def test_initialization_from_data(self):
n_e = 50
hs = N.ones(n_e)*1./n_e
n_cp = 3
nlp = NLPCollocationLagrangePolynomials(self.model, n_e, hs, n_cp)
nlp.set_initial_from_dymola(self.expected,hs,0,1)
nlp.export_result_dymola()
self.data = ResultDymolaTextual(
"NominalTests_NominalOptTest2_result.txt")
self.assert_all_trajectories(['x', 'der(x)', 'u'])
def test_init(self):
m = JMUModel(self.jn)
# Create a new collocation object
n_e = 30
coll = NLPCollocationLagrangePolynomials(m,n_e, N.ones(n_e)/n_e, 3)
# Initialize with optimization result
coll.set_initial_from_dymola(self.res.result_data,N.array([]),0,1)
# Write initial point to file
coll.export_result_dymola('Init_res.txt')
# Load result
res_init = ResultDymolaTextual('Init_res.txt')
# Load test fixture
res_init_fix = ResultDymolaTextual(self.curr_dir + '/../files/Results/MinTimeInit_init_fix.txt')
# Extract trajectories
dx = res_init.get_variable_data('der(x)')
dv = res_init.get_variable_data('der(v)')
x = res_init.get_variable_data('x')
v = res_init.get_variable_data('v')
u = res_init.get_variable_data('u')
dx_fix = res_init_fix.get_variable_data('der(x)')
dv_fix = res_init_fix.get_variable_data('der(v)')
x_fix = res_init_fix.get_variable_data('x')
v_fix = res_init_fix.get_variable_data('v')
u_fix = res_init_fix.get_variable_data('u')
# Comparison tests
N.testing.assert_array_almost_equal(dx_fix.x,dx.x)
N.testing.assert_array_almost_equal(dv_fix.x,dv.x)
N.testing.assert_array_almost_equal(x_fix.x,x.x)
N.testing.assert_array_almost_equal(v_fix.x,v.x)
N.testing.assert_array_almost_equal(u_fix.x,u.x)
if False:
plt.figure(1)
plt.subplot(2,1,1)
plt.plot(x.t,x.x,'r')
plt.hold(True)
plt.plot(v.t,v.x,'r')
plt.grid(True)
plt.subplot(2,1,2)
plt.plot(u.t,u.x,'r')
plt.grid(True)
def setUp(self):
resfile = os.path.join(get_files_path(), 'Results',
'BlockingInitPack_M_init_result.txt')
self.res_init = ResultDymolaTextual(resfile)
self.n_e = 5 # Number of elements
self.hs = N.ones(self.n_e)*1./self.n_e # Equidistant points
self.n_cp = 3; # Number of collocation points in each element
# Blocking factors for control parametrization
blocking_factors=N.ones(self.n_e,dtype=N.int)
self.nlp = NLPCollocationLagrangePolynomials(self.opt_model,
self.n_e,self.hs,self.n_cp,blocking_factors)
self.nlp.set_initial_from_dymola(self.res_init, self.hs, 0., 10.)
self.nlp.export_result_dymola("qwe.txt")
self.res_init2 = ResultDymolaTextual('qwe.txt')
def test_initialization_from_data(self):
n_e = 50
hs = N.ones(n_e) * 1. / n_e
n_cp = 3
nlp = NLPCollocationLagrangePolynomials(self.model, n_e, hs, n_cp)
nlp.set_initial_from_dymola(self.expected, hs, 0, 1)
nlp.export_result_dymola()
self.data = ResultDymolaTextual(
"NominalTests_NominalOptTest2_result.txt")
self.assert_all_trajectories(['x', 'der(x)', 'u'])
def test_init(self):
m = JMUModel(self.jn)
# Create a new collocation object
n_e = 30
coll = NLPCollocationLagrangePolynomials(m, n_e, N.ones(n_e) / n_e, 3)
# Initialize with optimization result
coll.set_initial_from_dymola(self.res.result_data, N.array([]), 0, 1)
# Write initial point to file
coll.export_result_dymola('Init_res.txt')
# Load result
res_init = ResultDymolaTextual('Init_res.txt')
# Load test fixture
res_init_fix = ResultDymolaTextual(
self.curr_dir + '/../files/Results/MinTimeInit_init_fix.txt')
# Extract trajectories
dx = res_init.get_variable_data('der(x)')
dv = res_init.get_variable_data('der(v)')
x = res_init.get_variable_data('x')
v = res_init.get_variable_data('v')
