How can I more efficiently use finite-differenced components in the ODE?#
Sometimes it’s overly burdensome to get the analytic partials for a component. In this case, OpenMDAO can use finite-differencing to approximate the partials of that component and then use those approximated partials when assembling the total derivatives. However, if a dense sub-jacobian pattern is prescribed somewhere within the ODE, it will effect all dependent calculations and cause related total jacobians to have dense patterns. In effect, a dense partial-derivative jacobian destroys the sparsity pattern of the problem. To alleviate this, OpenMDAO provides a mechanism to color the partials of a single component.
As an example, consider the minimum time-to-climb problem. The ODE of this problem consists of several components. In this case, we’re going to switch one of these components from using analytic derivatives to a finite-difference approximation. Here we use an option on the component so that we can toggle the use of partial coloring on and off for testing, but that’s not generally necessary.
class DynamicPressureCompFD(om.ExplicitComponent):
def initialize(self):
self.options.declare('num_nodes', types=int)
self.options.declare('partial_coloring', types=bool, default=False)
def setup(self):
nn = self.options['num_nodes']
self.add_input(name='rho', shape=(nn,), desc='atmospheric density', units='kg/m**3')
self.add_input(name='v', shape=(nn,), desc='air-relative velocity', units='m/s')
self.add_output(name='q', shape=(nn,), desc='dynamic pressure', units='N/m**2')
self.declare_partials(of='q', wrt='rho', method='fd')
self.declare_partials(of='q', wrt='v', method='fd')
if self.options['partial_coloring']:
self.declare_coloring(wrt=['*'], method='cs', tol=1.0E-6, num_full_jacs=2,
show_summary=True, show_sparsity=False, min_improve_pct=10.)
def compute(self, inputs, outputs):
outputs['q'] = 0.5 * inputs['rho'] * inputs['v'] ** 2
Note
When using finite-differenced partials, they should not be specified in the compute_partials method. In fact, if all partials in the component are being approximated, compute_partials should just be omitted.
In this usage of declare_coloring, we use the following arguments:
wrt=['*']This is used to specify that we wish to find sparse partials with respect to all inputs.method=['fd']We’re using finite differencing to approximate the partials for coloring. Using'cs'here (complex-step) will result in more accurate derivatives if the model supports the use of complex inputs.tol=1.0E-6Any value in the Jacobian with a value greater than this will be considered a non-zero. Since finite differencing is used and it generally encounters noise on the order of 1.0E-8, this tolerance should be larger than that. If using complex-step for the approximation method this tolerance can be smaller - as small as about 1.0E-15.num_full_jacsCompute the full jacobian this number of times before determining the partial sparsity pattern.min_improve_pctIf the number of solves required to compute the derivatives isn’t reduced by at least this amount, then coloring is ignored and the dense jacobian is used.show_summary = TruePrint the sparsity of the partial derivative jacobian. This will display something like:
Jacobian shape: (60, 120) ( 1.67% nonzero)
FWD solves: 2 REV solves: 0
Total colors vs. total size: 2 vs 120 (98.3% improvement)
Sparsity computed using tolerance: 1e-06
Time to compute sparsity: 0.011868 sec.
Time to compute coloring: 0.001385 sec.
show_sparsity=TrueDisplay the sparsity pattern in standard output to provide a visual indication whether or not it is working. Here, this outputs the jacobian ofrhowith two diagonal bands - one for each of the two inputs.
Approx coloring for 'traj.phases.phase0.rhs_col.aero.q_comp' (class DynamicPressureCompFD)
f.............................f............................. 0 q
.f.............................f............................ 1 q
..f.............................f........................... 2 q
...f.............................f.......................... 3 q
....f.............................f......................... 4 q
.....f.............................f........................ 5 q
......f.............................f....................... 6 q
.......f.............................f...................... 7 q
........f.............................f..................... 8 q
.........f.............................f.................... 9 q
..........f.............................f................... 10 q
...........f.............................f.................. 11 q
............f.............................f................. 12 q
.............f.............................f................ 13 q
..............f.............................f............... 14 q
...............f.............................f.............. 15 q
................f.............................f............. 16 q
.................f.............................f............ 17 q
..................f.............................f........... 18 q
...................f.............................f.......... 19 q
....................f.............................f......... 20 q
.....................f.............................f........ 21 q
......................f.............................f....... 22 q
.......................f.............................f...... 23 q
........................f.............................f..... 24 q
.........................f.............................f.... 25 q
..........................f.............................f... 26 q
...........................f.............................f.. 27 q
............................f.............................f. 28 q
.............................f.............................f 29 q
|rho
|v
The sparsity patterns of the resulting total-derivative jacobian matrices are shown below. Finite differencing without partial derivative coloring causes the sparsity pattern to be dense for a large portion of the matrix. Since the dynamic pressure affects all of the defect constraints, the algorithm treats each defect constraint as if it is potentially dependent upon all altitude and velocity values throughout the phase. However, if partial derivative coloring is used, OpenMDAO recovers the same sparsity pattern as seen in the analytic derivative case.
Show code cell outputs
class MinTimeClimbODE(om.Group):
def initialize(self):
self.options.declare('num_nodes', types=int)
self.options.declare('fd', types=bool, default=False, desc='If True, use fd for partials')
self.options.declare('partial_coloring', types=bool, default=False,
desc='If True and fd is True, color the approximated partials')
def setup(self):
nn = self.options['num_nodes']
self.add_subsystem(name='atmos',
subsys=USatm1976Comp(num_nodes=nn),
promotes_inputs=['h'])
self.add_subsystem(name='aero',
subsys=AeroGroup(num_nodes=nn,
fd=self.options['fd'],
partial_coloring=self.options['partial_coloring']),
promotes_inputs=['v', 'alpha', 'S'])
self.connect('atmos.sos', 'aero.sos')
self.connect('atmos.rho', 'aero.rho')
self.add_subsystem(name='prop',
subsys=PropGroup(num_nodes=nn),
promotes_inputs=['h', 'Isp', 'throttle'])
self.connect('aero.mach', 'prop.mach')
self.add_subsystem(name='flight_dynamics',
subsys=FlightPathEOM2D(num_nodes=nn),
promotes_inputs=['m', 'v', 'gam', 'alpha'])
self.connect('aero.f_drag', 'flight_dynamics.D')
self.connect('aero.f_lift', 'flight_dynamics.L')
self.connect('prop.thrust', 'flight_dynamics.T')
import os
import matplotlib
import matplotlib.pyplot as plt
import shutil
import openmdao.api as om
import dymos as dm
from dymos.examples.min_time_climb.doc.min_time_climb_ode_partial_coloring import MinTimeClimbODE
for fd in (False, True):
if fd:
pc_options = (False, True)
else:
pc_options = (False,)
for pc in pc_options:
header = 'Finite differenced component' if fd else 'Analytic derivatives in component'
header += ' with partial coloring' if pc else ''
#
# Instantiate the problem and configure the optimization driver
#
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = 'IPOPT'
p.driver.opt_settings['max_iter'] = 500
p.driver.opt_settings['print_level'] = 0
p.driver.opt_settings['nlp_scaling_method'] = 'gradient-based'
p.driver.opt_settings['tol'] = 1.0E-6
p.driver.opt_settings['mu_strategy'] = 'adaptive'
p.driver.opt_settings['bound_mult_init_method'] = 'mu-based'
p.driver.opt_settings['mu_init'] = 0.01
p.driver.declare_coloring(tol=1.0E-12)
#
# Instantiate the trajectory and phase
#
traj = dm.Trajectory()
phase = dm.Phase(ode_class=MinTimeClimbODE,
ode_init_kwargs={'fd': fd, 'partial_coloring': pc},
transcription=dm.GaussLobatto(num_segments=30))
traj.add_phase('phase0', phase)
p.model.add_subsystem('traj', traj)
#
# Set the options on the optimization variables
#
phase.set_time_options(fix_initial=True, duration_bounds=(50, 400),
duration_ref=100.0)
phase.add_state('r', fix_initial=True, lower=0, upper=1.0E6,
ref=1.0E3, defect_ref=1.0E3, units='m',
rate_source='flight_dynamics.r_dot')
phase.add_state('h', fix_initial=True, lower=0, upper=20000.0,
ref=1.0E2, defect_ref=1.0E2, units='m',
rate_source='flight_dynamics.h_dot')
phase.add_state('v', fix_initial=True, lower=10.0,
ref=1.0E2, defect_ref=1.0E2, units='m/s',
rate_source='flight_dynamics.v_dot')
phase.add_state('gam', fix_initial=True, lower=-1.5, upper=1.5,
ref=1.0, defect_ref=1.0, units='rad',
rate_source='flight_dynamics.gam_dot')
phase.add_state('m', fix_initial=True, lower=10.0, upper=1.0E5,
ref=1.0E3, defect_ref=1.0E3, units='kg',
rate_source='prop.m_dot')
phase.add_control('alpha', units='deg', lower=-8.0, upper=8.0, scaler=1.0,
rate_continuity=True, rate_continuity_scaler=100.0,
rate2_continuity=False, targets=['alpha'])
phase.add_parameter('S', val=49.2386, units='m**2', opt=False, targets=['S'])
phase.add_parameter('Isp', val=1600.0, units='s', opt=False, targets=['Isp'])
phase.add_parameter('throttle', val=1.0, opt=False, targets=['throttle'])
#
# Setup the boundary and path constraints
#
phase.add_boundary_constraint('h', loc='final', equals=20000, scaler=1.0E-3)
phase.add_boundary_constraint('aero.mach', loc='final', equals=1.0)
phase.add_boundary_constraint('gam', loc='final', equals=0.0)
phase.add_path_constraint(name='h', lower=100.0, upper=20000, ref=20000)
phase.add_path_constraint(name='aero.mach', lower=0.1, upper=1.8)
# Minimize time at the end of the phase
phase.add_objective('time', loc='final', ref=100.0)
p.model.options['assembled_jac_type'] = 'csc'
p.model.linear_solver = om.DirectSolver(assemble_jac=True)
#
# Setup the problem and set the initial guess
#
p.setup()
p['traj.phase0.t_initial'] = 0.0
p['traj.phase0.t_duration'] = 500
p['traj.phase0.states:r'] = phase.interp('r', [0.0, 50000.0])
p['traj.phase0.states:h'] = phase.interp('h', [100.0, 20000.0])
p['traj.phase0.states:v'] = phase.interp('v', [135.964, 283.159])
p['traj.phase0.states:gam'] = phase.interp('gam', [0.0, 0.0])
p['traj.phase0.states:m'] = phase.interp('m', [19030.468, 10000.])
p['traj.phase0.controls:alpha'] = phase.interp('alpha', [0.0, 0.0])
#
# Solve for the optimal trajectory
#
print(80 * '-')
print(f'{"--- " + header + " ":-<80}')
print(80 * '-', '\n')
dm.run_problem(p)
#
# This code is intended to save the coloring plots for the documentation.
# In practice, use the command line interface to view these files instead:
# `openmdao view_coloring coloring_files/total_coloring.pkl --view`
#
stfd = '_fd' if fd else ''
stpc = '_pc' if pc else ''
coloring_dir = f'coloring_files{stfd}{stpc}'
if fd or pc:
if os.path.exists(coloring_dir):
shutil.rmtree(coloring_dir)
shutil.move('coloring_files', coloring_dir)
_view_coloring(os.path.join(coloring_dir, 'total_coloring.pkl'));
--- Constraint Report [traj] ---
--- phase0 ---
[final] 2.0000e+04 == h [m]
[final] 1.0000e+00 == aero.mach [None]
[final] 0.0000e+00 == gam [rad]
[path] 1.0000e+02 <= h <= 2.0000e+04 [m]
[path] 1.0000e-01 <= aero.mach <= 1.8000e+00 [None]
--------------------------------------------------------------------------------
--- Analytic derivatives in component ------------------------------------------
--------------------------------------------------------------------------------
Model viewer data has already been recorded for Driver.
/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.
/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/core/driver.py:469: DriverWarning:The following design variable initial conditions are out of their specified bounds:
traj.phase0.t_duration
val: [500.]
lower: 50.0
upper: 400.0
Set the initial value of the design variable to a valid value or set the driver option['invalid_desvar_behavior'] to 'ignore'.
Model viewer data has already been recorded for Driver.
Full total jacobian was computed 3 times, taking 0.274424 seconds.
Total jacobian shape: (361, 212)
Jacobian shape: (361, 212) (3.44% nonzero)
FWD solves: 13 REV solves: 0
Total colors vs. total size: 13 vs 212 (93.87% improvement)
Sparsity computed using tolerance: 1e-12
Time to compute sparsity: 0.2744 sec
Time to compute coloring: 0.2213 sec
Memory to compute coloring: 0.7500 MB
Coloring created on: 2023-12-08 21:07:05
/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/core/total_jac.py:1759: DerivativesWarning:Constraints or objectives [('traj.phases.phase0.timeseries.timeseries_comp.h', inds=[(0, 0)]), ('traj.phases.phase0.timeseries.timeseries_comp.mach', inds=[(0, 0)])] cannot be impacted by the design variables of the problem.
