add einstein tests

Author: bobmyhill

tests/test_einstein.py

@@ -0,0 +1,38 @@
+import unittest
+from util import BurnManTest
+
+from burnman.eos import einstein
+
+
+class Einstein(BurnManTest):
+    def test_theta_derivatives(self):
+        T = 300.0
+        debye_T = 1100.0
+        n = 2.0
+
+        # Numerical derivatives
+        delta = 1e-6
+        dF_dTheta_num = (
+            einstein.helmholtz_energy(T, debye_T + delta, n)
+            - einstein.helmholtz_energy(T, debye_T - delta, n)
+        ) / (2 * delta)
+        d2F_dTheta2_num = (
+            einstein.dhelmholtz_dTheta(T, debye_T + delta, n)
+            - einstein.dhelmholtz_dTheta(T, debye_T - delta, n)
+        ) / (2 * delta)
+        dS_dTheta_num = (
+            einstein.entropy(T, debye_T + delta, n)
+            - einstein.entropy(T, debye_T - delta, n)
+        ) / (2 * delta)
+
+        # Analytical derivatives
+        dF_dTheta_analytical = einstein.dhelmholtz_dTheta(T, debye_T, n)
+        d2F_dTheta2_analytical = einstein.d2helmholtz_dTheta2(T, debye_T, n)
+        dS_dTheta_analytical = einstein.dentropy_dTheta(T, debye_T, n)
+        self.assertFloatEqual(dF_dTheta_num, dF_dTheta_analytical)
+        self.assertFloatEqual(d2F_dTheta2_num, d2F_dTheta2_analytical)
+        self.assertFloatEqual(dS_dTheta_num, dS_dTheta_analytical)
+
+
+if __name__ == "__main__":
+    unittest.main()