u = res_init.get_variable_data('u')
dx_fix = res_init_fix.get_variable_data('der(x)')
dv_fix = res_init_fix.get_variable_data('der(v)')
x_fix = res_init_fix.get_variable_data('x')
v_fix = res_init_fix.get_variable_data('v')
u_fix = res_init_fix.get_variable_data('u')
# Comparison tests
N.testing.assert_array_almost_equal(dx_fix.x, dx.x)
N.testing.assert_array_almost_equal(dv_fix.x, dv.x)
N.testing.assert_array_almost_equal(x_fix.x, x.x)
N.testing.assert_array_almost_equal(v_fix.x, v.x)
N.testing.assert_array_almost_equal(u_fix.x, u.x)
if False:
plt.figure(1)
plt.subplot(2, 1, 1)
plt.plot(x.t, x.x, 'r')
plt.hold(True)
plt.plot(v.t, v.x, 'r')
plt.grid(True)
plt.subplot(2, 1, 2)
plt.plot(u.t, u.x, 'r')
plt.grid(True)
def setUp(self):
resfile = os.path.join(get_files_path(), 'Results',
'BlockingInitPack_M_init_result.txt')
self.res_init = ResultDymolaTextual(resfile)
self.n_e = 5 # Number of elements
self.hs = N.ones(self.n_e)*1./self.n_e # Equidistant points
self.n_cp = 3; # Number of collocation points in each element
# Blocking factors for control parametrization
blocking_factors=N.ones(self.n_e,dtype=N.int)
self.nlp = NLPCollocationLagrangePolynomials(self.opt_model,
self.n_e,self.hs,self.n_cp,blocking_factors)
self.nlp.set_initial_from_dymola(self.res_init, self.hs, 0., 10.)
self.nlp.export_result_dymola("qwe.txt")
self.res_init2 = ResultDymolaTextual('qwe.txt')
class TestOptInitBlockingFactors:
@classmethod
def setUpClass(cls):
cls.curr_dir = os.path.dirname(os.path.abspath(__file__));
mofile = os.path.join(get_files_path(), 'Modelica',
'BlockingError.mop')
m = compile_jmu("BlockingInitPack.M_init", mofile)
cls.model = JMUModel(m)
m = compile_jmu("BlockingInitPack.M_Opt",mofile)
cls.opt_model = JMUModel(m)
@testattr(ipopt = True)
def setUp(self):
resfile = os.path.join(get_files_path(), 'Results',
'BlockingInitPack_M_init_result.txt')
self.res_init = ResultDymolaTextual(resfile)
self.n_e = 5 # Number of elements
self.hs = N.ones(self.n_e)*1./self.n_e # Equidistant points
self.n_cp = 3; # Number of collocation points in each element
# Blocking factors for control parametrization
blocking_factors=N.ones(self.n_e,dtype=N.int)
self.nlp = NLPCollocationLagrangePolynomials(self.opt_model,
self.n_e,self.hs,self.n_cp,blocking_factors)
self.nlp.set_initial_from_dymola(self.res_init, self.hs, 0., 10.)
self.nlp.export_result_dymola("qwe.txt")
self.res_init2 = ResultDymolaTextual('qwe.txt')
@testattr(ipopt = True)
def test_initialization(self):
m_x1_1 = self.res_init.get_variable_data("m.x[1]").x
m_x1_2 = self.res_init2.get_variable_data("m.x[1]").x
m_x2_1 = self.res_init.get_variable_data("m.x[2]").x
m_x2_2 = self.res_init2.get_variable_data("m.x[2]").x
m_y_1 = self.res_init.get_variable_data("m.y").x
m_y_2 = self.res_init2.get_variable_data("m.y").x
u_1 = self.res_init.get_variable_data("u").x
u_2 = self.res_init2.get_variable_data("u").x
(n_x, n_g, n_h, dg_n_nz, dh_n_nz) = self.nlp.opt_coll_get_dimensions()
x_init = N.zeros(n_x)
self.nlp.opt_coll_get_initial(x_init)
nbr_dx = self.nlp._model._n_real_dx.value
nbr_x = self.nlp._model._n_real_x.value
nbr_u = self.nlp._model._n_real_u.value
nbr_w = self.nlp._model._n_real_w.value
offs1 = nbr_dx + nbr_x + nbr_u + nbr_w
offs2 = offs1 - 1
#print nbr_dx, nbr_x, nbr_u, nbr_w, offs1, offs2
offs_x_el_junc = offs1 + offs2*self.n_e*self.n_cp + self.n_e
x_el_junc = N.zeros((self.n_e,3))
for i in range(self.n_e):
x_el_junc[i,:] = x_init[offs_x_el_junc + i*3:offs_x_el_junc + (i+1)*3]
t_f = 10.
