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16 changes: 8 additions & 8 deletions contributing/contributing.html
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Expand Up @@ -1055,21 +1055,21 @@ <h2>Notebook Creation<a class="headerlink" href="#notebook-creation" title="Perm
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| of &#39;&lt;variable&gt;&#39; | wrt &#39;&lt;variable&gt;&#39; | calc mag. | check mag. | a(cal-chk) | r(cal-chk) | error desc |
+=================+==================+=============+=============+=============+=============+============+
| &#39;check&#39; | &#39;theta&#39; | 2.5200e+04 | 2.5200e+04 | 2.8422e-14 | 1.1278e-18 | |
| &#39;check&#39; | &#39;theta&#39; | 2.1679e+02 | 2.1679e+02 | 8.8818e-16 | 4.0969e-18 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;check&#39; | &#39;v&#39; | 5.7293e+01 | 5.7293e+01 | 8.8818e-16 | 1.5502e-17 | |
| &#39;check&#39; | &#39;v&#39; | 7.3605e+00 | 7.3605e+00 | 2.2204e-16 | 3.0167e-17 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;vdot&#39; | &#39;theta&#39; | 9.3953e+00 | 9.3953e+00 | 1.2561e-15 | 1.3369e-16 | |
| &#39;vdot&#39; | &#39;theta&#39; | 1.4122e+01 | 1.4122e+01 | 1.9984e-15 | 1.4151e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;vdot&#39; | &#39;v&#39; | 0.0000e+00 | 0.0000e+00 | 0.0000e+00 | nan | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;xdot&#39; | &#39;theta&#39; | 1.3999e+01 | 1.3999e+01 | 2.4825e-16 | 1.7734e-17 | |
| &#39;xdot&#39; | &#39;theta&#39; | 1.1523e+01 | 1.1523e+01 | 2.1763e-15 | 1.8887e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;xdot&#39; | &#39;v&#39; | 9.5805e-01 | 9.5805e-01 | 0.0000e+00 | 0.0000e+00 | |
| &#39;xdot&#39; | &#39;v&#39; | 1.4401e+00 | 1.4401e+00 | 0.0000e+00 | 0.0000e+00 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;ydot&#39; | &#39;theta&#39; | 4.2202e+00 | 4.2202e+00 | 2.4825e-16 | 5.8825e-17 | |
| &#39;ydot&#39; | &#39;theta&#39; | 8.9304e+00 | 8.9304e+00 | 1.3323e-15 | 1.4918e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;ydot&#39; | &#39;v&#39; | 2.0204e+00 | 2.0204e+00 | 0.0000e+00 | 0.0000e+00 | |
| &#39;ydot&#39; | &#39;v&#39; | 1.7106e+00 | 1.7106e+00 | 1.1189e-16 | 6.5407e-17 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+

