# 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:

(107)#\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_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.

Hide 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

if self.options['static_gravity']:
tags=['dymos.static_target'])
else:
self.add_input('g', val=9.80665 * np.ones(nn), desc='grav. acceleration', units='m/s/s')

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'])

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)

#
# First Phase: Integrate the standard brachistochrone ODE
#
phase0 = dm.Phase(ode_class=BrachistochroneODE, transcription=tx0)

phase0.set_time_options(fix_initial=True, duration_bounds=(.5, 10))

units='deg', lower=0.01, upper=179.9)

# Add alternative timeseries output to provide control inputs for the next phase

#
# Second Phase: Integration of ArcLength
#
phase1 = dm.Phase(ode_class=BrachistochroneArclengthODE, transcription=tx1)

phase1.set_time_options(fix_initial=True, input_duration=True)

rate_source='Sdot', units='m')

#
# 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

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()

'rhs_checking' is disabled for 'DirectSolver in <model> <class Group>' but that solver has redundant adjoint solves. If it is expensive to compute derivatives for this solver, turning on 'rhs_checking' may improve performance.

INFO: checking out_of_order

INFO: checking system

INFO: checking solvers

INFO: checking dup_inputs

INFO: checking missing_recorders

WARNING: The Problem has no recorder of any kind attached

INFO: checking unserializable_options

INFO: checking comp_has_no_outputs

INFO: checking auto_ivc_warnings

Model viewer data has already been recorded for Driver.
INFO: checking out_of_order

INFO: checking system

INFO: checking solvers

INFO: checking dup_inputs

INFO: checking missing_recorders

WARNING: The Problem has no recorder of any kind attached

INFO: checking unserializable_options

INFO: checking comp_has_no_outputs

INFO: checking auto_ivc_warnings

/usr/share/miniconda/envs/test/lib/python3.11/site-packages/openmdao/recorders/sqlite_recorder.py:231: UserWarning:The existing case recorder file, problem_out/dymos_solution.db, is being overwritten.

Full total jacobian for problem 'problem' was computed 3 times, taking 0.16087582500006192 seconds.
Total jacobian shape: (222, 287)

Jacobian shape: (222, 287)  (8.14% nonzero)
FWD solves: 29   REV solves: 0
Total colors vs. total size: 29 vs 287  (89.90% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity:   0.1609 sec
Time to compute coloring:   0.2391 sec
Memory to compute coloring:   6.7656 MB
Coloring created on: 2024-08-29 21:52:31

Optimization Problem -- Optimization using pyOpt_sparse
================================================================================
Objective Function: _objfunc

Solution:
--------------------------------------------------------------------------------
Total Time:                    9.0683
User Objective Time :       0.2632
User Sensitivity Time :     2.2663
Interface Time :            0.5720
Opt Solver Time:            5.9667
Calls to Objective Function :     134
Calls to Sens Function :          103