t_x_el_junc = N.linspace(0,t_f,self.n_e+1)
t_x_el_junc = t_x_el_junc[1:]
offs_dx_p = offs1 + offs2*self.n_e*self.n_cp + 4*self.n_e
offs_x_p = offs_dx_p + nbr_dx
offs_u_p = offs_x_p + nbr_x
offs_w_p = offs_u_p + nbr_u
n_tp = 10
dx_p = N.zeros((n_tp,nbr_dx))
x_p = N.zeros((n_tp,nbr_x))
u_p = N.zeros((n_tp,nbr_u))
w_p = N.zeros((n_tp,nbr_w))
for i in range(n_tp):
dx_p[i,:] = x_init[offs_dx_p + i*offs1:offs_dx_p + i*offs1 + nbr_dx]
x_p[i,:] = x_init[offs_x_p + i*offs1:offs_x_p + i*offs1 + nbr_x]
u_p[i,:] = x_init[offs_u_p + i*offs1:offs_u_p + i*offs1 + nbr_u]
w_p[i,:] = x_init[offs_w_p + i*offs1:offs_w_p + i*offs1 + nbr_w]
t_tp = N.linspace(1,10,10)
h=N.zeros(n_h)
self.nlp.opt_coll_h(h)
#print N.max(N.abs(h))
# plt.figure(3)
# plt.clf()
# plt.plot(m_x1_1.t,m_x1_1.x)
# plt.plot(m_x1_2.t,m_x1_2.x)
# plt.plot(t_x_el_junc,x_el_junc[:,1],'x')
# plt.plot(t_tp,x_p[:,1],'o')
# plt.title("x[1]")
# plt.grid()
# plt.show()
# plt.figure(4)
# plt.clf()
# plt.plot(m_x2_1.t,m_x2_1.x)
# plt.plot(m_x2_2.t,m_x2_2.x)
# plt.plot(t_x_el_junc,x_el_junc[:,2],'x')
# plt.plot(t_tp,x_p[:,2],'o')
# plt.title("x[2]")
# plt.grid()
# plt.show()
# plt.figure(5)
# plt.clf()
# plt.plot(m_y_1.t,m_y_1.x)
# plt.plot(m_y_2.t,m_y_2.x)
# plt.plot(t_tp,w_p[:,0],'o')
# plt.title("y")
# plt.grid()
# plt.show()
# plt.figure(6)
# plt.clf()
# plt.plot(m_u_1.t,m_u_1.x)
# plt.plot(m_u_2.t,m_u_2.x)
# plt.plot(t_tp,u_p[:,0],'o')
# plt.title("u")
# plt.grid()
# plt.show()
m_x1_2_res = N.array([ 1. , 0.96503702, 0.80699964, 0.81708186, 0.82968423,
0.73425843, 0.4641878 , 0.30274918, -0.22539661, -0.45405707,
-0.47988416, -0.25883339, 0.07728009, 0.22367095, 0.49688434,
0.42028466])
m_x2_2_res = N.array([ 1. , 0.77648496, 0.75474237, 0.86572509, 0.85523243,
0.47651669, -0.02410645, -0.24417425, -0.68431665, -0.61607295,
-0.48363351, 0.15624317, 0.56793272, 0.66948745, 0.56283272,
0.14759305])
u_2_res = N.array([ 0. , 0.30515581, 0.30515581, 0.30515581, 0.73893649,
0.73893649, 0.73893649, -0.920168 , -0.920168 , -0.920168 ,
0.0269131 , 0.0269131 , 0.0269131 , 0.89776804, 0.89776804,
0.89776804])
m_y_2_res = N.array([ 2. , 1.74152198, 1.56174201, 1.68280695, 1.68491666,
1.21077512, 0.44008136, 0.05857493, -0.90971326, -1.07013001,
-0.96351767, -0.10259022, 0.64521281, 0.8931584 , 1.05971706,
0.56787771])
x_el_junc_res = N.array([[ 3.91403795, 0.81708186, 0.86572509],
[ 6.38519639, 0.4641878 , -0.02410645],
[ 8.53595865, -0.45405707, -0.61607295],
[ 9.99351048, 0.07728009, 0.56793272],
[ 11.69233416, 0.42028466, 0.14759305]])
dx_p_res = N.array([[ 1.89614716, -0.13108396, 0.13906756],
[ 2.24392408, 0.04864298, 0.04357222],
