adding expressions derived using complete instead of incomplete ellip…

…tic integrals
PlasmaControl · Feb 17, 2025 · 59da3fd · 59da3fd
1 parent 89cedb4
commit 59da3fd
Showing 1 changed file with 45 additions and 9 deletions.
diff --git a/tests/test_integrals.py b/tests/test_integrals.py
@@ -10,7 +10,7 @@
 from numpy.polynomial.legendre import leggauss
 from scipy import integrate
 from scipy.interpolate import CubicHermiteSpline
-from scipy.special import ellipe, ellipkm1
+from scipy.special import ellipe, ellipk, ellipkm1
 from tests.test_interp_utils import _f_1d, _f_1d_nyquist_freq, _f_2d, _f_2d_nyquist_freq
 from tests.test_plotting import tol_1d
 
@@ -995,14 +995,50 @@ def elliptic_incomplete(k2):
             E, TestBounceQuadrature._fixed_elliptic(E_integrand, k, 10)
         )
 
-        I_0 = 4 / k * K
-        I_1 = 4 * k * E
-        I_2 = 16 * k * E
-        I_3 = 16 * k / 9 * (2 * (-1 + 2 * k2) * E - (-1 + k2) * K)
-        I_4 = 16 * k / 3 * ((-1 + 2 * k2) * E - 2 * (-1 + k2) * K)
-        I_5 = 32 * k / 30 * (2 * (1 - k2 + k2**2) * E - (1 - 3 * k2 + 2 * k2**2) * K)
-        I_6 = 4 / k * (2 * k2 * E + (1 - 2 * k2) * K)
-        I_7 = 2 * k / 3 * ((-2 + 4 * k2) * E - 4 * (-1 + k2) * K)
+        E0 = ellipe(k2)
+        K0 = ellipk(k2)
+
+        I_00 = 4 / k * K  # Incomplete integral
+        I_0 = 4 * K0  # Complete integral
+
+        I_10 = 4 * k * E
+        I_1 = 4 * (E0 + (k2 - 1) * K0)
+
+        I_20 = 16 * k * E
+        I_2 = 16 * (E0 + (k2 - 1) * K0)
+
+        I_30 = 16 * k / 9 * (2 * (-1 + 2 * k2) * E - (-1 + k2) * K)
+        I_3 = 16 / 9 * (2 * (-1 + 2 * k2) * (E0 + (k2 - 1) * K0) - (-1 + k2) * k2 * K0)
+
+        I_40 = 16 * k / 3 * ((-1 + 2 * k2) * E - 2 * (-1 + k2) * K)
+        I_4 = 16 / 3 * ((-1 + 2 * k2) * E0 - (-1 + k2) * K0)
+
+        I_50 = 32 * k / 30 * (2 * (1 - k2 + k2**2) * E - (1 - 3 * k2 + 2 * k2**2) * K)
+        I_5 = (
+            32
+            / 30
+            * (
+                2 * (1 - k2 + k2**2) * (E0 + (k2 - 1) * K0)
+                - (1 - 3 * k2 + 2 * k2**2) * k2 * K0
+            )
+        )
+
+        I_60 = 4 / k * (2 * k2 * E + (1 - 2 * k2) * K)
+        I_6 = 4 * (2 * E0 - K0)
+
+        I_70 = 2 * k / 3 * ((-2 + 4 * k2) * E - 4 * (-1 + k2) * K)
+        I_7 = 4 / 3 * ((2 * k2 - 1) * E0 - (k2 - 1) * K0)
+
+        # Check if incomplete integral expressions match the complete integrals
+        np.testing.assert_allclose(I_0, I_00)
+        np.testing.assert_allclose(I_1, I_10)
+        np.testing.assert_allclose(I_2, I_20)
+        np.testing.assert_allclose(I_3, I_30)
+        np.testing.assert_allclose(I_4, I_40)
+        np.testing.assert_allclose(I_5, I_50)
+        np.testing.assert_allclose(I_6, I_60)
+        np.testing.assert_allclose(I_7, I_70)
+
         # Check for math mistakes.
         np.testing.assert_allclose(
             I_2,