solution = sv.fiber_solver(**fiber_kwargs)
V1 = np.concatenate(solution["Fiber trace"].points, axis=1)[:-1,::10]
FX1 = solution["Fixed points"]
z = solution["Fiber trace"].z_initial
print("Status: %s\n"%solution["Fiber trace"].status)
# Run in other direction (negate initial tangent)
fiber_kwargs["z"] = -z
solution = sv.fiber_solver(**fiber_kwargs)
V2 = np.concatenate(solution["Fiber trace"].points, axis=1)[:-1,::10]
FX2 = solution["Fixed points"]
print("Status: %s\n"%solution["Fiber trace"].status)
# Join fiber segments
V = np.concatenate((np.fliplr(V1), V2), axis=1)
FX = np.concatenate((FX1, FX2), axis=1)
X_grid, Y_grid = np.mgrid[-10:10:60j,-10:10:60j]
ax = pt.gcf().add_subplot(2,1,2)
tv.plot_fiber(X_grid, Y_grid, V[:,::20], f, ax=ax, scale_XY=10, scale_V=20)
pt.plot(FX[0],FX[1], 'ko')
pt.show()
# v = np.zeros((2,1))
# print(levy(v))
# print(f(v).T)
# v = np.ones((2,1))
# print(levy(v))
# print(f(v).T)
x_lork = (b+1)/(-2*a)*np.ones(2)
y_lork = np.array([-2, 2])
# Fixed points
x_fx = ((b+1) + np.array([-1, 1])*np.sqrt((b+1)**2 + 4*a))/(-2*a)
y_fx = b*x_fx
# Grids for fiber and attractor
X_fiber, Y_fiber = np.mgrid[-2:2:20j, -2:2:20j]
X_a, Y_a = np.mgrid[-1:1:100j, -1:1:100j]
# Compute attractor points
V_a = np.array([X_a.flatten(), Y_a.flatten()])
for u in range(11):
V_a = V_a + f(V_a)
V_a = V_a[:,np.isfinite(V_a).all(axis=0)]
V_a = V_a[:,(np.fabs(V_a) < 2).all(axis=0)]
# Visualize fiber and attractor
pt.figure(figsize=(3.5,3.5))
ax_fiber = pt.gca()
ax_fiber.scatter(*V_a, marker='o', s=2, color=((0.3, 0.3, 0.3),)) # attractor
tv.plot_fiber(X_fiber, Y_fiber, V[:,::10], f, ax=ax_fiber, scale_XY=10, scale_V=10)
ax_fiber.plot(x_fx, y_fx, 'ko') # fixed points
# ax_fiber.plot(x_lork, y_lork, 'r-') # low-rank Df points
ax_fiber.set_xlabel("x")
ax_fiber.set_ylabel("y",rotation=0)
pt.yticks(np.linspace(-2,2,5))
pt.tight_layout()
pt.show()
X_fiber, Y_fiber = np.mgrid[-2.5:3.5:40j, -1:4:40j]
X_surface, Y_surface = np.mgrid[-2.5:3.5:100j, -1:4:100j]
# Low rank Df curve
x_lork = np.linspace(-2.5, 3.5, 40)
y_lork = (2 + (12 - 8 * b) * x_lork**2) / (4 * b)
# Compute rosenbrock
R = (a - X_surface)**2 + b * (Y_surface - X_surface**2)**2
# Visualize fiber and surface
ax_fiber = pt.subplot(2, 1, 2)
tv.plot_fiber(X_fiber,
Y_fiber,
V,
f,
ax=ax_fiber,
scale_XY=500,
scale_V=25)
ax_fiber.plot([1], [1], 'ko') # global optimum
# ax_fiber.plot(x_lork, y_lork, 'r-') # low-rank Df points
ax_surface = pt.gcf().add_subplot(2, 1, 1, projection="3d")
ax_surface.plot_surface(X_surface,
Y_surface,
R,
linewidth=0,
antialiased=False,
color='gray')
ax_surface.view_init(azim=-98, elev=21)
for ax in [ax_fiber, ax_surface]:
ax.set_xlabel("x")
def sanity2D():
# Set up fiber arguments
v = np.array([[2], [.5]])
fiber_kwargs = {
"f": f,
"ef": ef,
"Df": Df,
