Adding a test for inner

tests/test_inner.py

@@ -0,0 +1,162 @@
+import pytest
+import sympy as sp
+import jax.numpy as jnp
+from jaxfun.Legendre import Legendre
+from jaxfun.Chebyshev import Chebyshev
+from jaxfun.arguments import TestFunction, TrialFunction
+from jaxfun.composite import Composite
+from jaxfun.utils.common import ulp
+from jaxfun.inner import inner
+
+x = sp.Symbol("x")
+
+
+@pytest.mark.parametrize("space", (Legendre, Chebyshev))
+def test_inner(space) -> None:
+    N = 10
+    V = space(N)
+    u = TrialFunction(x, V)
+    v = TestFunction(x, V)
+    M = inner(v * u, sparse=True, sparse_tol=1000)
+    M0 = V.mass_matrix()
+    assert jnp.allclose(M.data, M0.data)
+    M = inner(x * v * u, sparse=True)
+    answer = {  # data from shenfun
+        "Chebyshev": jnp.array(
+            [
+                1.570796326794896,
+                0.785398163397448,
+                0.785398163397448,
+                0.785398163397448,
+                0.785398163397448,
+                0.785398163397448,
+                0.785398163397448,
+                0.785398163397448,
+                0.785398163397448,
+                0.785398163397448,
+            ]
+        ),
+        "Legendre": jnp.array(
+            [
+                0.6666666666666666,
+                0.2666666666666666,
+                0.1714285714285713,
+                0.126984126984127,
+                0.101010101010101,
+                0.0839160839160839,
+                0.0717948717948718,
+                0.0627450980392157,
+                0.0557275541795665,
+                0.050125313283208,
+            ]
+        ),
+    }[space.__name__]
+    assert jnp.allclose(M.todense().diagonal(1), answer)
+    assert jnp.allclose(M.todense().diagonal(-1), answer)
+    M = inner(x * v * u + sp.diff(u, x) * v, sparse=True)
+
+    N = 10
+    C = Composite(space, N, {"left": {"D": 0}, "right": {"D": 0}})
+    u = TrialFunction(x, C)
+    v = TestFunction(x, C)
+    M = inner(x * v * u + sp.diff(u, x) * v, sparse=False)
+    answer = {
+        "Chebyshev": {
+            -3: jnp.array(
+                [
+                    -0.7853981633974483,
+                    -0.7853981633974483,
+                    -0.7853981633974483,
+                    -0.7853981633974483,
+                    -0.7853981633974483,
+                    -0.7853981633974483,
+                ]
+            ),
+            -1: jnp.array(
+                [
+                    -4.71238898038469,
+                    -8.63937979737193,
+                    -11.780972450961723,
+                    -14.922565104551516,
+                    -18.06415775814131,
+                    -21.205750411731103,
+                    -24.347343065320896,
+                    -27.48893571891069,
+                ]
+            ),
+            1: jnp.array(
+                [
+                    4.71238898038469,
+                    7.0685834705770345,
+                    10.210176124166829,
+                    13.351768777756622,
+                    16.493361431346415,
+                    19.634954084936208,
+                    22.776546738526,
+                    25.918139392115794,
+                ]
+            ),
+            3: jnp.array(
+                [
+                    -0.7853981633974483,
+                    -0.7853981633974483,
+                    -0.7853981633974483,
+                    -0.7853981633974483,
+                    -0.7853981633974483,
+                    -0.7853981633974483,
+                ]
+            ),
+        },
+        "Legendre": {
+            -3: jnp.array(
+                [
+                    -0.1714285714285714,
+                    -0.126984126984127,
+                    -0.101010101010101,
+                    -0.0839160839160839,
+                    -0.0717948717948718,
+                    -0.0627450980392157,
+                ]
+            ),
+            -1: jnp.array(
+                [
+                    -1.4285714285714286,
+                    -1.7777777777777777,
+                    -1.8545454545454545,
+                    -1.89010989010989,
+                    -1.9111111111111112,
+                    -1.9251336898395721,
+                    -1.9352226720647774,
+                    -1.9428571428571428,
+                ]
+            ),
+            1: jnp.array(
+                [
+                    2.571428571428571,
+                    2.2222222222222223,
+                    2.1454545454545455,
+                    2.10989010989011,
+                    2.088888888888889,
+                    2.0748663101604277,
+                    2.064777327935223,
+                    2.057142857142857,
+                ]
+            ),
+            3: jnp.array(
+                [
+                    -0.1714285714285714,
+                    -0.126984126984127,
+                    -0.101010101010101,
+                    -0.0839160839160839,
+                    -0.0717948717948718,
+                    -0.0627450980392157,
+                ]
+            ),
+        },
+    }[space.__name__]
+    for d in (-3, -1, 1, 3):
+        assert jnp.allclose(M.diagonal(d), answer[d], atol=1000 * ulp(1.0))
+
+
+if __name__ == "__main__":
+    test_inner(Chebyshev)