def test_sub(self):
for _ in range(10):
u1, u2, v1, v2 = np.random.randn(4)
u, v = sjs.Dvec2(u1, u2), sjs.Dvec2(v1, v2)
w = u - v
self.assertAlmostEqual(w.x, u1 - v1)
self.assertAlmostEqual(w.y, u2 - v2)
def test_outer(self):
for _ in range(10):
u_gt, v_gt = np.random.randn(2, 2)
u, v = sjs.Dvec2(*u_gt), sjs.Dvec2(*v_gt)
uv, uv_gt = sjs.outer(u, v), np.outer(u_gt, v_gt)
for i, j in it.product(range(2), repeat=2):
self.assertAlmostEqual(uv[i, j], uv_gt[i, j])
def test_cproj(self):
for _ in range(10):
u, v = np.random.randn(2, 2)
w = sjs.cproj(sjs.Dvec2(*u), sjs.Dvec2(*v))
w_gt = (np.eye(2) - np.outer(u, u)) @ v
self.assertAlmostEqual(w[0], w_gt[0])
self.assertAlmostEqual(w[1], w_gt[1])
def test_add(self):
for _ in range(10):
u1, u2, v1, v2 = np.random.randn(4)
u, v = sjs.Dvec2(u1, u2), sjs.Dvec2(v1, v2)
w = u + v
self.assertAlmostEqual(w.x, u1 + v1)
self.assertAlmostEqual(w.y, u2 + v2)
def test_hybrid_constant_slowness(self):
cubic = sjs.Cubic([0, 0, 0, 0])
xy0 = sjs.Dvec2(1, 0)
xy1 = sjs.Dvec2(0, 1)
xy = sjs.Dvec2(0, 0)
h = 1
slow = sjs.get_constant_slowness_field2()
context = sjs.F3Context(cubic, xy, xy0, xy1, slow)
def func(lam):
context.compute(lam)
return context.F3_eta
lam = sjs.hybrid(func, 0, 1)
self.assertAlmostEqual(lam, 0.5)
self.assertAlmostEqual(context.F3, 1.0 / np.sqrt(2))
self.assertAlmostEqual(context.F3_eta, 0.0)
context.T_cubic = sjs.Cubic([0, 1, 1, 1])
lam = sjs.hybrid(func, 0, 1)
self.assertAlmostEqual(lam, 0.0)
self.assertAlmostEqual(context.F3, 1.0)
self.assertAlmostEqual(context.F3_eta, 0.0)
context.T_cubic = sjs.Cubic([1, 0, -1, -1])
lam = sjs.hybrid(func, 0, 1)
self.assertAlmostEqual(lam, 1.0)
self.assertAlmostEqual(context.F3, 1.0)
self.assertAlmostEqual(context.F3_eta, 0.0)
context.T_cubic = sjs.Cubic([1, 1, -1, 1])
lam = sjs.hybrid(func, 0, 1)
self.assertAlmostEqual(lam, 0.5)
self.assertAlmostEqual(context.F3_eta, 0.0)
def test_dvec2_to_ivec2(self):
for _ in range(10):
u1, u2 = np.random.randn(2)
u = sjs.Dvec2(u1, u2)
v = sjs.Ivec2(u)
self.assertAlmostEqual(v.i, int(u1))
self.assertAlmostEqual(v.j, int(u2))
def test_dbl_div(self):
for _ in range(10):
u1, u2, a = np.random.randn(3)
u = sjs.Dvec2(u1, u2)
v = u / a
self.assertAlmostEqual(v.x, u1 / a)
self.assertAlmostEqual(v.y, u2 / a)
def test_floor(self):
for _ in range(10):
u1, u2 = np.random.randn(2)
u = sjs.Dvec2(u1, u2)
v = u.floor()
self.assertAlmostEqual(v.x, np.floor(u1))
self.assertAlmostEqual(v.y, np.floor(u2))