Optimization Problem -- Optimization using pyOpt_sparse
================================================================================
Objective Function: _objfunc
Solution:
--------------------------------------------------------------------------------
Total Time: 5.6808
User Objective Time : 2.3278
User Sensitivity Time : 1.7234
Interface Time : 0.8395
Opt Solver Time: 0.7901
Calls to Objective Function : 155
Calls to Sens Function : 128
Objectives
Index Name Value
0 traj.phase0.t 3.235052E+00
Variables (c - continuous, i - integer, d - discrete)
Index Name Type Lower Bound Value Upper Bound Status
0 traj.phase0.t_duration_0 c 5.000000E-01 3.235052E+00 4.000000E+00
1 traj.phase0.states:r_0 c 0.000000E+00 1.808251E+00 1.000000E+03
2 traj.phase0.states:r_1 c 0.000000E+00 4.338697E+00 1.000000E+03
3 traj.phase0.states:r_2 c 0.000000E+00 7.365706E+00 1.000000E+03
4 traj.phase0.states:r_3 c 0.000000E+00 1.015788E+01 1.000000E+03
5 traj.phase0.states:r_4 c 0.000000E+00 1.292803E+01 1.000000E+03
6 traj.phase0.states:r_5 c 0.000000E+00 1.576496E+01 1.000000E+03
7 traj.phase0.states:r_6 c 0.000000E+00 1.862485E+01 1.000000E+03
8 traj.phase0.states:r_7 c 0.000000E+00 2.150888E+01 1.000000E+03
9 traj.phase0.states:r_8 c 0.000000E+00 2.455480E+01 1.000000E+03
10 traj.phase0.states:r_9 c 0.000000E+00 2.786272E+01 1.000000E+03
11 traj.phase0.states:r_10 c 0.000000E+00 3.146517E+01 1.000000E+03
12 traj.phase0.states:r_11 c 0.000000E+00 3.545861E+01 1.000000E+03
13 traj.phase0.states:r_12 c 0.000000E+00 3.978517E+01 1.000000E+03
14 traj.phase0.states:r_13 c 0.000000E+00 4.429326E+01 1.000000E+03
15 traj.phase0.states:r_14 c 0.000000E+00 4.890013E+01 1.000000E+03
16 traj.phase0.states:r_15 c 0.000000E+00 5.358829E+01 1.000000E+03
17 traj.phase0.states:r_16 c 0.000000E+00 5.836102E+01 1.000000E+03
18 traj.phase0.states:r_17 c 0.000000E+00 6.322273E+01 1.000000E+03
19 traj.phase0.states:r_18 c 0.000000E+00 6.817595E+01 1.000000E+03
20 traj.phase0.states:r_19 c 0.000000E+00 7.322536E+01 1.000000E+03
21 traj.phase0.states:r_20 c 0.000000E+00 7.838310E+01 1.000000E+03
22 traj.phase0.states:r_21 c 0.000000E+00 8.366868E+01 1.000000E+03
23 traj.phase0.states:r_22 c 0.000000E+00 8.909743E+01 1.000000E+03
24 traj.phase0.states:r_23 c 0.000000E+00 9.464681E+01 1.000000E+03
25 traj.phase0.states:r_24 c 0.000000E+00 1.001550E+02 1.000000E+03
26 traj.phase0.states:r_25 c 0.000000E+00 1.052010E+02 1.000000E+03
27 traj.phase0.states:r_26 c 0.000000E+00 1.093951E+02 1.000000E+03
28 traj.phase0.states:r_27 c 0.000000E+00 1.128544E+02 1.000000E+03
29 traj.phase0.states:r_28 c 0.000000E+00 1.159927E+02 1.000000E+03
30 traj.phase0.states:r_29 c 0.000000E+00 1.191444E+02 1.000000E+03
31 traj.phase0.states:h_0 c 0.000000E+00 1.061278E+00 2.000000E+02
32 traj.phase0.states:h_1 c 0.000000E+00 1.138902E+00 2.000000E+02
33 traj.phase0.states:h_2 c 0.000000E+00 8.816830E+00 2.000000E+02
34 traj.phase0.states:h_3 c 0.000000E+00 2.664369E+01 2.000000E+02
35 traj.phase0.states:h_4 c 0.000000E+00 4.417009E+01 2.000000E+02
36 traj.phase0.states:h_5 c 0.000000E+00 5.944148E+01 2.000000E+02
37 traj.phase0.states:h_6 c 0.000000E+00 7.289264E+01 2.000000E+02
38 traj.phase0.states:h_7 c 0.000000E+00 8.421155E+01 2.000000E+02
39 traj.phase0.states:h_8 c 0.000000E+00 9.049624E+01 2.000000E+02
40 traj.phase0.states:h_9 c 0.000000E+00 8.884446E+01 2.000000E+02
41 traj.phase0.states:h_10 c 0.000000E+00 8.146821E+01 2.000000E+02
42 traj.phase0.states:h_11 c 0.000000E+00 7.428380E+01 2.000000E+02
43 traj.phase0.states:h_12 c 0.000000E+00 7.107999E+01 2.000000E+02
44 traj.phase0.states:h_13 c 0.000000E+00 7.161936E+01 2.000000E+02
45 traj.phase0.states:h_14 c 0.000000E+00 7.403049E+01 2.000000E+02
46 traj.phase0.states:h_15 c 0.000000E+00 7.692153E+01 2.000000E+02
47 traj.phase0.states:h_16 c 0.000000E+00 7.977242E+01 2.000000E+02
48 traj.phase0.states:h_17 c 0.000000E+00 8.255948E+01 2.000000E+02
49 traj.phase0.states:h_18 c 0.000000E+00 8.533795E+01 2.000000E+02
50 traj.phase0.states:h_19 c 0.000000E+00 8.797512E+01 2.000000E+02
51 traj.phase0.states:h_20 c 0.000000E+00 9.008134E+01 2.000000E+02
52 traj.phase0.states:h_21 c 0.000000E+00 9.124472E+01 2.000000E+02
53 traj.phase0.states:h_22 c 0.000000E+00 9.175883E+01 2.000000E+02
54 traj.phase0.states:h_23 c 0.000000E+00 9.384321E+01 2.000000E+02
55 traj.phase0.states:h_24 c 0.000000E+00 1.021996E+02 2.000000E+02
56 traj.phase0.states:h_25 c 0.000000E+00 1.207245E+02 2.000000E+02
57 traj.phase0.states:h_26 c 0.000000E+00 1.466428E+02 2.000000E+02
58 traj.phase0.states:h_27 c 0.000000E+00 1.725217E+02 2.000000E+02
59 traj.phase0.states:h_28 c 0.000000E+00 1.921027E+02 2.000000E+02
60 traj.phase0.states:h_29 c 0.000000E+00 2.000000E+02 2.000000E+02 u
61 traj.phase0.states:v_0 c 1.000000E-01 2.001423E+00 1.000000E+19
62 traj.phase0.states:v_1 c 1.000000E-01 2.688869E+00 1.000000E+19
63 traj.phase0.states:v_2 c 1.000000E-01 3.059784E+00 1.000000E+19
64 traj.phase0.states:v_3 c 1.000000E-01 3.065025E+00 1.000000E+19
65 traj.phase0.states:v_4 c 1.000000E-01 3.014447E+00 1.000000E+19
66 traj.phase0.states:v_5 c 1.000000E-01 2.961204E+00 1.000000E+19
67 traj.phase0.states:v_6 c 1.000000E-01 2.900122E+00 1.000000E+19
68 traj.phase0.states:v_7 c 1.000000E-01 2.859573E+00 1.000000E+19
69 traj.phase0.states:v_8 c 1.000000E-01 2.953760E+00 1.000000E+19
70 traj.phase0.states:v_9 c 1.000000E-01 3.228336E+00 1.000000E+19
71 traj.phase0.states:v_10 c 1.000000E-01 3.596380E+00 1.000000E+19
72 traj.phase0.states:v_11 c 1.000000E-01 3.914291E+00 1.000000E+19
73 traj.phase0.states:v_12 c 1.000000E-01 4.117634E+00 1.000000E+19
74 traj.phase0.states:v_13 c 1.000000E-01 4.235637E+00 1.000000E+19
75 traj.phase0.states:v_14 c 1.000000E-01 4.317737E+00 1.000000E+19
76 traj.phase0.states:v_15 c 1.000000E-01 4.394116E+00 1.000000E+19
77 traj.phase0.states:v_16 c 1.000000E-01 4.474295E+00 1.000000E+19
78 traj.phase0.states:v_17 c 1.000000E-01 4.557851E+00 1.000000E+19
79 traj.phase0.states:v_18 c 1.000000E-01 4.643788E+00 1.000000E+19
80 traj.phase0.states:v_19 c 1.000000E-01 4.735627E+00 1.000000E+19
81 traj.phase0.states:v_20 c 1.000000E-01 4.841483E+00 1.000000E+19
82 traj.phase0.states:v_21 c 1.000000E-01 4.967195E+00 1.000000E+19
83 traj.phase0.states:v_22 c 1.000000E-01 5.100051E+00 1.000000E+19
84 traj.phase0.states:v_23 c 1.000000E-01 5.186233E+00 1.000000E+19
85 traj.phase0.states:v_24 c 1.000000E-01 5.124419E+00 1.000000E+19
86 traj.phase0.states:v_25 c 1.000000E-01 4.823440E+00 1.000000E+19
87 traj.phase0.states:v_26 c 1.000000E-01 4.304507E+00 1.000000E+19
88 traj.phase0.states:v_27 c 1.000000E-01 3.708459E+00 1.000000E+19
89 traj.phase0.states:v_28 c 1.000000E-01 3.190597E+00 1.000000E+19
90 traj.phase0.states:v_29 c 1.000000E-01 2.950864E+00 1.000000E+19
91 traj.phase0.states:gam_0 c -1.500000E+00 1.135809E-02 1.500000E+00
92 traj.phase0.states:gam_1 c -1.500000E+00 3.607791E-02 1.500000E+00
93 traj.phase0.states:gam_2 c -1.500000E+00 4.740251E-01 1.500000E+00
94 traj.phase0.states:gam_3 c -1.500000E+00 5.938412E-01 1.500000E+00
95 traj.phase0.states:gam_4 c -1.500000E+00 5.275395E-01 1.500000E+00
96 traj.phase0.states:gam_5 c -1.500000E+00 4.638884E-01 1.500000E+00
97 traj.phase0.states:gam_6 c -1.500000E+00 4.145407E-01 1.500000E+00
98 traj.phase0.states:gam_7 c -1.500000E+00 3.138366E-01 1.500000E+00
99 traj.phase0.states:gam_8 c -1.500000E+00 7.801432E-02 1.500000E+00
100 traj.phase0.states:gam_9 c -1.500000E+00 -1.560140E-01 1.500000E+00
101 traj.phase0.states:gam_10 c -1.500000E+00 -2.145622E-01 1.500000E+00
102 traj.phase0.states:gam_11 c -1.500000E+00 -1.292557E-01 1.500000E+00
103 traj.phase0.states:gam_12 c -1.500000E+00 -2.367965E-02 1.500000E+00
104 traj.phase0.states:gam_13 c -1.500000E+00 3.907735E-02 1.500000E+00
105 traj.phase0.states:gam_14 c -1.500000E+00 6.021435E-02 1.500000E+00
106 traj.phase0.states:gam_15 c -1.500000E+00 6.123182E-02 1.500000E+00
107 traj.phase0.states:gam_16 c -1.500000E+00 5.815344E-02 1.500000E+00
108 traj.phase0.states:gam_17 c -1.500000E+00 5.665182E-02 1.500000E+00
109 traj.phase0.states:gam_18 c -1.500000E+00 5.500486E-02 1.500000E+00
110 traj.phase0.states:gam_19 c -1.500000E+00 4.806055E-02 1.500000E+00
111 traj.phase0.states:gam_20 c -1.500000E+00 3.219164E-02 1.500000E+00
112 traj.phase0.states:gam_21 c -1.500000E+00 1.263263E-02 1.500000E+00
113 traj.phase0.states:gam_22 c -1.500000E+00 1.284872E-02 1.500000E+00
114 traj.phase0.states:gam_23 c -1.500000E+00 7.684100E-02 1.500000E+00
115 traj.phase0.states:gam_24 c -1.500000E+00 2.410043E-01 1.500000E+00
116 traj.phase0.states:gam_25 c -1.500000E+00 4.652932E-01 1.500000E+00
117 traj.phase0.states:gam_26 c -1.500000E+00 6.245258E-01 1.500000E+00
118 traj.phase0.states:gam_27 c -1.500000E+00 6.312972E-01 1.500000E+00
119 traj.phase0.states:gam_28 c -1.500000E+00 4.419071E-01 1.500000E+00
120 traj.phase0.states:gam_29 c -1.500000E+00 0.000000E+00 1.500000E+00
121 traj.phase0.states:m_0 c 1.000000E-02 1.894029E+01 1.000000E+02
122 traj.phase0.states:m_1 c 1.000000E-02 1.883985E+01 1.000000E+02
123 traj.phase0.states:m_2 c 1.000000E-02 1.873364E+01 1.000000E+02
124 traj.phase0.states:m_3 c 1.000000E-02 1.863493E+01 1.000000E+02
125 traj.phase0.states:m_4 c 1.000000E-02 1.854905E+01 1.000000E+02
126 traj.phase0.states:m_5 c 1.000000E-02 1.847497E+01 1.000000E+02
127 traj.phase0.states:m_6 c 1.000000E-02 1.841103E+01 1.000000E+02
128 traj.phase0.states:m_7 c 1.000000E-02 1.835554E+01 1.000000E+02
129 traj.phase0.states:m_8 c 1.000000E-02 1.830503E+01 1.000000E+02
130 traj.phase0.states:m_9 c 1.000000E-02 1.825307E+01 1.000000E+02
131 traj.phase0.states:m_10 c 1.000000E-02 1.819242E+01 1.000000E+02
132 traj.phase0.states:m_11 c 1.000000E-02 1.811953E+01 1.000000E+02
133 traj.phase0.states:m_12 c 1.000000E-02 1.803719E+01 1.000000E+02
134 traj.phase0.states:m_13 c 1.000000E-02 1.795047E+01 1.000000E+02
135 traj.phase0.states:m_14 c 1.000000E-02 1.786276E+01 1.000000E+02
136 traj.phase0.states:m_15 c 1.000000E-02 1.777530E+01 1.000000E+02
137 traj.phase0.states:m_16 c 1.000000E-02 1.768824E+01 1.000000E+02
138 traj.phase0.states:m_17 c 1.000000E-02 1.760150E+01 1.000000E+02
139 traj.phase0.states:m_18 c 1.000000E-02 1.751506E+01 1.000000E+02
140 traj.phase0.states:m_19 c 1.000000E-02 1.742890E+01 1.000000E+02
141 traj.phase0.states:m_20 c 1.000000E-02 1.734266E+01 1.000000E+02
142 traj.phase0.states:m_21 c 1.000000E-02 1.725555E+01 1.000000E+02
143 traj.phase0.states:m_22 c 1.000000E-02 1.716672E+01 1.000000E+02
144 traj.phase0.states:m_23 c 1.000000E-02 1.707674E+01 1.000000E+02
145 traj.phase0.states:m_24 c 1.000000E-02 1.699011E+01 1.000000E+02
146 traj.phase0.states:m_25 c 1.000000E-02 1.691715E+01 1.000000E+02
147 traj.phase0.states:m_26 c 1.000000E-02 1.686890E+01 1.000000E+02
148 traj.phase0.states:m_27 c 1.000000E-02 1.684153E+01 1.000000E+02
149 traj.phase0.states:m_28 c 1.000000E-02 1.682677E+01 1.000000E+02
150 traj.phase0.states:m_29 c 1.000000E-02 1.681809E+01 1.000000E+02
151 traj.phase0.controls:alpha_0 c -8.000000E+00 4.973302E+00 8.000000E+00
152 traj.phase0.controls:alpha_1 c -8.000000E+00 3.717358E+00 8.000000E+00
153 traj.phase0.controls:alpha_2 c -8.000000E+00 2.438005E+00 8.000000E+00
154 traj.phase0.controls:alpha_3 c -8.000000E+00 1.745995E+00 8.000000E+00
155 traj.phase0.controls:alpha_4 c -8.000000E+00 2.252077E+00 8.000000E+00
156 traj.phase0.controls:alpha_5 c -8.000000E+00 2.787490E+00 8.000000E+00
157 traj.phase0.controls:alpha_6 c -8.000000E+00 2.183468E+00 8.000000E+00
158 traj.phase0.controls:alpha_7 c -8.000000E+00 1.279482E+00 8.000000E+00
159 traj.phase0.controls:alpha_8 c -8.000000E+00 9.149972E-01 8.000000E+00
160 traj.phase0.controls:alpha_9 c -8.000000E+00 8.886376E-01 8.000000E+00
161 traj.phase0.controls:alpha_10 c -8.000000E+00 9.990253E-01 8.000000E+00
162 traj.phase0.controls:alpha_11 c -8.000000E+00 1.188564E+00 8.000000E+00
163 traj.phase0.controls:alpha_12 c -8.000000E+00 1.399656E+00 8.000000E+00
164 traj.phase0.controls:alpha_13 c -8.000000E+00 1.593700E+00 8.000000E+00
165 traj.phase0.controls:alpha_14 c -8.000000E+00 1.732093E+00 8.000000E+00
166 traj.phase0.controls:alpha_15 c -8.000000E+00 1.676067E+00 8.000000E+00
167 traj.phase0.controls:alpha_16 c -8.000000E+00 1.286855E+00 8.000000E+00
168 traj.phase0.controls:alpha_17 c -8.000000E+00 8.313130E-01 8.000000E+00
169 traj.phase0.controls:alpha_18 c -8.000000E+00 5.762999E-01 8.000000E+00
170 traj.phase0.controls:alpha_19 c -8.000000E+00 6.234701E-01 8.000000E+00
171 traj.phase0.controls:alpha_20 c -8.000000E+00 1.074478E+00 8.000000E+00
172 traj.phase0.controls:alpha_21 c -8.000000E+00 1.617219E+00 8.000000E+00
173 traj.phase0.controls:alpha_22 c -8.000000E+00 1.939588E+00 8.000000E+00
174 traj.phase0.controls:alpha_23 c -8.000000E+00 2.067124E+00 8.000000E+00
175 traj.phase0.controls:alpha_24 c -8.000000E+00 2.025367E+00 8.000000E+00
176 traj.phase0.controls:alpha_25 c -8.000000E+00 1.885614E+00 8.000000E+00
177 traj.phase0.controls:alpha_26 c -8.000000E+00 1.719161E+00 8.000000E+00
178 traj.phase0.controls:alpha_27 c -8.000000E+00 1.555758E+00 8.000000E+00
179 traj.phase0.controls:alpha_28 c -8.000000E+00 1.425154E+00 8.000000E+00
180 traj.phase0.controls:alpha_29 c -8.000000E+00 1.329011E+00 8.000000E+00
181 traj.phase0.controls:alpha_30 c -8.000000E+00 1.268987E+00 8.000000E+00
182 traj.phase0.controls:alpha_31 c -8.000000E+00 1.237394E+00 8.000000E+00
183 traj.phase0.controls:alpha_32 c -8.000000E+00 1.226543E+00 8.000000E+00
184 traj.phase0.controls:alpha_33 c -8.000000E+00 1.229144E+00 8.000000E+00
185 traj.phase0.controls:alpha_34 c -8.000000E+00 1.237907E+00 8.000000E+00
186 traj.phase0.controls:alpha_35 c -8.000000E+00 1.248334E+00 8.000000E+00
187 traj.phase0.controls:alpha_36 c -8.000000E+00 1.255927E+00 8.000000E+00
188 traj.phase0.controls:alpha_37 c -8.000000E+00 1.258050E+00 8.000000E+00
189 traj.phase0.controls:alpha_38 c -8.000000E+00 1.252069E+00 8.000000E+00
190 traj.phase0.controls:alpha_39 c -8.000000E+00 1.237674E+00 8.000000E+00
191 traj.phase0.controls:alpha_40 c -8.000000E+00 1.214555E+00 8.000000E+00
192 traj.phase0.controls:alpha_41 c -8.000000E+00 1.187278E+00 8.000000E+00
193 traj.phase0.controls:alpha_42 c -8.000000E+00 1.160405E+00 8.000000E+00
194 traj.phase0.controls:alpha_43 c -8.000000E+00 1.147736E+00 8.000000E+00
195 traj.phase0.controls:alpha_44 c -8.000000E+00 1.163065E+00 8.000000E+00
196 traj.phase0.controls:alpha_45 c -8.000000E+00 1.227458E+00 8.000000E+00
197 traj.phase0.controls:alpha_46 c -8.000000E+00 1.361979E+00 8.000000E+00
198 traj.phase0.controls:alpha_47 c -8.000000E+00 1.582043E+00 8.000000E+00
199 traj.phase0.controls:alpha_48 c -8.000000E+00 1.903064E+00 8.000000E+00
200 traj.phase0.controls:alpha_49 c -8.000000E+00 2.303926E+00 8.000000E+00
201 traj.phase0.controls:alpha_50 c -8.000000E+00 2.763515E+00 8.000000E+00
202 traj.phase0.controls:alpha_51 c -8.000000E+00 3.222348E+00 8.000000E+00
203 traj.phase0.controls:alpha_52 c -8.000000E+00 3.620941E+00 8.000000E+00
204 traj.phase0.controls:alpha_53 c -8.000000E+00 3.885807E+00 8.000000E+00
205 traj.phase0.controls:alpha_54 c -8.000000E+00 3.943456E+00 8.000000E+00
206 traj.phase0.controls:alpha_55 c -8.000000E+00 3.728445E+00 8.000000E+00
207 traj.phase0.controls:alpha_56 c -8.000000E+00 3.175329E+00 8.000000E+00
208 traj.phase0.controls:alpha_57 c -8.000000E+00 1.953484E+00 8.000000E+00
209 traj.phase0.controls:alpha_58 c -8.000000E+00 -2.677161E-01 8.000000E+00
210 traj.phase0.controls:alpha_59 c -8.000000E+00 -3.185536E+00 8.000000E+00
211 traj.phase0.controls:alpha_60 c -8.000000E+00 -6.497240E+00 8.000000E+00
Constraints (i - inequality, e - equality)
Index Name Type Lower Value Upper Status Lagrange Multiplier (N/A)
0 traj.phases.phase0->final_boundary_constraint->h e 2.000000E+01 2.000000E+01 2.000000E+01 9.00000E+100
1 traj.phases.phase0->final_boundary_constraint->mach e 1.000000E+00 1.000000E+00 1.000000E+00 9.00000E+100
2 traj.phases.phase0->final_boundary_constraint->gam e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
3 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 4.597285E-16 0.000000E+00 9.00000E+100
4 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 8.085092E-13 0.000000E+00 9.00000E+100
5 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 2.895769E-11 0.000000E+00 9.00000E+100
6 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 5.817068E-11 0.000000E+00 9.00000E+100
7 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 4.074267E-11 0.000000E+00 9.00000E+100
8 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 1.365455E-11 0.000000E+00 9.00000E+100
9 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 3.469418E-13 0.000000E+00 9.00000E+100
10 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 1.505335E-11 0.000000E+00 9.00000E+100
11 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 1.327573E-10 0.000000E+00 9.00000E+100
12 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 1.303487E-10 0.000000E+00 9.00000E+100