[ 1.05980345, -0.15348176, -0.49911689],
[ 0.78887658, -0.48829925, -0.73269738],
[ 1.29975129, -0.52999439, -0.34773495],
[ 0.66373748, -0.16201457, 0.33665916],
[ 0.56780963, 0.31891731, 0.70407499],
[ 1.30735387, 0.49065263, 0.42142531],
[ 0.81705525, 0.20439241, -0.24969127],
[ 0.49438075, -0.27269124, -0.69161393]])
x_p_res = N.array([[ 1.71039492, 0.83348678, 0.70240363],
[ 3.91403795, 0.81708186, 0.86572509],
[ 5.61520049, 0.79371837, 0.64023676],
[ 6.38519639, 0.4641878 , -0.02410645],
[ 7.48469697, -0.08119087, -0.61118532],
[ 8.53595865, -0.45405707, -0.61607295],
[ 9.01802285, -0.36600637, -0.04708865],
[ 9.99351048, 0.07728009, 0.56793272],
[ 11.15957068, 0.45741668, 0.66180933],
[ 11.69233416, 0.42028466, 0.14759305]])
u_p_res = N.array([[ 0.84147098],
[ 0.90929742],
[ 0.14112001],
[-0.75680257],
[-0.95892497],
[-0.27941585],
[ 0.6569871 ],
[ 0.98935824],
[ 0.41211848],
[-0.54402111]])
w_p_res = N.array([[ 1.53589041, 0.84147098],
[ 1.68280695, 0.90929742],
[ 1.43395513, 0.14112001],
[ 0.44008136, -0.75680257],
[-0.69237618, -0.95892497],
[-1.07013001, -0.27941585],
[-0.41309502, 0.6569871 ],
[ 0.64521281, 0.98935824],
[ 1.11922602, 0.41211848],
[ 0.56787771, -0.54402111]])
assert N.sum(N.abs(m_x1_2-m_x1_2_res))<1e-3
assert N.sum(N.abs(m_x2_2-m_x2_2_res))<1e-3
assert N.sum(N.abs(u_2-u_2_res))<1e-3
assert N.sum(N.abs(m_y_2-m_y_2_res))<1e-3
assert N.sum(N.abs(x_el_junc-x_el_junc_res))<1e-3
assert N.sum(N.abs(dx_p-dx_p_res))<1e-3
assert N.sum(N.abs(x_p-x_p_res))<1e-3
assert N.sum(N.abs(u_p-u_p_res))<1e-3
assert N.sum(N.abs(w_p-w_p_res))<1e-3
optimizer = CollocationOptimizer(self.nlp)
optimizer.opt_coll_ipopt_solve()
class TestOptInitBlockingFactors:
@classmethod
def setUpClass(cls):
cls.curr_dir = os.path.dirname(os.path.abspath(__file__))
mofile = os.path.join(get_files_path(), 'Modelica',
'BlockingError.mop')
m = compile_jmu("BlockingInitPack.M_init", mofile)
cls.model = JMUModel(m)
m = compile_jmu("BlockingInitPack.M_Opt", mofile)
cls.opt_model = JMUModel(m)
@testattr(ipopt=True)
def setUp(self):
resfile = os.path.join(get_files_path(), 'Results',
'BlockingInitPack_M_init_result.txt')
self.res_init = ResultDymolaTextual(resfile)
self.n_e = 5 # Number of elements
self.hs = N.ones(self.n_e) * 1. / self.n_e # Equidistant points
self.n_cp = 3
# Number of collocation points in each element
# Blocking factors for control parametrization
blocking_factors = N.ones(self.n_e, dtype=N.int)
self.nlp = NLPCollocationLagrangePolynomials(self.opt_model, self.n_e,
self.hs, self.n_cp,
blocking_factors)
self.nlp.set_initial_from_dymola(self.res_init, self.hs, 0., 10.)
