add a notebook just for fun

docs/demo.ipynb

+%% Cell type:markdown id: tags:
+
+# NIFTy4 tutorial
+
+Import the necessary packages:
+
+%% Cell type:code id: tags:
+
+``` python
+# some voodoo to make the notebook run properly
+%matplotlib inline
+import nifty4 as ift
+import numpy as np
+```
+
+%% Cell type:markdown id: tags:
+
+Define a space for our data
+
+%% Cell type:code id: tags:
+
+``` python
+spc = ift.RGSpace(10)  # 1D Cartesian space, contains 10 points
+```
+
+%% Cell type:markdown id: tags:
+
+ask the space about its configuration:
+
+%% Cell type:code id: tags:
+
+``` python
+print(spc)
+```
+
+%% Cell type:markdown id: tags:
+
+Now, create a Field with Gaussian random numbers, living on that space
+
+%% Cell type:code id: tags:
+
+``` python
+fld = ift.Field.from_random("normal",spc)
+```
+
+%% Cell type:code id: tags:
+
+``` python
+ift.plot(fld)
+```
+
+%% Cell type:markdown id: tags:
+
+Now, let's do the same thing in two dimensions:
+
+%% Cell type:code id: tags:
+
+``` python
+spc = ift.RGSpace((10,10))
+fld = ift.Field.from_random("normal",spc)
+ift.plot(fld)
+```
+
+%% Cell type:markdown id: tags:
+
+Now, let's do some basic arithmetics with the field
+
+%% Cell type:code id: tags:
+
+``` python
+fld += 50
+fld *= -2
+ift.plot(fld)
+```
+
+%% Cell type:markdown id: tags:
+
+... and smooth it.
+
+%% Cell type:code id: tags:
+
+``` python
+smooth = ift.FFTSmoothingOperator(spc,sigma=0.1)
+fld_smooth = smooth(fld)
+ift.plot(fld_smooth)
+```
+
+%% Cell type:code id: tags:
+
+``` python
+    np.random.seed(43)
+    # Set up physical constants
+    # Total length of interval or volume the field lives on, e.g. in meters
+    L = 2.
+    # Typical distance over which the field is correlated (in same unit as L)
+    correlation_length = 0.1
+    # Variance of field in position space sqrt(<|s_x|^2>) (in unit of s)
+    field_variance = 2.
+    # Smoothing length of response (in same unit as L)
+    response_sigma = 0.1
+
+    # Define resolution (pixels per dimension)
+    N_pixels = 256
+
+    # Set up derived constants
+    k_0 = 1./correlation_length
+    # Note that field_variance**2 = a*k_0/4. for this analytic form of power
+    # spectrum
+    a = field_variance**2/k_0*4.
+    pow_spec = (lambda k: a / (1 + k/k_0) ** 4)
+    pixel_width = L/N_pixels
+
+    # Set up the geometry
+    s_space = ift.RGSpace([N_pixels, N_pixels], distances=pixel_width)
+    fft = ift.FFTOperator(s_space)
+    h_space = fft.target[0]
+    p_space = ift.PowerSpace(h_space)
+
+    # Create mock data
+
+    Sh = ift.create_power_operator(h_space, power_spectrum=pow_spec)
+
+    sp = ift.PS_field(p_space, pow_spec)
+    sh = ift.power_synthesize(sp, real_signal=True)
+    ss = fft.inverse_times(sh)
+
+    R = ift.FFTSmoothingOperator(s_space, sigma=response_sigma)
+
+    signal_to_noise = 1
+    diag = ift.Field(s_space, ss.var()/signal_to_noise).weight(1)
+    N = ift.DiagonalOperator(diag)
+    n = ift.Field.from_random(domain=s_space,
+                              random_type='normal',
+                              std=ss.std()/np.sqrt(signal_to_noise),
+                              mean=0)
+
+    d = R(ss) + n
+
+    # Wiener filter
+
+    j = R.adjoint_times(N.inverse_times(d))
+    IC = ift.GradientNormController(verbose=True, iteration_limit=500,
+                                    tol_abs_gradnorm=0.1)
+    inverter = ift.ConjugateGradient(controller=IC)
+    S_inv = fft.adjoint*Sh.inverse*fft
+    D = (R.adjoint*N.inverse*R + S_inv).inverse
+    # MR FIXME: we can/should provide a preconditioner here as well!
+    D = ift.InversionEnabler(D, inverter)
+    m = D(j)
+```
+
+%% Cell type:code id: tags:
+
+``` python
+ift.plot(m)
+```
+
+%% Cell type:code id: tags:
+
+``` python
+ift.plot(d)
+```
+
+%% Cell type:code id: tags:
+
+``` python
+ift.plot(ss)
+```
+
+%% Cell type:code id: tags:
+
+``` python
+```