13 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 7.708115E-13 0.000000E+00 9.00000E+100
14 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 9.969673E-12 0.000000E+00 9.00000E+100
15 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 9.159846E-11 0.000000E+00 9.00000E+100
16 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 2.548643E-11 0.000000E+00 9.00000E+100
17 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 5.931847E-11 0.000000E+00 9.00000E+100
18 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 1.855875E-10 0.000000E+00 9.00000E+100
19 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 2.892385E-10 0.000000E+00 9.00000E+100
20 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 2.521767E-10 0.000000E+00 9.00000E+100
21 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 1.781200E-10 0.000000E+00 9.00000E+100
22 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 8.582611E-11 0.000000E+00 9.00000E+100
23 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 5.980731E-11 0.000000E+00 9.00000E+100
24 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 4.602404E-11 0.000000E+00 9.00000E+100
25 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 5.604305E-11 0.000000E+00 9.00000E+100
26 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 3.396168E-11 0.000000E+00 9.00000E+100
27 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 4.046101E-11 0.000000E+00 9.00000E+100
28 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 3.912106E-11 0.000000E+00 9.00000E+100
29 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 1.367141E-11 0.000000E+00 9.00000E+100
30 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 -1.560625E-12 0.000000E+00 9.00000E+100
31 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 3.106232E-12 0.000000E+00 9.00000E+100
32 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 9.133273E-14 0.000000E+00 9.00000E+100
33 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 2.807457E-15 0.000000E+00 9.00000E+100
34 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -1.191643E-12 0.000000E+00 9.00000E+100
35 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 6.080868E-10 0.000000E+00 9.00000E+100
36 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 2.417712E-11 0.000000E+00 9.00000E+100
37 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 3.146122E-10 0.000000E+00 9.00000E+100
38 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 1.915076E-11 0.000000E+00 9.00000E+100
39 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 2.656695E-11 0.000000E+00 9.00000E+100
40 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 2.865480E-10 0.000000E+00 9.00000E+100
41 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 2.110422E-10 0.000000E+00 9.00000E+100
42 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 6.651601E-10 0.000000E+00 9.00000E+100
43 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -3.355076E-10 0.000000E+00 9.00000E+100
44 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 2.030759E-10 0.000000E+00 9.00000E+100
45 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -4.583756E-10 0.000000E+00 9.00000E+100
46 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 3.600244E-11 0.000000E+00 9.00000E+100
47 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 3.762370E-10 0.000000E+00 9.00000E+100
48 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 2.013824E-10 0.000000E+00 9.00000E+100
49 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 3.380642E-10 0.000000E+00 9.00000E+100
50 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 4.224712E-10 0.000000E+00 9.00000E+100
51 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -4.619735E-11 0.000000E+00 9.00000E+100
52 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 3.056836E-10 0.000000E+00 9.00000E+100
53 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -1.176668E-10 0.000000E+00 9.00000E+100
54 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 2.449461E-10 0.000000E+00 9.00000E+100
55 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -1.466362E-10 0.000000E+00 9.00000E+100
56 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 5.443856E-11 0.000000E+00 9.00000E+100
57 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 1.421956E-10 0.000000E+00 9.00000E+100
58 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 3.064642E-10 0.000000E+00 9.00000E+100
59 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -2.559155E-11 0.000000E+00 9.00000E+100
60 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 4.180618E-11 0.000000E+00 9.00000E+100
61 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -1.518943E-11 0.000000E+00 9.00000E+100
62 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -1.710956E-11 0.000000E+00 9.00000E+100
63 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 1.053545E-15 0.000000E+00 9.00000E+100
64 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 1.034677E-12 0.000000E+00 9.00000E+100
65 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 1.141535E-11 0.000000E+00 9.00000E+100
66 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 8.295823E-11 0.000000E+00 9.00000E+100
67 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 2.081626E-11 0.000000E+00 9.00000E+100
68 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 2.635059E-12 0.000000E+00 9.00000E+100
69 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 5.097090E-12 0.000000E+00 9.00000E+100
70 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 9.840226E-12 0.000000E+00 9.00000E+100
71 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 1.124002E-10 0.000000E+00 9.00000E+100
72 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 7.397018E-11 0.000000E+00 9.00000E+100
73 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 2.013623E-11 0.000000E+00 9.00000E+100
74 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 2.049008E-11 0.000000E+00 9.00000E+100
75 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 1.453759E-11 0.000000E+00 9.00000E+100
76 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 2.458780E-11 0.000000E+00 9.00000E+100
77 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 2.306512E-11 0.000000E+00 9.00000E+100
78 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 1.526567E-10 0.000000E+00 9.00000E+100
79 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 4.704566E-10 0.000000E+00 9.00000E+100
80 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 6.021516E-10 0.000000E+00 9.00000E+100
81 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 3.680209E-10 0.000000E+00 9.00000E+100
82 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 1.810507E-10 0.000000E+00 9.00000E+100
83 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 7.492563E-11 0.000000E+00 9.00000E+100
84 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 1.920446E-11 0.000000E+00 9.00000E+100
85 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 4.845621E-11 0.000000E+00 9.00000E+100
86 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 9.015125E-11 0.000000E+00 9.00000E+100
87 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 1.160774E-10 0.000000E+00 9.00000E+100
88 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 8.878675E-11 0.000000E+00 9.00000E+100
89 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 1.632889E-11 0.000000E+00 9.00000E+100
90 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 1.650425E-12 0.000000E+00 9.00000E+100
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265 traj.phases.phase0->path_constraint->h i 5.000000E-03 8.626086E-01 1.000000E+00 9.00000E+100
266 traj.phases.phase0->path_constraint->h i 5.000000E-03 8.626086E-01 1.000000E+00 9.00000E+100
267 traj.phases.phase0->path_constraint->h i 5.000000E-03 9.171160E-01 1.000000E+00 9.00000E+100
268 traj.phases.phase0->path_constraint->h i 5.000000E-03 9.605137E-01 1.000000E+00 9.00000E+100
269 traj.phases.phase0->path_constraint->h i 5.000000E-03 9.605137E-01 1.000000E+00 9.00000E+100
270 traj.phases.phase0->path_constraint->h i 5.000000E-03 9.894532E-01 1.000000E+00 9.00000E+100
271 traj.phases.phase0->path_constraint->mach i 1.000000E-01 4.000084E-01 1.800000E+00 9.00000E+100
272 traj.phases.phase0->path_constraint->mach i 1.000000E-01 4.928085E-01 1.800000E+00 9.00000E+100
273 traj.phases.phase0->path_constraint->mach i 1.000000E-01 5.888628E-01 1.800000E+00 9.00000E+100
274 traj.phases.phase0->path_constraint->mach i 1.000000E-01 5.888628E-01 1.800000E+00 9.00000E+100
275 traj.phases.phase0->path_constraint->mach i 1.000000E-01 6.907438E-01 1.800000E+00 9.00000E+100
276 traj.phases.phase0->path_constraint->mach i 1.000000E-01 7.911940E-01 1.800000E+00 9.00000E+100
277 traj.phases.phase0->path_constraint->mach i 1.000000E-01 7.911940E-01 1.800000E+00 9.00000E+100
278 traj.phases.phase0->path_constraint->mach i 1.000000E-01 8.675548E-01 1.800000E+00 9.00000E+100
279 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.082548E-01 1.800000E+00 9.00000E+100
280 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.082548E-01 1.800000E+00 9.00000E+100
281 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.235977E-01 1.800000E+00 9.00000E+100
282 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.290698E-01 1.800000E+00 9.00000E+100
283 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.290698E-01 1.800000E+00 9.00000E+100
284 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.318669E-01 1.800000E+00 9.00000E+100
285 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.335845E-01 1.800000E+00 9.00000E+100
286 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.335845E-01 1.800000E+00 9.00000E+100
287 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.348379E-01 1.800000E+00 9.00000E+100
288 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.351596E-01 1.800000E+00 9.00000E+100
289 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.351596E-01 1.800000E+00 9.00000E+100
290 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.342013E-01 1.800000E+00 9.00000E+100
291 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.323512E-01 1.800000E+00 9.00000E+100
292 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.323512E-01 1.800000E+00 9.00000E+100
293 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.308127E-01 1.800000E+00 9.00000E+100
294 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.336906E-01 1.800000E+00 9.00000E+100
295 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.336906E-01 1.800000E+00 9.00000E+100
296 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.466621E-01 1.800000E+00 9.00000E+100
297 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.729970E-01 1.800000E+00 9.00000E+100
298 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.729970E-01 1.800000E+00 9.00000E+100
299 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.012228E+00 1.800000E+00 9.00000E+100
300 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.060964E+00 1.800000E+00 9.00000E+100
301 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.060964E+00 1.800000E+00 9.00000E+100
302 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.115393E+00 1.800000E+00 9.00000E+100
303 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.169809E+00 1.800000E+00 9.00000E+100
304 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.169809E+00 1.800000E+00 9.00000E+100
305 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.219078E+00 1.800000E+00 9.00000E+100
306 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.260763E+00 1.800000E+00 9.00000E+100
307 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.260763E+00 1.800000E+00 9.00000E+100
308 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.294139E+00 1.800000E+00 9.00000E+100
309 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.320538E+00 1.800000E+00 9.00000E+100
310 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.320538E+00 1.800000E+00 9.00000E+100
311 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.341667E+00 1.800000E+00 9.00000E+100
312 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.359367E+00 1.800000E+00 9.00000E+100
313 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.359367E+00 1.800000E+00 9.00000E+100
314 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.375206E+00 1.800000E+00 9.00000E+100
315 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.390233E+00 1.800000E+00 9.00000E+100
316 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.390233E+00 1.800000E+00 9.00000E+100
317 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.405192E+00 1.800000E+00 9.00000E+100
318 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.420396E+00 1.800000E+00 9.00000E+100
319 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.420396E+00 1.800000E+00 9.00000E+100
320 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.436000E+00 1.800000E+00 9.00000E+100
321 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.451974E+00 1.800000E+00 9.00000E+100
322 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.451974E+00 1.800000E+00 9.00000E+100
323 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.468256E+00 1.800000E+00 9.00000E+100
324 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.484791E+00 1.800000E+00 9.00000E+100
325 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.484791E+00 1.800000E+00 9.00000E+100
326 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.501560E+00 1.800000E+00 9.00000E+100
327 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.518645E+00 1.800000E+00 9.00000E+100
328 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.518645E+00 1.800000E+00 9.00000E+100
329 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.536188E+00 1.800000E+00 9.00000E+100
330 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.554417E+00 1.800000E+00 9.00000E+100
331 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.554417E+00 1.800000E+00 9.00000E+100
332 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.573586E+00 1.800000E+00 9.00000E+100
333 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.593894E+00 1.800000E+00 9.00000E+100
334 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.593894E+00 1.800000E+00 9.00000E+100
335 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.615448E+00 1.800000E+00 9.00000E+100
336 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.637980E+00 1.800000E+00 9.00000E+100
337 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.637980E+00 1.800000E+00 9.00000E+100
338 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.660942E+00 1.800000E+00 9.00000E+100
339 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.683020E+00 1.800000E+00 9.00000E+100
340 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.683020E+00 1.800000E+00 9.00000E+100
341 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.702446E+00 1.800000E+00 9.00000E+100
342 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.716556E+00 1.800000E+00 9.00000E+100
343 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.716556E+00 1.800000E+00 9.00000E+100
344 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.722337E+00 1.800000E+00 9.00000E+100
345 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.716745E+00 1.800000E+00 9.00000E+100
346 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.716745E+00 1.800000E+00 9.00000E+100
347 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.696689E+00 1.800000E+00 9.00000E+100
348 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.634713E+00 1.800000E+00 9.00000E+100
349 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.634713E+00 1.800000E+00 9.00000E+100
350 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.553446E+00 1.800000E+00 9.00000E+100
351 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.458842E+00 1.800000E+00 9.00000E+100
352 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.458842E+00 1.800000E+00 9.00000E+100
353 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.357849E+00 1.800000E+00 9.00000E+100
354 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.256835E+00 1.800000E+00 9.00000E+100
355 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.256835E+00 1.800000E+00 9.00000E+100
356 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.162016E+00 1.800000E+00 9.00000E+100
357 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.081326E+00 1.800000E+00 9.00000E+100
358 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.081326E+00 1.800000E+00 9.00000E+100
359 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.024098E+00 1.800000E+00 9.00000E+100
Exit Status
Inform Description
0 Solve Succeeded
--------------------------------------------------------------------------------
/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/utils/coloring.py:812: OMDeprecationWarning:display is deprecated. Use display_bokeh for rich html displays of coloringor display_txt for a text-based display.
