Torsten asked me to incorporate a small Wiender Filter toy example incl. units...

Torsten asked me to incorporate a small Wiender Filter toy example incl. units and a proper distinction between data-space and signal space.

demos/wiener_filter_unit.py

+from nifty import *
+from mpi4py import MPI
+import plotly.offline as py
+import plotly.graph_objs as go
+
+
+comm = MPI.COMM_WORLD
+rank = comm.rank
+
+
+def plot_maps(x, name):
+
+    trace = [None]*len(x)
+
+    keys = x.keys()
+    field = x[keys[0]]
+    domain = field.domain[0]
+    shape = len(domain.shape)
+    max_n = domain.shape[0]*domain.distances[0]
+    step = domain.distances[0]
+    x_axis = np.arange(0, max_n, step)
+
+    if shape == 1:
+        for ii in xrange(len(x)):
+            trace[ii] = go.Scatter(x= x_axis, y=x[keys[ii]].val.get_full_data(), name=keys[ii])
+        fig = go.Figure(data=trace)
+
+        py.plot(fig, filename=name)
+
+    elif shape == 2:
+        for ii in xrange(len(x)):
+            py.plot([go.Heatmap(z=x[keys[ii]].val.get_full_data())], filename=keys[ii])
+    else:
+        raise TypeError("Only 1D and 2D field plots are supported")
+
+def plot_power(x, name):
+
+    layout = go.Layout(
+        xaxis=dict(
+            type='log',
+            autorange=True
+        ),
+        yaxis=dict(
+            type='log',
+            autorange=True
+        )
+    )
+
+    trace = [None]*len(x)
+
+    keys = x.keys()
+    field = x[keys[0]]
+    domain = field.domain[0]
+    x_axis = domain.kindex
+
+    for ii in xrange(len(x)):
+        trace[ii] = go.Scatter(x= x_axis, y=x[keys[ii]].val.get_full_data(), name=keys[ii])
+
+    fig = go.Figure(data=trace, layout=layout)
+    py.plot(fig, filename=name)
+
+np.random.seed(42)
+
+if __name__ == "__main__":
+
+    distribution_strategy = 'not'
+
+    # setting spaces
+    npix = np.array([500])  # number of pixels
+    total_volume = 1.  # total length
+
+    # setting signal parameters
+    lambda_s = .05  # signal correlation length
+    sigma_s = 10.  # signal variance
+
+
+    #setting response operator parameters
+    length_convolution = .025
+    exposure = 2000.
+
+
+
+    # calculating parameters
+    k_0 = 4. / (2 * np.pi * lambda_s)
+    a_s = sigma_s ** 2. * lambda_s * total_volume
+
+    # creation of spaces
+    x1 = RGSpace(npix, dtype=np.float64, distances=total_volume / npix,
+                 zerocenter=False)
+    k1 = RGRGTransformation.get_codomain(x1)
+    p1 = PowerSpace(harmonic_domain=k1, log=False, dtype=np.float64)
+
+    # creating Power Operator with given spectrum
+    spec = (lambda k: a_s / (1 + (k / k_0) ** 2) ** 2)
+    p_field = Field(p1, val=spec)
+    S_op = create_power_operator(k1, spec)
+
+    # creating FFT-Operator and Response-Operator with Gaussian convolution
+    Fft_op = FFTOperator(domain=x1, target=k1,
+                        domain_dtype=np.float64,
+                        target_dtype=np.complex128)
+    R_op = ResponseOperator(x1, sigma=length_convolution,
+                            exposure=exposure)
+
+    # drawing a random field
+    sk = p_field.power_synthesize(real_signal=True, mean=0.)
+    s = Fft_op.inverse_times(sk)
+
+    signal_to_noise = 1
+    N_op = DiagonalOperator(R_op.target, diagonal=s.var()/signal_to_noise, bare=True)
+    n = Field.from_random(domain=R_op.target,
+                          random_type='normal',
+                          std=s.std()/np.sqrt(signal_to_noise),
+                          mean=0)
+
+    d = R_op(s) + n
+
+    # Wiener filter
+    j = R_op.adjoint_times(N_op.inverse_times(d))
+    D = PropagatorOperator(S=S_op, N=N_op, R=R_op)
+
+    m = D(j)
+
+    z={}
+    z["signal"] = s
+    z["reconstructed_map"] = m
+    z["data"] = d
+    z["lambda"] = R_op(s)
+
+    plot_maps(z, "Wiener_filter.html")
+
+