def apply_flow(phi, u):
surf = sqp_problem.make_interp(phi)
out = np.empty_like(phi)
for i in range(out.shape[0]):
for j in range(out.shape[1]):
out[i,j] = surf.eval_xys(surf.to_xys([i,j])[0] - u[i,j,:])
return out
def __init__(self, init_phi):
self.phi_surf = sqp_problem.make_interp(init_phi)
self.curr_u = np.zeros(sqp_problem.Config.GRID_SHAPE + (2, ))
self.curr_obs = None
self.prob = None
self.phi_cmap = np.zeros((256, 3), dtype='uint8')
self.phi_cmap[:128, 0] = 255
self.phi_cmap[:128, 1] = np.linspace(0, 255, 128).astype(int)
self.phi_cmap[:128, 2] = np.linspace(0, 255, 128).astype(int)
self.phi_cmap[128:, 0] = np.linspace(255, 0, 128).astype(int)
self.phi_cmap[128:, 1] = np.linspace(255, 0, 128).astype(int)
self.phi_cmap[128:, 2] = 255
def __init__(self, init_phi):
self.phi_surf = sqp_problem.make_interp(init_phi)
self.curr_u = np.zeros(sqp_problem.Config.GRID_SHAPE + (2,))
self.curr_obs = None
self.prob = None
self.phi_cmap = np.zeros((256, 3), dtype='uint8')
self.phi_cmap[:128,0] = 255
self.phi_cmap[:128,1] = np.linspace(0, 255, 128).astype(int)
self.phi_cmap[:128,2] = np.linspace(0, 255, 128).astype(int)
self.phi_cmap[128:,0] = np.linspace(255, 0, 128).astype(int)
self.phi_cmap[128:,1] = np.linspace(255, 0, 128).astype(int)
self.phi_cmap[128:,2] = 255
def apply_flow_forwards(fig, N, phi, u, x=None, y=None, z=None):
# x goes to x + u(x)
# so we want out(x+u(x)) == phi(x)
surf = sqp_problem.make_interp(phi)
pts = np.empty((phi.shape + (2,)))
if x is None or y is None or z is None:
x, y, z = [], [], []
for i in range(phi.shape[0]):
for j in range(phi.shape[1]):
p = surf.to_xys([i,j])[0] + u[i,j,:]
x.append(p[0])
y.append(p[1])
z.append(phi[i,j])
ax = fig.add_subplot(N, aspect='equal')
#pts = pts.reshape((-1,2))
#ax.scatter(pts[:,0], pts[:,1], c=phi.reshape(-1), cmap='Greys_r')
ax.scatter(x, y, c=z, cmap='Greys_r')
def optimize_sqp(self):
if self.prob is None:
self.prob = sqp_problem.TrackingProblem()
self.prob.set_coeffs(flow_agree=0)
self.prob.set_obs_points(self.curr_obs)
self.prob.set_prev_phi_surf(self.phi_surf)
self.phi_surf, self.curr_u = self.prob.optimize(self.prob.prev_phi_surf.data, np.zeros((SIZE,SIZE,2)))
print 'phi max, min:', abs(self.phi_surf.data).max(), abs(self.phi_surf.data).min()
# rescale
self.phi_surf = sqp_problem.make_interp(self.phi_surf.data / abs(self.phi_surf.data).max())
# print 'smoothing'
# print self.phi_surf.data
# self.phi_surf = sqp_problem.make_interp(smooth_by_edt(self.phi_surf.data))
# print 'after'
# print self.phi_surf.data
# print 'done'
self.prob.set_coeffs(flow_agree=1)
def optimize_sqp(self):
if self.prob is None:
self.prob = sqp_problem.TrackingProblem()
self.prob.set_coeffs(flow_agree=0)
self.prob.set_obs_points(self.curr_obs)
self.prob.set_prev_phi_surf(self.phi_surf)
self.phi_surf, self.curr_u = self.prob.optimize(
self.prob.prev_phi_surf.data, np.zeros((SIZE, SIZE, 2)))
print 'phi max, min:', abs(self.phi_surf.data).max(), abs(
self.phi_surf.data).min()
# rescale
self.phi_surf = sqp_problem.make_interp(self.phi_surf.data /
abs(self.phi_surf.data).max())
# print 'smoothing'
# print self.phi_surf.data
# self.phi_surf = sqp_problem.make_interp(smooth_by_edt(self.phi_surf.data))
# print 'after'
# print self.phi_surf.data
# print 'done'
self.prob.set_coeffs(flow_agree=1)
def simple():
empty_phi = np.ones((SIZE, SIZE))
square_phi = np.ones_like(empty_phi)
square_phi[int(SIZE / 2.), int(SIZE / 4.):-int(SIZE / 4.)] = 0.