<Figure size 500x1000 with 1 Axes>
Jacobian shape: (361, 212) (3.44% nonzero)
FWD solves: 13 REV solves: 0
Total colors vs. total size: 13 vs 212 (93.87% improvement)
Sparsity computed using tolerance: 1e-12
Time to compute sparsity: 0.2744 sec
Time to compute coloring: 0.2213 sec
Memory to compute coloring: 0.7500 MB
Coloring created on: 2023-12-08 21:07:05
--- Constraint Report [traj] ---
--- phase0 ---
[final] 2.0000e+04 == h [m]
[final] 1.0000e+00 == aero.mach [None]
[final] 0.0000e+00 == gam [rad]
[path] 1.0000e+02 <= h <= 2.0000e+04 [m]
[path] 1.0000e-01 <= aero.mach <= 1.8000e+00 [None]
--------------------------------------------------------------------------------
--- Finite differenced component -----------------------------------------------
--------------------------------------------------------------------------------
/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.
Model viewer data has already been recorded for Driver.
Model viewer data has already been recorded for Driver.
/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/core/driver.py:469: DriverWarning:The following design variable initial conditions are out of their specified bounds:
traj.phase0.t_duration
val: [500.]
lower: 50.0
upper: 400.0
Set the initial value of the design variable to a valid value or set the driver option['invalid_desvar_behavior'] to 'ignore'.
Full total jacobian was computed 3 times, taking 0.320855 seconds.
Total jacobian shape: (361, 212)
Jacobian shape: (361, 212) (23.30% nonzero)
FWD solves: 154 REV solves: 0
Total colors vs. total size: 154 vs 212 (27.36% improvement)
Sparsity computed using tolerance: 1e-12
Time to compute sparsity: 0.3209 sec
Time to compute coloring: 1.0174 sec
Memory to compute coloring: 16.6406 MB
Coloring created on: 2023-12-08 21:07:14
/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/core/total_jac.py:1759: DerivativesWarning:Constraints or objectives [('traj.phases.phase0.timeseries.timeseries_comp.h', inds=[(0, 0)]), ('traj.phases.phase0.timeseries.timeseries_comp.mach', inds=[(0, 0)])] cannot be impacted by the design variables of the problem.
Optimization Problem -- Optimization using pyOpt_sparse
================================================================================
Objective Function: _objfunc
Solution:
--------------------------------------------------------------------------------
Total Time: 19.8643
User Objective Time : 3.4773
User Sensitivity Time : 13.4011
Interface Time : 0.9422
Opt Solver Time: 2.0438
Calls to Objective Function : 146
Calls to Sens Function : 136
Objectives
Index Name Value
0 traj.phase0.t 3.235052E+00
Variables (c - continuous, i - integer, d - discrete)
Index Name Type Lower Bound Value Upper Bound Status
0 traj.phase0.t_duration_0 c 5.000000E-01 3.235052E+00 4.000000E+00
1 traj.phase0.states:r_0 c 0.000000E+00 1.808252E+00 1.000000E+03
2 traj.phase0.states:r_1 c 0.000000E+00 4.338693E+00 1.000000E+03
3 traj.phase0.states:r_2 c 0.000000E+00 7.365630E+00 1.000000E+03
4 traj.phase0.states:r_3 c 0.000000E+00 1.015784E+01 1.000000E+03
5 traj.phase0.states:r_4 c 0.000000E+00 1.292801E+01 1.000000E+03
6 traj.phase0.states:r_5 c 0.000000E+00 1.576497E+01 1.000000E+03
7 traj.phase0.states:r_6 c 0.000000E+00 1.862493E+01 1.000000E+03
8 traj.phase0.states:r_7 c 0.000000E+00 2.150887E+01 1.000000E+03
9 traj.phase0.states:r_8 c 0.000000E+00 2.455439E+01 1.000000E+03
10 traj.phase0.states:r_9 c 0.000000E+00 2.786183E+01 1.000000E+03
11 traj.phase0.states:r_10 c 0.000000E+00 3.146370E+01 1.000000E+03
12 traj.phase0.states:r_11 c 0.000000E+00 3.545652E+01 1.000000E+03
13 traj.phase0.states:r_12 c 0.000000E+00 3.978277E+01 1.000000E+03
14 traj.phase0.states:r_13 c 0.000000E+00 4.429082E+01 1.000000E+03
15 traj.phase0.states:r_14 c 0.000000E+00 4.889773E+01 1.000000E+03
16 traj.phase0.states:r_15 c 0.000000E+00 5.358594E+01 1.000000E+03
17 traj.phase0.states:r_16 c 0.000000E+00 5.835871E+01 1.000000E+03
18 traj.phase0.states:r_17 c 0.000000E+00 6.322045E+01 1.000000E+03
19 traj.phase0.states:r_18 c 0.000000E+00 6.817368E+01 1.000000E+03
20 traj.phase0.states:r_19 c 0.000000E+00 7.322308E+01 1.000000E+03
21 traj.phase0.states:r_20 c 0.000000E+00 7.838081E+01 1.000000E+03
22 traj.phase0.states:r_21 c 0.000000E+00 8.366636E+01 1.000000E+03
23 traj.phase0.states:r_22 c 0.000000E+00 8.909509E+01 1.000000E+03
24 traj.phase0.states:r_23 c 0.000000E+00 9.464445E+01 1.000000E+03
25 traj.phase0.states:r_24 c 0.000000E+00 1.001527E+02 1.000000E+03
26 traj.phase0.states:r_25 c 0.000000E+00 1.051988E+02 1.000000E+03
27 traj.phase0.states:r_26 c 0.000000E+00 1.093930E+02 1.000000E+03
28 traj.phase0.states:r_27 c 0.000000E+00 1.128523E+02 1.000000E+03
29 traj.phase0.states:r_28 c 0.000000E+00 1.159906E+02 1.000000E+03
30 traj.phase0.states:r_29 c 0.000000E+00 1.191423E+02 1.000000E+03
31 traj.phase0.states:h_0 c 0.000000E+00 1.061205E+00 2.000000E+02
32 traj.phase0.states:h_1 c 0.000000E+00 1.139547E+00 2.000000E+02
33 traj.phase0.states:h_2 c 0.000000E+00 8.818493E+00 2.000000E+02
34 traj.phase0.states:h_3 c 0.000000E+00 2.664424E+01 2.000000E+02
35 traj.phase0.states:h_4 c 0.000000E+00 4.417020E+01 2.000000E+02
36 traj.phase0.states:h_5 c 0.000000E+00 5.944116E+01 2.000000E+02
37 traj.phase0.states:h_6 c 0.000000E+00 7.289166E+01 2.000000E+02
38 traj.phase0.states:h_7 c 0.000000E+00 8.421286E+01 2.000000E+02
39 traj.phase0.states:h_8 c 0.000000E+00 9.050666E+01 2.000000E+02
40 traj.phase0.states:h_9 c 0.000000E+00 8.886522E+01 2.000000E+02
41 traj.phase0.states:h_10 c 0.000000E+00 8.149107E+01 2.000000E+02
42 traj.phase0.states:h_11 c 0.000000E+00 7.430015E+01 2.000000E+02
43 traj.phase0.states:h_12 c 0.000000E+00 7.108702E+01 2.000000E+02
44 traj.phase0.states:h_13 c 0.000000E+00 7.162016E+01 2.000000E+02
45 traj.phase0.states:h_14 c 0.000000E+00 7.402915E+01 2.000000E+02
46 traj.phase0.states:h_15 c 0.000000E+00 7.692000E+01 2.000000E+02
47 traj.phase0.states:h_16 c 0.000000E+00 7.977137E+01 2.000000E+02
48 traj.phase0.states:h_17 c 0.000000E+00 8.255909E+01 2.000000E+02
49 traj.phase0.states:h_18 c 0.000000E+00 8.533828E+01 2.000000E+02
50 traj.phase0.states:h_19 c 0.000000E+00 8.797569E+01 2.000000E+02
51 traj.phase0.states:h_20 c 0.000000E+00 9.008237E+01 2.000000E+02
52 traj.phase0.states:h_21 c 0.000000E+00 9.124630E+01 2.000000E+02
53 traj.phase0.states:h_22 c 0.000000E+00 9.176050E+01 2.000000E+02
54 traj.phase0.states:h_23 c 0.000000E+00 9.384412E+01 2.000000E+02
55 traj.phase0.states:h_24 c 0.000000E+00 1.021987E+02 2.000000E+02
56 traj.phase0.states:h_25 c 0.000000E+00 1.207221E+02 2.000000E+02
57 traj.phase0.states:h_26 c 0.000000E+00 1.466401E+02 2.000000E+02
58 traj.phase0.states:h_27 c 0.000000E+00 1.725200E+02 2.000000E+02
59 traj.phase0.states:h_28 c 0.000000E+00 1.921022E+02 2.000000E+02
60 traj.phase0.states:h_29 c 0.000000E+00 2.000000E+02 2.000000E+02 u
61 traj.phase0.states:v_0 c 1.000000E-01 2.001428E+00 1.000000E+19
62 traj.phase0.states:v_1 c 1.000000E-01 2.688839E+00 1.000000E+19
63 traj.phase0.states:v_2 c 1.000000E-01 3.059732E+00 1.000000E+19
64 traj.phase0.states:v_3 c 1.000000E-01 3.065014E+00 1.000000E+19
65 traj.phase0.states:v_4 c 1.000000E-01 3.014447E+00 1.000000E+19
66 traj.phase0.states:v_5 c 1.000000E-01 2.961219E+00 1.000000E+19
67 traj.phase0.states:v_6 c 1.000000E-01 2.900156E+00 1.000000E+19
68 traj.phase0.states:v_7 c 1.000000E-01 2.859508E+00 1.000000E+19
69 traj.phase0.states:v_8 c 1.000000E-01 2.953401E+00 1.000000E+19
70 traj.phase0.states:v_9 c 1.000000E-01 3.227774E+00 1.000000E+19
71 traj.phase0.states:v_10 c 1.000000E-01 3.595835E+00 1.000000E+19
72 traj.phase0.states:v_11 c 1.000000E-01 3.913948E+00 1.000000E+19
73 traj.phase0.states:v_12 c 1.000000E-01 4.117519E+00 1.000000E+19
74 traj.phase0.states:v_13 c 1.000000E-01 4.235648E+00 1.000000E+19
75 traj.phase0.states:v_14 c 1.000000E-01 4.317785E+00 1.000000E+19
76 traj.phase0.states:v_15 c 1.000000E-01 4.394161E+00 1.000000E+19
77 traj.phase0.states:v_16 c 1.000000E-01 4.474328E+00 1.000000E+19
78 traj.phase0.states:v_17 c 1.000000E-01 4.557866E+00 1.000000E+19
79 traj.phase0.states:v_18 c 1.000000E-01 4.643789E+00 1.000000E+19
80 traj.phase0.states:v_19 c 1.000000E-01 4.735623E+00 1.000000E+19
81 traj.phase0.states:v_20 c 1.000000E-01 4.841467E+00 1.000000E+19
82 traj.phase0.states:v_21 c 1.000000E-01 4.967170E+00 1.000000E+19
83 traj.phase0.states:v_22 c 1.000000E-01 5.100028E+00 1.000000E+19
84 traj.phase0.states:v_23 c 1.000000E-01 5.186230E+00 1.000000E+19
85 traj.phase0.states:v_24 c 1.000000E-01 5.124452E+00 1.000000E+19
86 traj.phase0.states:v_25 c 1.000000E-01 4.823503E+00 1.000000E+19
87 traj.phase0.states:v_26 c 1.000000E-01 4.304577E+00 1.000000E+19
88 traj.phase0.states:v_27 c 1.000000E-01 3.708513E+00 1.000000E+19
89 traj.phase0.states:v_28 c 1.000000E-01 3.190622E+00 1.000000E+19
90 traj.phase0.states:v_29 c 1.000000E-01 2.950864E+00 1.000000E+19
91 traj.phase0.states:gam_0 c -1.500000E+00 1.134439E-02 1.500000E+00
92 traj.phase0.states:gam_1 c -1.500000E+00 3.614696E-02 1.500000E+00
93 traj.phase0.states:gam_2 c -1.500000E+00 4.740105E-01 1.500000E+00
94 traj.phase0.states:gam_3 c -1.500000E+00 5.938098E-01 1.500000E+00
95 traj.phase0.states:gam_4 c -1.500000E+00 5.275347E-01 1.500000E+00
96 traj.phase0.states:gam_5 c -1.500000E+00 4.638575E-01 1.500000E+00
97 traj.phase0.states:gam_6 c -1.500000E+00 4.145383E-01 1.500000E+00
98 traj.phase0.states:gam_7 c -1.500000E+00 3.140234E-01 1.500000E+00
99 traj.phase0.states:gam_8 c -1.500000E+00 7.840336E-02 1.500000E+00
100 traj.phase0.states:gam_9 c -1.500000E+00 -1.558399E-01 1.500000E+00
101 traj.phase0.states:gam_10 c -1.500000E+00 -2.146738E-01 1.500000E+00
102 traj.phase0.states:gam_11 c -1.500000E+00 -1.294798E-01 1.500000E+00
103 traj.phase0.states:gam_12 c -1.500000E+00 -2.387578E-02 1.500000E+00
104 traj.phase0.states:gam_13 c -1.500000E+00 3.899725E-02 1.500000E+00
105 traj.phase0.states:gam_14 c -1.500000E+00 6.019084E-02 1.500000E+00
106 traj.phase0.states:gam_15 c -1.500000E+00 6.124115E-02 1.500000E+00
107 traj.phase0.states:gam_16 c -1.500000E+00 5.816182E-02 1.500000E+00
108 traj.phase0.states:gam_17 c -1.500000E+00 5.666952E-02 1.500000E+00
109 traj.phase0.states:gam_18 c -1.500000E+00 5.501360E-02 1.500000E+00
110 traj.phase0.states:gam_19 c -1.500000E+00 4.806452E-02 1.500000E+00
111 traj.phase0.states:gam_20 c -1.500000E+00 3.220505E-02 1.500000E+00
112 traj.phase0.states:gam_21 c -1.500000E+00 1.263848E-02 1.500000E+00
113 traj.phase0.states:gam_22 c -1.500000E+00 1.284543E-02 1.500000E+00
114 traj.phase0.states:gam_23 c -1.500000E+00 7.681626E-02 1.500000E+00
115 traj.phase0.states:gam_24 c -1.500000E+00 2.409680E-01 1.500000E+00
116 traj.phase0.states:gam_25 c -1.500000E+00 4.652651E-01 1.500000E+00
117 traj.phase0.states:gam_26 c -1.500000E+00 6.245245E-01 1.500000E+00
118 traj.phase0.states:gam_27 c -1.500000E+00 6.313242E-01 1.500000E+00
119 traj.phase0.states:gam_28 c -1.500000E+00 4.419387E-01 1.500000E+00
120 traj.phase0.states:gam_29 c -1.500000E+00 4.242908E-30 1.500000E+00
121 traj.phase0.states:m_0 c 1.000000E-02 1.894029E+01 1.000000E+02
122 traj.phase0.states:m_1 c 1.000000E-02 1.883985E+01 1.000000E+02
123 traj.phase0.states:m_2 c 1.000000E-02 1.873364E+01 1.000000E+02
124 traj.phase0.states:m_3 c 1.000000E-02 1.863493E+01 1.000000E+02
125 traj.phase0.states:m_4 c 1.000000E-02 1.854905E+01 1.000000E+02
126 traj.phase0.states:m_5 c 1.000000E-02 1.847497E+01 1.000000E+02
127 traj.phase0.states:m_6 c 1.000000E-02 1.841103E+01 1.000000E+02
128 traj.phase0.states:m_7 c 1.000000E-02 1.835554E+01 1.000000E+02
129 traj.phase0.states:m_8 c 1.000000E-02 1.830504E+01 1.000000E+02
130 traj.phase0.states:m_9 c 1.000000E-02 1.825309E+01 1.000000E+02
131 traj.phase0.states:m_10 c 1.000000E-02 1.819247E+01 1.000000E+02
132 traj.phase0.states:m_11 c 1.000000E-02 1.811961E+01 1.000000E+02
133 traj.phase0.states:m_12 c 1.000000E-02 1.803728E+01 1.000000E+02
134 traj.phase0.states:m_13 c 1.000000E-02 1.795056E+01 1.000000E+02
135 traj.phase0.states:m_14 c 1.000000E-02 1.786285E+01 1.000000E+02
136 traj.phase0.states:m_15 c 1.000000E-02 1.777539E+01 1.000000E+02
137 traj.phase0.states:m_16 c 1.000000E-02 1.768833E+01 1.000000E+02
138 traj.phase0.states:m_17 c 1.000000E-02 1.760158E+01 1.000000E+02
139 traj.phase0.states:m_18 c 1.000000E-02 1.751514E+01 1.000000E+02
140 traj.phase0.states:m_19 c 1.000000E-02 1.742898E+01 1.000000E+02
141 traj.phase0.states:m_20 c 1.000000E-02 1.734274E+01 1.000000E+02
142 traj.phase0.states:m_21 c 1.000000E-02 1.725564E+01 1.000000E+02
143 traj.phase0.states:m_22 c 1.000000E-02 1.716681E+01 1.000000E+02
144 traj.phase0.states:m_23 c 1.000000E-02 1.707683E+01 1.000000E+02
145 traj.phase0.states:m_24 c 1.000000E-02 1.699020E+01 1.000000E+02
146 traj.phase0.states:m_25 c 1.000000E-02 1.691724E+01 1.000000E+02
147 traj.phase0.states:m_26 c 1.000000E-02 1.686899E+01 1.000000E+02
148 traj.phase0.states:m_27 c 1.000000E-02 1.684162E+01 1.000000E+02
149 traj.phase0.states:m_28 c 1.000000E-02 1.682685E+01 1.000000E+02
150 traj.phase0.states:m_29 c 1.000000E-02 1.681817E+01 1.000000E+02
151 traj.phase0.controls:alpha_0 c -8.000000E+00 4.973680E+00 8.000000E+00
152 traj.phase0.controls:alpha_1 c -8.000000E+00 3.717139E+00 8.000000E+00
153 traj.phase0.controls:alpha_2 c -8.000000E+00 2.438072E+00 8.000000E+00
154 traj.phase0.controls:alpha_3 c -8.000000E+00 1.746449E+00 8.000000E+00
155 traj.phase0.controls:alpha_4 c -8.000000E+00 2.252241E+00 8.000000E+00
156 traj.phase0.controls:alpha_5 c -8.000000E+00 2.787253E+00 8.000000E+00
157 traj.phase0.controls:alpha_6 c -8.000000E+00 2.183291E+00 8.000000E+00
158 traj.phase0.controls:alpha_7 c -8.000000E+00 1.279533E+00 8.000000E+00
159 traj.phase0.controls:alpha_8 c -8.000000E+00 9.151593E-01 8.000000E+00
160 traj.phase0.controls:alpha_9 c -8.000000E+00 8.887826E-01 8.000000E+00
161 traj.phase0.controls:alpha_10 c -8.000000E+00 9.990178E-01 8.000000E+00
162 traj.phase0.controls:alpha_11 c -8.000000E+00 1.188413E+00 8.000000E+00
163 traj.phase0.controls:alpha_12 c -8.000000E+00 1.399516E+00 8.000000E+00
164 traj.phase0.controls:alpha_13 c -8.000000E+00 1.593777E+00 8.000000E+00
165 traj.phase0.controls:alpha_14 c -8.000000E+00 1.732644E+00 8.000000E+00
166 traj.phase0.controls:alpha_15 c -8.000000E+00 1.677263E+00 8.000000E+00
167 traj.phase0.controls:alpha_16 c -8.000000E+00 1.288780E+00 8.000000E+00
168 traj.phase0.controls:alpha_17 c -8.000000E+00 8.332688E-01 8.000000E+00
169 traj.phase0.controls:alpha_18 c -8.000000E+00 5.768044E-01 8.000000E+00
170 traj.phase0.controls:alpha_19 c -8.000000E+00 6.223884E-01 8.000000E+00
171 traj.phase0.controls:alpha_20 c -8.000000E+00 1.073023E+00 8.000000E+00
172 traj.phase0.controls:alpha_21 c -8.000000E+00 1.616136E+00 8.000000E+00
173 traj.phase0.controls:alpha_22 c -8.000000E+00 1.939156E+00 8.000000E+00
