How do I run two phases parallel-in-time?#
Complex models sometimes encounter state variables which are best simulated on different time scales, with some state variables changing quickly (fast variables) and some evolving slowly (slow variables).
For instance, an aircraft trajectory optimization which includes vehicle component temperatures might see relatively gradual changes in altitude over the course of a two hour flight while temperatures of some components seem to exhibit step-function-like behavior on the same scale.
To accommodate both fast and slow variables in the same ODE, one would typically need to use a dense grid (with many segments/higher order segments). This can be unnecessarily burdensome when there are many slow variables or evaluating their rates is particularly expensive.
As a solution, Dymos allows the user to run two phases over the same range of times, where one phase may have a more sparse grid to accommodate the slow variables, and one has a more dense grid for the fast variables.
To connect the two phases, state variable values are passed from the first (slow) phase to the second (fast) phase as non-optimal dynamic control variables.
These values are then used to evaluate the rates of the fast variables.
Since outputs from the first phase in general will not fall on the appropriate grid points to be used by the second phase, interpolation is necessary.
This is one application of the interpolating timeseries component.
In the following example, we solve the brachistochrone problem but do so to minimize the arclength of the resulting wire instead of the time required for the bead to travel along the wire.
This is a trivial solution which should find a straight line from the starting point to the ending point.
There are two phases involved, the first utilizes the standard ODE for the brachistochrone problem. The second integrates the arclength (𝑆) of the wire using the equation:
(102)#\[\begin{align}
S = \int v \sin \theta \sqrt{1 + \frac{1}{\tan^2 \theta}} dt
\end{align}\]
The ODE for the wire arclength#
class BrachistochroneArclengthODE(om.ExplicitComponent):
def initialize(self):
self.options.declare('num_nodes', types=int)
def setup(self):
nn = self.options['num_nodes']
# Inputs
self.add_input('v', val=np.zeros(nn), desc='velocity', units='m/s')
self.add_input('theta', val=np.zeros(nn), desc='angle of wire', units='rad')
self.add_output('Sdot', val=np.zeros(nn), desc='rate of change of arclength', units='m/s')
# Setup partials
arange = np.arange(nn)
self.declare_partials(of='Sdot', wrt='v', rows=arange, cols=arange)
self.declare_partials(of='Sdot', wrt='theta', rows=arange, cols=arange)
def compute(self, inputs, outputs):
theta = inputs['theta']
v = inputs['v']
outputs['Sdot'] = np.sqrt(1.0 + (1.0/np.tan(theta))**2) * v * np.sin(theta)
def compute_partials(self, inputs, jacobian):
theta = inputs['theta']
v = inputs['v']
cos_theta = np.cos(theta)
sin_theta = np.sin(theta)
tan_theta = np.tan(theta)
cot_theta = 1.0 / tan_theta
csc_theta = 1.0 / sin_theta
jacobian['Sdot', 'v'] = sin_theta * np.sqrt(1.0 + cot_theta**2)
jacobian['Sdot', 'theta'] = v * (cos_theta * (cot_theta**2 + 1) - cot_theta * csc_theta) / \
(np.sqrt(1 + cot_theta**2))
The trick is that the bead velocity (\(v\)) is a state variable solved for in the first phase,
and the wire angle (\(\theta\)) is a control variable “owned” by the first phase. In the
second phase they are used as control variables with option opt=False so that their values are
expected as inputs for the second phase. We need to connect their values from the first phase
to the second phase, at the control_input node subset of the second phase.
In the following example, we instantiate two phases and add an interpolating timeseries to the first phase
which provides outputs at the control_input nodes of the second phase. Those values are
then connected and the entire problem run. The result is that the position and velocity variables
are solved on a relatively coarse grid while the arclength of the wire is solved on a much denser grid.
Show code cell outputs
import numpy as np
import openmdao.api as om
class BrachistochroneODE(om.ExplicitComponent):
def initialize(self):
self.options.declare('num_nodes', types=int)
self.options.declare('static_gravity', types=(bool,), default=False,
desc='If True, treat gravity as a static (scalar) input, rather than '
'having different values at each node.')
def setup(self):
nn = self.options['num_nodes']
# Inputs
self.add_input('v', val=np.zeros(nn), desc='velocity', units='m/s')
if self.options['static_gravity']:
self.add_input('g', val=9.80665, desc='grav. acceleration', units='m/s/s',
tags=['dymos.static_target'])
else:
self.add_input('g', val=9.80665 * np.ones(nn), desc='grav. acceleration', units='m/s/s')
self.add_input('theta', val=np.ones(nn), desc='angle of wire', units='rad')
self.add_output('xdot', val=np.zeros(nn), desc='velocity component in x', units='m/s',
tags=['dymos.state_rate_source:x', 'dymos.state_units:m'])
self.add_output('ydot', val=np.zeros(nn), desc='velocity component in y', units='m/s',
tags=['dymos.state_rate_source:y', 'dymos.state_units:m'])
self.add_output('vdot', val=np.zeros(nn), desc='acceleration magnitude', units='m/s**2',
tags=['dymos.state_rate_source:v', 'dymos.state_units:m/s'])
self.add_output('check', val=np.zeros(nn), desc='check solution: v/sin(theta) = constant',
units='m/s')
# Setup partials
arange = np.arange(self.options['num_nodes'])
self.declare_partials(of='vdot', wrt='theta', rows=arange, cols=arange)
self.declare_partials(of='xdot', wrt='v', rows=arange, cols=arange)
self.declare_partials(of='xdot', wrt='theta', rows=arange, cols=arange)
self.declare_partials(of='ydot', wrt='v', rows=arange, cols=arange)
self.declare_partials(of='ydot', wrt='theta', rows=arange, cols=arange)
self.declare_partials(of='check', wrt='v', rows=arange, cols=arange)
self.declare_partials(of='check', wrt='theta', rows=arange, cols=arange)
if self.options['static_gravity']:
c = np.zeros(self.options['num_nodes'])
self.declare_partials(of='vdot', wrt='g', rows=arange, cols=c)
else:
self.declare_partials(of='vdot', wrt='g', rows=arange, cols=arange)
def compute(self, inputs, outputs):
theta = inputs['theta']
cos_theta = np.cos(theta)
sin_theta = np.sin(theta)
g = inputs['g']