square_phi[int(SIZE / 2.):-int(SIZE / 4.), int(SIZE / 4.)] = 0.
square_phi[int(SIZE / 2.):-int(SIZE / 4.), -int(SIZE / 4.)] = 0.
square_phi[-int(SIZE / 4.), int(SIZE / 4.):-int(SIZE / 4.) + 1] = 0.
init_phi = square_phi
# init_phi = np.ones_like(empty_phi)
# init_phi[int(SIZE/2.),int(SIZE/4.):-int(SIZE/4.)] = 0.
# init_phi[int(SIZE/4.),int(SIZE/3.):-int(SIZE/3.)] = 0.
init_phi = smooth(init_phi)
# negate inside
init_phi[int(SIZE / 2.):-int(SIZE / 4.),
int(SIZE / 4.):-int(SIZE / 4.)] *= -1
# import cPickle
# with open('/tmp/init_phi.pkl', 'w') as f: cPickle.dump(init_phi, f)
init_phi_observed = np.ones_like(empty_phi)
init_phi_observed[int(SIZE / 2.), int(SIZE / 4.):-int(SIZE / 4.)] = 0.
# init_phi_observed = smooth(init_phi_observed)
new_phi_observed = init_phi_observed
new_phi_observed[int(SIZE / 2.),
int(SIZE / 10.):-int(SIZE / 10.)] = 0.
# new_phi_observed = sn.interpolation.zoom(init_phi_observed, 1.2, cval=1., order=0)
# new_phi_observed = sn.interpolation.shift(init_phi_observed, [2,0], cval=1., order=0)
# new_phi_observed = sn.interpolation.rotate(init_phi_observed, 5., cval=1., order=0)
# plt.imshow(new_phi_observed, cmap=cm.Greys_r)
# plt.show()
obs_pts = np.transpose(np.nonzero(new_phi_observed == 0))
# prob = sqp_problem.TrackingProblem()
prob = ctimbpy.TrackingProblem(WORLD_MIN[0], WORLD_MAX[0], WORLD_MIN[1],
WORLD_MAX[1], SIZE, SIZE)
prob.set_observation_points(obs_pts)
prob.set_prev_phi(init_phi)
# prob.set_coeffs(flow_norm=1e-9, flow_rigidity=1e-3, flow_tps=0, obs=1, flow_agree=1)
init_u = np.zeros(init_phi.shape + (2, ))
#init_u[:,:,0] = 1.
# out_phis, out_us, opt_result = prob.optimize(init_phi, init_u, return_full=True)
result = prob.optimize()
out_phis = [result.phi]
out_us = [result.u]
opt_result = result.opt_result
for out_phi, out_u in [zip(out_phis, out_us)[-1]]:
# import cPickle
# with open('/tmp/dump.pkl', 'w') as f:
# cPickle.dump((out_phi, out_u, opt_result), f)
global fig
fig = plt.figure(figsize=(15, 15))
init_phi[obs_pts[:, 0], obs_pts[:, 1]] = 0
plot_phi(221, sqp_problem.make_interp(init_phi))
ax = fig.add_subplot(224)
ax.plot(np.arange(len(opt_result.cost_over_iters)),
opt_result.cost_over_iters)
#out_phi = reintegrate(out_phi)
plot_phi(223, sqp_problem.make_interp(out_phi))
plot_u(222, out_u)
plt.show()
def rotate():
empty_phi = np.ones((SIZE, SIZE))
square_phi = np.ones_like(empty_phi)
square_phi[int(SIZE / 2.), int(SIZE / 4.):-int(SIZE / 4.)] = 0.
square_phi[int(SIZE / 2.):-int(SIZE / 4.), int(SIZE / 4.)] = 0.
square_phi[int(SIZE / 2.):-int(SIZE / 4.), -int(SIZE / 4.)] = 0.
square_phi[-int(SIZE / 4.), int(SIZE / 4.):-int(SIZE / 4.) + 1] = 0.