174 traj.phase0.controls:alpha_23 c -8.000000E+00 2.067300E+00 8.000000E+00
175 traj.phase0.controls:alpha_24 c -8.000000E+00 2.025783E+00 8.000000E+00
176 traj.phase0.controls:alpha_25 c -8.000000E+00 1.886118E+00 8.000000E+00
177 traj.phase0.controls:alpha_26 c -8.000000E+00 1.719822E+00 8.000000E+00
178 traj.phase0.controls:alpha_27 c -8.000000E+00 1.556473E+00 8.000000E+00
179 traj.phase0.controls:alpha_28 c -8.000000E+00 1.425653E+00 8.000000E+00
180 traj.phase0.controls:alpha_29 c -8.000000E+00 1.329250E+00 8.000000E+00
181 traj.phase0.controls:alpha_30 c -8.000000E+00 1.269155E+00 8.000000E+00
182 traj.phase0.controls:alpha_31 c -8.000000E+00 1.237541E+00 8.000000E+00
183 traj.phase0.controls:alpha_32 c -8.000000E+00 1.226577E+00 8.000000E+00
184 traj.phase0.controls:alpha_33 c -8.000000E+00 1.229088E+00 8.000000E+00
185 traj.phase0.controls:alpha_34 c -8.000000E+00 1.237897E+00 8.000000E+00
186 traj.phase0.controls:alpha_35 c -8.000000E+00 1.248386E+00 8.000000E+00
187 traj.phase0.controls:alpha_36 c -8.000000E+00 1.255935E+00 8.000000E+00
188 traj.phase0.controls:alpha_37 c -8.000000E+00 1.257993E+00 8.000000E+00
189 traj.phase0.controls:alpha_38 c -8.000000E+00 1.252009E+00 8.000000E+00
190 traj.phase0.controls:alpha_39 c -8.000000E+00 1.237656E+00 8.000000E+00
191 traj.phase0.controls:alpha_40 c -8.000000E+00 1.214607E+00 8.000000E+00
192 traj.phase0.controls:alpha_41 c -8.000000E+00 1.187367E+00 8.000000E+00
193 traj.phase0.controls:alpha_42 c -8.000000E+00 1.160443E+00 8.000000E+00
194 traj.phase0.controls:alpha_43 c -8.000000E+00 1.147711E+00 8.000000E+00
195 traj.phase0.controls:alpha_44 c -8.000000E+00 1.163048E+00 8.000000E+00
196 traj.phase0.controls:alpha_45 c -8.000000E+00 1.227454E+00 8.000000E+00
197 traj.phase0.controls:alpha_46 c -8.000000E+00 1.361931E+00 8.000000E+00
198 traj.phase0.controls:alpha_47 c -8.000000E+00 1.581948E+00 8.000000E+00
199 traj.phase0.controls:alpha_48 c -8.000000E+00 1.902978E+00 8.000000E+00
200 traj.phase0.controls:alpha_49 c -8.000000E+00 2.303872E+00 8.000000E+00
201 traj.phase0.controls:alpha_50 c -8.000000E+00 2.763482E+00 8.000000E+00
202 traj.phase0.controls:alpha_51 c -8.000000E+00 3.222345E+00 8.000000E+00
203 traj.phase0.controls:alpha_52 c -8.000000E+00 3.620997E+00 8.000000E+00
204 traj.phase0.controls:alpha_53 c -8.000000E+00 3.885939E+00 8.000000E+00
205 traj.phase0.controls:alpha_54 c -8.000000E+00 3.943673E+00 8.000000E+00
206 traj.phase0.controls:alpha_55 c -8.000000E+00 3.728709E+00 8.000000E+00
207 traj.phase0.controls:alpha_56 c -8.000000E+00 3.175556E+00 8.000000E+00
208 traj.phase0.controls:alpha_57 c -8.000000E+00 1.953397E+00 8.000000E+00
209 traj.phase0.controls:alpha_58 c -8.000000E+00 -2.685874E-01 8.000000E+00
210 traj.phase0.controls:alpha_59 c -8.000000E+00 -3.186808E+00 8.000000E+00
211 traj.phase0.controls:alpha_60 c -8.000000E+00 -6.497675E+00 8.000000E+00
Constraints (i - inequality, e - equality)
Index Name Type Lower Value Upper Status Lagrange Multiplier (N/A)
0 traj.phases.phase0->final_boundary_constraint->h e 2.000000E+01 2.000000E+01 2.000000E+01 9.00000E+100
1 traj.phases.phase0->final_boundary_constraint->mach e 1.000000E+00 1.000000E+00 1.000000E+00 9.00000E+100
2 traj.phases.phase0->final_boundary_constraint->gam e 0.000000E+00 4.242908E-30 0.000000E+00 9.00000E+100
3 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 1.385009E-12 0.000000E+00 9.00000E+100
4 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 4.310215E-11 0.000000E+00 9.00000E+100
5 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 4.911893E-11 0.000000E+00 9.00000E+100
6 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 1.992218E-10 0.000000E+00 9.00000E+100
7 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 6.604521E-11 0.000000E+00 9.00000E+100
8 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 4.698334E-11 0.000000E+00 9.00000E+100
9 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 7.246915E-11 0.000000E+00 9.00000E+100
10 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 1.224594E-11 0.000000E+00 9.00000E+100
11 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 6.362336E-12 0.000000E+00 9.00000E+100
12 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 2.970796E-11 0.000000E+00 9.00000E+100
13 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 3.308084E-11 0.000000E+00 9.00000E+100
14 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 4.397119E-11 0.000000E+00 9.00000E+100
15 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 2.939780E-11 0.000000E+00 9.00000E+100
16 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 1.559706E-12 0.000000E+00 9.00000E+100
17 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 4.970278E-12 0.000000E+00 9.00000E+100
18 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 1.398770E-11 0.000000E+00 9.00000E+100
19 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 7.007182E-11 0.000000E+00 9.00000E+100
20 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 5.077089E-11 0.000000E+00 9.00000E+100
21 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 6.132809E-11 0.000000E+00 9.00000E+100
22 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 -3.620822E-12 0.000000E+00 9.00000E+100
23 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 1.991768E-10 0.000000E+00 9.00000E+100
24 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 3.482637E-10 0.000000E+00 9.00000E+100
25 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 3.319329E-10 0.000000E+00 9.00000E+100
26 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 2.735605E-10 0.000000E+00 9.00000E+100
27 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 1.680958E-10 0.000000E+00 9.00000E+100
28 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 7.637838E-11 0.000000E+00 9.00000E+100
29 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 1.071198E-11 0.000000E+00 9.00000E+100
30 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 4.750222E-12 0.000000E+00 9.00000E+100
31 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 5.365645E-12 0.000000E+00 9.00000E+100
32 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 7.049171E-14 0.000000E+00 9.00000E+100
33 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 6.871843E-12 0.000000E+00 9.00000E+100
34 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 1.073123E-10 0.000000E+00 9.00000E+100
35 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 1.143774E-09 0.000000E+00 9.00000E+100
36 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 5.505464E-10 0.000000E+00 9.00000E+100
37 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 3.041242E-10 0.000000E+00 9.00000E+100
38 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 8.500687E-10 0.000000E+00 9.00000E+100
39 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -6.240585E-11 0.000000E+00 9.00000E+100
40 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 1.091357E-10 0.000000E+00 9.00000E+100
41 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -4.581769E-11 0.000000E+00 9.00000E+100
42 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 7.752287E-11 0.000000E+00 9.00000E+100
43 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -6.315367E-11 0.000000E+00 9.00000E+100
44 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -2.465371E-11 0.000000E+00 9.00000E+100
45 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -1.147885E-11 0.000000E+00 9.00000E+100
46 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -1.961547E-11 0.000000E+00 9.00000E+100
47 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -4.456302E-12 0.000000E+00 9.00000E+100
48 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 1.179062E-10 0.000000E+00 9.00000E+100
49 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 8.919423E-11 0.000000E+00 9.00000E+100
50 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 2.830051E-11 0.000000E+00 9.00000E+100
51 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 9.255274E-11 0.000000E+00 9.00000E+100
52 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 1.357467E-10 0.000000E+00 9.00000E+100
53 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 4.770982E-10 0.000000E+00 9.00000E+100
54 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 8.387824E-11 0.000000E+00 9.00000E+100
55 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 2.438822E-10 0.000000E+00 9.00000E+100
56 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 3.050199E-10 0.000000E+00 9.00000E+100
57 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 4.732239E-10 0.000000E+00 9.00000E+100
58 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 2.641861E-10 0.000000E+00 9.00000E+100
59 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 8.846403E-11 0.000000E+00 9.00000E+100
60 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 1.110919E-10 0.000000E+00 9.00000E+100
61 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 2.396718E-12 0.000000E+00 9.00000E+100
62 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -1.510974E-12 0.000000E+00 9.00000E+100
63 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 3.097565E-12 0.000000E+00 9.00000E+100
64 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 1.922039E-11 0.000000E+00 9.00000E+100
65 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 9.344540E-11 0.000000E+00 9.00000E+100
66 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 2.621567E-11 0.000000E+00 9.00000E+100
67 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 8.366646E-11 0.000000E+00 9.00000E+100
68 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 6.598384E-11 0.000000E+00 9.00000E+100
69 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 1.778286E-11 0.000000E+00 9.00000E+100
70 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 1.827033E-11 0.000000E+00 9.00000E+100
71 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 6.487464E-12 0.000000E+00 9.00000E+100
72 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 1.532637E-11 0.000000E+00 9.00000E+100
73 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 6.826140E-11 0.000000E+00 9.00000E+100
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247 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.562315E-01 1.000000E+00 9.00000E+100
248 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.562315E-01 1.000000E+00 9.00000E+100
249 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.574986E-01 1.000000E+00 9.00000E+100
250 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.588025E-01 1.000000E+00 9.00000E+100
251 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.588025E-01 1.000000E+00 9.00000E+100
252 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.617707E-01 1.000000E+00 9.00000E+100
253 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.692206E-01 1.000000E+00 9.00000E+100
254 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.692206E-01 1.000000E+00 9.00000E+100
255 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.845475E-01 1.000000E+00 9.00000E+100
256 traj.phases.phase0->path_constraint->h i 5.000000E-03 5.109937E-01 1.000000E+00 9.00000E+100
257 traj.phases.phase0->path_constraint->h i 5.000000E-03 5.109937E-01 1.000000E+00 9.00000E+100
258 traj.phases.phase0->path_constraint->h i 5.000000E-03 5.509587E-01 1.000000E+00 9.00000E+100
259 traj.phases.phase0->path_constraint->h i 5.000000E-03 6.036105E-01 1.000000E+00 9.00000E+100
260 traj.phases.phase0->path_constraint->h i 5.000000E-03 6.036105E-01 1.000000E+00 9.00000E+100
261 traj.phases.phase0->path_constraint->h i 5.000000E-03 6.660276E-01 1.000000E+00 9.00000E+100
262 traj.phases.phase0->path_constraint->h i 5.000000E-03 7.332006E-01 1.000000E+00 9.00000E+100
263 traj.phases.phase0->path_constraint->h i 5.000000E-03 7.332006E-01 1.000000E+00 9.00000E+100
264 traj.phases.phase0->path_constraint->h i 5.000000E-03 8.001116E-01 1.000000E+00 9.00000E+100
265 traj.phases.phase0->path_constraint->h i 5.000000E-03 8.625998E-01 1.000000E+00 9.00000E+100
266 traj.phases.phase0->path_constraint->h i 5.000000E-03 8.625998E-01 1.000000E+00 9.00000E+100
267 traj.phases.phase0->path_constraint->h i 5.000000E-03 9.171104E-01 1.000000E+00 9.00000E+100
268 traj.phases.phase0->path_constraint->h i 5.000000E-03 9.605112E-01 1.000000E+00 9.00000E+100
269 traj.phases.phase0->path_constraint->h i 5.000000E-03 9.605112E-01 1.000000E+00 9.00000E+100
270 traj.phases.phase0->path_constraint->h i 5.000000E-03 9.894526E-01 1.000000E+00 9.00000E+100
271 traj.phases.phase0->path_constraint->mach i 1.000000E-01 4.000084E-01 1.800000E+00 9.00000E+100
272 traj.phases.phase0->path_constraint->mach i 1.000000E-01 4.928085E-01 1.800000E+00 9.00000E+100
273 traj.phases.phase0->path_constraint->mach i 1.000000E-01 5.888644E-01 1.800000E+00 9.00000E+100
274 traj.phases.phase0->path_constraint->mach i 1.000000E-01 5.888644E-01 1.800000E+00 9.00000E+100
275 traj.phases.phase0->path_constraint->mach i 1.000000E-01 6.907438E-01 1.800000E+00 9.00000E+100
276 traj.phases.phase0->path_constraint->mach i 1.000000E-01 7.911859E-01 1.800000E+00 9.00000E+100
277 traj.phases.phase0->path_constraint->mach i 1.000000E-01 7.911859E-01 1.800000E+00 9.00000E+100
278 traj.phases.phase0->path_constraint->mach i 1.000000E-01 8.675398E-01 1.800000E+00 9.00000E+100
279 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.082411E-01 1.800000E+00 9.00000E+100
280 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.082411E-01 1.800000E+00 9.00000E+100
281 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.235899E-01 1.800000E+00 9.00000E+100
282 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.290669E-01 1.800000E+00 9.00000E+100
283 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.290669E-01 1.800000E+00 9.00000E+100
284 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.318663E-01 1.800000E+00 9.00000E+100
285 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.335845E-01 1.800000E+00 9.00000E+100
286 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.335845E-01 1.800000E+00 9.00000E+100
287 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.348393E-01 1.800000E+00 9.00000E+100
288 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.351641E-01 1.800000E+00 9.00000E+100
289 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.351641E-01 1.800000E+00 9.00000E+100
290 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.342098E-01 1.800000E+00 9.00000E+100
291 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.323608E-01 1.800000E+00 9.00000E+100
292 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.323608E-01 1.800000E+00 9.00000E+100
293 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.308148E-01 1.800000E+00 9.00000E+100
294 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.336711E-01 1.800000E+00 9.00000E+100