v = inputs['v']
outputs['vdot'] = g * cos_theta
outputs['xdot'] = v * sin_theta
outputs['ydot'] = -v * cos_theta
outputs['check'] = v / sin_theta
def compute_partials(self, inputs, partials):
theta = inputs['theta']
cos_theta = np.cos(theta)
sin_theta = np.sin(theta)
g = inputs['g']
v = inputs['v']
partials['vdot', 'g'] = cos_theta
partials['vdot', 'theta'] = -g * sin_theta
partials['xdot', 'v'] = sin_theta
partials['xdot', 'theta'] = v * cos_theta
partials['ydot', 'v'] = -cos_theta
partials['ydot', 'theta'] = v * sin_theta
partials['check', 'v'] = 1 / sin_theta
partials['check', 'theta'] = -v * cos_theta / sin_theta ** 2
from dymos.examples.brachistochrone.brachistochrone_ode import BrachistochroneODE
import numpy as np
import matplotlib.pyplot as plt
import openmdao.api as om
import dymos as dm
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = 'SLSQP'
p.driver.declare_coloring()
# The transcription of the first phase
tx0 = dm.GaussLobatto(num_segments=10, order=3, compressed=False)
# The transcription for the second phase (and the secondary timeseries outputs from the first phase)
tx1 = dm.Radau(num_segments=20, order=9, compressed=False)
#
# First Phase: Integrate the standard brachistochrone ODE
#
phase0 = dm.Phase(ode_class=BrachistochroneODE, transcription=tx0)
p.model.add_subsystem('phase0', phase0)
phase0.set_time_options(fix_initial=True, duration_bounds=(.5, 10))
phase0.add_state('x', fix_initial=True, fix_final=False)
phase0.add_state('y', fix_initial=True, fix_final=False)
phase0.add_state('v', fix_initial=True, fix_final=False)
phase0.add_control('theta', continuity=True, rate_continuity=True,
units='deg', lower=0.01, upper=179.9)
phase0.add_parameter('g', units='m/s**2', val=9.80665)
phase0.add_boundary_constraint('x', loc='final', equals=10)
phase0.add_boundary_constraint('y', loc='final', equals=5)
# Add alternative timeseries output to provide control inputs for the next phase
phase0.add_timeseries('timeseries2', transcription=tx1, subset='control_input')
#
# Second Phase: Integration of ArcLength
#
phase1 = dm.Phase(ode_class=BrachistochroneArclengthODE, transcription=tx1)
p.model.add_subsystem('phase1', phase1)
phase1.set_time_options(fix_initial=True, input_duration=True)
phase1.add_state('S', fix_initial=True, fix_final=False,
rate_source='Sdot', units='m')
phase1.add_control('theta', opt=False, units='deg', targets='theta')
phase1.add_control('v', opt=False, units='m/s', targets='v')
#
# Connect the two phases
#
p.model.connect('phase0.t_duration_val', 'phase1.t_duration')
p.model.connect('phase0.timeseries2.theta', 'phase1.controls:theta')
p.model.connect('phase0.timeseries2.v', 'phase1.controls:v')
# Minimize arclength at the end of the second phase
phase1.add_objective('S', loc='final', ref=1)
p.model.linear_solver = om.DirectSolver()
p.setup(check=True)
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 2.0
p.set_val('phase0.states:x', phase0.interp('x', ys=[0, 10]))
p.set_val('phase0.states:y', phase0.interp('y', ys=[10, 5]))
p.set_val('phase0.states:v', phase0.interp('v', ys=[0, 9.9]))
p.set_val('phase0.controls:theta', phase0.interp('theta', ys=[5, 100]))
p['phase0.parameters:g'] = 9.80665
p['phase1.states:S'] = 0.0
dm.run_problem(p)
fig, (ax0, ax1) = plt.subplots(2, 1)
fig.tight_layout()
ax0.plot(p.get_val('phase0.timeseries.x'), p.get_val('phase0.timeseries.y'), '.')
ax0.set_xlabel('x (m)')
ax0.set_ylabel('y (m)')
ax1.plot(p.get_val('phase1.timeseries.time'), p.get_val('phase1.timeseries.S'), '+')
ax1.set_xlabel('t (s)')
ax1.set_ylabel('S (m)')
plt.show()
INFO: checking out_of_order
/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/recorders/sqlite_recorder.py:227: UserWarning:The existing case recorder file, dymos_solution.db, is being overwritten.
INFO:check_config:checking out_of_order
INFO: checking system
INFO:check_config:checking system
INFO: checking solvers
INFO:check_config:checking solvers
INFO: checking dup_inputs
INFO:check_config:checking dup_inputs
INFO: checking missing_recorders
INFO:check_config:checking missing_recorders
WARNING: The Problem has no recorder of any kind attached
WARNING:check_config:The Problem has no recorder of any kind attached
INFO: checking unserializable_options
INFO:check_config:checking unserializable_options
INFO: checking comp_has_no_outputs
INFO:check_config:checking comp_has_no_outputs
INFO: checking auto_ivc_warnings
INFO:check_config:checking auto_ivc_warnings
Model viewer data has already been recorded for Driver.
INFO: checking out_of_order
INFO:check_config:checking out_of_order
INFO: checking system
INFO:check_config:checking system
INFO: checking solvers
INFO:check_config:checking solvers
INFO: checking dup_inputs
INFO:check_config:checking dup_inputs
INFO: checking missing_recorders
INFO:check_config:checking missing_recorders
WARNING: The Problem has no recorder of any kind attached
WARNING:check_config:The Problem has no recorder of any kind attached
INFO: checking unserializable_options
INFO:check_config:checking unserializable_options
INFO: checking comp_has_no_outputs
INFO:check_config:checking comp_has_no_outputs
INFO: checking auto_ivc_warnings
INFO:check_config:checking auto_ivc_warnings
Full total jacobian was computed 3 times, taking 0.286457 seconds.
Total jacobian shape: (222, 287)
Jacobian shape: (222, 287) ( 7.43% nonzero)
FWD solves: 26 REV solves: 0
Total colors vs. total size: 26 vs 287 (90.9% improvement)
Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.286457 sec.
Time to compute coloring: 0.425438 sec.
Memory to compute coloring: 3.875000 MB.
Optimization Problem -- Optimization using pyOpt_sparse
================================================================================
Objective Function: _objfunc
Solution:
--------------------------------------------------------------------------------
Total Time: 13.3099
User Objective Time : 0.4654
User Sensitivity Time : 2.5612
Interface Time : 0.9825
Opt Solver Time: 9.3008
Calls to Objective Function : 134
Calls to Sens Function : 103
Objectives
Index Name Value
0 phase1.indep_states.states:S 1.118119E+01
Variables (c - continuous, i - integer, d - discrete)
Index Name Type Lower Bound Value Upper Bound Status
0 phase0.t_duration_0 c 5.000000E-01 2.210247E+00 1.000000E+01
1 phase0.indep_states.states:x_0 c -1.000000E+21 1.390924E-01 1.000000E+21
