Update test_eigensolver.py

Added docstrings, added a line to make sure compared values are sorted

Author: yianzeng

tests/regression/test_eigensolver.py

@@ -8,8 +8,10 @@
 
 cwd = abspath(dirname(__file__))
 
-
-def poisson_1d(n, quadrilateral=False, degree=1, mesh=None):
+def evals(n, quadrilateral=False, degree=1, mesh=None):
+    '''We base this test on the 1D Poisson problem with Dirichlet boundary conditions,
+    outlined in part 1 of Daniele Boffi's 'Finite element approximation
+    of eigenvalue problems' Acta Numerica 2010'''
     # Create mesh and define function space
     if mesh is None:
         mesh = IntervalMesh(n, 0, pi)
@@ -26,7 +28,6 @@ def poisson_1d(n, quadrilateral=False, degree=1, mesh=None):
     # Create corresponding eigensolver, looking for n eigenvalues
     eigensolver = LinearEigensolver(eigenprob, n)
     ncov = eigensolver.solve()
-    print(ncov)
 
     # boffi solns 
     h = pi /n
@@ -38,64 +39,13 @@ def poisson_1d(n, quadrilateral=False, degree=1, mesh=None):
         true_values[k] = true_val
 
         estimates[k] = 1/eigensolver.eigenvalue(k).real # takes real part 
-    return true_values, estimates
-
-@pytest.mark.parametrize(('n', 'quadrilateral', 'degree', 'tolerance'),
-                         [(5, False, 1, 1e-14),
-                          (10, False, 1, 1e-14),
-                          (20, False, 1, 1e-14),
-                          (30, False, 1, 1e-14)])
-def test_poisson_eigenvalue_convergence(n, quadrilateral, degree, tolerance):
-    true_values, estimates = poisson_1d(n, quadrilateral=quadrilateral, degree=degree)
-    assert np.allclose(true_values, estimates, rtol=tolerance)
-
-
-# tests/regression/test_helmholtz.py
-
-from os.path import abspath, dirname, join
-import numpy as np
-import pytest
-
-from firedrake import *
-
-cwd = abspath(dirname(__file__))
-
-
-def poisson_2d(n, quadrilateral=False, degree=1, mesh=None):
-    # Create mesh and define function space
-    if mesh is None:
-        mesh = UnitSquareMesh(n, 0, pi)
-    V = FunctionSpace(mesh, "CG", degree)
-    # Define variational problem
-    u = TrialFunction(V)
-    v = TestFunction(V)
-    a = (inner(grad(u), grad(v))) * dx
-
-    # Create eigenproblem with boundary conditions
-    bc = DirichletBC(V, 0.0, "on_boundary")
-    eigenprob = LinearEigenproblem(a, bcs=bc)
-    
-    # Create corresponding eigensolver, looking for n eigenvalues
-    eigensolver = LinearEigensolver(eigenprob, n)
-    ncov = eigensolver.solve()
-    print(ncov)
-
-    # boffi solns 
-    h = pi /n
-    true_values = np.zeros(ncov-2)
-    estimates = np.zeros(ncov-2)
-    for k in range(ncov-2):
-        true_val = 6 / h**2
-        true_val *= (1-cos((k+1)*h))/(2+cos((k+1)*h)) # k+1 because we skip the trivial 0 eigenvalue
-        true_values[k] = true_val
-        estimates[k] = 1/eigensolver.eigenvalue(k).real # takes real part 
-    return true_values, estimates
+    return sorted(true_values), sorted(estimates) # sort in case order of evals returned differently
 
 @pytest.mark.parametrize(('n', 'quadrilateral', 'degree', 'tolerance'),
-                         [(5, False, 1, 1e-14),
-                          (10, False, 1, 1e-14),
-                          (20, False, 1, 1e-14),
-                          (30, False, 1, 1e-14)])
-def test_poisson_eigenvalue_convergence(n, quadrilateral, degree, tolerance):
-    true_values, estimates = poisson_1d(n, quadrilateral=quadrilateral, degree=degree)
+                         [(5, False, 1, 1e-13),
+                          (10, False, 1, 1e-13),
+                          (20, False, 1, 1e-13),
+                          (30, False, 1, 1e-13)])
+def test_evals_1d(n, quadrilateral, degree, tolerance):
+    true_values, estimates = evals(n, quadrilateral=quadrilateral, degree=degree)
     assert np.allclose(true_values, estimates, rtol=tolerance)