295 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.336711E-01 1.800000E+00 9.00000E+100
296 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.466033E-01 1.800000E+00 9.00000E+100
297 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.728930E-01 1.800000E+00 9.00000E+100
298 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.728930E-01 1.800000E+00 9.00000E+100
299 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.012091E+00 1.800000E+00 9.00000E+100
300 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.060811E+00 1.800000E+00 9.00000E+100
301 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.060811E+00 1.800000E+00 9.00000E+100
302 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.115238E+00 1.800000E+00 9.00000E+100
303 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.169668E+00 1.800000E+00 9.00000E+100
304 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.169668E+00 1.800000E+00 9.00000E+100
305 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.218964E+00 1.800000E+00 9.00000E+100
306 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.260680E+00 1.800000E+00 9.00000E+100
307 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.260680E+00 1.800000E+00 9.00000E+100
308 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.294087E+00 1.800000E+00 9.00000E+100
309 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.320514E+00 1.800000E+00 9.00000E+100
310 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.320514E+00 1.800000E+00 9.00000E+100
311 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.341661E+00 1.800000E+00 9.00000E+100
312 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.359372E+00 1.800000E+00 9.00000E+100
313 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.359372E+00 1.800000E+00 9.00000E+100
314 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.375217E+00 1.800000E+00 9.00000E+100
315 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.390246E+00 1.800000E+00 9.00000E+100
316 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.390246E+00 1.800000E+00 9.00000E+100
317 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.405205E+00 1.800000E+00 9.00000E+100
318 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.420407E+00 1.800000E+00 9.00000E+100
319 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.420407E+00 1.800000E+00 9.00000E+100
320 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.436010E+00 1.800000E+00 9.00000E+100
321 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.451982E+00 1.800000E+00 9.00000E+100
322 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.451982E+00 1.800000E+00 9.00000E+100
323 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.468263E+00 1.800000E+00 9.00000E+100
324 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.484795E+00 1.800000E+00 9.00000E+100
325 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.484795E+00 1.800000E+00 9.00000E+100
326 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.501562E+00 1.800000E+00 9.00000E+100
327 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.518646E+00 1.800000E+00 9.00000E+100
328 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.518646E+00 1.800000E+00 9.00000E+100
329 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.536188E+00 1.800000E+00 9.00000E+100
330 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.554417E+00 1.800000E+00 9.00000E+100
331 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.554417E+00 1.800000E+00 9.00000E+100
332 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.573585E+00 1.800000E+00 9.00000E+100
333 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.593891E+00 1.800000E+00 9.00000E+100
334 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.593891E+00 1.800000E+00 9.00000E+100
335 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.615444E+00 1.800000E+00 9.00000E+100
336 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.637975E+00 1.800000E+00 9.00000E+100
337 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.637975E+00 1.800000E+00 9.00000E+100
338 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.660938E+00 1.800000E+00 9.00000E+100
339 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.683016E+00 1.800000E+00 9.00000E+100
340 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.683016E+00 1.800000E+00 9.00000E+100
341 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.702444E+00 1.800000E+00 9.00000E+100
342 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.716557E+00 1.800000E+00 9.00000E+100
343 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.716557E+00 1.800000E+00 9.00000E+100
344 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.722342E+00 1.800000E+00 9.00000E+100
345 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.716754E+00 1.800000E+00 9.00000E+100
346 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.716754E+00 1.800000E+00 9.00000E+100
347 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.696704E+00 1.800000E+00 9.00000E+100
348 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.634735E+00 1.800000E+00 9.00000E+100
349 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.634735E+00 1.800000E+00 9.00000E+100
350 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.553470E+00 1.800000E+00 9.00000E+100
351 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.458866E+00 1.800000E+00 9.00000E+100
352 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.458866E+00 1.800000E+00 9.00000E+100
353 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.357871E+00 1.800000E+00 9.00000E+100
354 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.256853E+00 1.800000E+00 9.00000E+100
355 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.256853E+00 1.800000E+00 9.00000E+100
356 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.162029E+00 1.800000E+00 9.00000E+100
357 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.081335E+00 1.800000E+00 9.00000E+100
358 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.081335E+00 1.800000E+00 9.00000E+100
359 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.024102E+00 1.800000E+00 9.00000E+100
Exit Status
Inform Description
0 Solve Succeeded
--------------------------------------------------------------------------------
<Figure size 500x1000 with 1 Axes>
Jacobian shape: (361, 212) (23.30% nonzero)
FWD solves: 154 REV solves: 0
Total colors vs. total size: 154 vs 212 (27.36% improvement)
Sparsity computed using tolerance: 1e-12
Time to compute sparsity: 0.3209 sec
Time to compute coloring: 1.0174 sec
Memory to compute coloring: 16.6406 MB
Coloring created on: 2023-12-08 21:07:14
--- Constraint Report [traj] ---
--- phase0 ---
[final] 2.0000e+04 == h [m]
[final] 1.0000e+00 == aero.mach [None]
[final] 0.0000e+00 == gam [rad]
[path] 1.0000e+02 <= h <= 2.0000e+04 [m]
[path] 1.0000e-01 <= aero.mach <= 1.8000e+00 [None]
--------------------------------------------------------------------------------
--- Finite differenced component with partial coloring -------------------------
--------------------------------------------------------------------------------
Model viewer data has already been recorded for Driver.
Model viewer data has already been recorded for Driver.
/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/core/driver.py:469: DriverWarning:The following design variable initial conditions are out of their specified bounds:
traj.phase0.t_duration
val: [500.]
lower: 50.0
upper: 400.0
Set the initial value of the design variable to a valid value or set the driver option['invalid_desvar_behavior'] to 'ignore'.
Coloring for 'traj.phases.phase0.rhs_disc.aero.q_comp' (class DynamicPressureCompFD)
Jacobian shape: (60, 120) (1.67% nonzero)
FWD solves: 2 REV solves: 0
Total colors vs. total size: 2 vs 120 (98.33% improvement)
Sparsity computed using tolerance: 1e-06
Time to compute sparsity: 0.0078 sec
Time to compute coloring: 0.0094 sec
Memory to compute coloring: 0.0000 MB
Coloring for 'traj.phases.phase0.rhs_col.aero.q_comp' (class DynamicPressureCompFD)
Jacobian shape: (30, 60) (3.33% nonzero)
FWD solves: 2 REV solves: 0
Total colors vs. total size: 2 vs 60 (96.67% improvement)
Sparsity computed using tolerance: 1e-06
Time to compute sparsity: 0.0040 sec
Time to compute coloring: 0.0051 sec
Memory to compute coloring: 0.0000 MB
Full total jacobian was computed 3 times, taking 0.329502 seconds.
Total jacobian shape: (361, 212)
Jacobian shape: (361, 212) (3.44% nonzero)
FWD solves: 13 REV solves: 0
Total colors vs. total size: 13 vs 212 (93.87% improvement)
Sparsity computed using tolerance: 1e-12
Time to compute sparsity: 0.3295 sec
Time to compute coloring: 0.2213 sec
Memory to compute coloring: 0.0000 MB
Coloring created on: 2023-12-08 21:07:37
/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/core/total_jac.py:1759: DerivativesWarning:Constraints or objectives [('traj.phases.phase0.timeseries.timeseries_comp.h', inds=[(0, 0)]), ('traj.phases.phase0.timeseries.timeseries_comp.mach', inds=[(0, 0)])] cannot be impacted by the design variables of the problem.
Optimization Problem -- Optimization using pyOpt_sparse
================================================================================
Objective Function: _objfunc
Solution:
--------------------------------------------------------------------------------
Total Time: 5.0774
User Objective Time : 1.9598
User Sensitivity Time : 1.7779
Interface Time : 0.6857
Opt Solver Time: 0.6541
Calls to Objective Function : 128
Calls to Sens Function : 104
Objectives
Index Name Value
0 traj.phase0.t 3.235052E+00
Variables (c - continuous, i - integer, d - discrete)
Index Name Type Lower Bound Value Upper Bound Status
0 traj.phase0.t_duration_0 c 5.000000E-01 3.235052E+00 4.000000E+00
1 traj.phase0.states:r_0 c 0.000000E+00 1.808253E+00 1.000000E+03
2 traj.phase0.states:r_1 c 0.000000E+00 4.338690E+00 1.000000E+03
3 traj.phase0.states:r_2 c 0.000000E+00 7.365587E+00 1.000000E+03
4 traj.phase0.states:r_3 c 0.000000E+00 1.015778E+01 1.000000E+03
5 traj.phase0.states:r_4 c 0.000000E+00 1.292792E+01 1.000000E+03
6 traj.phase0.states:r_5 c 0.000000E+00 1.576490E+01 1.000000E+03
7 traj.phase0.states:r_6 c 0.000000E+00 1.862486E+01 1.000000E+03
8 traj.phase0.states:r_7 c 0.000000E+00 2.150884E+01 1.000000E+03
9 traj.phase0.states:r_8 c 0.000000E+00 2.455451E+01 1.000000E+03
10 traj.phase0.states:r_9 c 0.000000E+00 2.786213E+01 1.000000E+03
11 traj.phase0.states:r_10 c 0.000000E+00 3.146421E+01 1.000000E+03
12 traj.phase0.states:r_11 c 0.000000E+00 3.545724E+01 1.000000E+03
13 traj.phase0.states:r_12 c 0.000000E+00 3.978359E+01 1.000000E+03
14 traj.phase0.states:r_13 c 0.000000E+00 4.429165E+01 1.000000E+03
15 traj.phase0.states:r_14 c 0.000000E+00 4.889853E+01 1.000000E+03
16 traj.phase0.states:r_15 c 0.000000E+00 5.358666E+01 1.000000E+03
17 traj.phase0.states:r_16 c 0.000000E+00 5.835933E+01 1.000000E+03
18 traj.phase0.states:r_17 c 0.000000E+00 6.322096E+01 1.000000E+03
19 traj.phase0.states:r_18 c 0.000000E+00 6.817410E+01 1.000000E+03
20 traj.phase0.states:r_19 c 0.000000E+00 7.322345E+01 1.000000E+03
21 traj.phase0.states:r_20 c 0.000000E+00 7.838115E+01 1.000000E+03
22 traj.phase0.states:r_21 c 0.000000E+00 8.366670E+01 1.000000E+03
23 traj.phase0.states:r_22 c 0.000000E+00 8.909546E+01 1.000000E+03
24 traj.phase0.states:r_23 c 0.000000E+00 9.464483E+01 1.000000E+03
25 traj.phase0.states:r_24 c 0.000000E+00 1.001531E+02 1.000000E+03
26 traj.phase0.states:r_25 c 0.000000E+00 1.051991E+02 1.000000E+03
27 traj.phase0.states:r_26 c 0.000000E+00 1.093932E+02 1.000000E+03
28 traj.phase0.states:r_27 c 0.000000E+00 1.128526E+02 1.000000E+03
29 traj.phase0.states:r_28 c 0.000000E+00 1.159910E+02 1.000000E+03
30 traj.phase0.states:r_29 c 0.000000E+00 1.191426E+02 1.000000E+03
31 traj.phase0.states:h_0 c 0.000000E+00 1.061148E+00 2.000000E+02
32 traj.phase0.states:h_1 c 0.000000E+00 1.140002E+00 2.000000E+02
33 traj.phase0.states:h_2 c 0.000000E+00 8.819446E+00 2.000000E+02
34 traj.phase0.states:h_3 c 0.000000E+00 2.664496E+01 2.000000E+02
35 traj.phase0.states:h_4 c 0.000000E+00 4.417089E+01 2.000000E+02
36 traj.phase0.states:h_5 c 0.000000E+00 5.944139E+01 2.000000E+02
37 traj.phase0.states:h_6 c 0.000000E+00 7.289178E+01 2.000000E+02
38 traj.phase0.states:h_7 c 0.000000E+00 8.421214E+01 2.000000E+02
39 traj.phase0.states:h_8 c 0.000000E+00 9.050274E+01 2.000000E+02
40 traj.phase0.states:h_9 c 0.000000E+00 8.885772E+01 2.000000E+02
41 traj.phase0.states:h_10 c 0.000000E+00 8.148337E+01 2.000000E+02
42 traj.phase0.states:h_11 c 0.000000E+00 7.429505E+01 2.000000E+02
43 traj.phase0.states:h_12 c 0.000000E+00 7.108475E+01 2.000000E+02
44 traj.phase0.states:h_13 c 0.000000E+00 7.162005E+01 2.000000E+02
45 traj.phase0.states:h_14 c 0.000000E+00 7.403069E+01 2.000000E+02
46 traj.phase0.states:h_15 c 0.000000E+00 7.692316E+01 2.000000E+02
47 traj.phase0.states:h_16 c 0.000000E+00 7.977568E+01 2.000000E+02
48 traj.phase0.states:h_17 c 0.000000E+00 8.256333E+01 2.000000E+02
49 traj.phase0.states:h_18 c 0.000000E+00 8.534160E+01 2.000000E+02
50 traj.phase0.states:h_19 c 0.000000E+00 8.797806E+01 2.000000E+02
51 traj.phase0.states:h_20 c 0.000000E+00 9.008356E+01 2.000000E+02
52 traj.phase0.states:h_21 c 0.000000E+00 9.124568E+01 2.000000E+02
53 traj.phase0.states:h_22 c 0.000000E+00 9.175901E+01 2.000000E+02
54 traj.phase0.states:h_23 c 0.000000E+00 9.384372E+01 2.000000E+02
55 traj.phase0.states:h_24 c 0.000000E+00 1.021998E+02 2.000000E+02
56 traj.phase0.states:h_25 c 0.000000E+00 1.207240E+02 2.000000E+02
57 traj.phase0.states:h_26 c 0.000000E+00 1.466418E+02 2.000000E+02
58 traj.phase0.states:h_27 c 0.000000E+00 1.725207E+02 2.000000E+02
59 traj.phase0.states:h_28 c 0.000000E+00 1.921020E+02 2.000000E+02
60 traj.phase0.states:h_29 c 0.000000E+00 2.000000E+02 2.000000E+02 u
61 traj.phase0.states:v_0 c 1.000000E-01 2.001433E+00 1.000000E+19
62 traj.phase0.states:v_1 c 1.000000E-01 2.688819E+00 1.000000E+19
63 traj.phase0.states:v_2 c 1.000000E-01 3.059703E+00 1.000000E+19
64 traj.phase0.states:v_3 c 1.000000E-01 3.064991E+00 1.000000E+19
65 traj.phase0.states:v_4 c 1.000000E-01 3.014429E+00 1.000000E+19
66 traj.phase0.states:v_5 c 1.000000E-01 2.961215E+00 1.000000E+19
67 traj.phase0.states:v_6 c 1.000000E-01 2.900155E+00 1.000000E+19
68 traj.phase0.states:v_7 c 1.000000E-01 2.859541E+00 1.000000E+19
69 traj.phase0.states:v_8 c 1.000000E-01 2.953537E+00 1.000000E+19
70 traj.phase0.states:v_9 c 1.000000E-01 3.227977E+00 1.000000E+19
71 traj.phase0.states:v_10 c 1.000000E-01 3.596015E+00 1.000000E+19
72 traj.phase0.states:v_11 c 1.000000E-01 3.914054E+00 1.000000E+19
73 traj.phase0.states:v_12 c 1.000000E-01 4.117558E+00 1.000000E+19
74 traj.phase0.states:v_13 c 1.000000E-01 4.235639E+00 1.000000E+19