##################################################################
Expand All @@ -1078,7 +1078,7 @@ <h2>Notebook Creation<a class="headerlink" href="#notebook-creation" title="Perm
+-----------------+------------------+-------------+-------------+-------------+-------------+
| of &#39;&lt;variable&gt;&#39; | wrt &#39;&lt;variable&gt;&#39; | calc mag. | check mag. | a(cal-chk) | r(cal-chk) |
+=================+==================+=============+=============+=============+=============+
| &#39;vdot&#39; | &#39;theta&#39; | 9.3953e+00 | 9.3953e+00 | 1.2561e-15 | 1.3369e-16 |
| &#39;xdot&#39; | &#39;theta&#39; | 1.1523e+01 | 1.1523e+01 | 2.1763e-15 | 1.8887e-16 |
+-----------------+------------------+-------------+-------------+-------------+-------------+
</pre></div>
</div>
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67 changes: 33 additions & 34 deletions examples/balanced_field/balanced_field.html
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Expand Up @@ -941,13 +941,13 @@ <h2>The ODE System<a class="headerlink" href="#the-ode-system" title="Permalink
<h3>The Aerodynamic Model<a class="headerlink" href="#the-aerodynamic-model" title="Permalink to this heading">#</a></h3>
<p>Both sets of equations of motion have common aerodynamic models.</p>
<p>First, the lift coefficient is computed using a model which assumes linearity in lift wrt the angle of attack.</p>
<div class="amsmath math notranslate nohighlight" id="equation-b4e3869a-eb6f-4630-94b3-dde5a4590219">
<span class="eqno">(21)<a class="headerlink" href="#equation-b4e3869a-eb6f-4630-94b3-dde5a4590219" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-3f7fc140-e9b2-47c2-a73b-0c246550eb45">
<span class="eqno">(21)<a class="headerlink" href="#equation-3f7fc140-e9b2-47c2-a73b-0c246550eb45" title="Permalink to this equation">#</a></span>\[\begin{align}
C_L &amp;= C_{L0} + \frac{\alpha}{\alpha_{max}} \left(C_{L-max} - C_{L0}\right)
\end{align}\]</div>
<p>Next, the drag-due-to-lift factor is computed (Equations 12.48 and 12.61 in Raymer[&#64;raymer2012aircraft]).</p>
<div class="amsmath math notranslate nohighlight" id="equation-4f4ff000-668d-4948-a9b8-41b38c6fd6f4">
<span class="eqno">(22)<a class="headerlink" href="#equation-4f4ff000-668d-4948-a9b8-41b38c6fd6f4" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-b5286436-6829-4d8a-9e37-7c3e58fba157">
<span class="eqno">(22)<a class="headerlink" href="#equation-b5286436-6829-4d8a-9e37-7c3e58fba157" title="Permalink to this equation">#</a></span>\[\begin{align}
K_{nom} &amp;= \frac{1}{ \pi AR e} \\
b &amp;= \frac{span}{2} \\
K &amp;= 33 K_{nom} \frac{ \left(\frac{h + h_w}{b} \right) ^{\frac{3}{2}}}{1.0 + 33 \left( \frac{h + h_w}{b}\right) ^{\frac{3}{2}}}
Expand All @@ -956,8 +956,8 @@ <h3>The Aerodynamic Model<a class="headerlink" href="#the-aerodynamic-model" tit
This causes this problem to be difficult to solve using a shooting method.
If the optimizer proposes a combination of initial states and a control history that results in altitude dropping significantly below zero, the propagation will fail.</p>
<p>Finally, the lift and drag are computed after computing the dynamic pressure.</p>
<div class="amsmath math notranslate nohighlight" id="equation-43ce03a6-5cfb-47b3-a677-06c6f7de270f">
<span class="eqno">(23)<a class="headerlink" href="#equation-43ce03a6-5cfb-47b3-a677-06c6f7de270f" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-8434baeb-e506-472b-9cab-d620c3ed9d2e">
<span class="eqno">(23)<a class="headerlink" href="#equation-8434baeb-e506-472b-9cab-d620c3ed9d2e" title="Permalink to this equation">#</a></span>\[\begin{align}
q &amp;= 0.5 \rho v^2 \\
L &amp;= q S C_L \\
D &amp;= q S \left( C_{D0} + K C_{L}^2 \right)
Expand All @@ -968,17 +968,17 @@ <h3>Stall Speed<a class="headerlink" href="#stall-speed" title="Permalink to thi
<p>This model relies on the ratio of the current true airspeed to stall speed (<span class="math notranslate nohighlight">\(\frac{v}{v_{stall}}\)</span>).
This constraint is used to trigger the beginning of rotation and is used as a boundary constraint at the end of the initial climb.
Stall speed is given by Equation 5.6 in Raymer[&#64;raymer2012aircraft].</p>
<div class="amsmath math notranslate nohighlight" id="equation-85ab2e17-06c1-4987-a787-f8db06d88afd">
<span class="eqno">(24)<a class="headerlink" href="#equation-85ab2e17-06c1-4987-a787-f8db06d88afd" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-50328208-c75f-43c1-8d87-f24941d17c12">
<span class="eqno">(24)<a class="headerlink" href="#equation-50328208-c75f-43c1-8d87-f24941d17c12" title="Permalink to this equation">#</a></span>\[\begin{align}
W &amp;= m g \\
v_{stall} &amp;= \sqrt{\frac{2 * W}{\rho S C_{L-max}}}
\end{align}\]</div>
</section>
<section id="runway-equations-of-motion">
<h3>Runway Equations of Motion<a class="headerlink" href="#runway-equations-of-motion" title="Permalink to this heading">#</a></h3>
<p>The runway equations of motion are used to integrate range and speed as the vehicle rolls along the runway.</p>
<div class="amsmath math notranslate nohighlight" id="equation-f3c1b34a-f433-41f8-a415-fb8faa215c32">
<span class="eqno">(25)<a class="headerlink" href="#equation-f3c1b34a-f433-41f8-a415-fb8faa215c32" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-0e7f5337-b8bf-44e0-9d89-a42d969f3879">
<span class="eqno">(25)<a class="headerlink" href="#equation-0e7f5337-b8bf-44e0-9d89-a42d969f3879" title="Permalink to this equation">#</a></span>\[\begin{align}
F_r &amp;= mg - L \cos \alpha - T \sin \alpha \\
\dot{v} &amp;= \frac{T \cos \alpha - D - F_r \mu_r}{m} \\
\dot{r} &amp;= v
Expand All @@ -1005,8 +1005,8 @@ <h3>Runway Equations of Motion<a class="headerlink" href="#runway-equations-of-m
<section id="flight-equations-of-motion">
<h3>Flight Equations of Motion<a class="headerlink" href="#flight-equations-of-motion" title="Permalink to this heading">#</a></h3>
<p>The flight equations of motion include two additional state variables: the flight-path angle (<span class="math notranslate nohighlight">\(\gamma\)</span>) and altitude (<span class="math notranslate nohighlight">\(h\)</span>).</p>
<div class="amsmath math notranslate nohighlight" id="equation-f84f0155-1863-4071-a4f6-dbb6da3e59ab">
<span class="eqno">(26)<a class="headerlink" href="#equation-f84f0155-1863-4071-a4f6-dbb6da3e59ab" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-0d685d4f-945c-4f47-810b-e93918cd2935">
<span class="eqno">(26)<a class="headerlink" href="#equation-0d685d4f-945c-4f47-810b-e93918cd2935" title="Permalink to this equation">#</a></span>\[\begin{align}
\dot{v} &amp;= \frac{T}{m} \cos \alpha - \frac{D}{m} - g \sin \gamma \\
\dot{\gamma} &amp;= \frac{T}{m v} \sin \alpha + \frac{L}{m v} - \frac{g \cos \gamma}{v} \\
\dot{h} &amp;= v \sin \gamma \\
Expand Down Expand Up @@ -1531,7 +1531,7 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;dymos.phase.phase.Phase at 0x7f0e800f6b50&gt;
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;dymos.phase.phase.Phase at 0x7f9769437390&gt;
</pre></div>
</div>
</div>
Expand Down Expand Up @@ -1727,8 +1727,8 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.33% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.0157 sec
Time to compute coloring: 0.0099 sec
Time to compute sparsity: 0.0158 sec
Time to compute coloring: 0.0100 sec
Memory to compute coloring: 0.1250 MB

