def test_convert_tangent_euclidean_to_stereo():
solver = kmap.Solver()
n_steps = 10
s3_map = map_sens.Sensitivity(solver, n_steps)
n_runup = 10
u_init = solver.u_init
s0 = solver.s0
u_init = solver.primal_step(u_init, s0, n_runup)
u_trj = s3_map.solve_primal(solver,\
u_init, n_steps, solver.s0)
u_trj = u_trj.T
q = rand(2, n_steps)
q[0] = 0.
q[1] = 1.
q_euclidean = solver.convert_tangent_stereo_to_euclidean(u_trj, q)
q_euclidean = vstack(q_euclidean)
q_spherical = solver.convert_tangent_euclidean_to_spherical(u_trj,\
q_euclidean)
q_spherical = vstack(q_spherical)
p_euclidean = solver.convert_tangent_spherical_to_euclidean(
u_trj, q_spherical)
p_euclidean = vstack(p_euclidean)
p_stereo = solver.convert_tangent_euclidean_to_stereo(u_trj, p_euclidean)
p_stereo = vstack(p_stereo)
print(p_stereo)
assert (norm(p_stereo - q) < 1.e-10)
return
def test_step_primal():
holes = array([1./sqrt(2.),0,1./sqrt(2.0),\
-1./sqrt(2.),0,1./sqrt(2.0), \
1./sqrt(2.),0,-1./sqrt(2.0), \
-1./sqrt(2.),0,-1./sqrt(2.0)])
holes = holes.reshape(4, 3)
solver_map = kmap.Solver()
u_init = solver_map.u_init
n_map = solver_map.n_poincare
n_steps = 500
s0 = solver_map.s0
sens_object = map_sens.Sensitivity()
solve_primal = sens_object.solve_primal
u = solve_primal(solver_map,\
u_init,n_steps,s0)
flag = 1
epsi = 1.e-1
for i in range(1, n_steps):
if (not (flag)):
break
for j in range(holes.shape[0]):
if (norm(u[i, :3] - holes[j]) < epsi):
flag = 0
if (norm(u[i, :3]) > 1.0 + epsi):
flag = 0
assert (i == n_steps - 1)
def visualize_poincare_primal():
solver_map = kmap.Solver()
u_init = solver_map.u_init
n_steps = 500
s0 = solver_map.s0
sens_object = map_sens.Sensitivity()
solve_primal = sens_object.solve_primal
u_map = solve_primal(solver_map,\
u_init,n_steps,s0)
stereo_real, stereo_imag = \
solver_map.stereographic_projection(u_map.T)
figure()
plot(stereo_real, stereo_imag, '.')
savefig('st_proj_poincare_attractor.png')
def visualize_tangent_stereographic(u, v, c1="black"):
EPS = 1E-8
u_plus, u_minus = u + v * EPS, u - v * EPS
stereographic_projection = kmap.Solver().stereographic_projection
stereo_real, stereo_imag = stereographic_projection(u.T)
stereo_real_plus, stereo_imag_plus = stereographic_projection(u_plus.T)
stereo_real_minus, stereo_imag_minus = stereographic_projection(u_minus.T)
stereo_real_plus = extrapolate(stereo_real, stereo_real_plus, 1E6)
stereo_real_minus = extrapolate(stereo_real, stereo_real_minus, 1E6)
stereo_imag_plus = extrapolate(stereo_imag, stereo_imag_plus, 1E6)
stereo_imag_minus = extrapolate(stereo_imag, stereo_imag_minus, 1E6)
plot([stereo_real_plus, stereo_real_minus],
[stereo_imag_plus, stereo_imag_minus],
color=c1,
ms=10)
def visualize_unstable_direction():
solver_map = kmap.Solver()
u_init = solver_map.u_init
n_map = solver_map.n_poincare
n_steps = 500
s0 = solver_map.s0
sens_object = map_sens.Sensitivity()
solve_primal = sens_object.solve_primal
u_map = solve_primal(solver_map,\
u_init,n_steps,s0)
solve_unstable_direction = sens_object.\
solve_unstable_direction
v = solve_unstable_direction(solver_map,\
u_map, rand(solver_map.state_dim),n_steps,\
s0)
visualize_tangent_stereographic(u_map,\
v)
def test_convert_tangent_euclidean_to_spherical():
solver = kmap.Solver()
n_steps = 10
s3_map = map_sens.Sensitivity(solver, n_steps)
n_runup = 10