75 traj.phase0.states:v_14 c 1.000000E-01 4.317740E+00 1.000000E+19
76 traj.phase0.states:v_15 c 1.000000E-01 4.394082E+00 1.000000E+19
77 traj.phase0.states:v_16 c 1.000000E-01 4.474230E+00 1.000000E+19
78 traj.phase0.states:v_17 c 1.000000E-01 4.557776E+00 1.000000E+19
79 traj.phase0.states:v_18 c 1.000000E-01 4.643721E+00 1.000000E+19
80 traj.phase0.states:v_19 c 1.000000E-01 4.735577E+00 1.000000E+19
81 traj.phase0.states:v_20 c 1.000000E-01 4.841448E+00 1.000000E+19
82 traj.phase0.states:v_21 c 1.000000E-01 4.967188E+00 1.000000E+19
83 traj.phase0.states:v_22 c 1.000000E-01 5.100053E+00 1.000000E+19
84 traj.phase0.states:v_23 c 1.000000E-01 5.186228E+00 1.000000E+19
85 traj.phase0.states:v_24 c 1.000000E-01 5.124424E+00 1.000000E+19
86 traj.phase0.states:v_25 c 1.000000E-01 4.823460E+00 1.000000E+19
87 traj.phase0.states:v_26 c 1.000000E-01 4.304542E+00 1.000000E+19
88 traj.phase0.states:v_27 c 1.000000E-01 3.708498E+00 1.000000E+19
89 traj.phase0.states:v_28 c 1.000000E-01 3.190634E+00 1.000000E+19
90 traj.phase0.states:v_29 c 1.000000E-01 2.950864E+00 1.000000E+19
91 traj.phase0.states:gam_0 c -1.500000E+00 1.133397E-02 1.500000E+00
92 traj.phase0.states:gam_1 c -1.500000E+00 3.619449E-02 1.500000E+00
93 traj.phase0.states:gam_2 c -1.500000E+00 4.739946E-01 1.500000E+00
94 traj.phase0.states:gam_3 c -1.500000E+00 5.938262E-01 1.500000E+00
95 traj.phase0.states:gam_4 c -1.500000E+00 5.275194E-01 1.500000E+00
96 traj.phase0.states:gam_5 c -1.500000E+00 4.638511E-01 1.500000E+00
97 traj.phase0.states:gam_6 c -1.500000E+00 4.145307E-01 1.500000E+00
98 traj.phase0.states:gam_7 c -1.500000E+00 3.139588E-01 1.500000E+00
99 traj.phase0.states:gam_8 c -1.500000E+00 7.826395E-02 1.500000E+00
100 traj.phase0.states:gam_9 c -1.500000E+00 -1.558926E-01 1.500000E+00
101 traj.phase0.states:gam_10 c -1.500000E+00 -2.146177E-01 1.500000E+00
102 traj.phase0.states:gam_11 c -1.500000E+00 -1.294054E-01 1.500000E+00
103 traj.phase0.states:gam_12 c -1.500000E+00 -2.381777E-02 1.500000E+00
104 traj.phase0.states:gam_13 c -1.500000E+00 3.903665E-02 1.500000E+00
105 traj.phase0.states:gam_14 c -1.500000E+00 6.022618E-02 1.500000E+00
106 traj.phase0.states:gam_15 c -1.500000E+00 6.127488E-02 1.500000E+00
107 traj.phase0.states:gam_16 c -1.500000E+00 5.817559E-02 1.500000E+00
108 traj.phase0.states:gam_17 c -1.500000E+00 5.665727E-02 1.500000E+00
109 traj.phase0.states:gam_18 c -1.500000E+00 5.499396E-02 1.500000E+00
110 traj.phase0.states:gam_19 c -1.500000E+00 4.804656E-02 1.500000E+00
111 traj.phase0.states:gam_20 c -1.500000E+00 3.217589E-02 1.500000E+00
112 traj.phase0.states:gam_21 c -1.500000E+00 1.260508E-02 1.500000E+00
113 traj.phase0.states:gam_22 c -1.500000E+00 1.285007E-02 1.500000E+00
114 traj.phase0.states:gam_23 c -1.500000E+00 7.684480E-02 1.500000E+00
115 traj.phase0.states:gam_24 c -1.500000E+00 2.409912E-01 1.500000E+00
116 traj.phase0.states:gam_25 c -1.500000E+00 4.652774E-01 1.500000E+00
117 traj.phase0.states:gam_26 c -1.500000E+00 6.245111E-01 1.500000E+00
118 traj.phase0.states:gam_27 c -1.500000E+00 6.312943E-01 1.500000E+00
119 traj.phase0.states:gam_28 c -1.500000E+00 4.419195E-01 1.500000E+00
120 traj.phase0.states:gam_29 c -1.500000E+00 7.493683E-26 1.500000E+00
121 traj.phase0.states:m_0 c 1.000000E-02 1.894029E+01 1.000000E+02
122 traj.phase0.states:m_1 c 1.000000E-02 1.883985E+01 1.000000E+02
123 traj.phase0.states:m_2 c 1.000000E-02 1.873364E+01 1.000000E+02
124 traj.phase0.states:m_3 c 1.000000E-02 1.863493E+01 1.000000E+02
125 traj.phase0.states:m_4 c 1.000000E-02 1.854905E+01 1.000000E+02
126 traj.phase0.states:m_5 c 1.000000E-02 1.847498E+01 1.000000E+02
127 traj.phase0.states:m_6 c 1.000000E-02 1.841103E+01 1.000000E+02
128 traj.phase0.states:m_7 c 1.000000E-02 1.835554E+01 1.000000E+02
129 traj.phase0.states:m_8 c 1.000000E-02 1.830504E+01 1.000000E+02
130 traj.phase0.states:m_9 c 1.000000E-02 1.825309E+01 1.000000E+02
131 traj.phase0.states:m_10 c 1.000000E-02 1.819245E+01 1.000000E+02
132 traj.phase0.states:m_11 c 1.000000E-02 1.811959E+01 1.000000E+02
133 traj.phase0.states:m_12 c 1.000000E-02 1.803725E+01 1.000000E+02
134 traj.phase0.states:m_13 c 1.000000E-02 1.795054E+01 1.000000E+02
135 traj.phase0.states:m_14 c 1.000000E-02 1.786282E+01 1.000000E+02
136 traj.phase0.states:m_15 c 1.000000E-02 1.777536E+01 1.000000E+02
137 traj.phase0.states:m_16 c 1.000000E-02 1.768831E+01 1.000000E+02
138 traj.phase0.states:m_17 c 1.000000E-02 1.760157E+01 1.000000E+02
139 traj.phase0.states:m_18 c 1.000000E-02 1.751514E+01 1.000000E+02
140 traj.phase0.states:m_19 c 1.000000E-02 1.742898E+01 1.000000E+02
141 traj.phase0.states:m_20 c 1.000000E-02 1.734274E+01 1.000000E+02
142 traj.phase0.states:m_21 c 1.000000E-02 1.725564E+01 1.000000E+02
143 traj.phase0.states:m_22 c 1.000000E-02 1.716681E+01 1.000000E+02
144 traj.phase0.states:m_23 c 1.000000E-02 1.707683E+01 1.000000E+02
145 traj.phase0.states:m_24 c 1.000000E-02 1.699020E+01 1.000000E+02
146 traj.phase0.states:m_25 c 1.000000E-02 1.691723E+01 1.000000E+02
147 traj.phase0.states:m_26 c 1.000000E-02 1.686899E+01 1.000000E+02
148 traj.phase0.states:m_27 c 1.000000E-02 1.684162E+01 1.000000E+02
149 traj.phase0.states:m_28 c 1.000000E-02 1.682685E+01 1.000000E+02
150 traj.phase0.states:m_29 c 1.000000E-02 1.681817E+01 1.000000E+02
151 traj.phase0.controls:alpha_0 c -8.000000E+00 4.973967E+00 8.000000E+00
152 traj.phase0.controls:alpha_1 c -8.000000E+00 3.716974E+00 8.000000E+00
153 traj.phase0.controls:alpha_2 c -8.000000E+00 2.438122E+00 8.000000E+00
154 traj.phase0.controls:alpha_3 c -8.000000E+00 1.746779E+00 8.000000E+00
155 traj.phase0.controls:alpha_4 c -8.000000E+00 2.252311E+00 8.000000E+00
156 traj.phase0.controls:alpha_5 c -8.000000E+00 2.787036E+00 8.000000E+00
157 traj.phase0.controls:alpha_6 c -8.000000E+00 2.183271E+00 8.000000E+00
158 traj.phase0.controls:alpha_7 c -8.000000E+00 1.279755E+00 8.000000E+00
159 traj.phase0.controls:alpha_8 c -8.000000E+00 9.152228E-01 8.000000E+00
160 traj.phase0.controls:alpha_9 c -8.000000E+00 8.886373E-01 8.000000E+00
161 traj.phase0.controls:alpha_10 c -8.000000E+00 9.989608E-01 8.000000E+00
162 traj.phase0.controls:alpha_11 c -8.000000E+00 1.188516E+00 8.000000E+00
163 traj.phase0.controls:alpha_12 c -8.000000E+00 1.399627E+00 8.000000E+00
164 traj.phase0.controls:alpha_13 c -8.000000E+00 1.593789E+00 8.000000E+00
165 traj.phase0.controls:alpha_14 c -8.000000E+00 1.732498E+00 8.000000E+00
166 traj.phase0.controls:alpha_15 c -8.000000E+00 1.676885E+00 8.000000E+00
167 traj.phase0.controls:alpha_16 c -8.000000E+00 1.288082E+00 8.000000E+00
168 traj.phase0.controls:alpha_17 c -8.000000E+00 8.325160E-01 8.000000E+00
169 traj.phase0.controls:alpha_18 c -8.000000E+00 5.766166E-01 8.000000E+00
170 traj.phase0.controls:alpha_19 c -8.000000E+00 6.228389E-01 8.000000E+00
171 traj.phase0.controls:alpha_20 c -8.000000E+00 1.073638E+00 8.000000E+00
172 traj.phase0.controls:alpha_21 c -8.000000E+00 1.616594E+00 8.000000E+00
173 traj.phase0.controls:alpha_22 c -8.000000E+00 1.939285E+00 8.000000E+00
174 traj.phase0.controls:alpha_23 c -8.000000E+00 2.067129E+00 8.000000E+00
175 traj.phase0.controls:alpha_24 c -8.000000E+00 2.025542E+00 8.000000E+00
176 traj.phase0.controls:alpha_25 c -8.000000E+00 1.885919E+00 8.000000E+00
177 traj.phase0.controls:alpha_26 c -8.000000E+00 1.719655E+00 8.000000E+00
178 traj.phase0.controls:alpha_27 c -8.000000E+00 1.556346E+00 8.000000E+00
179 traj.phase0.controls:alpha_28 c -8.000000E+00 1.425590E+00 8.000000E+00
180 traj.phase0.controls:alpha_29 c -8.000000E+00 1.329252E+00 8.000000E+00
181 traj.phase0.controls:alpha_30 c -8.000000E+00 1.269199E+00 8.000000E+00
182 traj.phase0.controls:alpha_31 c -8.000000E+00 1.237594E+00 8.000000E+00
183 traj.phase0.controls:alpha_32 c -8.000000E+00 1.226600E+00 8.000000E+00
184 traj.phase0.controls:alpha_33 c -8.000000E+00 1.229069E+00 8.000000E+00
185 traj.phase0.controls:alpha_34 c -8.000000E+00 1.237851E+00 8.000000E+00
186 traj.phase0.controls:alpha_35 c -8.000000E+00 1.248341E+00 8.000000E+00
187 traj.phase0.controls:alpha_36 c -8.000000E+00 1.255933E+00 8.000000E+00
188 traj.phase0.controls:alpha_37 c -8.000000E+00 1.258045E+00 8.000000E+00
189 traj.phase0.controls:alpha_38 c -8.000000E+00 1.252093E+00 8.000000E+00
190 traj.phase0.controls:alpha_39 c -8.000000E+00 1.237738E+00 8.000000E+00
191 traj.phase0.controls:alpha_40 c -8.000000E+00 1.214639E+00 8.000000E+00
192 traj.phase0.controls:alpha_41 c -8.000000E+00 1.187338E+00 8.000000E+00
193 traj.phase0.controls:alpha_42 c -8.000000E+00 1.160377E+00 8.000000E+00
194 traj.phase0.controls:alpha_43 c -8.000000E+00 1.147674E+00 8.000000E+00
195 traj.phase0.controls:alpha_44 c -8.000000E+00 1.163147E+00 8.000000E+00
196 traj.phase0.controls:alpha_45 c -8.000000E+00 1.227674E+00 8.000000E+00
197 traj.phase0.controls:alpha_46 c -8.000000E+00 1.362135E+00 8.000000E+00
198 traj.phase0.controls:alpha_47 c -8.000000E+00 1.582065E+00 8.000000E+00
199 traj.phase0.controls:alpha_48 c -8.000000E+00 1.902998E+00 8.000000E+00
200 traj.phase0.controls:alpha_49 c -8.000000E+00 2.303834E+00 8.000000E+00
201 traj.phase0.controls:alpha_50 c -8.000000E+00 2.763473E+00 8.000000E+00
202 traj.phase0.controls:alpha_51 c -8.000000E+00 3.222355E+00 8.000000E+00
203 traj.phase0.controls:alpha_52 c -8.000000E+00 3.620922E+00 8.000000E+00
204 traj.phase0.controls:alpha_53 c -8.000000E+00 3.885781E+00 8.000000E+00
205 traj.phase0.controls:alpha_54 c -8.000000E+00 3.943539E+00 8.000000E+00
206 traj.phase0.controls:alpha_55 c -8.000000E+00 3.728606E+00 8.000000E+00
207 traj.phase0.controls:alpha_56 c -8.000000E+00 3.175394E+00 8.000000E+00
208 traj.phase0.controls:alpha_57 c -8.000000E+00 1.953686E+00 8.000000E+00
209 traj.phase0.controls:alpha_58 c -8.000000E+00 -2.667336E-01 8.000000E+00
210 traj.phase0.controls:alpha_59 c -8.000000E+00 -3.185446E+00 8.000000E+00
211 traj.phase0.controls:alpha_60 c -8.000000E+00 -6.502031E+00 8.000000E+00
Constraints (i - inequality, e - equality)
Index Name Type Lower Value Upper Status Lagrange Multiplier (N/A)
0 traj.phases.phase0->final_boundary_constraint->h e 2.000000E+01 2.000000E+01 2.000000E+01 9.00000E+100
1 traj.phases.phase0->final_boundary_constraint->mach e 1.000000E+00 1.000000E+00 1.000000E+00 9.00000E+100
2 traj.phases.phase0->final_boundary_constraint->gam e 0.000000E+00 7.493683E-26 0.000000E+00 9.00000E+100
3 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 9.210446E-11 0.000000E+00 9.00000E+100
4 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 2.549804E-09 0.000000E+00 9.00000E+100
5 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 2.547007E-09 0.000000E+00 9.00000E+100
6 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 3.905088E-09 0.000000E+00 9.00000E+100
7 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 -1.149661E-10 0.000000E+00 9.00000E+100
8 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 6.395623E-10 0.000000E+00 9.00000E+100
9 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 2.424522E-10 0.000000E+00 9.00000E+100
10 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 6.077274E-11 0.000000E+00 9.00000E+100
11 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 3.176111E-11 0.000000E+00 9.00000E+100
12 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 2.844324E-09 0.000000E+00 9.00000E+100
13 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 4.020264E-09 0.000000E+00 9.00000E+100
14 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 4.334368E-09 0.000000E+00 9.00000E+100
15 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 1.142818E-09 0.000000E+00 9.00000E+100
16 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 6.139820E-09 0.000000E+00 9.00000E+100
17 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 8.011687E-09 0.000000E+00 9.00000E+100
18 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 7.621069E-09 0.000000E+00 9.00000E+100
19 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 6.799731E-09 0.000000E+00 9.00000E+100
20 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 7.011951E-09 0.000000E+00 9.00000E+100
21 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 8.832823E-09 0.000000E+00 9.00000E+100
22 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 5.246138E-09 0.000000E+00 9.00000E+100
23 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 3.784948E-09 0.000000E+00 9.00000E+100
24 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 4.245526E-09 0.000000E+00 9.00000E+100
25 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 4.901554E-09 0.000000E+00 9.00000E+100
26 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 6.185141E-09 0.000000E+00 9.00000E+100
27 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 8.387891E-09 0.000000E+00 9.00000E+100
28 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 9.427325E-09 0.000000E+00 9.00000E+100
29 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 5.004700E-09 0.000000E+00 9.00000E+100
30 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 2.411733E-09 0.000000E+00 9.00000E+100
31 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 1.232590E-10 0.000000E+00 9.00000E+100
32 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 -7.993729E-11 0.000000E+00 9.00000E+100
33 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 4.558666E-10 0.000000E+00 9.00000E+100
34 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 6.810199E-09 0.000000E+00 9.00000E+100
35 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 4.247861E-08 0.000000E+00 9.00000E+100
36 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -1.354293E-08 0.000000E+00 9.00000E+100
37 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 3.869602E-09 0.000000E+00 9.00000E+100
38 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 2.581068E-09 0.000000E+00 9.00000E+100
39 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 8.510624E-10 0.000000E+00 9.00000E+100
40 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 7.591052E-10 0.000000E+00 9.00000E+100
41 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -1.408919E-09 0.000000E+00 9.00000E+100
42 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 1.018717E-08 0.000000E+00 9.00000E+100
43 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -8.188860E-09 0.000000E+00 9.00000E+100
44 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -6.768067E-09 0.000000E+00 9.00000E+100
45 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 1.537335E-09 0.000000E+00 9.00000E+100
46 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 1.283325E-08 0.000000E+00 9.00000E+100
47 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 5.407716E-09 0.000000E+00 9.00000E+100
48 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 9.116695E-09 0.000000E+00 9.00000E+100
49 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 1.145578E-08 0.000000E+00 9.00000E+100
