def test_Helmholtz(ST2): M = 4 * N kx = 12 points, weights = ST2.points_and_weights(M) fj = np.random.randn(M) f_hat = np.zeros(M) f_hat = ST2.fst(fj, f_hat) fj = ST2.ifst(f_hat, fj) if ST2.__class__.__name__ == "ShenDirichletBasis": A = ADDmat(np.arange(M).astype(np.float)) B = BDDmat(np.arange(M).astype(np.float), ST2.quad) s = slice(0, M - 2) elif ST2.__class__.__name__ == "ShenNeumannBasis": A = ANNmat(np.arange(M).astype(np.float)) B = BNNmat(np.arange(M).astype(np.float), ST2.quad) s = slice(1, M - 2) f_hat = np.zeros(M) f_hat = ST2.fastShenScalar(fj, f_hat) u_hat = np.zeros(M) u_hat[s] = la.spsolve(A.diags() + kx ** 2 * B.diags(), f_hat[s]) u1 = np.zeros(M) u1 = ST2.ifst(u_hat, u1) c = A.matvec(u_hat) + kx ** 2 * B.matvec(u_hat) c2 = np.dot(A.diags().toarray(), u_hat[s]) + kx ** 2 * np.dot(B.diags().toarray(), u_hat[s]) # from IPython import embed; embed() assert np.allclose(c, f_hat) assert np.allclose(c[s], c2) # Multidimensional f_hat = f_hat.repeat(16).reshape((M, 4, 4)) + 1j * f_hat.repeat(16).reshape((M, 4, 4)) kx = np.zeros((4, 4)) + 12 H = Helmholtz(M, kx, ST2.quad, ST2.__class__.__name__ == "ShenNeumannBasis") u0_hat = np.zeros((M, 4, 4), dtype=np.complex) u0_hat = H(u0_hat, f_hat) u0 = np.zeros((M, 4, 4), dtype=np.complex) u0 = ST2.ifst(u0_hat, u0) assert np.linalg.norm(u0[:, 2, 2].real - u1) / (M * 16) < 1e-12 assert np.linalg.norm(u0[:, 2, 2].imag - u1) / (M * 16) < 1e-12