Objectives
Index  Name                       Value
0  phase1.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.states:x_0             c    -1.000000E+21     1.390924E-01     1.000000E+21
2  phase0.states:x_1             c    -1.000000E+21     1.390924E-01     1.000000E+21
3  phase0.states:x_2             c    -1.000000E+21     4.697012E-01     1.000000E+21
4  phase0.states:x_3             c    -1.000000E+21     4.697012E-01     1.000000E+21
5  phase0.states:x_4             c    -1.000000E+21     9.890058E-01     1.000000E+21
6  phase0.states:x_5             c    -1.000000E+21     9.890058E-01     1.000000E+21
7  phase0.states:x_6             c    -1.000000E+21     1.698475E+00     1.000000E+21
8  phase0.states:x_7             c    -1.000000E+21     1.698475E+00     1.000000E+21
9  phase0.states:x_8             c    -1.000000E+21     2.605083E+00     1.000000E+21
10  phase0.states:x_9             c    -1.000000E+21     2.605083E+00     1.000000E+21
11  phase0.states:x_10            c    -1.000000E+21     3.704224E+00     1.000000E+21
12  phase0.states:x_11            c    -1.000000E+21     3.704224E+00     1.000000E+21
13  phase0.states:x_12            c    -1.000000E+21     4.986862E+00     1.000000E+21
14  phase0.states:x_13            c    -1.000000E+21     4.986862E+00     1.000000E+21
15  phase0.states:x_14            c    -1.000000E+21     6.463732E+00     1.000000E+21
16  phase0.states:x_15            c    -1.000000E+21     6.463732E+00     1.000000E+21
17  phase0.states:x_16            c    -1.000000E+21     8.135741E+00     1.000000E+21
18  phase0.states:x_17            c    -1.000000E+21     8.135741E+00     1.000000E+21
19  phase0.states:x_18            c    -1.000000E+21     1.000000E+01     1.000000E+21
20  phase0.states:y_0             c    -1.000000E+21     9.926172E+00     1.000000E+21
21  phase0.states:y_1             c    -1.000000E+21     9.926172E+00     1.000000E+21
22  phase0.states:y_2             c    -1.000000E+21     9.767443E+00     1.000000E+21
23  phase0.states:y_3             c    -1.000000E+21     9.767443E+00     1.000000E+21
24  phase0.states:y_4             c    -1.000000E+21     9.507601E+00     1.000000E+21
25  phase0.states:y_5             c    -1.000000E+21     9.507601E+00     1.000000E+21
26  phase0.states:y_6             c    -1.000000E+21     9.145739E+00     1.000000E+21
27  phase0.states:y_7             c    -1.000000E+21     9.145739E+00     1.000000E+21
28  phase0.states:y_8             c    -1.000000E+21     8.694668E+00     1.000000E+21
29  phase0.states:y_9             c    -1.000000E+21     8.694668E+00     1.000000E+21
30  phase0.states:y_10            c    -1.000000E+21     8.156003E+00     1.000000E+21
31  phase0.states:y_11            c    -1.000000E+21     8.156003E+00     1.000000E+21
32  phase0.states:y_12            c    -1.000000E+21     7.507055E+00     1.000000E+21
33  phase0.states:y_13            c    -1.000000E+21     7.507055E+00     1.000000E+21
34  phase0.states:y_14            c    -1.000000E+21     6.762417E+00     1.000000E+21
35  phase0.states:y_15            c    -1.000000E+21     6.762417E+00     1.000000E+21
36  phase0.states:y_16            c    -1.000000E+21     5.928277E+00     1.000000E+21
37  phase0.states:y_17            c    -1.000000E+21     5.928277E+00     1.000000E+21
38  phase0.states:y_18            c    -1.000000E+21     5.000000E+00     1.000000E+21
39  phase0.states:v_0             c    -1.000000E+21     1.212937E+00     1.000000E+21
40  phase0.states:v_1             c    -1.000000E+21     1.212937E+00     1.000000E+21
41  phase0.states:v_2             c    -1.000000E+21     2.141310E+00     1.000000E+21
42  phase0.states:v_3             c    -1.000000E+21     2.141310E+00     1.000000E+21
43  phase0.states:v_4             c    -1.000000E+21     3.111522E+00     1.000000E+21
44  phase0.states:v_5             c    -1.000000E+21     3.111522E+00     1.000000E+21
45  phase0.states:v_6             c    -1.000000E+21     4.096205E+00     1.000000E+21
46  phase0.states:v_7             c    -1.000000E+21     4.096205E+00     1.000000E+21
47  phase0.states:v_8             c    -1.000000E+21     5.062201E+00     1.000000E+21
48  phase0.states:v_9             c    -1.000000E+21     5.062201E+00     1.000000E+21
49  phase0.states:v_10            c    -1.000000E+21     6.015885E+00     1.000000E+21
50  phase0.states:v_11            c    -1.000000E+21     6.015885E+00     1.000000E+21
51  phase0.states:v_12            c    -1.000000E+21     6.994205E+00     1.000000E+21
52  phase0.states:v_13            c    -1.000000E+21     6.994205E+00     1.000000E+21
53  phase0.states:v_14            c    -1.000000E+21     7.970176E+00     1.000000E+21
54  phase0.states:v_15            c    -1.000000E+21     7.970176E+00     1.000000E+21
55  phase0.states:v_16            c    -1.000000E+21     8.937781E+00     1.000000E+21
56  phase0.states:v_17            c    -1.000000E+21     8.937781E+00     1.000000E+21
57  phase0.states:v_18            c    -1.000000E+21     9.904065E+00     1.000000E+21
58  phase0.controls:theta_0       c     1.000000E-02     1.671533E+01     1.799000E+02
59  phase0.controls:theta_1       c     1.000000E-02     5.933426E+01     1.799000E+02
60  phase0.controls:theta_2       c     1.000000E-02     6.891623E+01     1.799000E+02
61  phase0.controls:theta_3       c     1.000000E-02     6.891623E+01     1.799000E+02
62  phase0.controls:theta_4       c     1.000000E-02     6.396317E+01     1.799000E+02
63  phase0.controls:theta_5       c     1.000000E-02     6.297700E+01     1.799000E+02
64  phase0.controls:theta_6       c     1.000000E-02     6.297700E+01     1.799000E+02
65  phase0.controls:theta_7       c     1.000000E-02     6.355032E+01     1.799000E+02
66  phase0.controls:theta_8       c     1.000000E-02     6.327570E+01     1.799000E+02
67  phase0.controls:theta_9       c     1.000000E-02     6.327570E+01     1.799000E+02
68  phase0.controls:theta_10      c     1.000000E-02     6.287968E+01     1.799000E+02
69  phase0.controls:theta_11      c     1.000000E-02     6.308877E+01     1.799000E+02
70  phase0.controls:theta_12      c     1.000000E-02     6.308877E+01     1.799000E+02
71  phase0.controls:theta_13      c     1.000000E-02     6.355024E+01     1.799000E+02
72  phase0.controls:theta_14      c     1.000000E-02     6.391133E+01     1.799000E+02
73  phase0.controls:theta_15      c     1.000000E-02     6.391133E+01     1.799000E+02
74  phase0.controls:theta_16      c     1.000000E-02     6.397805E+01     1.799000E+02
75  phase0.controls:theta_17      c     1.000000E-02     6.355640E+01     1.799000E+02
76  phase0.controls:theta_18      c     1.000000E-02     6.355640E+01     1.799000E+02
77  phase0.controls:theta_19      c     1.000000E-02     6.309950E+01     1.799000E+02
78  phase0.controls:theta_20      c     1.000000E-02     6.306048E+01     1.799000E+02
79  phase0.controls:theta_21      c     1.000000E-02     6.306048E+01     1.799000E+02
80  phase0.controls:theta_22      c     1.000000E-02     6.323669E+01     1.799000E+02
81  phase0.controls:theta_23      c     1.000000E-02     6.342548E+01     1.799000E+02
82  phase0.controls:theta_24      c     1.000000E-02     6.342548E+01     1.799000E+02
83  phase0.controls:theta_25      c     1.000000E-02     6.351981E+01     1.799000E+02
84  phase0.controls:theta_26      c     1.000000E-02     6.341262E+01     1.799000E+02
85  phase0.controls:theta_27      c     1.000000E-02     6.341262E+01     1.799000E+02
86  phase0.controls:theta_28      c     1.000000E-02     6.344499E+01     1.799000E+02
87  phase0.controls:theta_29      c     1.000000E-02     6.395797E+01     1.799000E+02
88  phase1.states:S_0             c    -1.000000E+21     1.019016E-04     1.000000E+21
89  phase1.states:S_1             c    -1.000000E+21     1.053653E-03     1.000000E+21
90  phase1.states:S_2             c    -1.000000E+21     4.089151E-03     1.000000E+21
91  phase1.states:S_3             c    -1.000000E+21     1.007433E-02     1.000000E+21
92  phase1.states:S_4             c    -1.000000E+21     1.880365E-02     1.000000E+21
