Add unit tests for multiply_distributions()

tests/probability/test_multiply_distribution.py

@@ -0,0 +1,60 @@
+import numpy as np
+import scipy.stats
+
+import sdr
+
+
+def test_normal_normal():
+    X = scipy.stats.norm(loc=-1, scale=0.5)
+    Y = scipy.stats.norm(loc=2, scale=1.5)
+    _verify(X, Y)
+
+
+def test_rayleigh_rayleigh():
+    X = scipy.stats.rayleigh(scale=1)
+    Y = scipy.stats.rayleigh(loc=1, scale=2)
+    _verify(X, Y)
+
+
+def test_rician_rician():
+    X = scipy.stats.rice(2)
+    Y = scipy.stats.rice(3)
+    _verify(X, Y)
+
+
+def test_normal_rayleigh():
+    X = scipy.stats.norm(loc=-1, scale=0.5)
+    Y = scipy.stats.rayleigh(loc=2, scale=1.5)
+    _verify(X, Y)
+
+
+def test_rayleigh_rician():
+    X = scipy.stats.rayleigh(scale=1)
+    Y = scipy.stats.rice(3)
+    _verify(X, Y)
+
+
+def _verify(X, Y):
+    # Empirically compute the distribution
+    z = X.rvs(100_000) * Y.rvs(100_000)
+    hist, bins = np.histogram(z, bins=51, density=True)
+    x = bins[1:] - np.diff(bins) / 2
+
+    # Numerically compute the distribution, only do so over the histogram bins (for speed)
+    Z = sdr.multiply_distributions(X, Y, x)
+
+    if False:
+        import matplotlib.pyplot as plt
+
+        plt.figure()
+        plt.plot(x, X.pdf(x), label="X")
+        plt.plot(x, Y.pdf(x), label="Y")
+        plt.plot(x, Z.pdf(x), label="X * Y")
+        plt.hist(z, bins=101, cumulative=False, density=True, histtype="step", label="X * Y empirical")
+        plt.legend()
+        plt.xlabel("Random variable")
+        plt.ylabel("Probability density")
+        plt.title("Product of two distributions")
+        plt.show()
+
+    assert np.allclose(Z.pdf(x), hist, atol=np.max(hist) * 0.1)