2 phase0.indep_states.states:x_1 c -1.000000E+21 1.390924E-01 1.000000E+21
3 phase0.indep_states.states:x_2 c -1.000000E+21 4.697012E-01 1.000000E+21
4 phase0.indep_states.states:x_3 c -1.000000E+21 4.697012E-01 1.000000E+21
5 phase0.indep_states.states:x_4 c -1.000000E+21 9.890058E-01 1.000000E+21
6 phase0.indep_states.states:x_5 c -1.000000E+21 9.890058E-01 1.000000E+21
7 phase0.indep_states.states:x_6 c -1.000000E+21 1.698475E+00 1.000000E+21
8 phase0.indep_states.states:x_7 c -1.000000E+21 1.698475E+00 1.000000E+21
9 phase0.indep_states.states:x_8 c -1.000000E+21 2.605083E+00 1.000000E+21
10 phase0.indep_states.states:x_9 c -1.000000E+21 2.605083E+00 1.000000E+21
11 phase0.indep_states.states:x_10 c -1.000000E+21 3.704224E+00 1.000000E+21
12 phase0.indep_states.states:x_11 c -1.000000E+21 3.704224E+00 1.000000E+21
13 phase0.indep_states.states:x_12 c -1.000000E+21 4.986862E+00 1.000000E+21
14 phase0.indep_states.states:x_13 c -1.000000E+21 4.986862E+00 1.000000E+21
15 phase0.indep_states.states:x_14 c -1.000000E+21 6.463732E+00 1.000000E+21
16 phase0.indep_states.states:x_15 c -1.000000E+21 6.463732E+00 1.000000E+21
17 phase0.indep_states.states:x_16 c -1.000000E+21 8.135741E+00 1.000000E+21
18 phase0.indep_states.states:x_17 c -1.000000E+21 8.135741E+00 1.000000E+21
19 phase0.indep_states.states:x_18 c -1.000000E+21 1.000000E+01 1.000000E+21
20 phase0.indep_states.states:y_0 c -1.000000E+21 9.926172E+00 1.000000E+21
21 phase0.indep_states.states:y_1 c -1.000000E+21 9.926172E+00 1.000000E+21
22 phase0.indep_states.states:y_2 c -1.000000E+21 9.767443E+00 1.000000E+21
23 phase0.indep_states.states:y_3 c -1.000000E+21 9.767443E+00 1.000000E+21
24 phase0.indep_states.states:y_4 c -1.000000E+21 9.507601E+00 1.000000E+21
25 phase0.indep_states.states:y_5 c -1.000000E+21 9.507601E+00 1.000000E+21
26 phase0.indep_states.states:y_6 c -1.000000E+21 9.145739E+00 1.000000E+21
27 phase0.indep_states.states:y_7 c -1.000000E+21 9.145739E+00 1.000000E+21
28 phase0.indep_states.states:y_8 c -1.000000E+21 8.694668E+00 1.000000E+21
29 phase0.indep_states.states:y_9 c -1.000000E+21 8.694668E+00 1.000000E+21
30 phase0.indep_states.states:y_10 c -1.000000E+21 8.156003E+00 1.000000E+21
31 phase0.indep_states.states:y_11 c -1.000000E+21 8.156003E+00 1.000000E+21
32 phase0.indep_states.states:y_12 c -1.000000E+21 7.507055E+00 1.000000E+21
33 phase0.indep_states.states:y_13 c -1.000000E+21 7.507055E+00 1.000000E+21
34 phase0.indep_states.states:y_14 c -1.000000E+21 6.762417E+00 1.000000E+21
35 phase0.indep_states.states:y_15 c -1.000000E+21 6.762417E+00 1.000000E+21
36 phase0.indep_states.states:y_16 c -1.000000E+21 5.928277E+00 1.000000E+21
37 phase0.indep_states.states:y_17 c -1.000000E+21 5.928277E+00 1.000000E+21
38 phase0.indep_states.states:y_18 c -1.000000E+21 5.000000E+00 1.000000E+21
39 phase0.indep_states.states:v_0 c -1.000000E+21 1.212937E+00 1.000000E+21
40 phase0.indep_states.states:v_1 c -1.000000E+21 1.212937E+00 1.000000E+21
41 phase0.indep_states.states:v_2 c -1.000000E+21 2.141310E+00 1.000000E+21
42 phase0.indep_states.states:v_3 c -1.000000E+21 2.141310E+00 1.000000E+21
43 phase0.indep_states.states:v_4 c -1.000000E+21 3.111522E+00 1.000000E+21
44 phase0.indep_states.states:v_5 c -1.000000E+21 3.111522E+00 1.000000E+21
45 phase0.indep_states.states:v_6 c -1.000000E+21 4.096205E+00 1.000000E+21
46 phase0.indep_states.states:v_7 c -1.000000E+21 4.096205E+00 1.000000E+21
47 phase0.indep_states.states:v_8 c -1.000000E+21 5.062201E+00 1.000000E+21
48 phase0.indep_states.states:v_9 c -1.000000E+21 5.062201E+00 1.000000E+21
49 phase0.indep_states.states:v_10 c -1.000000E+21 6.015885E+00 1.000000E+21
50 phase0.indep_states.states:v_11 c -1.000000E+21 6.015885E+00 1.000000E+21
51 phase0.indep_states.states:v_12 c -1.000000E+21 6.994205E+00 1.000000E+21
52 phase0.indep_states.states:v_13 c -1.000000E+21 6.994205E+00 1.000000E+21
53 phase0.indep_states.states:v_14 c -1.000000E+21 7.970176E+00 1.000000E+21
54 phase0.indep_states.states:v_15 c -1.000000E+21 7.970176E+00 1.000000E+21
55 phase0.indep_states.states:v_16 c -1.000000E+21 8.937781E+00 1.000000E+21
56 phase0.indep_states.states:v_17 c -1.000000E+21 8.937781E+00 1.000000E+21
57 phase0.indep_states.states:v_18 c -1.000000E+21 9.904065E+00 1.000000E+21
58 phase0.control_group.indep_controls.controls:theta_0 c 1.000000E-02 1.671533E+01 1.799000E+02
59 phase0.control_group.indep_controls.controls:theta_1 c 1.000000E-02 5.933426E+01 1.799000E+02
60 phase0.control_group.indep_controls.controls:theta_2 c 1.000000E-02 6.891623E+01 1.799000E+02
61 phase0.control_group.indep_controls.controls:theta_3 c 1.000000E-02 6.891623E+01 1.799000E+02
62 phase0.control_group.indep_controls.controls:theta_4 c 1.000000E-02 6.396317E+01 1.799000E+02
63 phase0.control_group.indep_controls.controls:theta_5 c 1.000000E-02 6.297700E+01 1.799000E+02
64 phase0.control_group.indep_controls.controls:theta_6 c 1.000000E-02 6.297700E+01 1.799000E+02
65 phase0.control_group.indep_controls.controls:theta_7 c 1.000000E-02 6.355032E+01 1.799000E+02
66 phase0.control_group.indep_controls.controls:theta_8 c 1.000000E-02 6.327570E+01 1.799000E+02
67 phase0.control_group.indep_controls.controls:theta_9 c 1.000000E-02 6.327570E+01 1.799000E+02
68 phase0.control_group.indep_controls.controls:theta_10 c 1.000000E-02 6.287968E+01 1.799000E+02
69 phase0.control_group.indep_controls.controls:theta_11 c 1.000000E-02 6.308877E+01 1.799000E+02
70 phase0.control_group.indep_controls.controls:theta_12 c 1.000000E-02 6.308877E+01 1.799000E+02
71 phase0.control_group.indep_controls.controls:theta_13 c 1.000000E-02 6.355024E+01 1.799000E+02
72 phase0.control_group.indep_controls.controls:theta_14 c 1.000000E-02 6.391133E+01 1.799000E+02
73 phase0.control_group.indep_controls.controls:theta_15 c 1.000000E-02 6.391133E+01 1.799000E+02
74 phase0.control_group.indep_controls.controls:theta_16 c 1.000000E-02 6.397805E+01 1.799000E+02
75 phase0.control_group.indep_controls.controls:theta_17 c 1.000000E-02 6.355640E+01 1.799000E+02
76 phase0.control_group.indep_controls.controls:theta_18 c 1.000000E-02 6.355640E+01 1.799000E+02
77 phase0.control_group.indep_controls.controls:theta_19 c 1.000000E-02 6.309950E+01 1.799000E+02
78 phase0.control_group.indep_controls.controls:theta_20 c 1.000000E-02 6.306048E+01 1.799000E+02
