N_pixels)\n",
- "fft = FFTOperator(s_space)\n",
- "h_space = fft.target[0]\n",
- "p_space = PowerSpace(h_space)\n",
- "\n",
+ "s_space = ift.RGSpace(N_pixels)\n",
+ "h_space = s_space.get_default_codomain()\n",
+ "HT = ift.HarmonicTransformOperator(h_space, target=s_space)\n",
+ "p_space = ift.PowerSpace(h_space)\n",
"\n",
"# Operators\n",
- "Sh = create_power_operator(h_space, power_spectrum=pow_spec)\n",
- "N = DiagonalOperator(s_space, diagonal=sigma2, bare=True)\n",
- "R = DiagonalOperator(s_space, diagonal=1.)\n",
- "D = PropagatorOperator(R=R, N=N, Sh=Sh)\n",
+ "Sh = ift.create_power_operator(h_space, power_spectrum=pow_spec)\n",
+ "R = HT #*ift.create_harmonic_smoothing_operator((h_space,), 0, 0.02)\n",
"\n",
"# Fields and data\n",
- "sh = Field(p_space, val=pow_spec).power_synthesize(real_signal=True)\n",
- "s = fft.adjoint_times(sh)\n",
- "n = Field.from_random(domain=s_space, random_type='normal',\n",
- " std=np.sqrt(sigma2), mean=0)\n",
- "d = R(s) + n\n",
- "j = R.adjoint_times(N.inverse_times(d))"
+ "sh = ift.power_synthesize(ift.PS_field(p_space, pow_spec),real_signal=True)\n",
+ "noiseless_data=R(sh)\n",
+ "signal_to_noise = 5\n",
+ "noise_amplitude = noiseless_data.std()/signal_to_noise\n",
+ "N = ift.ScalingOperator(noise_amplitude**2, s_space)\n",
+ "\n",
+ "n = ift.Field.from_random(domain=s_space, random_type='normal',\n",
+ " std=noise_amplitude, mean=0)\n",
+ "ift.plot(n)\n",
+ "d = noiseless_data + n\n",
+ "ift.plot(d)\n",
+ "j = R.adjoint_times(N.inverse_times(d))\n",
+ "ift.plot(HT(j))\n",
+ "D = PropagatorOperator(R=R, N=N, Sh=Sh)"
]
},
{
@@ -288,7 +266,6 @@
"cell_type": "code",
"execution_count": null,
"metadata": {
- "collapsed": true,
"slideshow": {
"slide_type": "-"
}
@@ -313,23 +290,22 @@
"cell_type": "code",
"execution_count": null,
"metadata": {
- "collapsed": true,
"slideshow": {
"slide_type": "-"
}
},
"outputs": [],
"source": [
- "s_power = sh.power_analyze()\n",
- "m_power = fft(m).power_analyze()\n",
- "s_power_data = s_power.val.get_full_data().real\n",
- "m_power_data = m_power.val.get_full_data().real\n",
+ "s_power = ift.power_analyze(sh)\n",
+ "m_power = ift.power_analyze(m)\n",
+ "s_power_data = s_power.val.real\n",
+ "m_power_data = m_power.val.real\n",
"\n",
"# Get signal data and reconstruction data\n",
- "s_data = s.val.get_full_data().real\n",
- "m_data = m.val.get_full_data().real\n",
+ "s_data = HT(sh).val.real\n",
+ "m_data = HT(m).val.real\n",
"\n",
- "d_data = d.val.get_full_data().real"
+ "d_data = d.val.real"
]
},
{
@@ -375,7 +351,7 @@
"plt.plot(s_data - s_data, 'k', label=\"Signal\", alpha=.5, linewidth=.5)\n",
"plt.plot(d_data - s_data, 'k+', label=\"Data\")\n",
"plt.plot(m_data - s_data, 'r', label=\"Reconstruction\")\n",
- "plt.axhspan(-np.sqrt(sigma2),np.sqrt(sigma2), facecolor='0.9', alpha=.5)\n",
+ "plt.axhspan(-noise_amplitude,noise_amplitude, facecolor='0.9', alpha=.5)\n",
"plt.title(\"Residuals\")\n",
"plt.legend()\n",
"plt.show()"
@@ -410,8 +386,8 @@
"plt.plot(xs, pow_spec(xs), label=\"True Power Spectrum\", linewidth=.7, color='k')\n",
"plt.plot(s_power_data, 'k', label=\"Signal\", alpha=.5, linewidth=.5)\n",
"plt.plot(m_power_data, 'r', label=\"Reconstruction\")\n",
- "plt.axhline(sigma2 / N_pixels, color=\"k\", linestyle='--', label=\"Noise level\", alpha=.5)\n",
- "plt.axhspan(sigma2 / N_pixels, ymin, facecolor='0.9', alpha=.5)\n",
+ "plt.axhline(noise_amplitude**2 / N_pixels, color=\"k\", linestyle='--', label=\"Noise level\", alpha=.5)\n",
+ "plt.axhspan(noise_amplitude**2 / N_pixels, ymin, facecolor='0.9', alpha=.5)\n",
"plt.title(\"Power Spectrum\")\n",
"plt.legend()\n",
"plt.show()"
@@ -432,7 +408,6 @@
"cell_type": "code",
"execution_count": null,
"metadata": {
- "collapsed": true,
"slideshow": {
"slide_type": "skip"
}
@@ -440,15 +415,15 @@
"outputs": [],
"source": [
"# Operators\n",
- "Sh = create_power_operator(h_space, power_spectrum=pow_spec)\n",
- "N = DiagonalOperator(s_space, diagonal=sigma2, bare=True)\n",
+ "Sh = ift.create_power_operator(h_space, power_spectrum=pow_spec)\n",
+ "N = ift.ScalingOperator(noise_amplitude**2,s_space)\n",
