def test_cg_2x2():
A = np.array([4.0, 1.0, 1.0, 3.0])
A = A.reshape((2, 2))
def Ax(x):
return np.dot(A, x)
b = np.array([1.0, 2.0])
x, niter = cg(Ax, b)
assert niter <= 2
assert (np.round(x, decimals=4) == np.array([0.0909, 0.6364])).all()
def test_cg_20x20():
n = 20
A = np.random.rand(n, n)
A = (A + A.T) / 2.0
def Ax(x):
return np.dot(A, x)
b = np.random.rand(n)
x, niter = cg(Ax, b)
np_x = np.linalg.solve(A, b)
assert np.allclose(x, np_x, atol=1e-8)
def test_single_element_cg_sin_3d():
N = 10
n = N + 1
mesh = load_mesh("box001.msh")
mesh.find_physical_coordinates(N)
mesh.calc_geometric_factors()
mesh.establish_global_numbering()
mesh.setup_mask()
G = mesh.get_geom()
J = mesh.get_jaco()
B = mesh.get_mass()
def mask(W):
W = W.reshape((n, n, n))
W[0, :, :] = 0
W[n - 1, :, :] = 0
W[:, 0, :] = 0
W[:, n - 1, :] = 0
W[:, :, 0] = 0
W[:, :, n - 1] = 0
W = W.reshape((n * n * n,))
return W
def Ax(x):
Ux, Uy, Uz = gradient(x, n)
Wx = G[0, 0, 0, :] * Ux + G[0, 0, 1, :] * Uy + G[0, 0, 2, :] * Uz
Wy = G[0, 1, 0, :] * Ux + G[0, 1, 1, :] * Uy + G[0, 1, 2, :] * Uz
Wz = G[0, 2, 0, :] * Ux + G[0, 2, 1, :] * Uy + G[0, 2, 2, :] * Uz
W = gradient_transpose(Wx, Wy, Wz, n)
return mask(W)
X = mesh.get_x()
Y = mesh.get_y()
Z = mesh.get_z()
x = np.sin(np.pi * X) * np.sin(np.pi * Y) * np.sin(np.pi * Z)
x = mask(x)
b = 3 * np.pi * np.pi * np.sin(np.pi * X) * np.sin(np.pi * Y) * np.sin(np.pi * Z)
b = b * B * J
b = mask(b)
x_cg, niter = cg(Ax, b, tol=1e-8, maxit=100, verbose=0)
assert np.allclose(x, x_cg, 1e-8)
def test_cg_3x3():
A = np.array([1.0, 2.0, -1.0, 2.0, 2.0, 2.0, 1.0, -1.0, 2.0])
A = A.reshape((3, 3))
A = (A + A.T) / 2.0
def Ax(x):
return np.dot(A, x)
b = np.array([2.0, 12.0, 5.0])
x, niter = cg(Ax, b)
np_x = np.linalg.solve(A, b)
assert niter <= 3
assert np.allclose(x, np_x, atol=1e-8)
if example_2d:
b = np.exp(10 * Y) * np.sin(10 * X)
b = mask(b.reshape((n * n, )) * B * J)
else:
b = np.exp(10 * Y * Z) * np.sin(10 * X)
b = mask(b.reshape((n * n * n, )) * B * J)
tol = 1.0e-8
maxit = 1000
verbose = 0
t = time.process_time()
if example_2d:
x_cg, niter_cg = cg(Ax_2d, b, tol, maxit, verbose)
x_mass, niter_mass = pcg(Ax_2d, precon_mass, b, tol, maxit, verbose)
x_jacobi, niter_jacobi = pcg(Ax_2d, precon_jacobi_2d, b, tol, maxit,
verbose)
x_fdm, niter_fdm = pcg(Ax_2d, precon_fdm_2d, b, tol, maxit, verbose)
else:
x_cg, niter_cg = cg(Ax, b, tol, maxit, verbose)
tt = time.process_time() - t
elapsed_cg.append(tt)
# x_mass ,niter_mass =pcg(Ax,precon_mass ,b,tol,maxit,verbose)
# x_jacobi,niter_jacobi=pcg(Ax,precon_jacobi,b,tol,maxit,verbose)
t = time.process_time()
x_fdm, niter_fdm = pcg(Ax, precon_fdm, b, tol, maxit, verbose)
tt = time.process_time() - t
elapsed_fdm.append(tt)