def test_get_fy_on_edge(self):
for _ in range(10):
data = np.random.randn(4, 4)
bicubic = sjs.Bicubic(data)
cubic = bicubic.get_fy_on_edge(sjs.BicubicVariable.Lambda, 0)
self.assertAlmostEqual(cubic.f(0), data[0, 2])
self.assertAlmostEqual(cubic.f(1), data[1, 2])
for _ in range(10):
lam = np.random.rand()
self.assertAlmostEqual(cubic.f(lam), bicubic.fy(lam, 0))
cubic = bicubic.get_fy_on_edge(sjs.BicubicVariable.Lambda, 1)
self.assertAlmostEqual(cubic.f(0), data[0, 3])
self.assertAlmostEqual(cubic.f(1), data[1, 3])
for _ in range(10):
lam = np.random.rand()
self.assertAlmostEqual(cubic.f(lam), bicubic.fy(lam, 1))
cubic = bicubic.get_fy_on_edge(sjs.BicubicVariable.Mu, 0)
self.assertAlmostEqual(cubic.f(0), data[0, 2])
self.assertAlmostEqual(cubic.f(1), data[0, 3])
for _ in range(10):
mu = np.random.rand()
self.assertAlmostEqual(cubic.f(mu), bicubic.fy(0, mu))
cubic = bicubic.get_fy_on_edge(sjs.BicubicVariable.Mu, 1)
self.assertAlmostEqual(cubic.f(0), data[1, 2])
self.assertAlmostEqual(cubic.f(1), data[1, 3])
for _ in range(10):
mu = np.random.rand()
self.assertAlmostEqual(cubic.f(mu), bicubic.fy(1, mu))
def test_ctor(self):
for _ in range(10):
data = np.random.randn(4, 4)
bicubic = sjs.Bicubic(data)
for (i, lam), (j, mu) in it.product(enumerate([0.0,1.0]), repeat=2):
self.assertAlmostEqual(bicubic.f(lam, mu), data[i, j])
self.assertAlmostEqual(bicubic.fx(lam, mu), data[2 + i, j])
self.assertAlmostEqual(bicubic.fy(lam, mu), data[i, 2 + j])
self.assertAlmostEqual(bicubic.fxy(lam, mu), data[2 + i, 2 + j])
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_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)