changed initial value for krylov sampling CG and changed demo to actually use...

changed initial value for krylov sampling CG and changed demo to actually use the krylov sampling method supplied by NIFTy

demos/krylov_sampling.py

@@ -30,46 +30,12 @@ d = R(s_x) + n
 
 R_p = R * FFT * A
 j = R_p.adjoint(N.inverse(d))
-D_inv = R_p.adjoint * N.inverse * R_p + S.inverse
-
-history = []
-
-
-def sample(D_inv, S, j,  N_samps, N_iter):
-    global history
-    space = D_inv.domain
-    x = ift.Field.zeros(space)
-    r = j.copy()
-    p = r.copy()
-    d = p.vdot(D_inv(p))
-    y = []
-    for i in range(N_samps):
-        y += [S.draw_sample()]
-    for k in range(1, 1 + N_iter):
-        history += [y[0].copy()]
-        gamma = r.vdot(r) / d
-        if gamma == 0.:
-            break
-        x += gamma * p
-        #print(p.vdot(D_inv(j)))
-        for i in range(N_samps):
-            y[i] -= p.vdot(D_inv(y[i])) * p / d
-            y[i] += np.random.randn() / np.sqrt(d) * p
-        print("variance iteration "+str(k)+":", np.sqrt(p.vdot(p)/d))
-        #r_new = j - D_inv(x)
-        r_new = r - gamma * D_inv(p)
-        beta = r_new.vdot(r_new) / (r.vdot(r))
-        r = r_new
-        p = r + beta * p
-        d = p.vdot(D_inv(p))
-        if d == 0.:
-            break
-    return x, y
+D_inv = ift.SandwichOperator(R_p, N.inverse) + S.inverse
 
 
 N_samps = 200
 N_iter = 10
-m, samps = sample(D_inv, S, j, N_samps, N_iter)
+m, samps = ift.library.generate_krylov_samples(D_inv, S, j, N_samps, N_iter)
 m_x = sky(m)
 IC = ift.GradientNormController(iteration_limit=N_iter)
 inverter = ift.ConjugateGradient(IC)
@@ -117,9 +83,3 @@ plt.legend()
 plt.savefig('Krylov_uncertainty.png')
 plt.close()
 
-for i in range(min(6, len(history))):
-    plt.plot(sky(history[i]).val, label="step " + str(i+1))
-plt.plot(s_x.val-m_x.val, 'k-', label="residual")
-plt.legend()
-plt.savefig('iterations.png')
-plt.close()

nifty4/library/krylov_sampling.py

@@ -32,7 +32,7 @@ def generate_krylov_samples(D_inv, S, j=None,  N_samps=1, N_iter=10,
     ----------
     D_inv : EndomorphicOperator
         The curvature which will be the inverse of the covarianc
-        of the generated samples
+        of the generated samples 
     S : EndomorphicOperator (from which one can sample)
         A prior covariance operator which is used to generate prior
         samples that are then iteratively updated
@@ -54,7 +54,7 @@ def generate_krylov_samples(D_inv, S, j=None,  N_samps=1, N_iter=10,
         and the second entry are a list of samples from D_inv.inverse
     """
     j = S.draw_sample(from_inverse=True) if j is None else j
-    x = S.draw_sample()
+    x = j*0
     r = j.copy()
     p = r.copy()
     d = p.vdot(D_inv(p))