93  phase1.states:S_5             c    -1.000000E+21     2.884538E-02     1.000000E+21
94  phase1.states:S_6             c    -1.000000E+21     3.797642E-02     1.000000E+21
95  phase1.states:S_7             c    -1.000000E+21     4.394894E-02     1.000000E+21
96  phase1.states:S_8             c    -1.000000E+21     4.544833E-02     1.000000E+21
97  phase1.states:S_9             c    -1.000000E+21     4.544833E-02     1.000000E+21
98  phase1.states:S_10            c    -1.000000E+21     4.930524E-02     1.000000E+21
99  phase1.states:S_11            c    -1.000000E+21     5.838955E-02     1.000000E+21
100  phase1.states:S_12            c    -1.000000E+21     7.242388E-02     1.000000E+21
101  phase1.states:S_13            c    -1.000000E+21     9.044517E-02     1.000000E+21
102  phase1.states:S_14            c    -1.000000E+21     1.105293E-01     1.000000E+21
103  phase1.states:S_15            c    -1.000000E+21     1.299675E-01     1.000000E+21
104  phase1.states:S_16            c    -1.000000E+21     1.458122E-01     1.000000E+21
105  phase1.states:S_17            c    -1.000000E+21     1.555406E-01     1.000000E+21
106  phase1.states:S_18            c    -1.000000E+21     1.579190E-01     1.000000E+21
107  phase1.states:S_19            c    -1.000000E+21     1.579190E-01     1.000000E+21
108  phase1.states:S_20            c    -1.000000E+21     1.639474E-01     1.000000E+21
109  phase1.states:S_21            c    -1.000000E+21     1.777488E-01     1.000000E+21
110  phase1.states:S_22            c    -1.000000E+21     1.982656E-01     1.000000E+21
111  phase1.states:S_23            c    -1.000000E+21     2.236927E-01     1.000000E+21
112  phase1.states:S_24            c    -1.000000E+21     2.513423E-01     1.000000E+21
113  phase1.states:S_25            c    -1.000000E+21     2.777794E-01     1.000000E+21
114  phase1.states:S_26            c    -1.000000E+21     2.992698E-01     1.000000E+21
115  phase1.states:S_27            c    -1.000000E+21     3.124872E-01     1.000000E+21
116  phase1.states:S_28            c    -1.000000E+21     3.157241E-01     1.000000E+21
117  phase1.states:S_29            c    -1.000000E+21     3.157241E-01     1.000000E+21
118  phase1.states:S_30            c    -1.000000E+21     3.239214E-01     1.000000E+21
119  phase1.states:S_31            c    -1.000000E+21     3.426097E-01     1.000000E+21
120  phase1.states:S_32            c    -1.000000E+21     3.702048E-01     1.000000E+21
121  phase1.states:S_33            c    -1.000000E+21     4.041265E-01     1.000000E+21
122  phase1.states:S_34            c    -1.000000E+21     4.407045E-01     1.000000E+21
123  phase1.states:S_35            c    -1.000000E+21     4.754121E-01     1.000000E+21
124  phase1.states:S_36            c    -1.000000E+21     5.034534E-01     1.000000E+21
125  phase1.states:S_37            c    -1.000000E+21     5.206290E-01     1.000000E+21
126  phase1.states:S_38            c    -1.000000E+21     5.248275E-01     1.000000E+21
127  phase1.states:S_39            c    -1.000000E+21     5.248275E-01     1.000000E+21
128  phase1.states:S_40            c    -1.000000E+21     5.354434E-01     1.000000E+21
129  phase1.states:S_41            c    -1.000000E+21     5.595519E-01     1.000000E+21
130  phase1.states:S_42            c    -1.000000E+21     5.949177E-01     1.000000E+21
131  phase1.states:S_43            c    -1.000000E+21     6.380243E-01     1.000000E+21
132  phase1.states:S_44            c    -1.000000E+21     6.840715E-01     1.000000E+21
133  phase1.states:S_45            c    -1.000000E+21     7.273651E-01     1.000000E+21
134  phase1.states:S_46            c    -1.000000E+21     7.620708E-01     1.000000E+21
135  phase1.states:S_47            c    -1.000000E+21     7.832121E-01     1.000000E+21
136  phase1.states:S_48            c    -1.000000E+21     7.883667E-01     1.000000E+21
137  phase1.states:S_49            c    -1.000000E+21     7.883667E-01     1.000000E+21
138  phase1.states:S_50            c    -1.000000E+21     8.013814E-01     1.000000E+21
139  phase1.states:S_51            c    -1.000000E+21     8.308479E-01     1.000000E+21
140  phase1.states:S_52            c    -1.000000E+21     8.738621E-01     1.000000E+21
141  phase1.states:S_53            c    -1.000000E+21     9.259807E-01     1.000000E+21
142  phase1.states:S_54            c    -1.000000E+21     9.813141E-01     1.000000E+21
143  phase1.states:S_55            c    -1.000000E+21     1.033049E+00     1.000000E+21
144  phase1.states:S_56            c    -1.000000E+21     1.074336E+00     1.000000E+21
145  phase1.states:S_57            c    -1.000000E+21     1.099411E+00     1.000000E+21
146  phase1.states:S_58            c    -1.000000E+21     1.105516E+00     1.000000E+21
147  phase1.states:S_59            c    -1.000000E+21     1.105516E+00     1.000000E+21
148  phase1.states:S_60            c    -1.000000E+21     1.120918E+00     1.000000E+21
149  phase1.states:S_61            c    -1.000000E+21     1.155723E+00     1.000000E+21
150  phase1.states:S_62            c    -1.000000E+21     1.206376E+00     1.000000E+21
151  phase1.states:S_63            c    -1.000000E+21     1.267521E+00     1.000000E+21
152  phase1.states:S_64            c    -1.000000E+21     1.332189E+00     1.000000E+21
153  phase1.states:S_65            c    -1.000000E+21     1.392440E+00     1.000000E+21
154  phase1.states:S_66            c    -1.000000E+21     1.440388E+00     1.000000E+21
155  phase1.states:S_67            c    -1.000000E+21     1.469454E+00     1.000000E+21
156  phase1.states:S_68            c    -1.000000E+21     1.476525E+00     1.000000E+21
157  phase1.states:S_69            c    -1.000000E+21     1.476525E+00     1.000000E+21
158  phase1.states:S_70            c    -1.000000E+21     1.494351E+00     1.000000E+21
159  phase1.states:S_71            c    -1.000000E+21     1.534576E+00     1.000000E+21
160  phase1.states:S_72            c    -1.000000E+21     1.592973E+00     1.000000E+21
161  phase1.states:S_73            c    -1.000000E+21     1.663254E+00     1.000000E+21
162  phase1.states:S_74            c    -1.000000E+21     1.737350E+00     1.000000E+21
163  phase1.states:S_75            c    -1.000000E+21     1.806183E+00     1.000000E+21
164  phase1.states:S_76            c    -1.000000E+21     1.860830E+00     1.000000E+21
165  phase1.states:S_77            c    -1.000000E+21     1.893903E+00     1.000000E+21
166  phase1.states:S_78            c    -1.000000E+21     1.901943E+00     1.000000E+21
167  phase1.states:S_79            c    -1.000000E+21     1.901943E+00     1.000000E+21
168  phase1.states:S_80            c    -1.000000E+21     1.922202E+00     1.000000E+21
169  phase1.states:S_81            c    -1.000000E+21     1.967859E+00     1.000000E+21
170  phase1.states:S_82            c    -1.000000E+21     2.034007E+00     1.000000E+21
171  phase1.states:S_83            c    -1.000000E+21     2.113417E+00     1.000000E+21
172  phase1.states:S_84            c    -1.000000E+21     2.196905E+00     1.000000E+21
173  phase1.states:S_85            c    -1.000000E+21     2.274261E+00     1.000000E+21
174  phase1.states:S_86            c    -1.000000E+21     2.335542E+00     1.000000E+21
175  phase1.states:S_87            c    -1.000000E+21     2.372573E+00     1.000000E+21
176  phase1.states:S_88            c    -1.000000E+21     2.381569E+00     1.000000E+21
177  phase1.states:S_89            c    -1.000000E+21     2.381569E+00     1.000000E+21
178  phase1.states:S_90            c    -1.000000E+21     2.404227E+00     1.000000E+21
179  phase1.states:S_91            c    -1.000000E+21     2.455239E+00     1.000000E+21
180  phase1.states:S_92            c    -1.000000E+21     2.529022E+00     1.000000E+21
181  phase1.states:S_93            c    -1.000000E+21     2.617415E+00     1.000000E+21
182  phase1.states:S_94            c    -1.000000E+21     2.710146E+00     1.000000E+21
183  phase1.states:S_95            c    -1.000000E+21     2.795891E+00     1.000000E+21
184  phase1.states:S_96            c    -1.000000E+21     2.863703E+00     1.000000E+21
