Add Poisson demo

demos/getting_started_2.py

+import nifty5 as ift
+import sys
+import numpy as np
+import global_newton as gn
+from nifty5.library.nonlinearities import Exponential
+
+np.random.seed(42)
+
+N = 2
+Nsamples = 5
+
+s_space = ift.RGSpace(10024)
+h_space = s_space.get_default_codomain()
+
+domain = ift.MultiDomain.make({'xi': h_space})
+position = ift.from_random('normal', domain)
+HT = ift.HarmonicTransformOperator(h_space, s_space)
+
+def sqrtpspec(k):
+    return 16. / (20.+k**2)
+
+
+# Define amplitude model
+p_space = ift.PowerSpace(h_space)
+pd = ift.PowerDistributor(h_space, p_space)
+a = ift.PS_field(p_space, sqrtpspec)
+A = pd(a)
+
+# Define sky model
+xi = ift.Variable(position)['xi']
+logsky_h = xi * A
+logsky = HT(logsky_h)
+nonlin = Exponential()
+sky = ift.PointwiseExponential(logsky)
+R = ift.ScalingOperator(1., s_space)
+d_space = R.target[0]
+lamb = R(sky)
+
+# Generate mock data
+MOCK_POSITION = ift.from_random('normal', lamb.position.domain)
+data = np.random.poisson(lamb.at(MOCK_POSITION).value.val.astype(np.float64))
+data = ift.Field.from_local_data(d_space, data)
+
+# Define Hamiltonian
+position = ift.from_random('normal', lamb.position.domain)
+likelihood = ift.library.PoissonLogLikelihood(lamb, data)
+
+ic_cg = ift.GradientNormController(iteration_limit=50)
+ic_samps = ift.GradientNormController(iteration_limit=500, tol_abs_gradnorm=1e-4)
+
+ic_newton = ift.GradientNormController(name='Newton', tol_abs_gradnorm=1e-3)
+minimizer = ift.RelaxedNewton(ic_newton)
+
+H = gn.Hamiltonian(likelihood, ic_cg, ic_samps)
+
+for _ in range(N):
+    samples = [H.curvature.draw_sample(from_inverse=True)
+               for _ in range(Nsamples)]
+    sc_samplesky = ift.StatCalculator()
+    for s in samples:
+        sc_samplesky.add(sky.at(s+position).value)
+    ift.plot(sc_samplesky.mean, name='sample_mean.png')
+
+    KL = gn.SampledKullbachLeiblerDivergence(H, samples, ic_cg)
+    KL, convergence = minimizer(KL)
+    position = KL.position
+
+# Plot results
+E = KL
+l1 = lamb.at(E.position).value
+l2 = lamb.at(MOCK_POSITION).value
+ift.plot([data, l2, l1], name="poisson.png",
+         label=['Data', 'Mock signal', 'Reconstruction'],
+         alpha=[.5, 1, 1])
+if power_spectrum_estimation:
+    a_mock = a.at(MOCK_POSITION).value
+    a_recon = a.at(E.position).value
+else:
+    a_mock = a
+    a_recon = a
+ift.plot([a_mock**2, a_recon**2, ift.power_analyze(logsky_h.at(E.position).value)],
+         name='power_spectrum.png', label=['Mock', 'Reconstruction', 'power_analyze'])
+