orig_phi = smooth(square_phi)
init_phi = np.ones_like(empty_phi)
init_obs_inds = calc_observable_inds(square_phi)
init_phi[init_obs_inds[:, 0], init_obs_inds[:, 1]] = 0.
init_phi = smooth(init_phi)
# go through a rotation of the square
prob = sqp_problem.TrackingProblem()
prob.set_coeffs(flow_norm=1e-9, flow_rigidity=1, obs=1, flow_agree=1)
for i_iter, angle in enumerate(np.arange(0, 359, 5)):
if i_iter == 0:
prob.set_coeffs(flow_agree=0)
else:
prob.set_coeffs(flow_agree=1)
print 'Current angle:', angle
# make an observation
rotated = sn.interpolation.rotate(square_phi,
angle,
cval=1.,
order=0,
reshape=False)
print rotated.shape, square_phi.shape
obs_inds = calc_observable_inds(rotated)
prob.set_obs_points(obs_inds)
prob.set_prev_phi(init_phi)
init_u = np.zeros(init_phi.shape + (2, ))
out_phis, out_us, opt_result = prob.optimize(init_phi,
init_u,
return_full=True)
for out_phi, out_u in [zip(out_phis, out_us)[-1]]:
global fig
fig = plt.figure()
not_oob = (0 <= obs_inds[:, 0]) & (
obs_inds[:, 0] < init_phi.shape[0]) & (0 <= obs_inds[:, 1]) & (
obs_inds[:, 1] < init_phi.shape[1])
init_phi[obs_inds[:, 0][not_oob], obs_inds[:, 1][not_oob]] = .5
plot_phi(231, sqp_problem.make_interp(init_phi))
ax = fig.add_subplot(234)
tmp = rotated.copy()
tmp[obs_inds[:, 0], obs_inds[:, 1]] = .5
tmp = np.flipud(tmp.T)
ax.imshow(tmp, cmap=cm.Greys_r).set_interpolation('nearest')
# ax = fig.add_subplot(224)
# ax.plot(np.arange(len(opt_result.costs_over_iters)), opt_result.costs_over_iters)
plot_phi(232, sqp_problem.make_interp(out_phi))
plot_u(233, out_u)
# zero_thresh = sqp_problem.make_interp(out_phi).eval_ijs(obs_inds).mean()
# print 'zero thresh', zero_thresh
out_phi = reintegrate(out_phi) #, zero_thresh)
plot_phi(235, sqp_problem.make_interp(out_phi))
plt.show()
# TODO: REINTEGRATE HERE
init_phi = out_phi
def rotate_full_obs():
square_phi = make_square_phi()
init_phi = square_phi.copy()
# go through a rotation of the square
prob = sqp_problem.TrackingProblem()
prob.set_coeffs(flow_norm=1e-9,
flow_rigidity=1e-3,
flow_tps=1e-5,
obs=1,
flow_agree=1)
for i_iter, angle in enumerate(np.arange(0, 359, 5)):
print 'Current angle:', angle
# make an observation
rotated = sn.interpolation.rotate(square_phi,
angle,
cval=1.,
order=0,
reshape=False)
print rotated.shape, square_phi.shape
obs_inds = calc_observable_inds(rotated)
prob.set_obs_points(obs_inds)
prob.set_prev_phi(init_phi)
init_u = np.zeros(init_phi.shape + (2, ))
out_phis, out_us, opt_result = prob.optimize(init_phi,
init_u,
return_full=True)
for out_phi, out_u in [zip(out_phis, out_us)[-1]]:
global fig
fig = plt.figure()
# superimpose observation drawing
not_oob = (0 <= obs_inds[:, 0]) & (
obs_inds[:, 0] < init_phi.shape[0]) & (0 <= obs_inds[:, 1]) & (
obs_inds[:, 1] < init_phi.shape[1])
init_phi[obs_inds[:, 0][not_oob], obs_inds[:, 1][not_oob]] = 0
plot_phi(231, sqp_problem.make_interp(init_phi))
# ax = fig.add_subplot(234)
# tmp = rotated.copy()
# tmp[obs_inds[:,0],obs_inds[:,1]] = .5
# tmp = np.flipud(tmp.T)
# ax.imshow(tmp, cmap=cm.Greys_r).set_interpolation('nearest')
ax = fig.add_subplot(234)
ax.plot(np.arange(len(opt_result.costs_over_iters)),
opt_result.costs_over_iters)
plot_phi(232, sqp_problem.make_interp(out_phi))
plot_u(233, out_u)
out_phi = reintegrate(out_phi)
plot_phi(235, sqp_problem.make_interp(out_phi))
plt.show()
init_phi = out_phi
init_phi_observed = np.ones_like(empty_phi)
init_phi_observed[int(SIZE / 2.), int(SIZE / 4.):-int(SIZE / 4.)] = 0.