self.nlp.export_result_dymola("qwe.txt")
self.res_init2 = ResultDymolaTextual('qwe.txt')
@testattr(ipopt=True)
def test_initialization(self):
m_x1_1 = self.res_init.get_variable_data("m.x[1]").x
m_x1_2 = self.res_init2.get_variable_data("m.x[1]").x
m_x2_1 = self.res_init.get_variable_data("m.x[2]").x
m_x2_2 = self.res_init2.get_variable_data("m.x[2]").x
m_y_1 = self.res_init.get_variable_data("m.y").x
m_y_2 = self.res_init2.get_variable_data("m.y").x
u_1 = self.res_init.get_variable_data("u").x
u_2 = self.res_init2.get_variable_data("u").x
(n_x, n_g, n_h, dg_n_nz, dh_n_nz) = self.nlp.opt_coll_get_dimensions()
x_init = N.zeros(n_x)
self.nlp.opt_coll_get_initial(x_init)
nbr_dx = self.nlp._model._n_real_dx.value
nbr_x = self.nlp._model._n_real_x.value
nbr_u = self.nlp._model._n_real_u.value
nbr_w = self.nlp._model._n_real_w.value
offs1 = nbr_dx + nbr_x + nbr_u + nbr_w
offs2 = offs1 - 1
#print nbr_dx, nbr_x, nbr_u, nbr_w, offs1, offs2
offs_x_el_junc = offs1 + offs2 * self.n_e * self.n_cp + self.n_e
x_el_junc = N.zeros((self.n_e, 3))
for i in range(self.n_e):
x_el_junc[i, :] = x_init[offs_x_el_junc + i * 3:offs_x_el_junc +
(i + 1) * 3]
t_f = 10.
t_x_el_junc = N.linspace(0, t_f, self.n_e + 1)
t_x_el_junc = t_x_el_junc[1:]
offs_dx_p = offs1 + offs2 * self.n_e * self.n_cp + 4 * self.n_e
offs_x_p = offs_dx_p + nbr_dx
offs_u_p = offs_x_p + nbr_x
offs_w_p = offs_u_p + nbr_u
n_tp = 10
dx_p = N.zeros((n_tp, nbr_dx))
x_p = N.zeros((n_tp, nbr_x))
u_p = N.zeros((n_tp, nbr_u))
w_p = N.zeros((n_tp, nbr_w))
for i in range(n_tp):
dx_p[i, :] = x_init[offs_dx_p + i * offs1:offs_dx_p + i * offs1 +
nbr_dx]
x_p[i, :] = x_init[offs_x_p + i * offs1:offs_x_p + i * offs1 +
nbr_x]
u_p[i, :] = x_init[offs_u_p + i * offs1:offs_u_p + i * offs1 +
nbr_u]
w_p[i, :] = x_init[offs_w_p + i * offs1:offs_w_p + i * offs1 +
nbr_w]
t_tp = N.linspace(1, 10, 10)
h = N.zeros(n_h)
self.nlp.opt_coll_h(h)
#print N.max(N.abs(h))
# plt.figure(3)
# plt.clf()
# plt.plot(m_x1_1.t,m_x1_1.x)
# plt.plot(m_x1_2.t,m_x1_2.x)
# plt.plot(t_x_el_junc,x_el_junc[:,1],'x')
# plt.plot(t_tp,x_p[:,1],'o')
# plt.title("x[1]")
# plt.grid()
# plt.show()
# plt.figure(4)
# plt.clf()
# plt.plot(m_x2_1.t,m_x2_1.x)
# plt.plot(m_x2_2.t,m_x2_2.x)
# plt.plot(t_x_el_junc,x_el_junc[:,2],'x')
# plt.plot(t_tp,x_p[:,2],'o')
# plt.title("x[2]")
# plt.grid()
# plt.show()
# plt.figure(5)
# plt.clf()
# plt.plot(m_y_1.t,m_y_1.x)
# plt.plot(m_y_2.t,m_y_2.x)
# plt.plot(t_tp,w_p[:,0],'o')
# plt.title("y")
# plt.grid()
# plt.show()
# plt.figure(6)
# plt.clf()
# plt.plot(m_u_1.t,m_u_1.x)
# plt.plot(m_u_2.t,m_u_2.x)
# plt.plot(t_tp,u_p[:,0],'o')
# plt.title("u")
# plt.grid()
# plt.show()
m_x1_2_res = N.array([
1., 0.96503702, 0.80699964, 0.81708186, 0.82968423, 0.73425843,