"# R is defined below\n",
"\n",
"# Fields\n",
- "sh = Field(p_space, val=pow_spec).power_synthesize(real_signal=True)\n",
- "s = fft.adjoint_times(sh)\n",
- "n = Field.from_random(domain=s_space, random_type='normal',\n",
- " std=np.sqrt(sigma2), mean=0)"
+ "sh = ift.power_synthesize(ift.PS_field(p_space,pow_spec),real_signal=True)\n",
+ "s = HT(sh)\n",
+ "n = ift.Field.from_random(domain=s_space, random_type='normal',\n",
+ " std=noise_amplitude, mean=0)"
]
},
{
@@ -466,7 +441,6 @@
"cell_type": "code",
"execution_count": null,
"metadata": {
- "collapsed": true,
"slideshow": {
"slide_type": "-"
}
@@ -474,22 +448,21 @@
"outputs": [],
"source": [
"l = int(N_pixels * 0.2)\n",
- "h = int(N_pixels * 0.2 * 4)\n",
+ "h = int(N_pixels * 0.2 * 2)\n",
"\n",
- "mask = Field(s_space, val=1)\n",
+ "mask = ift.Field(s_space, val=1)\n",
"mask.val[ l : h] = 0\n",
"\n",
- "R = DiagonalOperator(s_space, diagonal = mask)\n",
+ "R = ift.DiagonalOperator(mask)*HT\n",
"n.val[l:h] = 0\n",
"\n",
- "d = R(s) + n"
+ "d = R(sh) + n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
- "collapsed": true,
"slideshow": {
"slide_type": "skip"
}
@@ -516,17 +489,21 @@
"cell_type": "code",
"execution_count": null,
"metadata": {
- "collapsed": true
+ "scrolled": true
},
"outputs": [],
"source": [
- "class DiagonalProber(DiagonalProberMixin, Prober):\n",
- " def __init__(self, *args, **kwargs):\n",
- " super(DiagonalProber,self).__init__(*args, **kwargs)\n",
+ "sc = ift.probing.utils.StatCalculator()\n",
"\n",
- "diagProber = DiagonalProber(domain=s_space, probe_dtype=np.complex, probe_count=200)\n",
- "diagProber(D)\n",
- "m_var = Field(s_space,val=diagProber.diagonal.val).weight(-1)"
+ "IC = ift.GradientNormController(name=\"inverter\", iteration_limit=50000,\n",
+ " tol_abs_gradnorm=0.1)\n",
+ "inverter = ift.ConjugateGradient(controller=IC)\n",
+ "curv = ift.library.wiener_filter_curvature.WienerFilterCurvature(R,N,Sh,inverter)\n",
+ "\n",
+ "for i in range(200):\n",
+ " sc.add(HT(curv.generate_posterior_sample()))\n",
+ "\n",
+ "m_var = sc.var"
]
},
{
@@ -544,25 +521,24 @@
"cell_type": "code",
"execution_count": null,
"metadata": {
- "collapsed": true,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
- "s_power = sh.power_analyze()\n",
- "m_power = fft(m).power_analyze()\n",
- "s_power_data = s_power.val.get_full_data().real\n",
- "m_power_data = m_power.val.get_full_data().real\n",
+ "s_power = ift.power_analyze(sh)\n",
+ "m_power = ift.power_analyze(m)\n",
+ "s_power_data = s_power.val.real\n",
+ "m_power_data = m_power.val.real\n",
"\n",
"# Get signal data and reconstruction data\n",
- "s_data = s.val.get_full_data().real\n",
- "m_data = m.val.get_full_data().real\n",
- "m_var_data = m_var.val.get_full_data().real\n",
+ "s_data = s.val.real\n",
+ "m_data = HT(m).val.real\n",
+ "m_var_data = m_var.val.real\n",
"uncertainty = np.sqrt(np.abs(m_var_data))\n",
- "\n",
- "d_data = d.val.get_full_data().real\n",
+ "ift.plot(ift.sqrt(m_var))\n",
+ "d_data = d.val.real\n",
"\n",
"# Set lost data to NaN for proper plotting\n",
"d_data[d_data == 0] = np.nan"
@@ -646,9 +622,7 @@
{
"cell_type": "code",
"execution_count": null,
- "metadata": {
- "collapsed": true
- },
+ "metadata": {},
"outputs": [],
"source": [
"N_pixels = 256 # Number of pixels\n",
@@ -660,14 +634,13 @@
" return P0 * (1. + (k/k0)**2)**(- gamma / 2)\n",
"\n",
"\n",
- "s_space = RGSpace([N_pixels, N_pixels])"
+ "s_space = ift.RGSpace([N_pixels, N_pixels])"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
- "collapsed": true,
"slideshow": {
"slide_type": "skip"
}
@@ -857,21 +830,21 @@
"metadata": {
"celltoolbar": "Slideshow",
"kernelspec": {
- "display_name": "Python 3",
+ "display_name": "Python 2",
"language": "python",
- "name": "python3"
+ "name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
- "version": 3
+ "version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
- "pygments_lexer": "ipython3",
- "version": "3.6.4"
+ "pygments_lexer": "ipython2",
+ "version": "2.7.12"
}
},
"nbformat": 4,
--
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