X-Git-Url: https://www.fleuret.org/cgi-bin/gitweb/gitweb.cgi?a=blobdiff_plain;f=ddpol.py;h=645f47cfee373e9cb51d12cc5637021469c0d549;hb=47525ec795faca1ab72aee13956a553d070c81b7;hp=9d14d2ad7d5ad75b979e16477e5047f9e690276e;hpb=fbc0246e209dd03b9c9865904039b565d7fa9f96;p=pytorch.git

diff --git a/ddpol.py b/ddpol.py
index 9d14d2a..645f47c 100755
--- a/ddpol.py
+++ b/ddpol.py
@@ -50,15 +50,18 @@ def fit_alpha(x, y, D, a = 0, b = 1, rho = 1e-12):
         r = q.view(-1,  1)
         beta = x.new_zeros(D + 1, D + 1)
         beta[2:, 2:] = (q-1) * q * (r-1) * r * (b**(q+r-3) - a**(q+r-3))/(q+r-3)
-        l, U = beta.eig(eigenvectors = True)
-        Q = U @ torch.diag(l[:, 0].clamp(min = 0) ** 0.5) # clamp deals with ~0 negative values
+        W = torch.linalg.eig(beta)
+        l, U = W.eigenvalues.real, W.eigenvectors.real
+        Q = U @ torch.diag(l.clamp(min = 0) ** 0.5) # clamp deals with ~0 negative values
         B = torch.cat((B, y.new_zeros(Q.size(0))), 0)
         M = torch.cat((M, math.sqrt(rho) * Q.t()), 0)
 
-    return torch.lstsq(B, M).solution[:D+1, 0]
+    return torch.linalg.lstsq(M, B).solution[:D+1]
 
 ######################################################################
 
+# The "ground truth"
+
 def phi(x):
     return torch.abs(torch.abs(x - 0.4) - 0.2) + x/2 - 0.1
 
@@ -97,7 +100,7 @@ ax.set_ylabel('MSE', labelpad = 10)
 ax.axvline(x = args.nb_train_samples - 1,
            color = 'gray', linewidth = 0.5, linestyle = '--')
 
-ax.text(args.nb_train_samples - 1.2, 1e-4, 'Nb. params = nb. samples',
+ax.text(args.nb_train_samples - 1.2, 1e-4, 'nb. params = nb. samples',
         fontsize = 10, color = 'gray',
         rotation = 90, rotation_mode='anchor')
 
@@ -111,6 +114,33 @@ fig.savefig('dd-mse.pdf', bbox_inches='tight')
 
 plt.close(fig)
 
+######################################################################
+# Plot multiple MSE vs. degree curves
+
+fig = plt.figure()
+
+ax = fig.add_subplot(1, 1, 1)
+ax.set_yscale('log')
+ax.set_ylim(1e-5, 1)
+ax.set_xlabel('Polynomial degree', labelpad = 10)
+ax.set_ylabel('MSE', labelpad = 10)
+
+nb_train_samples_min = args.nb_train_samples - 4
+nb_train_samples_max = args.nb_train_samples
+
+for nb_train_samples in range(nb_train_samples_min, nb_train_samples_max + 1, 2):
+    mse_train, mse_test = compute_mse(nb_train_samples)
+    e = float(nb_train_samples - nb_train_samples_min) / float(nb_train_samples_max - nb_train_samples_min)
+    e = 0.15 + 0.7 * e
+    ax.plot(torch.arange(args.D_max + 1), mse_train, color = (e, e, 1.0), label = f'Train N={nb_train_samples}')
+    ax.plot(torch.arange(args.D_max + 1), mse_test, color = (1.0, e, e), label = f'Test N={nb_train_samples}')
+
+ax.legend(frameon = False)
+
+fig.savefig('dd-multi-mse.pdf', bbox_inches='tight')
+
+plt.close(fig)
+
 ######################################################################
 # Plot some examples of train / test