79 phase0.control_group.indep_controls.controls:theta_21 c 1.000000E-02 6.306048E+01 1.799000E+02
80 phase0.control_group.indep_controls.controls:theta_22 c 1.000000E-02 6.323669E+01 1.799000E+02
81 phase0.control_group.indep_controls.controls:theta_23 c 1.000000E-02 6.342548E+01 1.799000E+02
82 phase0.control_group.indep_controls.controls:theta_24 c 1.000000E-02 6.342548E+01 1.799000E+02
83 phase0.control_group.indep_controls.controls:theta_25 c 1.000000E-02 6.351981E+01 1.799000E+02
84 phase0.control_group.indep_controls.controls:theta_26 c 1.000000E-02 6.341262E+01 1.799000E+02
85 phase0.control_group.indep_controls.controls:theta_27 c 1.000000E-02 6.341262E+01 1.799000E+02
86 phase0.control_group.indep_controls.controls:theta_28 c 1.000000E-02 6.344499E+01 1.799000E+02
87 phase0.control_group.indep_controls.controls:theta_29 c 1.000000E-02 6.395797E+01 1.799000E+02
88 phase1.indep_states.states:S_0 c -1.000000E+21 1.019016E-04 1.000000E+21
89 phase1.indep_states.states:S_1 c -1.000000E+21 1.053653E-03 1.000000E+21
90 phase1.indep_states.states:S_2 c -1.000000E+21 4.089151E-03 1.000000E+21
91 phase1.indep_states.states:S_3 c -1.000000E+21 1.007433E-02 1.000000E+21
92 phase1.indep_states.states:S_4 c -1.000000E+21 1.880365E-02 1.000000E+21
93 phase1.indep_states.states:S_5 c -1.000000E+21 2.884538E-02 1.000000E+21
94 phase1.indep_states.states:S_6 c -1.000000E+21 3.797642E-02 1.000000E+21
95 phase1.indep_states.states:S_7 c -1.000000E+21 4.394894E-02 1.000000E+21
96 phase1.indep_states.states:S_8 c -1.000000E+21 4.544833E-02 1.000000E+21
97 phase1.indep_states.states:S_9 c -1.000000E+21 4.544833E-02 1.000000E+21
98 phase1.indep_states.states:S_10 c -1.000000E+21 4.930524E-02 1.000000E+21
99 phase1.indep_states.states:S_11 c -1.000000E+21 5.838955E-02 1.000000E+21
100 phase1.indep_states.states:S_12 c -1.000000E+21 7.242388E-02 1.000000E+21
101 phase1.indep_states.states:S_13 c -1.000000E+21 9.044517E-02 1.000000E+21
102 phase1.indep_states.states:S_14 c -1.000000E+21 1.105293E-01 1.000000E+21
103 phase1.indep_states.states:S_15 c -1.000000E+21 1.299675E-01 1.000000E+21
104 phase1.indep_states.states:S_16 c -1.000000E+21 1.458122E-01 1.000000E+21
105 phase1.indep_states.states:S_17 c -1.000000E+21 1.555406E-01 1.000000E+21
106 phase1.indep_states.states:S_18 c -1.000000E+21 1.579190E-01 1.000000E+21
107 phase1.indep_states.states:S_19 c -1.000000E+21 1.579190E-01 1.000000E+21
108 phase1.indep_states.states:S_20 c -1.000000E+21 1.639474E-01 1.000000E+21
109 phase1.indep_states.states:S_21 c -1.000000E+21 1.777488E-01 1.000000E+21
110 phase1.indep_states.states:S_22 c -1.000000E+21 1.982656E-01 1.000000E+21
111 phase1.indep_states.states:S_23 c -1.000000E+21 2.236927E-01 1.000000E+21
112 phase1.indep_states.states:S_24 c -1.000000E+21 2.513423E-01 1.000000E+21
113 phase1.indep_states.states:S_25 c -1.000000E+21 2.777794E-01 1.000000E+21
114 phase1.indep_states.states:S_26 c -1.000000E+21 2.992698E-01 1.000000E+21
115 phase1.indep_states.states:S_27 c -1.000000E+21 3.124872E-01 1.000000E+21
116 phase1.indep_states.states:S_28 c -1.000000E+21 3.157241E-01 1.000000E+21
117 phase1.indep_states.states:S_29 c -1.000000E+21 3.157241E-01 1.000000E+21
118 phase1.indep_states.states:S_30 c -1.000000E+21 3.239214E-01 1.000000E+21
119 phase1.indep_states.states:S_31 c -1.000000E+21 3.426097E-01 1.000000E+21
120 phase1.indep_states.states:S_32 c -1.000000E+21 3.702048E-01 1.000000E+21
121 phase1.indep_states.states:S_33 c -1.000000E+21 4.041265E-01 1.000000E+21
122 phase1.indep_states.states:S_34 c -1.000000E+21 4.407045E-01 1.000000E+21
123 phase1.indep_states.states:S_35 c -1.000000E+21 4.754121E-01 1.000000E+21
124 phase1.indep_states.states:S_36 c -1.000000E+21 5.034534E-01 1.000000E+21
125 phase1.indep_states.states:S_37 c -1.000000E+21 5.206290E-01 1.000000E+21
126 phase1.indep_states.states:S_38 c -1.000000E+21 5.248275E-01 1.000000E+21
127 phase1.indep_states.states:S_39 c -1.000000E+21 5.248275E-01 1.000000E+21
128 phase1.indep_states.states:S_40 c -1.000000E+21 5.354434E-01 1.000000E+21
129 phase1.indep_states.states:S_41 c -1.000000E+21 5.595519E-01 1.000000E+21
130 phase1.indep_states.states:S_42 c -1.000000E+21 5.949177E-01 1.000000E+21
131 phase1.indep_states.states:S_43 c -1.000000E+21 6.380243E-01 1.000000E+21
132 phase1.indep_states.states:S_44 c -1.000000E+21 6.840715E-01 1.000000E+21
133 phase1.indep_states.states:S_45 c -1.000000E+21 7.273651E-01 1.000000E+21
134 phase1.indep_states.states:S_46 c -1.000000E+21 7.620708E-01 1.000000E+21
135 phase1.indep_states.states:S_47 c -1.000000E+21 7.832121E-01 1.000000E+21
136 phase1.indep_states.states:S_48 c -1.000000E+21 7.883667E-01 1.000000E+21
137 phase1.indep_states.states:S_49 c -1.000000E+21 7.883667E-01 1.000000E+21
138 phase1.indep_states.states:S_50 c -1.000000E+21 8.013814E-01 1.000000E+21
139 phase1.indep_states.states:S_51 c -1.000000E+21 8.308479E-01 1.000000E+21
140 phase1.indep_states.states:S_52 c -1.000000E+21 8.738621E-01 1.000000E+21
141 phase1.indep_states.states:S_53 c -1.000000E+21 9.259807E-01 1.000000E+21
142 phase1.indep_states.states:S_54 c -1.000000E+21 9.813141E-01 1.000000E+21
143 phase1.indep_states.states:S_55 c -1.000000E+21 1.033049E+00 1.000000E+21
144 phase1.indep_states.states:S_56 c -1.000000E+21 1.074336E+00 1.000000E+21
145 phase1.indep_states.states:S_57 c -1.000000E+21 1.099411E+00 1.000000E+21
146 phase1.indep_states.states:S_58 c -1.000000E+21 1.105516E+00 1.000000E+21
147 phase1.indep_states.states:S_59 c -1.000000E+21 1.105516E+00 1.000000E+21
148 phase1.indep_states.states:S_60 c -1.000000E+21 1.120918E+00 1.000000E+21
149 phase1.indep_states.states:S_61 c -1.000000E+21 1.155723E+00 1.000000E+21
150 phase1.indep_states.states:S_62 c -1.000000E+21 1.206376E+00 1.000000E+21
151 phase1.indep_states.states:S_63 c -1.000000E+21 1.267521E+00 1.000000E+21
152 phase1.indep_states.states:S_64 c -1.000000E+21 1.332189E+00 1.000000E+21
153 phase1.indep_states.states:S_65 c -1.000000E+21 1.392440E+00 1.000000E+21
154 phase1.indep_states.states:S_66 c -1.000000E+21 1.440388E+00 1.000000E+21
155 phase1.indep_states.states:S_67 c -1.000000E+21 1.469454E+00 1.000000E+21
156 phase1.indep_states.states:S_68 c -1.000000E+21 1.476525E+00 1.000000E+21
157 phase1.indep_states.states:S_69 c -1.000000E+21 1.476525E+00 1.000000E+21