185  phase1.states:S_97            c    -1.000000E+21     2.904635E+00     1.000000E+21
186  phase1.states:S_98            c    -1.000000E+21     2.914573E+00     1.000000E+21
187  phase1.states:S_99            c    -1.000000E+21     2.914573E+00     1.000000E+21
188  phase1.states:S_100           c    -1.000000E+21     2.939595E+00     1.000000E+21
189  phase1.states:S_101           c    -1.000000E+21     2.995883E+00     1.000000E+21
190  phase1.states:S_102           c    -1.000000E+21     3.077188E+00     1.000000E+21
191  phase1.states:S_103           c    -1.000000E+21     3.174433E+00     1.000000E+21
192  phase1.states:S_104           c    -1.000000E+21     3.276279E+00     1.000000E+21
193  phase1.states:S_105           c    -1.000000E+21     3.370306E+00     1.000000E+21
194  phase1.states:S_106           c    -1.000000E+21     3.444579E+00     1.000000E+21
195  phase1.states:S_107           c    -1.000000E+21     3.489374E+00     1.000000E+21
196  phase1.states:S_108           c    -1.000000E+21     3.500247E+00     1.000000E+21
197  phase1.states:S_109           c    -1.000000E+21     3.500247E+00     1.000000E+21
198  phase1.states:S_110           c    -1.000000E+21     3.527613E+00     1.000000E+21
199  phase1.states:S_111           c    -1.000000E+21     3.589143E+00     1.000000E+21
200  phase1.states:S_112           c    -1.000000E+21     3.677943E+00     1.000000E+21
201  phase1.states:S_113           c    -1.000000E+21     3.784033E+00     1.000000E+21
202  phase1.states:S_114           c    -1.000000E+21     3.895010E+00     1.000000E+21
203  phase1.states:S_115           c    -1.000000E+21     3.997355E+00     1.000000E+21
204  phase1.states:S_116           c    -1.000000E+21     4.078123E+00     1.000000E+21
205  phase1.states:S_117           c    -1.000000E+21     4.126805E+00     1.000000E+21
206  phase1.states:S_118           c    -1.000000E+21     4.138617E+00     1.000000E+21
207  phase1.states:S_119           c    -1.000000E+21     4.138617E+00     1.000000E+21
208  phase1.states:S_120           c    -1.000000E+21     4.168344E+00     1.000000E+21
209  phase1.states:S_121           c    -1.000000E+21     4.235155E+00     1.000000E+21
210  phase1.states:S_122           c    -1.000000E+21     4.331513E+00     1.000000E+21
211  phase1.states:S_123           c    -1.000000E+21     4.446541E+00     1.000000E+21
212  phase1.states:S_124           c    -1.000000E+21     4.566765E+00     1.000000E+21
213  phase1.states:S_125           c    -1.000000E+21     4.677548E+00     1.000000E+21
214  phase1.states:S_126           c    -1.000000E+21     4.764916E+00     1.000000E+21
215  phase1.states:S_127           c    -1.000000E+21     4.817552E+00     1.000000E+21
216  phase1.states:S_128           c    -1.000000E+21     4.830321E+00     1.000000E+21
217  phase1.states:S_129           c    -1.000000E+21     4.830321E+00     1.000000E+21
218  phase1.states:S_130           c    -1.000000E+21     4.862452E+00     1.000000E+21
219  phase1.states:S_131           c    -1.000000E+21     4.934635E+00     1.000000E+21
220  phase1.states:S_132           c    -1.000000E+21     5.038675E+00     1.000000E+21
221  phase1.states:S_133           c    -1.000000E+21     5.162774E+00     1.000000E+21
222  phase1.states:S_134           c    -1.000000E+21     5.292368E+00     1.000000E+21
223  phase1.states:S_135           c    -1.000000E+21     5.411686E+00     1.000000E+21
224  phase1.states:S_136           c    -1.000000E+21     5.505723E+00     1.000000E+21
225  phase1.states:S_137           c    -1.000000E+21     5.562350E+00     1.000000E+21
226  phase1.states:S_138           c    -1.000000E+21     5.576084E+00     1.000000E+21
227  phase1.states:S_139           c    -1.000000E+21     5.576084E+00     1.000000E+21
228  phase1.states:S_140           c    -1.000000E+21     5.610638E+00     1.000000E+21
229  phase1.states:S_141           c    -1.000000E+21     5.688237E+00     1.000000E+21
230  phase1.states:S_142           c    -1.000000E+21     5.800015E+00     1.000000E+21
231  phase1.states:S_143           c    -1.000000E+21     5.933238E+00     1.000000E+21
232  phase1.states:S_144           c    -1.000000E+21     6.072236E+00     1.000000E+21
233  phase1.states:S_145           c    -1.000000E+21     6.200104E+00     1.000000E+21
234  phase1.states:S_146           c    -1.000000E+21     6.300804E+00     1.000000E+21
235  phase1.states:S_147           c    -1.000000E+21     6.361412E+00     1.000000E+21
236  phase1.states:S_148           c    -1.000000E+21     6.376108E+00     1.000000E+21
237  phase1.states:S_149           c    -1.000000E+21     6.376108E+00     1.000000E+21
238  phase1.states:S_150           c    -1.000000E+21     6.413076E+00     1.000000E+21
239  phase1.states:S_151           c    -1.000000E+21     6.496067E+00     1.000000E+21
240  phase1.states:S_152           c    -1.000000E+21     6.615542E+00     1.000000E+21
241  phase1.states:S_153           c    -1.000000E+21     6.757831E+00     1.000000E+21
242  phase1.states:S_154           c    -1.000000E+21     6.906171E+00     1.000000E+21
243  phase1.states:S_155           c    -1.000000E+21     7.042528E+00     1.000000E+21
244  phase1.states:S_156           c    -1.000000E+21     7.149846E+00     1.000000E+21
245  phase1.states:S_157           c    -1.000000E+21     7.214408E+00     1.000000E+21
246  phase1.states:S_158           c    -1.000000E+21     7.230060E+00     1.000000E+21
247  phase1.states:S_159           c    -1.000000E+21     7.230060E+00     1.000000E+21
248  phase1.states:S_160           c    -1.000000E+21     7.269427E+00     1.000000E+21
249  phase1.states:S_161           c    -1.000000E+21     7.357776E+00     1.000000E+21
250  phase1.states:S_162           c    -1.000000E+21     7.484895E+00     1.000000E+21
251  phase1.states:S_163           c    -1.000000E+21     7.636190E+00     1.000000E+21
252  phase1.states:S_164           c    -1.000000E+21     7.793808E+00     1.000000E+21
253  phase1.states:S_165           c    -1.000000E+21     7.938600E+00     1.000000E+21
254  phase1.states:S_166           c    -1.000000E+21     8.052495E+00     1.000000E+21
255  phase1.states:S_167           c    -1.000000E+21     8.120990E+00     1.000000E+21
256  phase1.states:S_168           c    -1.000000E+21     8.137592E+00     1.000000E+21
257  phase1.states:S_169           c    -1.000000E+21     8.137592E+00     1.000000E+21
258  phase1.states:S_170           c    -1.000000E+21     8.179346E+00     1.000000E+21
259  phase1.states:S_171           c    -1.000000E+21     8.273026E+00     1.000000E+21
260  phase1.states:S_172           c    -1.000000E+21     8.407762E+00     1.000000E+21
261  phase1.states:S_173           c    -1.000000E+21     8.568038E+00     1.000000E+21
262  phase1.states:S_174           c    -1.000000E+21     8.734919E+00     1.000000E+21
263  phase1.states:S_175           c    -1.000000E+21     8.888139E+00     1.000000E+21
264  phase1.states:S_176           c    -1.000000E+21     9.008610E+00     1.000000E+21
265  phase1.states:S_177           c    -1.000000E+21     9.081037E+00     1.000000E+21
266  phase1.states:S_178           c    -1.000000E+21     9.098591E+00     1.000000E+21
267  phase1.states:S_179           c    -1.000000E+21     9.098591E+00     1.000000E+21
268  phase1.states:S_180           c    -1.000000E+21     9.142731E+00     1.000000E+21
269  phase1.states:S_181           c    -1.000000E+21     9.241748E+00     1.000000E+21
270  phase1.states:S_182           c    -1.000000E+21     9.384113E+00     1.000000E+21
271  phase1.states:S_183           c    -1.000000E+21     9.553393E+00     1.000000E+21
272  phase1.states:S_184           c    -1.000000E+21     9.729566E+00     1.000000E+21
273  phase1.states:S_185           c    -1.000000E+21     9.891243E+00     1.000000E+21
274  phase1.states:S_186           c    -1.000000E+21     1.001831E+01     1.000000E+21
275  phase1.states:S_187           c    -1.000000E+21     1.009469E+01     1.000000E+21
276  phase1.states:S_188           c    -1.000000E+21     1.011319E+01     1.000000E+21
