solvers: maked todo expose eigenvalues for generalized eigen solver

Author: Lucas-Haubert

include/eigenpy/decompositions/GeneralizedEigenSolver.hpp

@@ -32,10 +32,16 @@ struct GeneralizedEigenSolverVisitor
             "Computes the generalized eigendecomposition of given matrix "
             "pair. "))
 
+        .def("eigenvectors", &Solver::eigenvectors, bp::arg("self"),
+             "Returns an expression of the computed generalized eigenvectors. ")
+        // TODO: Expose so that the return type are convertible to np arrays
+        .def("eigenvalues", &Solver::eigenvalues, bp::arg("self"),
+             "Returns an expression of the computed generalized eigenvalues. ")
+
         .def("alphas", &Solver::alphas, bp::arg("self"),
-             "Returns the vectors containing the alpha values ")
+             "Returns the vectors containing the alpha values. ")
         .def("betas", &Solver::betas, bp::arg("self"),
-             "Returns the vectors containing the beta values ")
+             "Returns the vectors containing the beta values. ")
 
         .def("compute",
              &GeneralizedEigenSolverVisitor::compute_proxy<MatrixType>,
@@ -50,9 +56,6 @@ struct GeneralizedEigenSolverVisitor
              "Computes generalized eigendecomposition of given matrix. .",
              bp::return_self<>())
 
-        .def("eigenvectors", &Solver::eigenvectors, bp::arg("self"),
-             "Returns an expression of the computed generalized eigenvectors. ")
-
         .def("info", &Solver::info, bp::arg("self"),
              "NumericalIssue if the input contains INF or NaN values or "
              "overflow occured. Returns Success otherwise.")

unittest/python/test_generalized_eigen_solver.py

@@ -6,21 +6,24 @@
 rng = np.random.default_rng()
 A = rng.random((dim, dim))
 B = rng.random((dim, dim))
+B = (B + B.T) * 0.5 + np.diag(10.0 + rng.random(dim))  # Make B not singular
 
 ges = eigenpy.GeneralizedEigenSolver(A, B)
 
+assert ges.info() == eigenpy.ComputationInfo.Success
+
 alphas = ges.alphas()
 betas = ges.betas()
-V = ges.eigenvectors()
 
-eigenvalues = alphas / betas
-if np.all(np.abs(betas) >= 1e-15):
-    for i in range(dim):
-        v = V[:, i]
-        lam = eigenvalues[i]
+vec = ges.eigenvectors()
+
+val_est = alphas / betas
+for i in range(dim):
+    v = vec[:, i]
+    lam = val_est[i]
 
-        Av = A @ v
-        lam_Bv = lam * (B @ v)
+    Av = A @ v
+    lam_Bv = lam * (B @ v)
 
-        assert eigenpy.is_approx(Av.real, lam_Bv.real)
-        assert eigenpy.is_approx(Av.imag, lam_Bv.imag)
+    assert eigenpy.is_approx(Av.real, lam_Bv.real)
+    assert eigenpy.is_approx(Av.imag, lam_Bv.imag)