158 phase1.indep_states.states:S_70 c -1.000000E+21 1.494351E+00 1.000000E+21
159 phase1.indep_states.states:S_71 c -1.000000E+21 1.534576E+00 1.000000E+21
160 phase1.indep_states.states:S_72 c -1.000000E+21 1.592973E+00 1.000000E+21
161 phase1.indep_states.states:S_73 c -1.000000E+21 1.663254E+00 1.000000E+21
162 phase1.indep_states.states:S_74 c -1.000000E+21 1.737350E+00 1.000000E+21
163 phase1.indep_states.states:S_75 c -1.000000E+21 1.806183E+00 1.000000E+21
164 phase1.indep_states.states:S_76 c -1.000000E+21 1.860830E+00 1.000000E+21
165 phase1.indep_states.states:S_77 c -1.000000E+21 1.893903E+00 1.000000E+21
166 phase1.indep_states.states:S_78 c -1.000000E+21 1.901943E+00 1.000000E+21
167 phase1.indep_states.states:S_79 c -1.000000E+21 1.901943E+00 1.000000E+21
168 phase1.indep_states.states:S_80 c -1.000000E+21 1.922202E+00 1.000000E+21
169 phase1.indep_states.states:S_81 c -1.000000E+21 1.967859E+00 1.000000E+21
170 phase1.indep_states.states:S_82 c -1.000000E+21 2.034007E+00 1.000000E+21
171 phase1.indep_states.states:S_83 c -1.000000E+21 2.113417E+00 1.000000E+21
172 phase1.indep_states.states:S_84 c -1.000000E+21 2.196905E+00 1.000000E+21
173 phase1.indep_states.states:S_85 c -1.000000E+21 2.274261E+00 1.000000E+21
174 phase1.indep_states.states:S_86 c -1.000000E+21 2.335542E+00 1.000000E+21
175 phase1.indep_states.states:S_87 c -1.000000E+21 2.372573E+00 1.000000E+21
176 phase1.indep_states.states:S_88 c -1.000000E+21 2.381569E+00 1.000000E+21
177 phase1.indep_states.states:S_89 c -1.000000E+21 2.381569E+00 1.000000E+21
178 phase1.indep_states.states:S_90 c -1.000000E+21 2.404227E+00 1.000000E+21
179 phase1.indep_states.states:S_91 c -1.000000E+21 2.455239E+00 1.000000E+21
180 phase1.indep_states.states:S_92 c -1.000000E+21 2.529022E+00 1.000000E+21
181 phase1.indep_states.states:S_93 c -1.000000E+21 2.617415E+00 1.000000E+21
182 phase1.indep_states.states:S_94 c -1.000000E+21 2.710146E+00 1.000000E+21
183 phase1.indep_states.states:S_95 c -1.000000E+21 2.795891E+00 1.000000E+21
184 phase1.indep_states.states:S_96 c -1.000000E+21 2.863703E+00 1.000000E+21
185 phase1.indep_states.states:S_97 c -1.000000E+21 2.904635E+00 1.000000E+21
186 phase1.indep_states.states:S_98 c -1.000000E+21 2.914573E+00 1.000000E+21
187 phase1.indep_states.states:S_99 c -1.000000E+21 2.914573E+00 1.000000E+21
188 phase1.indep_states.states:S_100 c -1.000000E+21 2.939595E+00 1.000000E+21
189 phase1.indep_states.states:S_101 c -1.000000E+21 2.995883E+00 1.000000E+21
190 phase1.indep_states.states:S_102 c -1.000000E+21 3.077188E+00 1.000000E+21
191 phase1.indep_states.states:S_103 c -1.000000E+21 3.174433E+00 1.000000E+21
192 phase1.indep_states.states:S_104 c -1.000000E+21 3.276279E+00 1.000000E+21
193 phase1.indep_states.states:S_105 c -1.000000E+21 3.370306E+00 1.000000E+21
194 phase1.indep_states.states:S_106 c -1.000000E+21 3.444579E+00 1.000000E+21
195 phase1.indep_states.states:S_107 c -1.000000E+21 3.489374E+00 1.000000E+21
196 phase1.indep_states.states:S_108 c -1.000000E+21 3.500247E+00 1.000000E+21
197 phase1.indep_states.states:S_109 c -1.000000E+21 3.500247E+00 1.000000E+21
198 phase1.indep_states.states:S_110 c -1.000000E+21 3.527613E+00 1.000000E+21
199 phase1.indep_states.states:S_111 c -1.000000E+21 3.589143E+00 1.000000E+21
200 phase1.indep_states.states:S_112 c -1.000000E+21 3.677943E+00 1.000000E+21
201 phase1.indep_states.states:S_113 c -1.000000E+21 3.784033E+00 1.000000E+21
202 phase1.indep_states.states:S_114 c -1.000000E+21 3.895010E+00 1.000000E+21
203 phase1.indep_states.states:S_115 c -1.000000E+21 3.997355E+00 1.000000E+21
204 phase1.indep_states.states:S_116 c -1.000000E+21 4.078123E+00 1.000000E+21
205 phase1.indep_states.states:S_117 c -1.000000E+21 4.126805E+00 1.000000E+21
206 phase1.indep_states.states:S_118 c -1.000000E+21 4.138617E+00 1.000000E+21
207 phase1.indep_states.states:S_119 c -1.000000E+21 4.138617E+00 1.000000E+21
208 phase1.indep_states.states:S_120 c -1.000000E+21 4.168344E+00 1.000000E+21
209 phase1.indep_states.states:S_121 c -1.000000E+21 4.235155E+00 1.000000E+21
210 phase1.indep_states.states:S_122 c -1.000000E+21 4.331513E+00 1.000000E+21
211 phase1.indep_states.states:S_123 c -1.000000E+21 4.446541E+00 1.000000E+21
212 phase1.indep_states.states:S_124 c -1.000000E+21 4.566765E+00 1.000000E+21
213 phase1.indep_states.states:S_125 c -1.000000E+21 4.677548E+00 1.000000E+21
214 phase1.indep_states.states:S_126 c -1.000000E+21 4.764916E+00 1.000000E+21
215 phase1.indep_states.states:S_127 c -1.000000E+21 4.817552E+00 1.000000E+21
216 phase1.indep_states.states:S_128 c -1.000000E+21 4.830321E+00 1.000000E+21
217 phase1.indep_states.states:S_129 c -1.000000E+21 4.830321E+00 1.000000E+21
218 phase1.indep_states.states:S_130 c -1.000000E+21 4.862452E+00 1.000000E+21
219 phase1.indep_states.states:S_131 c -1.000000E+21 4.934635E+00 1.000000E+21
220 phase1.indep_states.states:S_132 c -1.000000E+21 5.038675E+00 1.000000E+21
221 phase1.indep_states.states:S_133 c -1.000000E+21 5.162774E+00 1.000000E+21
222 phase1.indep_states.states:S_134 c -1.000000E+21 5.292368E+00 1.000000E+21
223 phase1.indep_states.states:S_135 c -1.000000E+21 5.411686E+00 1.000000E+21
224 phase1.indep_states.states:S_136 c -1.000000E+21 5.505723E+00 1.000000E+21
225 phase1.indep_states.states:S_137 c -1.000000E+21 5.562350E+00 1.000000E+21
226 phase1.indep_states.states:S_138 c -1.000000E+21 5.576084E+00 1.000000E+21
227 phase1.indep_states.states:S_139 c -1.000000E+21 5.576084E+00 1.000000E+21
228 phase1.indep_states.states:S_140 c -1.000000E+21 5.610638E+00 1.000000E+21
229 phase1.indep_states.states:S_141 c -1.000000E+21 5.688237E+00 1.000000E+21
230 phase1.indep_states.states:S_142 c -1.000000E+21 5.800015E+00 1.000000E+21
231 phase1.indep_states.states:S_143 c -1.000000E+21 5.933238E+00 1.000000E+21
232 phase1.indep_states.states:S_144 c -1.000000E+21 6.072236E+00 1.000000E+21
233 phase1.indep_states.states:S_145 c -1.000000E+21 6.200104E+00 1.000000E+21
234 phase1.indep_states.states:S_146 c -1.000000E+21 6.300804E+00 1.000000E+21
235 phase1.indep_states.states:S_147 c -1.000000E+21 6.361412E+00 1.000000E+21
236 phase1.indep_states.states:S_148 c -1.000000E+21 6.376108E+00 1.000000E+21
237 phase1.indep_states.states:S_149 c -1.000000E+21 6.376108E+00 1.000000E+21