277  phase1.states:S_189           c    -1.000000E+21     1.011319E+01     1.000000E+21
278  phase1.states:S_190           c    -1.000000E+21     1.015973E+01     1.000000E+21
279  phase1.states:S_191           c    -1.000000E+21     1.026409E+01     1.000000E+21
280  phase1.states:S_192           c    -1.000000E+21     1.041408E+01     1.000000E+21
281  phase1.states:S_193           c    -1.000000E+21     1.059234E+01     1.000000E+21
282  phase1.states:S_194           c    -1.000000E+21     1.077776E+01     1.000000E+21
283  phase1.states:S_195           c    -1.000000E+21     1.094784E+01     1.000000E+21
284  phase1.states:S_196           c    -1.000000E+21     1.108145E+01     1.000000E+21
285  phase1.states:S_197           c    -1.000000E+21     1.116174E+01     1.000000E+21
286  phase1.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    1.409761E-10    0.000000E+00              9.00000E+100
4  phase0.collocation_constraint.defects:x                   e   0.000000E+00    1.105384E-11    0.000000E+00              9.00000E+100
5  phase0.collocation_constraint.defects:x                   e   0.000000E+00    1.603156E-11    0.000000E+00              9.00000E+100
6  phase0.collocation_constraint.defects:x                   e   0.000000E+00    1.546153E-11    0.000000E+00              9.00000E+100
7  phase0.collocation_constraint.defects:x                   e   0.000000E+00    3.141736E-11    0.000000E+00              9.00000E+100
8  phase0.collocation_constraint.defects:x                   e   0.000000E+00    3.950099E-11    0.000000E+00              9.00000E+100
9  phase0.collocation_constraint.defects:x                   e   0.000000E+00    1.601237E-11    0.000000E+00              9.00000E+100
10  phase0.collocation_constraint.defects:x                   e   0.000000E+00    5.979771E-11    0.000000E+00              9.00000E+100
11  phase0.collocation_constraint.defects:x                   e   0.000000E+00    1.328779E-11    0.000000E+00              9.00000E+100
12  phase0.collocation_constraint.defects:y                   e   0.000000E+00    1.210079E-10    0.000000E+00              9.00000E+100
13  phase0.collocation_constraint.defects:y                   e   0.000000E+00    7.331001E-11    0.000000E+00              9.00000E+100
14  phase0.collocation_constraint.defects:y                   e   0.000000E+00   -1.323573E-10    0.000000E+00              9.00000E+100
15  phase0.collocation_constraint.defects:y                   e   0.000000E+00   -3.740524E-11    0.000000E+00              9.00000E+100
16  phase0.collocation_constraint.defects:y                   e   0.000000E+00   -7.183501E-12    0.000000E+00              9.00000E+100
17  phase0.collocation_constraint.defects:y                   e   0.000000E+00   -5.728701E-12    0.000000E+00              9.00000E+100
18  phase0.collocation_constraint.defects:y                   e   0.000000E+00   -1.960287E-11    0.000000E+00              9.00000E+100
19  phase0.collocation_constraint.defects:y                   e   0.000000E+00    1.141147E-12    0.000000E+00              9.00000E+100
20  phase0.collocation_constraint.defects:y                   e   0.000000E+00    1.458260E-11    0.000000E+00              9.00000E+100
21  phase0.collocation_constraint.defects:y                   e   0.000000E+00   -4.961014E-11    0.000000E+00              9.00000E+100
22  phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.339416E-09    0.000000E+00              9.00000E+100
23  phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.610132E-10    0.000000E+00              9.00000E+100
24  phase0.collocation_constraint.defects:v                   e   0.000000E+00   -5.227523E-12    0.000000E+00              9.00000E+100
25  phase0.collocation_constraint.defects:v                   e   0.000000E+00   -1.358834E-11    0.000000E+00              9.00000E+100
26  phase0.collocation_constraint.defects:v                   e   0.000000E+00    4.582745E-12    0.000000E+00              9.00000E+100
27  phase0.collocation_constraint.defects:v                   e   0.000000E+00    3.323705E-11    0.000000E+00              9.00000E+100
28  phase0.collocation_constraint.defects:v                   e   0.000000E+00   -1.354604E-11    0.000000E+00              9.00000E+100
29  phase0.collocation_constraint.defects:v                   e   0.000000E+00   -9.883590E-12    0.000000E+00              9.00000E+100
30  phase0.collocation_constraint.defects:v                   e   0.000000E+00   -1.244238E-11    0.000000E+00              9.00000E+100
31  phase0.collocation_constraint.defects:v                   e   0.000000E+00    4.786858E-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
33  phase0.continuity_comp.defect_states:x                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
34  phase0.continuity_comp.defect_states:x                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
35  phase0.continuity_comp.defect_states:x                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
36  phase0.continuity_comp.defect_states:x                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
37  phase0.continuity_comp.defect_states:x                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
38  phase0.continuity_comp.defect_states:x                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
39  phase0.continuity_comp.defect_states:x                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
40  phase0.continuity_comp.defect_states:x                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
41  phase0.continuity_comp.defect_states:y                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
42  phase0.continuity_comp.defect_states:y                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
43  phase0.continuity_comp.defect_states:y                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
44  phase0.continuity_comp.defect_states:y                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
45  phase0.continuity_comp.defect_states:y                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
46  phase0.continuity_comp.defect_states:y                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
47  phase0.continuity_comp.defect_states:y                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
48  phase0.continuity_comp.defect_states:y                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
49  phase0.continuity_comp.defect_states:y                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
50  phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
51  phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
52  phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
53  phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
54  phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
55  phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
56  phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
57  phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
58  phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
59  phase0.continuity_comp.defect_control_rates:theta_rate    e   0.000000E+00   -1.963094E-13    0.000000E+00              9.00000E+100
60  phase0.continuity_comp.defect_control_rates:theta_rate    e   0.000000E+00   -7.067139E-14    0.000000E+00              9.00000E+100
61  phase0.continuity_comp.defect_control_rates:theta_rate    e   0.000000E+00   -1.452690E-13    0.000000E+00              9.00000E+100
62  phase0.continuity_comp.defect_control_rates:theta_rate    e   0.000000E+00    1.423243E-13    0.000000E+00              9.00000E+100
63  phase0.continuity_comp.defect_control_rates:theta_rate    e   0.000000E+00   -2.522576E-13    0.000000E+00              9.00000E+100
64  phase0.continuity_comp.defect_control_rates:theta_rate    e   0.000000E+00    1.344719E-13    0.000000E+00              9.00000E+100
65  phase0.continuity_comp.defect_control_rates:theta_rate    e   0.000000E+00    7.116216E-14    0.000000E+00              9.00000E+100