new_phi_observed = init_phi_observed
new_phi_observed[int(SIZE / 2.),
int(SIZE / 10.):-int(SIZE / 10.)] = 0.
obs_pts = np.transpose(np.nonzero(new_phi_observed == 0))
prob = sqp_problem.TrackingProblem()
prob.set_obs_points(obs_pts)
prob.set_prev_phi(init_phi)
prob.set_coeffs(flow_norm=1e-9,
flow_rigidity=1e-8,
flow_tps=1e-5,
obs=1,
flow_agree=1)
init_u = np.zeros(init_phi.shape + (2, ))
#init_u[:,:,0] = 1.
out_phis, out_us, opt_result = prob.optimize(init_phi,
init_u,
return_full=True)
for out_phi, out_u in [zip(out_phis, out_us)[-1]]:
# import cPickle
# with open('/tmp/dump.pkl', 'w') as f:
# cPickle.dump((out_phi, out_u, opt_result), f)
global fig
fig = plt.figure(figsize=(15, 15))
init_phi[obs_pts[:, 0], obs_pts[:, 1]] = 0
plot_phi(221, sqp_problem.make_interp(init_phi))
ax = fig.add_subplot(224)
ax.plot(np.arange(len(opt_result.costs_over_iters)),
opt_result.costs_over_iters)
out_phi = reintegrate(out_phi)
plot_phi(223, sqp_problem.make_interp(out_phi))
plot_u(222, out_u)
plt.show()
def simple():
empty_phi = np.ones((SIZE, SIZE))
square_phi = np.ones_like(empty_phi)
square_phi[int(SIZE/2.),int(SIZE/4.):-int(SIZE/4.)] = 0.
square_phi[int(SIZE/2.):-int(SIZE/4.),int(SIZE/4.)] = 0.
square_phi[int(SIZE/2.):-int(SIZE/4.),-int(SIZE/4.)] = 0.
square_phi[-int(SIZE/4.),int(SIZE/4.):-int(SIZE/4.)+1] = 0.
init_phi = square_phi
# init_phi = np.ones_like(empty_phi)
# init_phi[int(SIZE/2.),int(SIZE/4.):-int(SIZE/4.)] = 0.
# init_phi[int(SIZE/4.),int(SIZE/3.):-int(SIZE/3.)] = 0.
init_phi = smooth(init_phi)
# negate inside
init_phi[int(SIZE/2.):-int(SIZE/4.),int(SIZE/4.):-int(SIZE/4.)] *= -1
# import cPickle
# with open('/tmp/init_phi.pkl', 'w') as f: cPickle.dump(init_phi, f)
init_phi_observed = np.ones_like(empty_phi)
init_phi_observed[int(SIZE/2.),int(SIZE/4.):-int(SIZE/4.)] = 0.
# init_phi_observed = smooth(init_phi_observed)
new_phi_observed = init_phi_observed; new_phi_observed[int(SIZE/2.),int(SIZE/10.):-int(SIZE/10.)] = 0.
# new_phi_observed = sn.interpolation.zoom(init_phi_observed, 1.2, cval=1., order=0)
# new_phi_observed = sn.interpolation.shift(init_phi_observed, [2,0], cval=1., order=0)
# new_phi_observed = sn.interpolation.rotate(init_phi_observed, 5., cval=1., order=0)
# plt.imshow(new_phi_observed, cmap=cm.Greys_r)
# plt.show()
obs_pts = np.transpose(np.nonzero(new_phi_observed == 0))
# prob = sqp_problem.TrackingProblem()
prob = ctimbpy.TrackingProblem(WORLD_MIN[0], WORLD_MAX[0], WORLD_MIN[1], WORLD_MAX[1], SIZE, SIZE)
prob.set_observation_points(obs_pts)
prob.set_prev_phi(init_phi)
# prob.set_coeffs(flow_norm=1e-9, flow_rigidity=1e-3, flow_tps=0, obs=1, flow_agree=1)
init_u = np.zeros(init_phi.shape + (2,))
#init_u[:,:,0] = 1.