def test_solve(self):
for _ in range(10):
A_gt = np.random.randn(2, 2)
b_gt = np.random.randn(2)
A, b = sjs.Dmat22(A_gt), sjs.Dvec2(*b_gt)
x, x_gt = A.solve(b), np.linalg.solve(A_gt, b_gt)
self.assertAlmostEqual(x[0], x_gt[0])
self.assertAlmostEqual(x[1], x_gt[1])
def test_evaluate_linear_speed(self):
for _ in range(10):
h = 0.1
x0, y0 = np.random.uniform(-1, 1 - h, (2, ))
x1, y1 = x0 + h, y0 + h
x, y = x0 - h, y0
xy = sjs.Dvec2(x, y)
xy0 = sjs.Dvec2(x0, y0)
xy1 = sjs.Dvec2(x0, y1)
vx, vy = np.random.uniform(-0.05, 0.05, (2, ))
tau_xy = get_linear_speed_tau(vx, vy)
tau = lambda eta: tau_xy(x0, y0 + eta * (y1 - y0))
tau_eta = autograd.grad(tau)
s_gt = get_linear_speed_s(vx, vy)
slow = sjs.get_linear_speed_field2(vx, vy)
cubic = sjs.Cubic([tau(0.0), tau(1.0), tau_eta(0.0), tau_eta(1.0)])
context = sjs.F3Context(cubic, xy, xy0, xy1, slow)
a_T = np.array([cubic.a[0], cubic.a[1], cubic.a[2], cubic.a[3]])
p, p0, p1 = np.array([x, y]), np.array([x0,
y0]), np.array([x0, y1])
context_gt = F3(s_gt, a_T, p, p0, p1)
for _ in range(10):
eta = np.random.random()
T, T_gt = cubic.f(eta), context_gt.T(eta)
T_eta, T_eta_gt = cubic.df(eta), context_gt.T_eta(eta)
self.assertAlmostEqual(T, T_gt)
self.assertAlmostEqual(T_eta, T_eta_gt)
context.compute(eta)
f3, f3_eta = context.F3, context.F3_eta
f3_gt, f3_eta_gt = context_gt.F3(eta), context_gt.grad_F3(eta)
self.assertAlmostEqual(f3, f3_gt)
self.assertAlmostEqual(f3_eta, f3_eta_gt)
def test_evaluate(self):
eps = 1e-7
for _ in range(10):
vx, vy = np.random.uniform(-0.05, 0.05, (2,))
s_gt = get_linear_speed_s(vx, vy)
slow = sjs.get_linear_speed_field2(vx, vy)
data = np.random.randn(4, 4)
h = np.random.random()
H = np.diag([1, 1, h, h])
data = H@data@H
p = np.random.randn(2)
p0 = p + h*np.random.randn(2)
p1 = p + h*np.random.randn(2)
bicubic = sjs.Bicubic(data)
T = bicubic.get_f_on_edge(sjs.BicubicVariable.Lambda, 0)
Tx = bicubic.get_fx_on_edge(sjs.BicubicVariable.Lambda, 0)
Ty = bicubic.get_fy_on_edge(sjs.BicubicVariable.Lambda, 0)
a_T = np.array([T.a[i] for i in range(4)])
a_Tx = np.array([Tx.a[i] for i in range(4)])
a_Ty = np.array([Ty.a[i] for i in range(4)])
context_gt = F4(s_gt, a_T, a_Tx, a_Ty, p, p0, p1)
xy = sjs.Dvec2(*p)
xy0 = sjs.Dvec2(*p0)
xy1 = sjs.Dvec2(*p1)
context = sjs.F4Context(T, Tx, Ty, xy, xy0, xy1, slow)
for _ in range(10):
args = np.random.random(2)
args[1] *= 2*np.pi
context.compute(*args)
f4_gt = context_gt.F4(args)
