Commit b9909ca9 by Martin Reinecke

add a notebook just for fun

parent 3d4b1b18
Pipeline #23919 passed with stage
in 4 minutes and 42 seconds
docs/demo.ipynb 0 → 100644
 %% 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 ```
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