loss function changes

Development/Random Testing/loss func integral/loss_integral.py

@@ -0,0 +1,34 @@
+# This file is part of Frhodo. Copyright © 2020, UChicago Argonne, LLC
+# and licensed under BSD-3-Clause. See License.txt in the top-level 
+# directory for license and copyright information.
+
+import numpy as np
+from scipy import integrate      # used to integrate weights numerically
+
+def generalized_loss_fcn(x, mu=0, a=2, c=1):    # defaults to L2 loss
+    x_c_2 = ((x-mu)/c)**2
+
+    if a == 1:          # generalized function reproduces
+        loss = (x_c_2 + 1)**(0.5) - 1
+    if a == 2:
+        loss = 0.5*x_c_2
+    elif a == 0:
+        loss = np.log(0.5*x_c_2+1)
+    elif a == -2:       # generalized function reproduces
+        loss = 2*x_c_2/(x_c_2 + 4)
+    elif a <= -1000:    # supposed to be negative infinity
+        loss = 1 - np.exp(-0.5*x_c_2)
+    else:
+        loss = np.abs(a-2)/a*((x_c_2/np.abs(a-2) + 1)**(a/2) - 1)
+
+    return loss*c**a + mu  # multiplying by c^2 is not necessary, but makes order appropriate
+
+alpha_vec = np.geomspace(-60, -1, 1000)
+alpha_vec = np.concatenate([alpha_vec, np.linspace(-1,2, int(3/(alpha_vec[-1] - alpha_vec[-2])-1))[1:]])
+tau = 100
+for alpha in alpha_vec:
+    for c in np.geomspace(1, 5, 100):
+        int_func = lambda x: np.exp(-generalized_loss_fcn(x, a=alpha, c=c))
+        val, err = integrate.quadrature(int_func, -tau, tau, tol=1E-14, maxiter=10000)
+        print(f'{alpha:0.3f} {c:0.3f} {val:0.14e}')
+