50 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 1.949017E-08 0.000000E+00 9.00000E+100
51 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 1.569674E-08 0.000000E+00 9.00000E+100
52 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -8.329104E-09 0.000000E+00 9.00000E+100
53 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 3.705141E-09 0.000000E+00 9.00000E+100
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228 traj.phases.phase0->path_constraint->h i 5.000000E-03 3.773227E-01 1.000000E+00 9.00000E+100
229 traj.phases.phase0->path_constraint->h i 5.000000E-03 3.846158E-01 1.000000E+00 9.00000E+100
230 traj.phases.phase0->path_constraint->h i 5.000000E-03 3.846158E-01 1.000000E+00 9.00000E+100
231 traj.phases.phase0->path_constraint->h i 5.000000E-03 3.918073E-01 1.000000E+00 9.00000E+100
232 traj.phases.phase0->path_constraint->h i 5.000000E-03 3.988784E-01 1.000000E+00 9.00000E+100
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236 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.128167E-01 1.000000E+00 9.00000E+100
237 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.197815E-01 1.000000E+00 9.00000E+100
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240 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.334866E-01 1.000000E+00 9.00000E+100
241 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.398903E-01 1.000000E+00 9.00000E+100
242 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.398903E-01 1.000000E+00 9.00000E+100
243 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.456372E-01 1.000000E+00 9.00000E+100
244 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.504178E-01 1.000000E+00 9.00000E+100
245 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.504178E-01 1.000000E+00 9.00000E+100
246 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.539508E-01 1.000000E+00 9.00000E+100
247 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.562284E-01 1.000000E+00 9.00000E+100
248 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.562284E-01 1.000000E+00 9.00000E+100
249 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.574920E-01 1.000000E+00 9.00000E+100
250 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.587951E-01 1.000000E+00 9.00000E+100
251 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.587951E-01 1.000000E+00 9.00000E+100
252 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.617652E-01 1.000000E+00 9.00000E+100
253 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.692186E-01 1.000000E+00 9.00000E+100
254 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.692186E-01 1.000000E+00 9.00000E+100
255 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.845494E-01 1.000000E+00 9.00000E+100
256 traj.phases.phase0->path_constraint->h i 5.000000E-03 5.109990E-01 1.000000E+00 9.00000E+100
257 traj.phases.phase0->path_constraint->h i 5.000000E-03 5.109990E-01 1.000000E+00 9.00000E+100
258 traj.phases.phase0->path_constraint->h i 5.000000E-03 5.509665E-01 1.000000E+00 9.00000E+100
259 traj.phases.phase0->path_constraint->h i 5.000000E-03 6.036199E-01 1.000000E+00 9.00000E+100
260 traj.phases.phase0->path_constraint->h i 5.000000E-03 6.036199E-01 1.000000E+00 9.00000E+100
261 traj.phases.phase0->path_constraint->h i 5.000000E-03 6.660371E-01 1.000000E+00 9.00000E+100
262 traj.phases.phase0->path_constraint->h i 5.000000E-03 7.332088E-01 1.000000E+00 9.00000E+100
263 traj.phases.phase0->path_constraint->h i 5.000000E-03 7.332088E-01 1.000000E+00 9.00000E+100
264 traj.phases.phase0->path_constraint->h i 5.000000E-03 8.001177E-01 1.000000E+00 9.00000E+100
265 traj.phases.phase0->path_constraint->h i 5.000000E-03 8.626033E-01 1.000000E+00 9.00000E+100
266 traj.phases.phase0->path_constraint->h i 5.000000E-03 8.626033E-01 1.000000E+00 9.00000E+100
267 traj.phases.phase0->path_constraint->h i 5.000000E-03 9.171112E-01 1.000000E+00 9.00000E+100
268 traj.phases.phase0->path_constraint->h i 5.000000E-03 9.605099E-01 1.000000E+00 9.00000E+100
269 traj.phases.phase0->path_constraint->h i 5.000000E-03 9.605099E-01 1.000000E+00 9.00000E+100
270 traj.phases.phase0->path_constraint->h i 5.000000E-03 9.894516E-01 1.000000E+00 9.00000E+100
271 traj.phases.phase0->path_constraint->mach i 1.000000E-01 4.000084E-01 1.800000E+00 9.00000E+100
272 traj.phases.phase0->path_constraint->mach i 1.000000E-01 4.928086E-01 1.800000E+00 9.00000E+100
273 traj.phases.phase0->path_constraint->mach i 1.000000E-01 5.888656E-01 1.800000E+00 9.00000E+100
274 traj.phases.phase0->path_constraint->mach i 1.000000E-01 5.888656E-01 1.800000E+00 9.00000E+100
275 traj.phases.phase0->path_constraint->mach i 1.000000E-01 6.907437E-01 1.800000E+00 9.00000E+100
276 traj.phases.phase0->path_constraint->mach i 1.000000E-01 7.911803E-01 1.800000E+00 9.00000E+100
277 traj.phases.phase0->path_constraint->mach i 1.000000E-01 7.911803E-01 1.800000E+00 9.00000E+100
278 traj.phases.phase0->path_constraint->mach i 1.000000E-01 8.675306E-01 1.800000E+00 9.00000E+100
279 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.082336E-01 1.800000E+00 9.00000E+100
280 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.082336E-01 1.800000E+00 9.00000E+100
281 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.235844E-01 1.800000E+00 9.00000E+100
282 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.290609E-01 1.800000E+00 9.00000E+100
283 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.290609E-01 1.800000E+00 9.00000E+100
284 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.318600E-01 1.800000E+00 9.00000E+100
285 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.335799E-01 1.800000E+00 9.00000E+100
286 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.335799E-01 1.800000E+00 9.00000E+100
287 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.348370E-01 1.800000E+00 9.00000E+100
288 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.351630E-01 1.800000E+00 9.00000E+100
289 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.351630E-01 1.800000E+00 9.00000E+100
290 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.342089E-01 1.800000E+00 9.00000E+100
291 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.323605E-01 1.800000E+00 9.00000E+100
292 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.323605E-01 1.800000E+00 9.00000E+100
293 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.308175E-01 1.800000E+00 9.00000E+100
294 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.336812E-01 1.800000E+00 9.00000E+100
295 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.336812E-01 1.800000E+00 9.00000E+100
296 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.466270E-01 1.800000E+00 9.00000E+100
297 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.729325E-01 1.800000E+00 9.00000E+100
298 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.729325E-01 1.800000E+00 9.00000E+100
299 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.012142E+00 1.800000E+00 9.00000E+100
300 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.060866E+00 1.800000E+00 9.00000E+100
301 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.060866E+00 1.800000E+00 9.00000E+100
302 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.115292E+00 1.800000E+00 9.00000E+100
303 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.169715E+00 1.800000E+00 9.00000E+100
304 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.169715E+00 1.800000E+00 9.00000E+100
305 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.219000E+00 1.800000E+00 9.00000E+100
306 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.260706E+00 1.800000E+00 9.00000E+100
307 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.260706E+00 1.800000E+00 9.00000E+100
308 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.294103E+00 1.800000E+00 9.00000E+100
309 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.320522E+00 1.800000E+00 9.00000E+100
310 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.320522E+00 1.800000E+00 9.00000E+100
311 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.341663E+00 1.800000E+00 9.00000E+100
312 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.359369E+00 1.800000E+00 9.00000E+100
313 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.359369E+00 1.800000E+00 9.00000E+100
314 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.375209E+00 1.800000E+00 9.00000E+100
315 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.390234E+00 1.800000E+00 9.00000E+100
316 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.390234E+00 1.800000E+00 9.00000E+100
317 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.405189E+00 1.800000E+00 9.00000E+100
318 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.420388E+00 1.800000E+00 9.00000E+100
319 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.420388E+00 1.800000E+00 9.00000E+100
320 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.435987E+00 1.800000E+00 9.00000E+100
321 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.451959E+00 1.800000E+00 9.00000E+100
322 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.451959E+00 1.800000E+00 9.00000E+100
323 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.468240E+00 1.800000E+00 9.00000E+100
324 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.484775E+00 1.800000E+00 9.00000E+100
325 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.484775E+00 1.800000E+00 9.00000E+100
326 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.501545E+00 1.800000E+00 9.00000E+100
327 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.518632E+00 1.800000E+00 9.00000E+100
328 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.518632E+00 1.800000E+00 9.00000E+100
329 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.536176E+00 1.800000E+00 9.00000E+100
330 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.554407E+00 1.800000E+00 9.00000E+100
331 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.554407E+00 1.800000E+00 9.00000E+100
332 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.573578E+00 1.800000E+00 9.00000E+100
333 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.593888E+00 1.800000E+00 9.00000E+100
334 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.593888E+00 1.800000E+00 9.00000E+100
335 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.615445E+00 1.800000E+00 9.00000E+100
336 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.637980E+00 1.800000E+00 9.00000E+100
337 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.637980E+00 1.800000E+00 9.00000E+100
338 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.660944E+00 1.800000E+00 9.00000E+100
339 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.683021E+00 1.800000E+00 9.00000E+100
340 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.683021E+00 1.800000E+00 9.00000E+100
341 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.702446E+00 1.800000E+00 9.00000E+100
342 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.716556E+00 1.800000E+00 9.00000E+100
343 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.716556E+00 1.800000E+00 9.00000E+100
344 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.722337E+00 1.800000E+00 9.00000E+100
345 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.716748E+00 1.800000E+00 9.00000E+100
346 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.716748E+00 1.800000E+00 9.00000E+100
347 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.696693E+00 1.800000E+00 9.00000E+100
348 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.634720E+00 1.800000E+00 9.00000E+100
349 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.634720E+00 1.800000E+00 9.00000E+100
350 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.553456E+00 1.800000E+00 9.00000E+100
351 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.458854E+00 1.800000E+00 9.00000E+100
352 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.458854E+00 1.800000E+00 9.00000E+100
353 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.357862E+00 1.800000E+00 9.00000E+100
354 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.256848E+00 1.800000E+00 9.00000E+100
355 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.256848E+00 1.800000E+00 9.00000E+100
356 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.162029E+00 1.800000E+00 9.00000E+100
357 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.081339E+00 1.800000E+00 9.00000E+100
358 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.081339E+00 1.800000E+00 9.00000E+100
359 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.024108E+00 1.800000E+00 9.00000E+100
Exit Status
Inform Description
0 Solve Succeeded
--------------------------------------------------------------------------------
<Figure size 500x1000 with 1 Axes>
Jacobian shape: (361, 212) (3.44% nonzero)
FWD solves: 13 REV solves: 0
Total colors vs. total size: 13 vs 212 (93.87% improvement)
Sparsity computed using tolerance: 1e-12
Time to compute sparsity: 0.3295 sec
Time to compute coloring: 0.2213 sec
Memory to compute coloring: 0.0000 MB
Coloring created on: 2023-12-08 21:07:37
Performance comparison#
In this instance, the following performance was noted for the minimum time-to-climb case with 30 Gauss-Lobatto segments.
Using OpenMDAO’s partial derivative coloring buys back a signficant amount of performance lost to finite differencing.
It should be noted that the IPOPT option alpha_for_y can have a signficant impact on performance here.
The default ‘primal’ step results in faster convergence for the sparse analytic case, but results in problematic convergence for the finite-differenced versions.
Switching the option using p.driver.opt_settings['alpha_for_y'] = 'safer-min-dual-infeas' results in a ‘safer’ step size and faster convergence of the finite-differenced versions, at the expense of some time in the analytic case.
The table below shows approximate run times normalized by the analytic version of the problem’s run time.
Derivative Type |
Normalized Optimization Time |
|---|---|
Sparse Analytic |
1.0 |
Finite Difference (Dense) |
~1.5 to ~2.5 |
Finite Difference (with Coloring) |
~1.0 to ~1.5 |
Another note is that even in the finite differencing cases only a single component, the dynamic pressure component, is being switch to use finite differencing. Doing so completely destroys the sparsity of the system, requiring over 10x as many solves of the resulting linear system to compute the total derivatives across the model. This is an important lesson: Failing to employ sparsity everywhere in a complex model can completely negate its benefit. However, you can buy back a significant portion of this lost performance using partial coloring.