# out_phis, out_us, opt_result = prob.optimize(init_phi, init_u, return_full=True)
result = prob.optimize()
out_phis = [result.phi]
out_us = [result.u]
opt_result = result.opt_result
for out_phi, out_u in [zip(out_phis, out_us)[-1]]:
# import cPickle
# with open('/tmp/dump.pkl', 'w') as f:
# cPickle.dump((out_phi, out_u, opt_result), f)
global fig
fig = plt.figure(figsize=(15,15))
init_phi[obs_pts[:,0],obs_pts[:,1]] = 0
plot_phi(221, sqp_problem.make_interp(init_phi))
ax = fig.add_subplot(224)
ax.plot(np.arange(len(opt_result.cost_over_iters)), opt_result.cost_over_iters)
#out_phi = reintegrate(out_phi)
plot_phi(223, sqp_problem.make_interp(out_phi))
plot_u(222, out_u)
plt.show()
def rotate():
empty_phi = np.ones((SIZE, SIZE))
square_phi = np.ones_like(empty_phi)
square_phi[int(SIZE/2.),int(SIZE/4.):-int(SIZE/4.)] = 0.
square_phi[int(SIZE/2.):-int(SIZE/4.),int(SIZE/4.)] = 0.
square_phi[int(SIZE/2.):-int(SIZE/4.),-int(SIZE/4.)] = 0.
square_phi[-int(SIZE/4.),int(SIZE/4.):-int(SIZE/4.)+1] = 0.
orig_phi = smooth(square_phi)
init_phi = np.ones_like(empty_phi)
init_obs_inds = calc_observable_inds(square_phi)
init_phi[init_obs_inds[:,0],init_obs_inds[:,1]] = 0.
init_phi = smooth(init_phi)
# go through a rotation of the square
prob = sqp_problem.TrackingProblem()
prob.set_coeffs(flow_norm=1e-9, flow_rigidity=1, obs=1, flow_agree=1)
for i_iter, angle in enumerate(np.arange(0, 359, 5)):
if i_iter == 0:
prob.set_coeffs(flow_agree=0)
else:
prob.set_coeffs(flow_agree=1)
print 'Current angle:', angle
# make an observation
rotated = sn.interpolation.rotate(square_phi, angle, cval=1., order=0, reshape=False)
print rotated.shape, square_phi.shape
obs_inds = calc_observable_inds(rotated)
prob.set_obs_points(obs_inds)
prob.set_prev_phi(init_phi)
init_u = np.zeros(init_phi.shape + (2,))
out_phis, out_us, opt_result = prob.optimize(init_phi, init_u, return_full=True)
for out_phi, out_u in [zip(out_phis, out_us)[-1]]:
global fig
fig = plt.figure()
not_oob = (0 <= obs_inds[:,0]) & (obs_inds[:,0] < init_phi.shape[0]) & (0 <= obs_inds[:,1]) & (obs_inds[:,1] < init_phi.shape[1])
init_phi[obs_inds[:,0][not_oob],obs_inds[:,1][not_oob]] = .5
plot_phi(231, sqp_problem.make_interp(init_phi))
ax = fig.add_subplot(234)
tmp = rotated.copy()
tmp[obs_inds[:,0],obs_inds[:,1]] = .5
tmp = np.flipud(tmp.T)
ax.imshow(tmp, cmap=cm.Greys_r).set_interpolation('nearest')
# ax = fig.add_subplot(224)
# ax.plot(np.arange(len(opt_result.costs_over_iters)), opt_result.costs_over_iters)
plot_phi(232, sqp_problem.make_interp(out_phi))
plot_u(233, out_u)
# zero_thresh = sqp_problem.make_interp(out_phi).eval_ijs(obs_inds).mean()
# print 'zero thresh', zero_thresh
out_phi = reintegrate(out_phi)#, zero_thresh)
plot_phi(235, sqp_problem.make_interp(out_phi))
plt.show()
# TODO: REINTEGRATE HERE
init_phi = out_phi
def rotate_full_obs():
square_phi = make_square_phi()
init_phi = square_phi.copy()
# go through a rotation of the square
prob = sqp_problem.TrackingProblem()
prob.set_coeffs(flow_norm=1e-9, flow_rigidity=1e-3, flow_tps=1e-5, obs=1, flow_agree=1)
for i_iter, angle in enumerate(np.arange(0, 359, 5)):