f4_eta_gt, f4_th_gt = context_gt.grad_F4(args)
self.assertAlmostEqual(f4_gt, context.F4)
self.assertAlmostEqual(f4_eta_gt, context.F4_eta)
self.assertAlmostEqual(f4_th_gt, context.F4_th)
def test_dbl_mul(self):
for _ in range(10):
u1, u2, a = np.random.randn(3)
u = sjs.Dvec2(u1, u2)
v = u * a
self.assertAlmostEqual(v.x, a * u1)
self.assertAlmostEqual(v.y, a * u2)
u *= a
self.assertAlmostEqual(v.x, u.x)
self.assertAlmostEqual(v.y, u.y)
def test_evaluate_constant_slowness(self):
cubic = sjs.Cubic([0, 0, 0, 0])
xy0 = sjs.Dvec2(1, 0)
xy1 = sjs.Dvec2(0, 1)
xy = sjs.Dvec2(0, 0)
h = 1
slow = sjs.get_constant_slowness_field2()
context = sjs.F3Context(cubic, xy, xy0, xy1, slow)
context.compute(0)
self.assertAlmostEqual(context.F3, 1.0)
self.assertAlmostEqual(context.F3_eta, -1.0)
context.compute(1)
self.assertAlmostEqual(context.F3, 1.0)
self.assertAlmostEqual(context.F3_eta, 1.0)
context.compute(1 / 2)
self.assertAlmostEqual(context.F3, 1.0 / np.sqrt(2))
def test_mul(self):
for _ in range(10):
A_data, B_data = np.random.randn(2, 2, 2)
C_gt = A_data @ B_data
A = sjs.Dmat22(A_data)
B = sjs.Dmat22(B_data)
C = A @ B
for i, j in it.product(range(2), repeat=2):
self.assertAlmostEqual(C[i, j], C_gt[i, j])
x_data = np.random.randn(2)
x = sjs.Dvec2(*x_data)
y, y_gt = A @ x, A_data @ x_data
self.assertAlmostEqual(y[0], y_gt[0])
self.assertAlmostEqual(y[1], y_gt[1])
def test_dot(self):
for _ in range(10):
u1, u2, v1, v2 = np.random.randn(4)
u, v = sjs.Dvec2(u1, u2), sjs.Dvec2(v1, v2)
self.assertAlmostEqual(u * v, u1 * v1 + u2 * v2)
def test_bfgs_linear_speed(self):
for _ in range(10):
h = 0.1
x0, y0 = np.random.uniform(-1, 1 - h, (2,))
x1, y1 = x0 + h, y0 + h
x, y = x0 - h, y0
vx, vy = np.random.uniform(-0.05, 0.05, (2,))
s_gt = get_linear_speed_s(vx, vy)
slow = sjs.get_linear_speed_field2(vx, vy)
tau_Omega = get_linear_speed_tau(vx, vy)
tau = lambda lam, mu: tau_Omega(
(1 - lam)*x0 + lam*x1,
(1 - mu)*y0 + mu*y1
)
grad_tau = autograd.grad(lambda args: tau(args[0], args[1]))
hess_tau = autograd.hessian(lambda args: tau(args[0], args[1]))
tau_x = lambda lam, mu: grad_tau(np.array([lam, mu]))[0]
tau_y = lambda lam, mu: grad_tau(np.array([lam, mu]))[1]
tau_xy = lambda lam, mu: hess_tau(np.array([lam, mu]))[1][0]
data = np.array([
[ tau(0., 0.), tau(0., 1.), tau_y(0., 0.), tau_y(0., 1.)],
[ tau(1., 0.), tau(1., 1.), tau_y(1., 0.), tau_y(1., 1.)],
[tau_x(0., 0.), tau_x(0., 1.), tau_xy(0., 0.), tau_xy(0., 1.)],
