Added demos from paper.

demos/paper_demos/cartesian_wiener_filter.py

+# -*- coding: utf-8 -*-
+
+import numpy as np
+import nifty as ift
+
+from keepers import Repository
+
+if __name__ == "__main__":
+
+    signal_to_noise = 1.5 # The signal to noise ratioa
+
+
+    # Setting up parameters    |\label{code:wf_parameters}|
+    correlation_length_1 = 1. # Typical distance over which the field is correlated
+    field_variance_1 = 2. # Variance of field in position space
+
+    response_sigma_1 = 0.05 # Smoothing length of response (in same unit as L)
+
+    def power_spectrum_1(k): # note: field_variance**2 = a*k_0/4.
+        a = 4 * correlation_length_1 * field_variance_1**2
+        return a / (1 + k * correlation_length_1) ** 4.
+
+    # Setting up the geometry |\label{code:wf_geometry}|
+    L_1 = 2. # Total side-length of the domain
+    N_pixels_1 = 512 # Grid resolution (pixels per axis)
+
+    signal_space_1 = ift.RGSpace([N_pixels_1], distances=L_1/N_pixels_1)
+    harmonic_space_1 = ift.FFTOperator.get_default_codomain(signal_space_1)
+    fft_1 = ift.FFTOperator(harmonic_space_1, target=signal_space_1,
+                            domain_dtype=np.complex, target_dtype=np.complex)
+    power_space_1 = ift.PowerSpace(harmonic_space_1, distribution_strategy='fftw')
+
+    mock_power_1 = ift.Field(power_space_1, val=power_spectrum_1,
+                             distribution_strategy='not')
+
+
+
+    # Setting up parameters    |\label{code:wf_parameters}|
+    correlation_length_2 = 1. # Typical distance over which the field is correlated
+    field_variance_2 = 2. # Variance of field in position space
+
+    response_sigma_2 = 0.01 # Smoothing length of response (in same unit as L)
+
+    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
+
+    # Setting up the geometry |\label{code:wf_geometry}|
+    L_2 = 2. # Total side-length of the domain
+    N_pixels_2 = 512 # Grid resolution (pixels per axis)
+
+    signal_space_2 = ift.RGSpace([N_pixels_2], distances=L_2/N_pixels_2)
+    harmonic_space_2 = ift.FFTOperator.get_default_codomain(signal_space_2)
+    fft_2 = ift.FFTOperator(harmonic_space_2, target=signal_space_2,
+                            domain_dtype=np.complex, target_dtype=np.complex)
+    power_space_2 = PowerSpace(harmonic_space_2, distribution_strategy='not')
+
+    mock_power_2 = ift.Field(power_space_2, val=power_spectrum_2,
+                         distribution_strategy='not')
+
+    fft = ift.ComposedOperator((fft_1, fft_2))
+
+    mock_power = ift.Field(domain=(power_space_1, power_space_2),
+                           val=np.outer(mock_power_1.val.get_full_data(),
+                                        mock_power_2.val.get_full_data()),
+                                        distribution_strategy='not')
+
+    diagonal = mock_power.power_synthesize(spaces=(0, 1), mean=1, std=0,
+                                           real_signal=False,
+                                           distribution_strategy='fftw')**2
+
+    S = ift.DiagonalOperator(domain=(harmonic_space_1, harmonic_space_2),
+                             diagonal=diagonal)
+
+
+    np.random.seed(10)
+    mock_signal = fft(mock_power.power_synthesize(real_signal=True,
+                                                  distribution_strategy='fftw'))
+
+    # Setting up a exemplary response
+    N1_10 = int(N_pixels_1/10)
+    mask_1 = ift.Field(signal_space_1, val=1., distribution_strategy='fftw')
+    mask_1.val[N1_10*7:N1_10*9] = 0.
+
+    N2_10 = int(N_pixels_2/10)
+    mask_2 = ift.Field(signal_space_2, val=1., distribution_strategy='not')
+    mask_2.val[N2_10*7:N2_10*9] = 0.