0.4641878, 0.30274918, -0.22539661, -0.45405707, -0.47988416,
-0.25883339, 0.07728009, 0.22367095, 0.49688434, 0.42028466
])
m_x2_2_res = N.array([
1., 0.77648496, 0.75474237, 0.86572509, 0.85523243, 0.47651669,
-0.02410645, -0.24417425, -0.68431665, -0.61607295, -0.48363351,
0.15624317, 0.56793272, 0.66948745, 0.56283272, 0.14759305
])
u_2_res = N.array([
0., 0.30515581, 0.30515581, 0.30515581, 0.73893649, 0.73893649,
0.73893649, -0.920168, -0.920168, -0.920168, 0.0269131, 0.0269131,
0.0269131, 0.89776804, 0.89776804, 0.89776804
])
m_y_2_res = N.array([
2., 1.74152198, 1.56174201, 1.68280695, 1.68491666, 1.21077512,
0.44008136, 0.05857493, -0.90971326, -1.07013001, -0.96351767,
-0.10259022, 0.64521281, 0.8931584, 1.05971706, 0.56787771
])
x_el_junc_res = N.array([[3.91403795, 0.81708186, 0.86572509],
[6.38519639, 0.4641878, -0.02410645],
[8.53595865, -0.45405707, -0.61607295],
[9.99351048, 0.07728009, 0.56793272],
[11.69233416, 0.42028466, 0.14759305]])
dx_p_res = N.array([[1.89614716, -0.13108396, 0.13906756],
[2.24392408, 0.04864298, 0.04357222],
[1.05980345, -0.15348176, -0.49911689],
[0.78887658, -0.48829925, -0.73269738],
[1.29975129, -0.52999439, -0.34773495],
[0.66373748, -0.16201457, 0.33665916],
[0.56780963, 0.31891731, 0.70407499],
[1.30735387, 0.49065263, 0.42142531],
[0.81705525, 0.20439241, -0.24969127],
[0.49438075, -0.27269124, -0.69161393]])
x_p_res = N.array([[1.71039492, 0.83348678, 0.70240363],
[3.91403795, 0.81708186, 0.86572509],
[5.61520049, 0.79371837, 0.64023676],
[6.38519639, 0.4641878, -0.02410645],
[7.48469697, -0.08119087, -0.61118532],
[8.53595865, -0.45405707, -0.61607295],
[9.01802285, -0.36600637, -0.04708865],
[9.99351048, 0.07728009, 0.56793272],
[11.15957068, 0.45741668, 0.66180933],
[11.69233416, 0.42028466, 0.14759305]])
u_p_res = N.array([[0.84147098], [0.90929742], [0.14112001],
[-0.75680257], [-0.95892497], [-0.27941585],
[0.6569871], [0.98935824], [0.41211848],
[-0.54402111]])
w_p_res = N.array([[1.53589041, 0.84147098], [1.68280695, 0.90929742],
[1.43395513, 0.14112001], [0.44008136, -0.75680257],
[-0.69237618, -0.95892497],
[-1.07013001,
-0.27941585], [-0.41309502, 0.6569871],
[0.64521281, 0.98935824], [1.11922602, 0.41211848],
[0.56787771, -0.54402111]])
assert N.sum(N.abs(m_x1_2 - m_x1_2_res)) < 1e-3
assert N.sum(N.abs(m_x2_2 - m_x2_2_res)) < 1e-3
assert N.sum(N.abs(u_2 - u_2_res)) < 1e-3
assert N.sum(N.abs(m_y_2 - m_y_2_res)) < 1e-3
assert N.sum(N.abs(x_el_junc - x_el_junc_res)) < 1e-3
assert N.sum(N.abs(dx_p - dx_p_res)) < 1e-3
assert N.sum(N.abs(x_p - x_p_res)) < 1e-3
assert N.sum(N.abs(u_p - u_p_res)) < 1e-3
assert N.sum(N.abs(w_p - w_p_res)) < 1e-3
optimizer = CollocationOptimizer(self.nlp)
optimizer.opt_coll_ipopt_solve()