u_init = solver.u_init
s0 = solver.s0
u_init = solver.primal_step(u_init, s0, n_runup)
u_trj = s3_map.solve_primal(solver,\
u_init, n_steps, solver.s0)
q = rand(2, n_steps)
q_euclidean = solver.convert_tangent_spherical_to_euclidean(u_trj.T, q)
q_euclidean = vstack(q_euclidean)
q_spherical = solver.convert_tangent_euclidean_to_spherical(u_trj.T,\
q_euclidean)
assert (norm(q - q_spherical) < 1.e-10)
return
def test_convert_tangent_stereo_to_euclidean():
solver = kmap.Solver()
n_steps = 10
s3_map = map_sens.Sensitivity(solver, n_steps)
n_runup = 10
u_init = solver.u_init
s0 = solver.s0
u_init = solver.primal_step(u_init, s0, n_runup)
u_trj = s3_map.solve_primal(solver,\
u_init, n_steps, solver.s0)
p1 = solver.convert_tangent_stereo_to_euclidean(u_trj.T,\
vstack((ones(n_steps),zeros(n_steps))))
p2 = solver.convert_tangent_stereo_to_euclidean(u_trj.T,\
vstack((zeros(n_steps),ones(n_steps))))
p1 = vstack(p1)
p2 = vstack(p2)
dot_product_p1_p2 = sum(p1 * p2, axis=0)
print(norm(dot_product_p1_p2))
assert (norm(dot_product_p1_p2) <= 1.e-10)
return
def test_convert_tangent_spherical_to_euclidean():
solver = kmap.Solver()
n_steps = 10
s3_map = map_sens.Sensitivity(solver, n_steps)
n_runup = 10
u_init = solver.u_init
s0 = solver.s0
u_init = solver.primal_step(u_init, s0, n_runup)
u_trj = s3_map.solve_primal(solver,\
u_init, n_steps, solver.s0)
q1 = solver.convert_tangent_spherical_to_euclidean(u_trj.T,\
vstack((ones(n_steps),zeros(n_steps))))
q2 = solver.convert_tangent_spherical_to_euclidean(u_trj.T,\
vstack((zeros(n_steps),ones(n_steps))))
q1 = array(q1)
q2 = array(q2)
dot_product_q1_q2 = sum(q1 * q2, axis=0)
print(norm(dot_product_q1_q2))
assert (norm(dot_product_q1_q2) <= 1.e-10)
return
import sys
sys.path.insert(0, '../examples/')
import kuznetsov_poincare as kmap
import kuznetsov as kode
import map_sens as map_sens
import flow_sens as flow_sens
from time import clock
if __name__ == "__main__":
solver_ode = kode.Solver()
solver_map = kmap.Solver()
n_map = solver_ode.n_poincare
n_steps_map = 50
n_steps = n_map * n_steps_map
plykin = flow_sens.Sensitivity(solver_ode, n_steps)
t0 = clock()
u_ode = plykin.solve_primal(solver_ode,solver_ode.u_init,\
n_steps,
solver_ode.s0)
t1 = clock()
print('{:<60s}{:>16.10f}'.format(\
"Time to solve primal: ",\
t1-t0))
t2 = clock()
plykin.precompute_sources(solver_ode, u_ode)
t3 = clock()
print('{:<60s}{:>16.10f}'.format(\
"Time for flow precomputations: ",\
t3-t2))
poincare_plykin = map_sens.Sensitivity(solver_map, n_steps_map)
import sys
sys.path.insert(0, '../examples/')
import kuznetsov_poincare as kp
from objective import *
import scipy
from scipy.interpolate import griddata
import alt_map_sens as map_sens
from time import clock
from pylab import *
from mpl_toolkits.mplot3d import Axes3D
#def compute_sensitivity():
if __name__ == "__main__":
solver = kp.Solver()
n_steps = 5
s3_map = map_sens.Sensitivity(solver,n_steps)
n_runup = s3_map.n_runup
n_runup_forward_adjoint = 10
u_init = solver.u_init
s0 = solver.s0
state_dim = solver.state_dim
param_dim = s0.size
u_init = solver.primal_step(u_init, s0, n_runup)
u_trj = s3_map.solve_primal(solver,\
u_init, n_steps, solver.s0)
ds0 = zeros(param_dim)
ds1 = copy(ds0)
ds1[0] = 1.0
dJ0 = zeros(state_dim)
detJac = s3_map.compute_jacobian_determinant(solver,\