+
+    R = ift.ResponseOperator((signal_space_1, signal_space_2),
+                             sigma=(response_sigma_1, response_sigma_2),
+                             exposure=(mask_1, mask_2)) #|\label{code:wf_response}|
+    data_domain = R.target
+    R_harmonic = ComposedOperator([fft, R], default_spaces=(0, 1, 0, 1))
+
+    # Setting up the noise covariance and drawing a random noise realization
+    N = ift.DiagonalOperator(data_domain, diagonal=mock_signal.var()/signal_to_noise,
+                             bare=True,
+                             distribution_strategy='fftw')
+    noise = ift.Field.from_random(domain=data_domain, random_type='normal',
+                                  std=mock_signal.std()/np.sqrt(signal_to_noise),
+                                  mean=0,
+                                  distribution_strategy='fftw')
+    data = R(mock_signal) + noise #|\label{code:wf_mock_data}|
+
+    # Wiener filter
+    j = R_harmonic.adjoint_times(N.inverse_times(data))
+    wiener_curvature = ift.library.WienerFilterCurvature(S=S, N=N, R=R_harmonic)
+    wiener_curvature._InvertibleOperatorMixin__inverter.convergence_tolerance = 1e-3
+
+    m_k = wiener_curvature.inverse_times(j) #|\label{code:wf_wiener_filter}|
+    m = fft(m_k)
+
+    # Probing the variance
+    class Proby(ift.DiagonalProberMixin, ift.Prober): pass
+    proby = Proby((signal_space_1, signal_space_2), probe_count=100)
+    proby(lambda z: fft(wiener_curvature.inverse_times(fft.inverse_times(z))))
+#    sm = SmoothingOperator(signal_space, sigma=0.02)
+#    variance = sm(proby.diagonal.weight(-1))
+    variance = proby.diagonal.weight(-1)
+
+    repo = Repository('repo_100.h5')
+    repo.add(mock_signal, 'mock_signal')
+    repo.add(data, 'data')
+    repo.add(m, 'm')
+    repo.add(variance, 'variance')
+    repo.commit()
+
+    plot_space = ift.RGSpace((N_pixels_1, N_pixels_2))
+    plotter = ift.plotting.RG2DPlotter(color_map=plotting.colormaps.PlankCmap())
+    plotter.figure.xaxis = ift.plotting.Axis(label='Pixel Index')
+    plotter.figure.yaxis = ift.plotting.Axis(label='Pixel Index')
+
+    plotter.plot.zmin = 0.
+    plotter.plot.zmax = 3.
+    sm = ift.SmoothingOperator(plot_space, sigma=0.03)
+    plotter(ift.log(sqrt(sm(ift.Field(plot_space, val=variance.val.real)))), path='uncertainty.html')
+
+    plotter.plot.zmin = np.real(mock_signal.min());
+    plotter.plot.zmax = np.real(mock_signal.max());
+    plotter(ift.Field(plot_space, val=mock_signal.val.real), path='mock_signal.html')
+    plotter(ift.Field(plot_space, val=data.val.get_full_data().real), path = 'data.html')
+    plotter(ift.Field(plot_space, val=m.val.real), path = 'map.html')
+

demos/paper_demos/wiener_filter.py

+# -*- coding: utf-8 -*-
+
+import nifty as ift
+import numpy as np
+from keepers import Repository
+
+
+if __name__ == "__main__":
+    ift.nifty_configuration['default_distribution_strategy'] = 'fftw'
+
+    # Setting up parameters    |\label{code:wf_parameters}|
+    correlation_length_scale = 1.  # Typical distance over which the field is correlated
+    fluctuation_scale = 2.         # Variance of field in position space
+    response_sigma = 0.05          # Smoothing length of response (in same unit as L)
+    signal_to_noise = 1.5          # The signal to noise ratio
+    np.random.seed(43)             # Fixing the random seed
+    def power_spectrum(k):         # Defining the power spectrum
+        a = 4 * correlation_length_scale * fluctuation_scale**2
+        return a / (1 + (k * correlation_length_scale)**2) ** 2
+
+    # Setting up the geometry |\label{code:wf_geometry}|
+    L = 2.  # Total side-length of the domain
+    N_pixels = 512  # Grid resolution (pixels per axis)
+    signal_space = ift.RGSpace([N_pixels, N_pixels], distances=L/N_pixels)
+    harmonic_space = ift.FFTOperator.get_default_codomain(signal_space)
+    fft = ift.FFTOperator(harmonic_space, target=signal_space, target_dtype=np.float)
+    power_space = ift.PowerSpace(harmonic_space)
+
+    # Creating the mock signal |\label{code:wf_mock_signal}|
+    S = ift.create_power_operator(harmonic_space, power_spectrum=power_spectrum)
+    mock_power = ift.Field(power_space, val=power_spectrum)
+    mock_signal = fft(mock_power.power_synthesize(real_signal=True))
+
+    # Setting up an exemplary response
+    mask = ift.Field(signal_space, val=1.)