print 'Current angle:', angle
# make an observation
rotated = sn.interpolation.rotate(square_phi, angle, cval=1., order=0, reshape=False)
print rotated.shape, square_phi.shape
obs_inds = calc_observable_inds(rotated)
prob.set_obs_points(obs_inds)
prob.set_prev_phi(init_phi)
init_u = np.zeros(init_phi.shape + (2,))
out_phis, out_us, opt_result = prob.optimize(init_phi, init_u, return_full=True)
for out_phi, out_u in [zip(out_phis, out_us)[-1]]:
global fig
fig = plt.figure()
# superimpose observation drawing
not_oob = (0 <= obs_inds[:,0]) & (obs_inds[:,0] < init_phi.shape[0]) & (0 <= obs_inds[:,1]) & (obs_inds[:,1] < init_phi.shape[1])
init_phi[obs_inds[:,0][not_oob],obs_inds[:,1][not_oob]] = 0
plot_phi(231, sqp_problem.make_interp(init_phi))
# ax = fig.add_subplot(234)
# tmp = rotated.copy()
# tmp[obs_inds[:,0],obs_inds[:,1]] = .5
# tmp = np.flipud(tmp.T)
# ax.imshow(tmp, cmap=cm.Greys_r).set_interpolation('nearest')
ax = fig.add_subplot(234)
ax.plot(np.arange(len(opt_result.costs_over_iters)), opt_result.costs_over_iters)
plot_phi(232, sqp_problem.make_interp(out_phi))
plot_u(233, out_u)
out_phi = reintegrate(out_phi)
plot_phi(235, sqp_problem.make_interp(out_phi))
plt.show()
init_phi = out_phi
init_phi_observed = np.ones_like(empty_phi)
init_phi_observed[int(SIZE/2.),int(SIZE/4.):-int(SIZE/4.)] = 0.
new_phi_observed = init_phi_observed; new_phi_observed[int(SIZE/2.),int(SIZE/10.):-int(SIZE/10.)] = 0.
obs_pts = np.transpose(np.nonzero(new_phi_observed == 0))
prob = sqp_problem.TrackingProblem()
prob.set_obs_points(obs_pts)
prob.set_prev_phi(init_phi)
prob.set_coeffs(flow_norm=1e-9, flow_rigidity=1e-8, flow_tps=1e-5, obs=1, flow_agree=1)
init_u = np.zeros(init_phi.shape + (2,))
#init_u[:,:,0] = 1.
out_phis, out_us, opt_result = prob.optimize(init_phi, init_u, return_full=True)
for out_phi, out_u in [zip(out_phis, out_us)[-1]]:
# import cPickle
# with open('/tmp/dump.pkl', 'w') as f:
# cPickle.dump((out_phi, out_u, opt_result), f)
global fig
fig = plt.figure(figsize=(15,15))
init_phi[obs_pts[:,0],obs_pts[:,1]] = 0
plot_phi(221, sqp_problem.make_interp(init_phi))
ax = fig.add_subplot(224)
ax.plot(np.arange(len(opt_result.costs_over_iters)), opt_result.costs_over_iters)
out_phi = reintegrate(out_phi)
plot_phi(223, sqp_problem.make_interp(out_phi))
plot_u(222, out_u)
plt.show()
#u2 = np.empty_like(u) #u2[:,:,0] = u[:,:,1] #u2[:,:,1] = u[:,:,0] #u = u2 fig = plt.figure() ax = fig.add_subplot(221, aspect='equal') #mask = Y[:,:] == 15 #u[:,:,0][np.logical_not(mask)] = 0 #u[:,:,1][np.logical_not(mask)] = 0 print u ax.quiver(X, Y, u[:,:,0], u[:,:,1], angles='xy', scale_units='xy', scale=1.) init_phi_surf = sqp_problem.make_interp(init_phi) plot_phi(fig, 222, init_phi_surf) out_phi = apply_flow(init_phi, u) apply_flow_forwards(fig, 224, init_phi, u, X2.ravel(), Y2.ravel(), init_phi.ravel()) #for i in range(20): # print i # out_phi = apply_flow(out_phi, u) out_phi_surf = sqp_problem.make_interp(out_phi) ax = plot_phi(fig, 223, out_phi_surf) # ax.quiver(X, Y, np.fliplr(u[:,:,0].T), u[:,:,1].T, pivot='tip') plt.show()