66  phase0.continuity_comp.defect_control_rates:theta_rate    e   0.000000E+00   -2.844033E-13    0.000000E+00              9.00000E+100
67  phase0.continuity_comp.defect_control_rates:theta_rate    e   0.000000E+00   -3.197390E-13    0.000000E+00              9.00000E+100
68  phase0.continuity_comp.defect_controls:theta              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
69  phase0.continuity_comp.defect_controls:theta              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
70  phase0.continuity_comp.defect_controls:theta              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
71  phase0.continuity_comp.defect_controls:theta              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
72  phase0.continuity_comp.defect_controls:theta              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
73  phase0.continuity_comp.defect_controls:theta              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
74  phase0.continuity_comp.defect_controls:theta              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
75  phase0.continuity_comp.defect_controls:theta              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
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    2.775558E-17    0.000000E+00              9.00000E+100
78  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -3.823801E-13    0.000000E+00              9.00000E+100
79  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -1.123312E-12    0.000000E+00              9.00000E+100
80  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -1.909805E-12    0.000000E+00              9.00000E+100
81  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -2.426148E-12    0.000000E+00              9.00000E+100
82  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -2.492860E-12    0.000000E+00              9.00000E+100
83  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -2.142502E-12    0.000000E+00              9.00000E+100
84  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -1.597186E-12    0.000000E+00              9.00000E+100
85  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -1.157103E-12    0.000000E+00              9.00000E+100
86  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -1.037827E-12    0.000000E+00              9.00000E+100
87  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -7.168483E-13    0.000000E+00              9.00000E+100
88  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.143134E-13    0.000000E+00              9.00000E+100
89  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.573076E-12    0.000000E+00              9.00000E+100
90  phase1.collocation_constraint.defects:S                   e   0.000000E+00    3.704579E-12    0.000000E+00              9.00000E+100
91  phase1.collocation_constraint.defects:S                   e   0.000000E+00    6.368596E-12    0.000000E+00              9.00000E+100
92  phase1.collocation_constraint.defects:S                   e   0.000000E+00    9.203734E-12    0.000000E+00              9.00000E+100
93  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.168699E-11    0.000000E+00              9.00000E+100
94  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.328575E-11    0.000000E+00              9.00000E+100
95  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.368614E-11    0.000000E+00              9.00000E+100
96  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.458342E-11    0.000000E+00              9.00000E+100
97  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.644516E-11    0.000000E+00              9.00000E+100
98  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.876301E-11    0.000000E+00              9.00000E+100
99  phase1.collocation_constraint.defects:S                   e   0.000000E+00    2.097980E-11    0.000000E+00              9.00000E+100
100  phase1.collocation_constraint.defects:S                   e   0.000000E+00    2.267977E-11    0.000000E+00              9.00000E+100
101  phase1.collocation_constraint.defects:S                   e   0.000000E+00    2.371030E-11    0.000000E+00              9.00000E+100
102  phase1.collocation_constraint.defects:S                   e   0.000000E+00    2.417222E-11    0.000000E+00              9.00000E+100
103  phase1.collocation_constraint.defects:S                   e   0.000000E+00    2.430434E-11    0.000000E+00              9.00000E+100
104  phase1.collocation_constraint.defects:S                   e   0.000000E+00    2.432218E-11    0.000000E+00              9.00000E+100
105  phase1.collocation_constraint.defects:S                   e   0.000000E+00    2.433386E-11    0.000000E+00              9.00000E+100
106  phase1.collocation_constraint.defects:S                   e   0.000000E+00    2.421960E-11    0.000000E+00              9.00000E+100
107  phase1.collocation_constraint.defects:S                   e   0.000000E+00    2.371425E-11    0.000000E+00              9.00000E+100
108  phase1.collocation_constraint.defects:S                   e   0.000000E+00    2.260201E-11    0.000000E+00              9.00000E+100
109  phase1.collocation_constraint.defects:S                   e   0.000000E+00    2.086942E-11    0.000000E+00              9.00000E+100
110  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.877520E-11    0.000000E+00              9.00000E+100
111  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.680124E-11    0.000000E+00              9.00000E+100
112  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.547637E-11    0.000000E+00              9.00000E+100
113  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.514292E-11    0.000000E+00              9.00000E+100
114  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.500795E-11    0.000000E+00              9.00000E+100
115  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.471062E-11    0.000000E+00              9.00000E+100
116  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.428747E-11    0.000000E+00              9.00000E+100
117  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.378725E-11    0.000000E+00              9.00000E+100
118  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.327260E-11    0.000000E+00              9.00000E+100
119  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.280296E-11    0.000000E+00              9.00000E+100
120  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.243728E-11    0.000000E+00              9.00000E+100
121  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.221987E-11    0.000000E+00              9.00000E+100
122  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.215999E-11    0.000000E+00              9.00000E+100
123  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.203372E-11    0.000000E+00              9.00000E+100
124  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.173638E-11    0.000000E+00              9.00000E+100
125  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.131316E-11    0.000000E+00              9.00000E+100
126  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.081169E-11    0.000000E+00              9.00000E+100
127  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.029672E-11    0.000000E+00              9.00000E+100
128  phase1.collocation_constraint.defects:S                   e   0.000000E+00    9.825384E-12    0.000000E+00              9.00000E+100
129  phase1.collocation_constraint.defects:S                   e   0.000000E+00    9.461426E-12    0.000000E+00              9.00000E+100
130  phase1.collocation_constraint.defects:S                   e   0.000000E+00    9.239989E-12    0.000000E+00              9.00000E+100
131  phase1.collocation_constraint.defects:S                   e   0.000000E+00    9.184508E-12    0.000000E+00              9.00000E+100
132  phase1.collocation_constraint.defects:S                   e   0.000000E+00    9.084684E-12    0.000000E+00              9.00000E+100
133  phase1.collocation_constraint.defects:S                   e   0.000000E+00    8.855517E-12    0.000000E+00              9.00000E+100