"compute_step_amount": compute_step_amount,
"v": v,
"c": f(v),
"max_step_size": 1,
"max_traverse_steps": 2000,
"max_solve_iterations": 2**5,
}
# Run in one direction
solution = sv.fiber_solver(**fiber_kwargs)
V1 = np.concatenate(solution["Fiber trace"].points, axis=1)[:-1, ::10]
z = solution["Fiber trace"].z_initial
# Run in other direction (negate initial tangent)
fiber_kwargs["z"] = -z
solution = sv.fiber_solver(**fiber_kwargs)
V2 = np.concatenate(solution["Fiber trace"].points, axis=1)[:-1, ::10]
# Join fiber segments
V = np.concatenate((np.fliplr(V1), V2), axis=1)
# Grids for fiber and surface
X_fiber, Y_fiber = np.mgrid[-2.5:3.5:40j, -1:4:40j]
X_surface, Y_surface = np.mgrid[-2.5:3.5:100j, -1:4:100j]
# Compute rosenbrock
R_surface = R(np.array([X_surface.flatten(), Y_surface.flatten()]))
R_surface = R_surface.reshape(X_surface.shape)
# Visualize fiber and surface
ax_fiber = pt.subplot(2, 1, 2)
tv.plot_fiber(X_fiber,
Y_fiber,
V,
f,
ax=ax_fiber,
scale_XY=500,
scale_V=25)
ax_fiber.plot([1], [1], 'ko') # global optimum
ax_surface = pt.gcf().add_subplot(2, 1, 1, projection="3d")
ax_surface.plot_surface(X_surface,
Y_surface,
R_surface,
linewidth=0,
antialiased=False,
color='gray')
ax_surface.view_init(azim=-98, elev=21)
for ax in [ax_fiber, ax_surface]:
ax.set_xlabel("x")
ax.set_ylabel("y")
if ax == ax_surface:
ax.set_zlabel("R(x,y)", rotation=90)
ax.set_zlim([0, 10000])
ax.view_init(elev=40, azim=-106)
ax.set_xlim([-2.5, 3.5])
pt.show()
if __name__ == "__main__":
# Set up 2D network
N = 2
W = 1.25 * np.eye(N) + 0.1 * np.random.randn(N, N)
logger = lu.Logger(sys.stdout)
fxpts, solution = run_fiber_solver(
W,
# max_history=100,
compute_step_amount=compute_step_amount_factory3(W),
logger=logger,
abs_alpha_min=True,
within_fiber=True)
# Extract steps along fiber and corresponding f(v)'s
trace = solution["Fiber trace"]
X = np.concatenate(trace.points, axis=1)
X = np.concatenate((-np.fliplr(X), X), axis=1)
V = X[:-1, :]
# Plot fiber and fixed points
X_grid, Y_grid = np.mgrid[-1.15:1.15:20j, -1.15:1.15:20j]
plt.figure(figsize=(5, 4.5))
tv.plot_fiber(X_grid, Y_grid, V, f_factory(W), scale_XY=1, scale_V=1)
plt.scatter(*fxpts, color='k', marker='o')
plt.xlabel("v1")
plt.ylabel("v2", rotation=0)
plt.tight_layout()
plt.show()
fxpts = fx.sanitize_points(
V_fx,
f,
ef,
Df,
duplicates=lambda V, v: (np.fabs(V - v) < 10**-6).all(axis=0),
)
print("Fxpts:")
print(fxpts)
print("Residuals:")
print(ef(fxpts))
# Visualize fiber if 2d
if N == 2:
X_f, Y_f = np.mgrid[-2:2:15j, -2:2:15j]
V = V[:, \
(V[0,:] >= X_f.min()) & \
(V[0,:] <= X_f.max()) & \
(V[1,:] >= Y_f.min()) & \
(V[1,:] <= Y_f.max())]
# V = V[:,::20]
tv.plot_fiber(X_f, Y_f, V, f, scale_XY=8, scale_V=5)
pt.plot(*fxpts, marker='o', color='k', linestyle='none')
pt.xlabel("x")
pt.ylabel("y")
pt.show()