238 phase1.indep_states.states:S_150 c -1.000000E+21 6.413076E+00 1.000000E+21
239 phase1.indep_states.states:S_151 c -1.000000E+21 6.496067E+00 1.000000E+21
240 phase1.indep_states.states:S_152 c -1.000000E+21 6.615542E+00 1.000000E+21
241 phase1.indep_states.states:S_153 c -1.000000E+21 6.757831E+00 1.000000E+21
242 phase1.indep_states.states:S_154 c -1.000000E+21 6.906171E+00 1.000000E+21
243 phase1.indep_states.states:S_155 c -1.000000E+21 7.042528E+00 1.000000E+21
244 phase1.indep_states.states:S_156 c -1.000000E+21 7.149846E+00 1.000000E+21
245 phase1.indep_states.states:S_157 c -1.000000E+21 7.214408E+00 1.000000E+21
246 phase1.indep_states.states:S_158 c -1.000000E+21 7.230060E+00 1.000000E+21
247 phase1.indep_states.states:S_159 c -1.000000E+21 7.230060E+00 1.000000E+21
248 phase1.indep_states.states:S_160 c -1.000000E+21 7.269427E+00 1.000000E+21
249 phase1.indep_states.states:S_161 c -1.000000E+21 7.357776E+00 1.000000E+21
250 phase1.indep_states.states:S_162 c -1.000000E+21 7.484895E+00 1.000000E+21
251 phase1.indep_states.states:S_163 c -1.000000E+21 7.636190E+00 1.000000E+21
252 phase1.indep_states.states:S_164 c -1.000000E+21 7.793808E+00 1.000000E+21
253 phase1.indep_states.states:S_165 c -1.000000E+21 7.938600E+00 1.000000E+21
254 phase1.indep_states.states:S_166 c -1.000000E+21 8.052495E+00 1.000000E+21
255 phase1.indep_states.states:S_167 c -1.000000E+21 8.120990E+00 1.000000E+21
256 phase1.indep_states.states:S_168 c -1.000000E+21 8.137592E+00 1.000000E+21
257 phase1.indep_states.states:S_169 c -1.000000E+21 8.137592E+00 1.000000E+21
258 phase1.indep_states.states:S_170 c -1.000000E+21 8.179346E+00 1.000000E+21
259 phase1.indep_states.states:S_171 c -1.000000E+21 8.273026E+00 1.000000E+21
260 phase1.indep_states.states:S_172 c -1.000000E+21 8.407762E+00 1.000000E+21
261 phase1.indep_states.states:S_173 c -1.000000E+21 8.568038E+00 1.000000E+21
262 phase1.indep_states.states:S_174 c -1.000000E+21 8.734919E+00 1.000000E+21
263 phase1.indep_states.states:S_175 c -1.000000E+21 8.888139E+00 1.000000E+21
264 phase1.indep_states.states:S_176 c -1.000000E+21 9.008610E+00 1.000000E+21
265 phase1.indep_states.states:S_177 c -1.000000E+21 9.081037E+00 1.000000E+21
266 phase1.indep_states.states:S_178 c -1.000000E+21 9.098591E+00 1.000000E+21
267 phase1.indep_states.states:S_179 c -1.000000E+21 9.098591E+00 1.000000E+21
268 phase1.indep_states.states:S_180 c -1.000000E+21 9.142731E+00 1.000000E+21
269 phase1.indep_states.states:S_181 c -1.000000E+21 9.241748E+00 1.000000E+21
270 phase1.indep_states.states:S_182 c -1.000000E+21 9.384113E+00 1.000000E+21
271 phase1.indep_states.states:S_183 c -1.000000E+21 9.553393E+00 1.000000E+21
272 phase1.indep_states.states:S_184 c -1.000000E+21 9.729566E+00 1.000000E+21
273 phase1.indep_states.states:S_185 c -1.000000E+21 9.891243E+00 1.000000E+21
274 phase1.indep_states.states:S_186 c -1.000000E+21 1.001831E+01 1.000000E+21
275 phase1.indep_states.states:S_187 c -1.000000E+21 1.009469E+01 1.000000E+21
276 phase1.indep_states.states:S_188 c -1.000000E+21 1.011319E+01 1.000000E+21
277 phase1.indep_states.states:S_189 c -1.000000E+21 1.011319E+01 1.000000E+21
278 phase1.indep_states.states:S_190 c -1.000000E+21 1.015973E+01 1.000000E+21
279 phase1.indep_states.states:S_191 c -1.000000E+21 1.026409E+01 1.000000E+21
280 phase1.indep_states.states:S_192 c -1.000000E+21 1.041408E+01 1.000000E+21
281 phase1.indep_states.states:S_193 c -1.000000E+21 1.059234E+01 1.000000E+21
282 phase1.indep_states.states:S_194 c -1.000000E+21 1.077776E+01 1.000000E+21
283 phase1.indep_states.states:S_195 c -1.000000E+21 1.094784E+01 1.000000E+21
284 phase1.indep_states.states:S_196 c -1.000000E+21 1.108145E+01 1.000000E+21
285 phase1.indep_states.states:S_197 c -1.000000E+21 1.116174E+01 1.000000E+21
286 phase1.indep_states.states:S_198 c -1.000000E+21 1.118119E+01 1.000000E+21
Constraints (i - inequality, e - equality)
Index Name Type Lower Value Upper Status Lagrange Multiplier (N/A)
0 phase0->final_boundary_constraint->x e 1.000000E+01 1.000000E+01 1.000000E+01 9.00000E+100
1 phase0->final_boundary_constraint->y e 5.000000E+00 5.000000E+00 5.000000E+00 9.00000E+100
2 phase0.collocation_constraint.defects:x e 0.000000E+00 2.755816E-10 0.000000E+00 9.00000E+100
3 phase0.collocation_constraint.defects:x e 0.000000E+00 1.409762E-10 0.000000E+00 9.00000E+100
4 phase0.collocation_constraint.defects:x e 0.000000E+00 1.105399E-11 0.000000E+00 9.00000E+100
5 phase0.collocation_constraint.defects:x e 0.000000E+00 1.603117E-11 0.000000E+00 9.00000E+100
6 phase0.collocation_constraint.defects:x e 0.000000E+00 1.546172E-11 0.000000E+00 9.00000E+100
7 phase0.collocation_constraint.defects:x e 0.000000E+00 3.141697E-11 0.000000E+00 9.00000E+100
8 phase0.collocation_constraint.defects:x e 0.000000E+00 3.950148E-11 0.000000E+00 9.00000E+100
9 phase0.collocation_constraint.defects:x e 0.000000E+00 1.601384E-11 0.000000E+00 9.00000E+100
10 phase0.collocation_constraint.defects:x e 0.000000E+00 5.979585E-11 0.000000E+00 9.00000E+100
11 phase0.collocation_constraint.defects:x e 0.000000E+00 1.328877E-11 0.000000E+00 9.00000E+100
12 phase0.collocation_constraint.defects:y e 0.000000E+00 1.210078E-10 0.000000E+00 9.00000E+100
13 phase0.collocation_constraint.defects:y e 0.000000E+00 7.331046E-11 0.000000E+00 9.00000E+100
14 phase0.collocation_constraint.defects:y e 0.000000E+00 -1.323581E-10 0.000000E+00 9.00000E+100
15 phase0.collocation_constraint.defects:y e 0.000000E+00 -3.740308E-11 0.000000E+00 9.00000E+100
16 phase0.collocation_constraint.defects:y e 0.000000E+00 -7.185023E-12 0.000000E+00 9.00000E+100
17 phase0.collocation_constraint.defects:y e 0.000000E+00 -5.729634E-12 0.000000E+00 9.00000E+100
18 phase0.collocation_constraint.defects:y e 0.000000E+00 -1.960140E-11 0.000000E+00 9.00000E+100
19 phase0.collocation_constraint.defects:y e 0.000000E+00 1.141048E-12 0.000000E+00 9.00000E+100
20 phase0.collocation_constraint.defects:y e 0.000000E+00 1.458329E-11 0.000000E+00 9.00000E+100
21 phase0.collocation_constraint.defects:y e 0.000000E+00 -4.961102E-11 0.000000E+00 9.00000E+100
22 phase0.collocation_constraint.defects:v e 0.000000E+00 1.339415E-09 0.000000E+00 9.00000E+100
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24 phase0.collocation_constraint.defects:v e 0.000000E+00 -5.228112E-12 0.000000E+00 9.00000E+100