+    N10 = int(N_pixels/10)
+    mask.val[N10*5:N10*9, N10*5:N10*9] = 0.
+    R = ift.ResponseOperator(signal_space, sigma=(response_sigma,), exposure=(mask,))  #|\label{code:wf_response}|
+    data_domain = R.target[0]
+    R_harmonic = ift.ComposedOperator([fft, R], default_spaces=[0, 0])
+
+    # Setting up the noise covariance and drawing a random noise realization
+    N = ift.DiagonalOperator(data_domain, diagonal=mock_signal.var()/signal_to_noise, bare=True)
+    noise = ift.Field.from_random(domain=data_domain, random_type='normal',
+                                  std=mock_signal.std()/np.sqrt(signal_to_noise), mean=0)
+    data = R(mock_signal) + noise  #|\label{code:wf_mock_data}|
+
+    # Wiener filter
+    j = R_harmonic.adjoint_times(N.inverse_times(data))
+    wiener_curvature = ift.library.WienerFilterCurvature(S=S, N=N, R=R_harmonic)
+    m_k = wiener_curvature.inverse_times(j)  #|\label{code:wf_wiener_filter}|
+    m = fft(m_k)
+
+    # Probing the uncertainty |\label{code:wf_uncertainty_probing}|
+    class Proby(ift.DiagonalProberMixin, ift.Prober): pass
+    proby = Proby(signal_space, probe_count=800)
+    proby(lambda z: fft(wiener_curvature.inverse_times(fft.inverse_times(z))))  #|\label{code:wf_variance_fft_wrap}|
+
+    sm = ift.SmoothingOperator(signal_space, sigma=0.03)
+    variance = ift.sqrt(sm(proby.diagonal.weight(-1)))  #|\label{code:wf_variance_weighting}|
+
+    repo = Repository('repo_800.h5')
+    repo.add(mock_signal, 'mock_signal')
+    repo.add(data, 'data')
+    repo.add(m, 'm')
+    repo.add(variance, 'variance')
+    repo.commit()
+
+    # Plotting #|\label{code:wf_plotting}|
+    plotter = ift.plotting.RG2DPlotter(color_map=plotting.colormaps.PlankCmap())
+    plotter.figure.xaxis = ift.plotting.Axis(label='Pixel Index')
+    plotter.figure.yaxis = ift.plotting.Axis(label='Pixel Index')
+    plotter.plot.zmax = variance.max(); plotter.plot.zmin = 0
+    plotter(variance, path = 'uncertainty.html')
+    plotter.plot.zmax = mock_signal.max(); plotter.plot.zmin = mock_signal.min()
+    plotter(mock_signal, path='mock_signal.html')
+    plotter(ift.Field(signal_space, val=data.val), path='data.html')
+    plotter(m, path='map.html')