Initial commit.

diff --git a/ddpol.py b/ddpol.py
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+#!/usr/bin/env python
+
+# Any copyright is dedicated to the Public Domain.
+# https://creativecommons.org/publicdomain/zero/1.0/
+
+# Written by Francois Fleuret <francois@fleuret.org>
+
+import math
+import matplotlib.pyplot as plt
+import torch
+
+######################################################################
+
+def compute_alpha(x, y, D, a = 0, b = 1, rho = 1e-11):
+    M = x.view(-1, 1) ** torch.arange(D + 1).view(1, -1)
+    B = y
+
+    if D+1 > 2:
+        q = torch.arange(2, D + 1).view( 1, -1).to(x.dtype)
+        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].pow(0.5))
+        B = torch.cat((B, y.new_zeros(Q.size(0))), 0)
+        M = torch.cat((M, math.sqrt(rho) * Q.t()), 0)
+
+    alpha = torch.lstsq(B, M).solution.view(-1)[:D+1]
+
+    return alpha
+
+######################################################################
+
+def phi(x):
+    return 4 * (x - 0.5) ** 2 * (x >= 0.5)
+
+######################################################################
+
+torch.manual_seed(0)
+
+nb_train_samples = 7
+D_max = 16
+nb_runs = 250
+
+mse_train = torch.zeros(nb_runs, D_max + 1)
+mse_test = torch.zeros(nb_runs, D_max + 1)
+
+for k in range(nb_runs):
+    x_train = torch.rand(nb_train_samples, dtype = torch.float64)
+    y_train = phi(x_train)
+    y_train = y_train + torch.empty(y_train.size(), dtype = y_train.dtype).normal_(0, 0.1)
+    x_test = torch.linspace(0, 1, 100, dtype = x_train.dtype)
+    y_test = phi(x_test)
+
+    for D in range(D_max + 1):
+        alpha = compute_alpha(x_train, y_train, D)
+        X_train = x_train.view(-1, 1) ** torch.arange(D + 1).view(1, -1)
+        X_test = x_test.view(-1, 1) ** torch.arange(D + 1).view(1, -1)
+        mse_train[k, D] = ((X_train @ alpha - y_train)**2).mean()
+        mse_test[k, D] = ((X_test @ alpha - y_test)**2).mean()
+
+mse_train = mse_train.median(0).values
+mse_test = mse_test.median(0).values
+
+######################################################################
+
+torch.manual_seed(4) # I picked that for pretty
+
+x_train = torch.rand(nb_train_samples, dtype = torch.float64)
+y_train = phi(x_train)
+y_train = y_train + torch.empty(y_train.size(), dtype = y_train.dtype).normal_(0, 0.1)
+x_test = torch.linspace(0, 1, 100, dtype = x_train.dtype)
+y_test = phi(x_test)
+
+for D in range(D_max + 1):
+    fig = plt.figure()
+
+    ax = fig.add_subplot(1, 1, 1)
+    ax.set_title(f'Degree {D}')
+    ax.set_ylim(-0.1, 1.1)
+    ax.plot(x_test, y_test, color = 'blue', label = 'Test values')
+    ax.scatter(x_train, y_train, color = 'blue', label = 'Training examples')
+
+    alpha = compute_alpha(x_train, y_train, D)
+    X_test = x_test.view(-1, 1) ** torch.arange(D + 1).view(1, -1)
+    ax.plot(x_test, X_test @ alpha, color = 'red', label = 'Fitted polynomial')
+
+    ax.legend(frameon = False)
+
+    fig.savefig(f'dd-example-{D:02d}.pdf', bbox_inches='tight')
+
+######################################################################
+
+fig = plt.figure()
+
+ax = fig.add_subplot(1, 1, 1)
+ax.set_yscale('log')
+ax.set_xlabel('Polynomial degree', labelpad = 10)
+ax.set_ylabel('MSE', labelpad = 10)
+
+ax.axvline(x = nb_train_samples - 1, color = 'gray', linewidth = 0.5)
+ax.plot(torch.arange(D_max + 1), mse_train, color = 'blue', label = 'Train error')
+ax.plot(torch.arange(D_max + 1), mse_test, color = 'red', label = 'Test error')
+
+ax.legend(frameon = False)
+
+fig.savefig('dd-mse.pdf', bbox_inches='tight')
+
+######################################################################