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26 phase0.collocation_constraint.defects:v e 0.000000E+00 4.582843E-12 0.000000E+00 9.00000E+100
27 phase0.collocation_constraint.defects:v e 0.000000E+00 3.323666E-11 0.000000E+00 9.00000E+100
28 phase0.collocation_constraint.defects:v e 0.000000E+00 -1.354672E-11 0.000000E+00 9.00000E+100
29 phase0.collocation_constraint.defects:v e 0.000000E+00 -9.884473E-12 0.000000E+00 9.00000E+100
30 phase0.collocation_constraint.defects:v e 0.000000E+00 -1.244032E-11 0.000000E+00 9.00000E+100
31 phase0.collocation_constraint.defects:v e 0.000000E+00 4.786711E-11 0.000000E+00 9.00000E+100
32 phase0.continuity_comp.defect_states:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
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35 phase0.continuity_comp.defect_states:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
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38 phase0.continuity_comp.defect_states:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
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42 phase0.continuity_comp.defect_states:y e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
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59 phase0.continuity_comp.defect_control_rates:theta_rate e 0.000000E+00 2.355713E-14 0.000000E+00 9.00000E+100
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67 phase0.continuity_comp.defect_control_rates:theta_rate e 0.000000E+00 1.064979E-13 0.000000E+00 9.00000E+100
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72 phase0.continuity_comp.defect_controls:theta e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
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76 phase0.continuity_comp.defect_controls:theta e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
77 phase1.collocation_constraint.defects:S e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
78 phase1.collocation_constraint.defects:S e 0.000000E+00 -3.823716E-13 0.000000E+00 9.00000E+100
79 phase1.collocation_constraint.defects:S e 0.000000E+00 -1.123315E-12 0.000000E+00 9.00000E+100
80 phase1.collocation_constraint.defects:S e 0.000000E+00 -1.909796E-12 0.000000E+00 9.00000E+100
81 phase1.collocation_constraint.defects:S e 0.000000E+00 -2.426151E-12 0.000000E+00 9.00000E+100
82 phase1.collocation_constraint.defects:S e 0.000000E+00 -2.492847E-12 0.000000E+00 9.00000E+100
83 phase1.collocation_constraint.defects:S e 0.000000E+00 -2.142460E-12 0.000000E+00 9.00000E+100
84 phase1.collocation_constraint.defects:S e 0.000000E+00 -1.597118E-12 0.000000E+00 9.00000E+100
85 phase1.collocation_constraint.defects:S e 0.000000E+00 -1.157029E-12 0.000000E+00 9.00000E+100
86 phase1.collocation_constraint.defects:S e 0.000000E+00 -1.038011E-12 0.000000E+00 9.00000E+100
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89 phase1.collocation_constraint.defects:S e 0.000000E+00 1.573113E-12 0.000000E+00 9.00000E+100
90 phase1.collocation_constraint.defects:S e 0.000000E+00 3.704567E-12 0.000000E+00 9.00000E+100
91 phase1.collocation_constraint.defects:S e 0.000000E+00 6.368719E-12 0.000000E+00 9.00000E+100
92 phase1.collocation_constraint.defects:S e 0.000000E+00 9.203599E-12 0.000000E+00 9.00000E+100
93 phase1.collocation_constraint.defects:S e 0.000000E+00 1.168737E-11 0.000000E+00 9.00000E+100
94 phase1.collocation_constraint.defects:S e 0.000000E+00 1.328583E-11 0.000000E+00 9.00000E+100
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96 phase1.collocation_constraint.defects:S e 0.000000E+00 1.458325E-11 0.000000E+00 9.00000E+100
97 phase1.collocation_constraint.defects:S e 0.000000E+00 1.644518E-11 0.000000E+00 9.00000E+100
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100 phase1.collocation_constraint.defects:S e 0.000000E+00 2.268022E-11 0.000000E+00 9.00000E+100
101 phase1.collocation_constraint.defects:S e 0.000000E+00 2.371046E-11 0.000000E+00 9.00000E+100
102 phase1.collocation_constraint.defects:S e 0.000000E+00 2.417225E-11 0.000000E+00 9.00000E+100
103 phase1.collocation_constraint.defects:S e 0.000000E+00 2.430384E-11 0.000000E+00 9.00000E+100
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109 phase1.collocation_constraint.defects:S e 0.000000E+00 2.086944E-11 0.000000E+00 9.00000E+100
110 phase1.collocation_constraint.defects:S e 0.000000E+00 1.877538E-11 0.000000E+00 9.00000E+100
111 phase1.collocation_constraint.defects:S e 0.000000E+00 1.680092E-11 0.000000E+00 9.00000E+100
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119 phase1.collocation_constraint.defects:S e 0.000000E+00 1.280384E-11 0.000000E+00 9.00000E+100
120 phase1.collocation_constraint.defects:S e 0.000000E+00 1.243875E-11 0.000000E+00 9.00000E+100
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122 phase1.collocation_constraint.defects:S e 0.000000E+00 1.216605E-11 0.000000E+00 9.00000E+100
123 phase1.collocation_constraint.defects:S e 0.000000E+00 1.203276E-11 0.000000E+00 9.00000E+100
124 phase1.collocation_constraint.defects:S e 0.000000E+00 1.173771E-11 0.000000E+00 9.00000E+100
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128 phase1.collocation_constraint.defects:S e 0.000000E+00 9.828402E-12 0.000000E+00 9.00000E+100
129 phase1.collocation_constraint.defects:S e 0.000000E+00 9.459856E-12 0.000000E+00 9.00000E+100
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132 phase1.collocation_constraint.defects:S e 0.000000E+00 9.082893E-12 0.000000E+00 9.00000E+100
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134 phase1.collocation_constraint.defects:S e 0.000000E+00 8.543533E-12 0.000000E+00 9.00000E+100
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210 phase1.collocation_constraint.defects:S e 0.000000E+00 1.820328E-12 0.000000E+00 9.00000E+100
211 phase1.collocation_constraint.defects:S e 0.000000E+00 1.777631E-12 0.000000E+00 9.00000E+100
212 phase1.collocation_constraint.defects:S e 0.000000E+00 1.752405E-12 0.000000E+00 9.00000E+100
213 phase1.collocation_constraint.defects:S e 0.000000E+00 1.712751E-12 0.000000E+00 9.00000E+100
214 phase1.collocation_constraint.defects:S e 0.000000E+00 1.639134E-12 0.000000E+00 9.00000E+100
215 phase1.collocation_constraint.defects:S e 0.000000E+00 1.533324E-12 0.000000E+00 9.00000E+100
