Kernel tests

localreg/localreg.py

@@ -64,13 +64,13 @@ def biweight(t):
 def triweight(t):
     res = np.zeros_like(t)
     ind = np.where(np.abs(t)<=1)
-    res[ind] = (35/32)*(1-t[ind]**2)**2
+    res[ind] = (35/32)*(1-t[ind]**2)**3
     return res
 
 def tricube(t):
     res = np.zeros_like(t)
     ind = np.where(np.abs(t)<=1)
-    res[ind] = (1-np.abs(t[ind])**3)**3
+    res[ind] = (70/81)*(1-np.abs(t[ind])**3)**3
     return res
 
 def gaussian(t):

test/test_localreg.py

@@ -18,7 +18,90 @@
 """
 
 from localreg import *
+import numpy as np
 import pytest
 
-def test_dummy():
-    return True
+#
+# PARAMETRIC KERNEL TESTS
+#
+
+all_kernels = [rectangular
+              ,triangular
+              ,epanechnikov
+              ,biweight
+              ,triweight
+              ,tricube
+              ,gaussian
+              ,cosine
+              ,logistic
+              ,sigmoid
+              ,silverman]
+
+@pytest.mark.parametrize("kernel", [k for k in all_kernels if k!=silverman])
+def test_nonnegative(kernel):
+    t = np.linspace(-5, 5, 100)
+    assert np.all(kernel(t)>=0)
+
+@pytest.mark.parametrize("kernel", all_kernels)
+def test_symmetry(kernel):
+    t = np.linspace(-5, 5, 100)
+    assert np.allclose(kernel(t), kernel(-t))
+
+@pytest.mark.parametrize("kernel", all_kernels)
+def test_normalized(kernel):
+    t = np.linspace(-20, 20, 5000)
+    dt = t[1]-t[0]
+    int = np.sum(kernel(t))*dt
+    assert int == pytest.approx(1, 1e-3)
+
+#
+# SIMPLE KERNEL TESTS
+#
+
+@pytest.fixture
+def t():
+    return np.array([-1.5, -1, -0.5, 0, 0.5, 1, 1.5])
+
+def test_rectangular(t):
+    assert np.allclose(rectangular(t),
+                       np.array([0, 0.5, 0.5, 0.5, 0.5, 0.5, 0]))
+
+def test_triangular(t):
+    assert np.allclose(triangular(t),
+                       np.array([0, 0, 0.5, 1, 0.5, 0, 0]))
+
+def test_epanechnikov(t):
+    assert np.allclose(epanechnikov(t),
+                       0.75*np.array([0, 0, 0.75, 1, 0.75, 0, 0]))
+
+def test_biweight(t):
+    assert np.allclose(biweight(t),
+                       (15/16)*np.array([0, 0, 0.75**2, 1, 0.75**2, 0, 0]))
+
+def test_triweight(t):
+    assert np.allclose(triweight(t),
+                       (35/32)*np.array([0, 0, 0.75**3, 1, 0.75**3, 0, 0]))
+
+def test_tricube(t):
+    assert np.allclose(tricube(t),
+                       (70/81)*np.array([0, 0, 0.875**3, 1, 0.875**3, 0, 0]))
+
+def test_gaussian(t):
+    assert np.allclose(gaussian(t),
+                       (1/np.sqrt(2*np.pi))*np.array([np.exp(-1.125), np.exp(-0.5), np.exp(-0.125), 1, np.exp(-0.125), np.exp(-0.5), np.exp(-1.125)]))
+
+def test_cosine(t):
+    assert np.allclose(cosine(t),
+                       (np.pi/4)*np.array([0, 0, np.sqrt(2)/2, 1, np.sqrt(2)/2, 0, 0]))
+
+def test_logistic(t):
+    assert np.allclose(logistic(t),
+                       np.array([0.149146, 0.196612, 0.235004, 0.25, 0.235004, 0.196612, 0.149146]))
+
+def test_sigmoid(t):
+    assert np.allclose(sigmoid(t),
+                       (2/np.pi)*np.array([0.212548, 0.324027, 0.443409, 0.5, 0.443409, 0.324027, 0.212548]))
+
+def test_silverman(t):
+    assert np.allclose(silverman(t),
+                       0.5*np.array([0.333193, 0.491558, 0.637724, np.sqrt(2)/2, 0.637724, 0.491558, 0.333193]))