134  phase1.collocation_constraint.defects:S                   e   0.000000E+00    8.544612E-12    0.000000E+00              9.00000E+100
135  phase1.collocation_constraint.defects:S                   e   0.000000E+00    8.197390E-12    0.000000E+00              9.00000E+100
136  phase1.collocation_constraint.defects:S                   e   0.000000E+00    7.861137E-12    0.000000E+00              9.00000E+100
137  phase1.collocation_constraint.defects:S                   e   0.000000E+00    7.574574E-12    0.000000E+00              9.00000E+100
138  phase1.collocation_constraint.defects:S                   e   0.000000E+00    7.362707E-12    0.000000E+00              9.00000E+100
139  phase1.collocation_constraint.defects:S                   e   0.000000E+00    7.251571E-12    0.000000E+00              9.00000E+100
140  phase1.collocation_constraint.defects:S                   e   0.000000E+00    7.214027E-12    0.000000E+00              9.00000E+100
141  phase1.collocation_constraint.defects:S                   e   0.000000E+00    7.145172E-12    0.000000E+00              9.00000E+100
142  phase1.collocation_constraint.defects:S                   e   0.000000E+00    6.996885E-12    0.000000E+00              9.00000E+100
143  phase1.collocation_constraint.defects:S                   e   0.000000E+00    6.792453E-12    0.000000E+00              9.00000E+100
144  phase1.collocation_constraint.defects:S                   e   0.000000E+00    6.571458E-12    0.000000E+00              9.00000E+100
145  phase1.collocation_constraint.defects:S                   e   0.000000E+00    6.367492E-12    0.000000E+00              9.00000E+100
146  phase1.collocation_constraint.defects:S                   e   0.000000E+00    6.198838E-12    0.000000E+00              9.00000E+100
147  phase1.collocation_constraint.defects:S                   e   0.000000E+00    6.089567E-12    0.000000E+00              9.00000E+100
148  phase1.collocation_constraint.defects:S                   e   0.000000E+00    6.011190E-12    0.000000E+00              9.00000E+100
149  phase1.collocation_constraint.defects:S                   e   0.000000E+00    6.008982E-12    0.000000E+00              9.00000E+100
150  phase1.collocation_constraint.defects:S                   e   0.000000E+00    5.923440E-12    0.000000E+00              9.00000E+100
151  phase1.collocation_constraint.defects:S                   e   0.000000E+00    5.743866E-12    0.000000E+00              9.00000E+100
152  phase1.collocation_constraint.defects:S                   e   0.000000E+00    5.517276E-12    0.000000E+00              9.00000E+100
153  phase1.collocation_constraint.defects:S                   e   0.000000E+00    5.280821E-12    0.000000E+00              9.00000E+100
154  phase1.collocation_constraint.defects:S                   e   0.000000E+00    5.082254E-12    0.000000E+00              9.00000E+100
155  phase1.collocation_constraint.defects:S                   e   0.000000E+00    4.937672E-12    0.000000E+00              9.00000E+100
156  phase1.collocation_constraint.defects:S                   e   0.000000E+00    4.849677E-12    0.000000E+00              9.00000E+100
157  phase1.collocation_constraint.defects:S                   e   0.000000E+00    4.803004E-12    0.000000E+00              9.00000E+100
158  phase1.collocation_constraint.defects:S                   e   0.000000E+00    4.789263E-12    0.000000E+00              9.00000E+100
159  phase1.collocation_constraint.defects:S                   e   0.000000E+00    4.782343E-12    0.000000E+00              9.00000E+100
160  phase1.collocation_constraint.defects:S                   e   0.000000E+00    4.739891E-12    0.000000E+00              9.00000E+100
161  phase1.collocation_constraint.defects:S                   e   0.000000E+00    4.715499E-12    0.000000E+00              9.00000E+100
162  phase1.collocation_constraint.defects:S                   e   0.000000E+00    4.720162E-12    0.000000E+00              9.00000E+100
163  phase1.collocation_constraint.defects:S                   e   0.000000E+00    4.764282E-12    0.000000E+00              9.00000E+100
164  phase1.collocation_constraint.defects:S                   e   0.000000E+00    4.844573E-12    0.000000E+00              9.00000E+100
165  phase1.collocation_constraint.defects:S                   e   0.000000E+00    4.931538E-12    0.000000E+00              9.00000E+100
166  phase1.collocation_constraint.defects:S                   e   0.000000E+00    4.992197E-12    0.000000E+00              9.00000E+100
167  phase1.collocation_constraint.defects:S                   e   0.000000E+00    5.009031E-12    0.000000E+00              9.00000E+100
168  phase1.collocation_constraint.defects:S                   e   0.000000E+00    5.081862E-12    0.000000E+00              9.00000E+100
169  phase1.collocation_constraint.defects:S                   e   0.000000E+00    5.232971E-12    0.000000E+00              9.00000E+100
170  phase1.collocation_constraint.defects:S                   e   0.000000E+00    5.434924E-12    0.000000E+00              9.00000E+100
171  phase1.collocation_constraint.defects:S                   e   0.000000E+00    5.630399E-12    0.000000E+00              9.00000E+100
172  phase1.collocation_constraint.defects:S                   e   0.000000E+00    5.798097E-12    0.000000E+00              9.00000E+100
173  phase1.collocation_constraint.defects:S                   e   0.000000E+00    5.910582E-12    0.000000E+00              9.00000E+100
174  phase1.collocation_constraint.defects:S                   e   0.000000E+00    5.976689E-12    0.000000E+00              9.00000E+100
175  phase1.collocation_constraint.defects:S                   e   0.000000E+00    6.004418E-12    0.000000E+00              9.00000E+100
176  phase1.collocation_constraint.defects:S                   e   0.000000E+00    6.009865E-12    0.000000E+00              9.00000E+100
177  phase1.collocation_constraint.defects:S                   e   0.000000E+00    6.032294E-12    0.000000E+00              9.00000E+100
178  phase1.collocation_constraint.defects:S                   e   0.000000E+00    6.052170E-12    0.000000E+00              9.00000E+100
179  phase1.collocation_constraint.defects:S                   e   0.000000E+00    6.057667E-12    0.000000E+00              9.00000E+100
180  phase1.collocation_constraint.defects:S                   e   0.000000E+00    6.038036E-12    0.000000E+00              9.00000E+100
181  phase1.collocation_constraint.defects:S                   e   0.000000E+00    5.970800E-12    0.000000E+00              9.00000E+100
182  phase1.collocation_constraint.defects:S                   e   0.000000E+00    5.876424E-12    0.000000E+00              9.00000E+100
183  phase1.collocation_constraint.defects:S                   e   0.000000E+00    5.784060E-12    0.000000E+00              9.00000E+100
184  phase1.collocation_constraint.defects:S                   e   0.000000E+00    5.693709E-12    0.000000E+00              9.00000E+100
185  phase1.collocation_constraint.defects:S                   e   0.000000E+00    5.690470E-12    0.000000E+00              9.00000E+100
186  phase1.collocation_constraint.defects:S                   e   0.000000E+00    5.643405E-12    0.000000E+00              9.00000E+100
187  phase1.collocation_constraint.defects:S                   e   0.000000E+00    5.527484E-12    0.000000E+00              9.00000E+100
188  phase1.collocation_constraint.defects:S                   e   0.000000E+00    5.350560E-12    0.000000E+00              9.00000E+100
189  phase1.collocation_constraint.defects:S                   e   0.000000E+00    5.134669E-12    0.000000E+00              9.00000E+100
190  phase1.collocation_constraint.defects:S                   e   0.000000E+00    4.896889E-12    0.000000E+00              9.00000E+100
191  phase1.collocation_constraint.defects:S                   e   0.000000E+00    4.663625E-12    0.000000E+00              9.00000E+100
192  phase1.collocation_constraint.defects:S                   e   0.000000E+00    4.470407E-12    0.000000E+00              9.00000E+100