Coloring for &#39;traj.phases.rto.rhs_all&#39; (class BalancedFieldODEComp)
Expand All @@ -1738,20 +1738,19 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.33% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.0154 sec
Time to compute coloring: 0.0096 sec
Time to compute sparsity: 0.0155 sec
Time to compute coloring: 0.0097 sec
Memory to compute coloring: 0.0000 MB
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Coloring for &#39;traj.phases.v1_to_vr.rhs_all&#39; (class BalancedFieldODEComp)

Coloring for &#39;traj.phases.v1_to_vr.rhs_all&#39; (class BalancedFieldODEComp)

Jacobian shape: (132, 60) (10.15% nonzero)
FWD solves: 16 REV solves: 0
Total colors vs. total size: 16 vs 60 (73.33% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.0157 sec
Time to compute coloring: 0.0098 sec
Time to compute sparsity: 0.0156 sec
Time to compute coloring: 0.0097 sec
Memory to compute coloring: 0.0000 MB

Coloring for &#39;traj.phases.rotate.rhs_all&#39; (class BalancedFieldODEComp)
Expand All @@ -1761,8 +1760,8 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.33% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.0154 sec
Time to compute coloring: 0.0097 sec
Time to compute sparsity: 0.0155 sec
Time to compute coloring: 0.0096 sec
Memory to compute coloring: 0.0000 MB

Coloring for &#39;traj.phases.climb.rhs_all&#39; (class BalancedFieldODEComp)
Expand All @@ -1772,12 +1771,12 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 111 (85.59% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.0323 sec
Time to compute coloring: 0.0182 sec
Memory to compute coloring: 0.2500 MB
Time to compute sparsity: 0.0325 sec
Time to compute coloring: 0.0185 sec
Memory to compute coloring: 0.0000 MB
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Full total jacobian for problem &#39;problem&#39; was computed 3 times, taking 0.9825835510000047 seconds.
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Full total jacobian for problem &#39;problem&#39; was computed 3 times, taking 1.009388161000004 seconds.
Total jacobian shape: (178, 166)