216 phase1.collocation_constraint.defects:S e 0.000000E+00 1.406655E-12 0.000000E+00 9.00000E+100
217 phase1.collocation_constraint.defects:S e 0.000000E+00 1.271103E-12 0.000000E+00 9.00000E+100
218 phase1.collocation_constraint.defects:S e 0.000000E+00 1.133540E-12 0.000000E+00 9.00000E+100
219 phase1.collocation_constraint.defects:S e 0.000000E+00 1.038624E-12 0.000000E+00 9.00000E+100
220 phase1.collocation_constraint.defects:S e 0.000000E+00 9.970555E-13 0.000000E+00 9.00000E+100
221 phase1.collocation_constraint.defects:S e 0.000000E+00 1.006478E-12 0.000000E+00 9.00000E+100
222 phase1.collocation_constraint.defects:S e 0.000000E+00 8.704850E-13 0.000000E+00 9.00000E+100
223 phase1.collocation_constraint.defects:S e 0.000000E+00 6.703966E-13 0.000000E+00 9.00000E+100
224 phase1.collocation_constraint.defects:S e 0.000000E+00 3.716137E-13 0.000000E+00 9.00000E+100
225 phase1.collocation_constraint.defects:S e 0.000000E+00 6.674520E-14 0.000000E+00 9.00000E+100
226 phase1.collocation_constraint.defects:S e 0.000000E+00 -2.416569E-13 0.000000E+00 9.00000E+100
227 phase1.collocation_constraint.defects:S e 0.000000E+00 -4.888104E-13 0.000000E+00 9.00000E+100
228 phase1.collocation_constraint.defects:S e 0.000000E+00 -6.926778E-13 0.000000E+00 9.00000E+100
229 phase1.collocation_constraint.defects:S e 0.000000E+00 -7.578525E-13 0.000000E+00 9.00000E+100
230 phase1.collocation_constraint.defects:S e 0.000000E+00 -8.215549E-13 0.000000E+00 9.00000E+100
231 phase1.collocation_constraint.defects:S e 0.000000E+00 -8.921281E-13 0.000000E+00 9.00000E+100
232 phase1.collocation_constraint.defects:S e 0.000000E+00 -1.002847E-12 0.000000E+00 9.00000E+100
233 phase1.collocation_constraint.defects:S e 0.000000E+00 -1.184040E-12 0.000000E+00 9.00000E+100
234 phase1.collocation_constraint.defects:S e 0.000000E+00 -1.378387E-12 0.000000E+00 9.00000E+100
235 phase1.collocation_constraint.defects:S e 0.000000E+00 -1.573518E-12 0.000000E+00 9.00000E+100
236 phase1.collocation_constraint.defects:S e 0.000000E+00 -1.688065E-12 0.000000E+00 9.00000E+100
237 phase1.collocation_constraint.defects:S e 0.000000E+00 -1.814292E-12 0.000000E+00 9.00000E+100
238 phase1.collocation_constraint.defects:S e 0.000000E+00 -1.841873E-12 0.000000E+00 9.00000E+100
239 phase1.collocation_constraint.defects:S e 0.000000E+00 -1.860424E-12 0.000000E+00 9.00000E+100
240 phase1.collocation_constraint.defects:S e 0.000000E+00 -1.891539E-12 0.000000E+00 9.00000E+100
241 phase1.collocation_constraint.defects:S e 0.000000E+00 -1.922556E-12 0.000000E+00 9.00000E+100
242 phase1.collocation_constraint.defects:S e 0.000000E+00 -1.936003E-12 0.000000E+00 9.00000E+100
243 phase1.collocation_constraint.defects:S e 0.000000E+00 -1.931292E-12 0.000000E+00 9.00000E+100
244 phase1.collocation_constraint.defects:S e 0.000000E+00 -1.879761E-12 0.000000E+00 9.00000E+100
245 phase1.collocation_constraint.defects:S e 0.000000E+00 -1.799372E-12 0.000000E+00 9.00000E+100
246 phase1.collocation_constraint.defects:S e 0.000000E+00 -1.716824E-12 0.000000E+00 9.00000E+100
247 phase1.collocation_constraint.defects:S e 0.000000E+00 -1.621810E-12 0.000000E+00 9.00000E+100
248 phase1.collocation_constraint.defects:S e 0.000000E+00 -1.713094E-12 0.000000E+00 9.00000E+100
249 phase1.collocation_constraint.defects:S e 0.000000E+00 -1.597762E-12 0.000000E+00 9.00000E+100
250 phase1.collocation_constraint.defects:S e 0.000000E+00 -1.482332E-12 0.000000E+00 9.00000E+100
251 phase1.collocation_constraint.defects:S e 0.000000E+00 -1.312525E-12 0.000000E+00 9.00000E+100
252 phase1.collocation_constraint.defects:S e 0.000000E+00 -1.087063E-12 0.000000E+00 9.00000E+100
253 phase1.collocation_constraint.defects:S e 0.000000E+00 -7.879860E-13 0.000000E+00 9.00000E+100
254 phase1.collocation_constraint.defects:S e 0.000000E+00 -5.096192E-13 0.000000E+00 9.00000E+100
255 phase1.collocation_constraint.defects:S e 0.000000E+00 -2.734590E-13 0.000000E+00 9.00000E+100
256 phase1.collocation_constraint.defects:S e 0.000000E+00 -1.286808E-13 0.000000E+00 9.00000E+100
257 phase1.continuity_comp.defect_states:S e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
258 phase1.continuity_comp.defect_states:S e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
259 phase1.continuity_comp.defect_states:S e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
260 phase1.continuity_comp.defect_states:S e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
261 phase1.continuity_comp.defect_states:S e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
262 phase1.continuity_comp.defect_states:S e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
263 phase1.continuity_comp.defect_states:S e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
264 phase1.continuity_comp.defect_states:S e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
265 phase1.continuity_comp.defect_states:S e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
266 phase1.continuity_comp.defect_states:S e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
267 phase1.continuity_comp.defect_states:S e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
268 phase1.continuity_comp.defect_states:S e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
269 phase1.continuity_comp.defect_states:S e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
270 phase1.continuity_comp.defect_states:S e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
271 phase1.continuity_comp.defect_states:S e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
272 phase1.continuity_comp.defect_states:S e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
273 phase1.continuity_comp.defect_states:S e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
274 phase1.continuity_comp.defect_states:S e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
275 phase1.continuity_comp.defect_states:S e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
Exit Status
Inform Description
0 Optimization terminated successfully.
--------------------------------------------------------------------------------
/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/visualization/opt_report/opt_report.py:634: UserWarning: Attempting to set identical low and high ylims makes transformation singular; automatically expanding.
ax.set_ylim([ymin_plot, ymax_plot])