193  phase1.collocation_constraint.defects:S                   e   0.000000E+00    4.357480E-12    0.000000E+00              9.00000E+100
194  phase1.collocation_constraint.defects:S                   e   0.000000E+00    4.320427E-12    0.000000E+00              9.00000E+100
195  phase1.collocation_constraint.defects:S                   e   0.000000E+00    4.251129E-12    0.000000E+00              9.00000E+100
196  phase1.collocation_constraint.defects:S                   e   0.000000E+00    4.087211E-12    0.000000E+00              9.00000E+100
197  phase1.collocation_constraint.defects:S                   e   0.000000E+00    3.835935E-12    0.000000E+00              9.00000E+100
198  phase1.collocation_constraint.defects:S                   e   0.000000E+00    3.533422E-12    0.000000E+00              9.00000E+100
199  phase1.collocation_constraint.defects:S                   e   0.000000E+00    3.203671E-12    0.000000E+00              9.00000E+100
200  phase1.collocation_constraint.defects:S                   e   0.000000E+00    2.884620E-12    0.000000E+00              9.00000E+100
201  phase1.collocation_constraint.defects:S                   e   0.000000E+00    2.645564E-12    0.000000E+00              9.00000E+100
202  phase1.collocation_constraint.defects:S                   e   0.000000E+00    2.471781E-12    0.000000E+00              9.00000E+100
203  phase1.collocation_constraint.defects:S                   e   0.000000E+00    2.443758E-12    0.000000E+00              9.00000E+100
204  phase1.collocation_constraint.defects:S                   e   0.000000E+00    2.420593E-12    0.000000E+00              9.00000E+100
205  phase1.collocation_constraint.defects:S                   e   0.000000E+00    2.356498E-12    0.000000E+00              9.00000E+100
206  phase1.collocation_constraint.defects:S                   e   0.000000E+00    2.256528E-12    0.000000E+00              9.00000E+100
207  phase1.collocation_constraint.defects:S                   e   0.000000E+00    2.148508E-12    0.000000E+00              9.00000E+100
208  phase1.collocation_constraint.defects:S                   e   0.000000E+00    2.019926E-12    0.000000E+00              9.00000E+100
209  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.910827E-12    0.000000E+00              9.00000E+100
210  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.820917E-12    0.000000E+00              9.00000E+100
211  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.757411E-12    0.000000E+00              9.00000E+100
212  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.753583E-12    0.000000E+00              9.00000E+100
213  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.721241E-12    0.000000E+00              9.00000E+100
214  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.646447E-12    0.000000E+00              9.00000E+100
215  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.532538E-12    0.000000E+00              9.00000E+100
216  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.408373E-12    0.000000E+00              9.00000E+100
217  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.271447E-12    0.000000E+00              9.00000E+100
218  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.134325E-12    0.000000E+00              9.00000E+100
219  phase1.collocation_constraint.defects:S                   e   0.000000E+00    1.050206E-12    0.000000E+00              9.00000E+100
220  phase1.collocation_constraint.defects:S                   e   0.000000E+00    9.660877E-13    0.000000E+00              9.00000E+100
221  phase1.collocation_constraint.defects:S                   e   0.000000E+00    9.754615E-13    0.000000E+00              9.00000E+100
222  phase1.collocation_constraint.defects:S                   e   0.000000E+00    8.821654E-13    0.000000E+00              9.00000E+100
223  phase1.collocation_constraint.defects:S                   e   0.000000E+00    6.662741E-13    0.000000E+00              9.00000E+100
224  phase1.collocation_constraint.defects:S                   e   0.000000E+00    3.803495E-13    0.000000E+00              9.00000E+100
225  phase1.collocation_constraint.defects:S                   e   0.000000E+00    5.987437E-14    0.000000E+00              9.00000E+100
226  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -2.285042E-13    0.000000E+00              9.00000E+100
227  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -4.929329E-13    0.000000E+00              9.00000E+100
228  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -6.714763E-13    0.000000E+00              9.00000E+100
229  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -8.288183E-13    0.000000E+00              9.00000E+100
230  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -7.858266E-13    0.000000E+00              9.00000E+100
231  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -8.598352E-13    0.000000E+00              9.00000E+100
232  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -1.005693E-12    0.000000E+00              9.00000E+100
233  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -1.191696E-12    0.000000E+00              9.00000E+100
234  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -1.378288E-12    0.000000E+00              9.00000E+100
235  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -1.553004E-12    0.000000E+00              9.00000E+100
236  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -1.698960E-12    0.000000E+00              9.00000E+100
237  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -1.810365E-12    0.000000E+00              9.00000E+100
238  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -1.880153E-12    0.000000E+00              9.00000E+100
239  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -1.884472E-12    0.000000E+00              9.00000E+100
240  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -1.890165E-12    0.000000E+00              9.00000E+100
241  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -1.923832E-12    0.000000E+00              9.00000E+100
242  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -1.934433E-12    0.000000E+00              9.00000E+100
243  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -1.923243E-12    0.000000E+00              9.00000E+100
244  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -1.885257E-12    0.000000E+00              9.00000E+100
245  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -1.790146E-12    0.000000E+00              9.00000E+100
246  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -1.714468E-12    0.000000E+00              9.00000E+100
247  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -1.655085E-12    0.000000E+00              9.00000E+100
248  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -1.611308E-12    0.000000E+00              9.00000E+100
249  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -1.584708E-12    0.000000E+00              9.00000E+100
250  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -1.487240E-12    0.000000E+00              9.00000E+100
251  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -1.307126E-12    0.000000E+00              9.00000E+100
252  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -1.078818E-12    0.000000E+00              9.00000E+100
253  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -7.948568E-13    0.000000E+00              9.00000E+100
254  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -5.072635E-13    0.000000E+00              9.00000E+100
255  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -2.542207E-13    0.000000E+00              9.00000E+100
256  phase1.collocation_constraint.defects:S                   e   0.000000E+00   -1.103259E-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/python3.11/site-packages/openmdao/visualization/opt_report/opt_report.py:625: UserWarning: Attempting to set identical low and high ylims makes transformation singular; automatically expanding.
ax.set_ylim([ymin_plot, ymax_plot])