Expand All @@ -1786,10 +1785,10 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 14 vs 166 (91.57% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.9826 sec
Time to compute coloring: 0.0679 sec
Time to compute sparsity: 1.0094 sec
Time to compute coloring: 0.0774 sec
Memory to compute coloring: 0.0000 MB
Coloring created on: 2024-11-04 21:26:53
Coloring created on: 2024-11-06 01:20:37
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/usr/share/miniconda/envs/test/lib/python3.11/site-packages/openmdao/core/total_jac.py:1652: DerivativesWarning:Constraints or objectives [(&#39;traj.phases.climb-&gt;path_constraint-&gt;gam&#39;, inds=[(0, 0)])] cannot be impacted by the design variables of the problem.
Expand All @@ -1810,11 +1809,11 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Driver: pyOptSparseDriver
success : True
iterations : 25
runtime : 3.0100E+00 s
runtime : 3.0421E+00 s
model_evals : 25
model_time : 6.8689E-02 s
model_time : 6.6774E-02 s
deriv_evals : 24
deriv_time : 1.1846E+00 s
deriv_time : 1.1653E+00 s
exit_status : SUCCESS
</pre></div>
</div>
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30 changes: 15 additions & 15 deletions examples/balanced_field/balanced_field_funccomp.html
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Expand Up @@ -1255,9 +1255,9 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.33% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.2289 sec
Time to compute coloring: 0.0105 sec
Memory to compute coloring: 0.1250 MB
Time to compute sparsity: 0.2249 sec
Time to compute coloring: 0.0104 sec
Memory to compute coloring: 0.2500 MB
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/usr/share/miniconda/envs/test/lib/python3.11/site-packages/openmdao/core/system.py:1701: DerivativesWarning:&#39;traj.phases.rto.rhs_all&#39; &lt;class ExplicitFuncComp&gt;: No partials found but coloring was requested. Declaring ALL partials as dense (method=&#39;jax&#39;)
Expand All @@ -1270,8 +1270,8 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.33% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.1954 sec
Time to compute coloring: 0.0112 sec
Time to compute sparsity: 0.1889 sec
Time to compute coloring: 0.0102 sec
Memory to compute coloring: 0.0000 MB
</pre></div>
</div>
Expand All @@ -1285,8 +1285,8 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.33% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.1907 sec
Time to compute coloring: 0.0115 sec
Time to compute sparsity: 0.1871 sec
Time to compute coloring: 0.0106 sec
Memory to compute coloring: 0.0000 MB
</pre></div>
</div>
Expand All @@ -1300,8 +1300,8 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.33% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.2837 sec
Time to compute coloring: 0.0106 sec
Time to compute sparsity: 0.2829 sec
Time to compute coloring: 0.0105 sec
Memory to compute coloring: 0.0000 MB
</pre></div>
</div>
Expand All @@ -1315,12 +1315,12 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 111 (85.59% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.2751 sec
Time to compute coloring: 0.0195 sec
Time to compute sparsity: 0.2732 sec
Time to compute coloring: 0.0192 sec
Memory to compute coloring: 0.1250 MB
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Full total jacobian for problem &#39;problem&#39; was computed 3 times, taking 3.2737298330000044 seconds.
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Full total jacobian for problem &#39;problem&#39; was computed 3 times, taking 3.247299850000047 seconds.
Total jacobian shape: (178, 166)


Expand All @@ -1329,10 +1329,10 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 14 vs 166 (91.57% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 3.2737 sec
Time to compute sparsity: 3.2473 sec
Time to compute coloring: 0.0681 sec
Memory to compute coloring: 0.1250 MB
Coloring created on: 2024-11-04 21:27:04
Memory to compute coloring: 0.2500 MB
Coloring created on: 2024-11-06 01:20:48
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/usr/share/miniconda/envs/test/lib/python3.11/site-packages/openmdao/core/total_jac.py:1652: DerivativesWarning:Constraints or objectives [(&#39;traj.phases.climb-&gt;path_constraint-&gt;gam&#39;, inds=[(0, 0)])] cannot be impacted by the design variables of the problem.
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