[tau_x(1., 0.), tau_x(1., 1.), tau_xy(1., 0.), tau_xy(1., 1.)],
])
bicubic = sjs.Bicubic(data)
T = bicubic.get_f_on_edge(sjs.BicubicVariable.Lambda, 0)
Tx = bicubic.get_fx_on_edge(sjs.BicubicVariable.Lambda, 0)
Ty = bicubic.get_fy_on_edge(sjs.BicubicVariable.Lambda, 0)
a_T = np.array([T.a[i] for i in range(4)])
a_Tx = np.array([Tx.a[i] for i in range(4)])
a_Ty = np.array([Ty.a[i] for i in range(4)])
p, p0, p1 = np.array([x, y]), np.array([x0, y0]), np.array([x0, y1])
context_gt = F4(s_gt, a_T, a_Tx, a_Ty, p, p0, p1)
xy = sjs.Dvec2(*p)
xy0 = sjs.Dvec2(*p0)
xy1 = sjs.Dvec2(*p1)
context = sjs.F4Context(T, Tx, Ty, xy, xy0, xy1, slow)
context3 = sjs.F3Context(T, xy, xy0, xy1, slow)
def F3(eta):
context3.compute(eta)
return context3.F3
def F3_eta(eta):
context3.compute(eta)
return context3.F3_eta
if np.sign(F3_eta(0.)) == np.sign(F3_eta(1.)):
argeta3 = 0. if F3(0.) < F3(1.) else 1.
else:
argeta3 = brentq(F3_eta, 0, 1)
lp = (p - p0 - argeta3*(p1 - p0))
lp /= np.linalg.norm(lp)
argth3 = np.arctan2(*reversed(lp))
xk_gt = np.array([argeta3, argth3])
eps = 1e-7
hess_gt = context_gt.hess_F4(xk_gt)
hess_fd = context.hess_fd(argeta3, argth3, eps)
self.assertTrue(abs(hess_gt[0, 0] - hess_fd[0, 0]) < eps)
self.assertTrue(abs(hess_gt[1, 0] - hess_fd[1, 0]) < eps)
self.assertTrue(abs(hess_gt[0, 1] - hess_fd[0, 1]) < eps)
self.assertTrue(abs(hess_gt[1, 1] - hess_fd[1, 1]) < eps)
gk_gt = context_gt.grad_F4(xk_gt)
Hk_gt = np.linalg.inv(hess_gt)
xk, gk, Hk = context.bfgs_init(*xk_gt)
eps = 1e-6
self.assertTrue(abs(Hk_gt[0, 0] - Hk[0, 0]) < eps)
self.assertTrue(abs(Hk_gt[1, 0] - Hk[1, 0]) < eps)
self.assertTrue(abs(Hk_gt[0, 1] - Hk[0, 1]) < eps)
self.assertTrue(abs(Hk_gt[1, 1] - Hk[1, 1]) < eps)
def test_normalize(self):
for _ in range(10):
u = sjs.Dvec2(*np.random.randn(2))
u.normalize()
self.assertAlmostEqual(u.norm(), 1.0)
def test_ccomb(self):
u, v = sjs.Dvec2(2, 0), sjs.Dvec2(1, 3)
w = sjs.ccomb(u, v, 0.1)
self.assertAlmostEqual(w.x, 1.9)
self.assertAlmostEqual(w.y, 0.3)
def test_ctor(self):
v = sjs.Dvec2(1, 2)
self.assertEqual(v.x, 1)
self.assertEqual(v.y, 2)
def test_dist(self):
for _ in range(10):
u1, u2, v1, v2 = np.random.randn(4)
u, v = sjs.Dvec2(u1, u2), sjs.Dvec2(v1, v2)
d = np.sqrt((v1 - u1)**2 + (v2 - u2)**2)
self.assertAlmostEqual(sjs.dist(u, v), d)
def test_norm(self):
for _ in range(10):
u1, u2 = np.random.randn(2)
u = sjs.Dvec2(u1, u2)
d = np.sqrt(u1**2 + u2**2)
self.assertAlmostEqual(u.norm(), d)