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16 changes: 8 additions & 8 deletions contributing/contributing.html
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Expand Up @@ -729,21 +729,21 @@ <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; | 4.3029e+01 | 4.3029e+01 | 7.3911e-15 | 1.7177e-16 | |
| &#39;check&#39; | &#39;theta&#39; | 9.8147e+02 | 9.8147e+02 | 2.2749e-13 | 2.3179e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;check&#39; | &#39;v&#39; | 4.4915e+00 | 4.4915e+00 | 4.9651e-16 | 1.1054e-16 | |
| &#39;check&#39; | &#39;v&#39; | 1.2709e+01 | 1.2709e+01 | 1.1322e-15 | 8.9090e-17 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;vdot&#39; | &#39;theta&#39; | 1.7366e+01 | 1.7366e+01 | 2.6645e-15 | 1.5343e-16 | |
| &#39;vdot&#39; | &#39;theta&#39; | 1.4431e+01 | 1.4431e+01 | 2.8109e-15 | 1.9477e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;vdot&#39; | &#39;v&#39; | 0.0000e+00 | 0.0000e+00 | 0.0000e+00 | nan | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;xdot&#39; | &#39;theta&#39; | 5.6296e+00 | 5.6296e+00 | 1.7764e-15 | 3.1554e-16 | |
| &#39;xdot&#39; | &#39;theta&#39; | 8.5390e+00 | 8.5390e+00 | 2.8262e-15 | 3.3097e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;xdot&#39; | &#39;v&#39; | 1.7708e+00 | 1.7708e+00 | 3.3307e-16 | 1.8808e-16 | |
| &#39;xdot&#39; | &#39;v&#39; | 1.4716e+00 | 1.4716e+00 | 2.0015e-16 | 1.3601e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;ydot&#39; | &#39;theta&#39; | 1.3868e+01 | 1.3868e+01 | 3.9783e-15 | 2.8686e-16 | |
| &#39;ydot&#39; | &#39;theta&#39; | 1.1471e+01 | 1.1471e+01 | 8.9164e-16 | 7.7733e-17 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;ydot&#39; | &#39;v&#39; | 1.3653e+00 | 1.3653e+00 | 3.7649e-16 | 2.7576e-16 | |
| &#39;ydot&#39; | &#39;v&#39; | 1.6836e+00 | 1.6836e+00 | 2.4980e-16 | 1.4837e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+

##################################################################
Expand All @@ -752,7 +752,7 @@ <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;xdot&#39; | &#39;theta&#39; | 5.6296e+00 | 5.6296e+00 | 1.7764e-15 | 3.1554e-16 |
| &#39;xdot&#39; | &#39;theta&#39; | 8.5390e+00 | 8.5390e+00 | 2.8262e-15 | 3.3097e-16 |
+-----------------+------------------+-------------+-------------+-------------+-------------+
</pre></div>
</div>
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57 changes: 28 additions & 29 deletions examples/balanced_field/balanced_field.html
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Expand Up @@ -576,13 +576,13 @@ <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-b4e751f8-bae2-497d-b2c3-4c410f1a1696">
<span class="eqno">(21)<a class="headerlink" href="#equation-b4e751f8-bae2-497d-b2c3-4c410f1a1696" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-eb13c583-d2ff-40f0-b2bd-a104fc6be1ad">
<span class="eqno">(21)<a class="headerlink" href="#equation-eb13c583-d2ff-40f0-b2bd-a104fc6be1ad" 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-d5cad48a-0bca-40a8-a629-f5e1862e6440">
<span class="eqno">(22)<a class="headerlink" href="#equation-d5cad48a-0bca-40a8-a629-f5e1862e6440" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-e3d3fb68-6c7e-4bb2-b159-eee7de9f8f96">
<span class="eqno">(22)<a class="headerlink" href="#equation-e3d3fb68-6c7e-4bb2-b159-eee7de9f8f96" 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 @@ -591,8 +591,8 @@ <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-eb90d3f0-fa94-4558-b8b9-2cc8c3ff7f32">
<span class="eqno">(23)<a class="headerlink" href="#equation-eb90d3f0-fa94-4558-b8b9-2cc8c3ff7f32" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-d923400c-f294-4b54-a143-815eb3c84770">
<span class="eqno">(23)<a class="headerlink" href="#equation-d923400c-f294-4b54-a143-815eb3c84770" 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 @@ -603,17 +603,17 @@ <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-8bda7cf4-b64c-4043-a935-11bf7d7f5e48">
<span class="eqno">(24)<a class="headerlink" href="#equation-8bda7cf4-b64c-4043-a935-11bf7d7f5e48" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-2e71e0bc-15ca-4303-b515-772f138adaa7">
<span class="eqno">(24)<a class="headerlink" href="#equation-2e71e0bc-15ca-4303-b515-772f138adaa7" 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-f0c0432d-1595-43c8-8eba-e2c48f98de96">
<span class="eqno">(25)<a class="headerlink" href="#equation-f0c0432d-1595-43c8-8eba-e2c48f98de96" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-b9acdf38-8b25-493c-835f-22a6eb8abb3e">
<span class="eqno">(25)<a class="headerlink" href="#equation-b9acdf38-8b25-493c-835f-22a6eb8abb3e" 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 @@ -640,8 +640,8 @@ <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-10f06305-999b-498c-a408-9e477f147edf">
<span class="eqno">(26)<a class="headerlink" href="#equation-10f06305-999b-498c-a408-9e477f147edf" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-f08a6c7e-ad29-4026-9cf0-b9bc251239b9">
<span class="eqno">(26)<a class="headerlink" href="#equation-f08a6c7e-ad29-4026-9cf0-b9bc251239b9" 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 @@ -1165,7 +1165,7 @@ <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 0x7fe128b7ad10&gt;
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;dymos.phase.phase.Phase at 0x7f01bcf53af0&gt;
</pre></div>
</div>
</div>
Expand Down Expand Up @@ -1309,9 +1309,8 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
[final] 5.0000e+00 == gam [deg]
[final] 1.2500e+00 &lt;= v_over_v_stall [None]
[path] 0.0000e+00 &lt;= gam &lt;= 5.0000e+00 [deg]
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>INFO: checking out_of_order

INFO: checking out_of_order
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>INFO:check_config:checking out_of_order
Expand Down Expand Up @@ -1427,8 +1426,8 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.3% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.020643 sec.
Time to compute coloring: 0.015187 sec.
Time to compute sparsity: 0.022397 sec.
Time to compute coloring: 0.015122 sec.
Memory to compute coloring: 0.000000 MB.
</pre></div>
</div>
Expand All @@ -1439,8 +1438,8 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.3% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.022303 sec.
Time to compute coloring: 0.016201 sec.
Time to compute sparsity: 0.020197 sec.
Time to compute coloring: 0.014614 sec.
Memory to compute coloring: 0.000000 MB.

Coloring for &#39;traj.phases.v1_to_vr.rhs_all&#39; (class BalancedFieldODEComp)
Expand All @@ -1450,8 +1449,8 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.3% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.020355 sec.
Time to compute coloring: 0.015141 sec.
Time to compute sparsity: 0.019348 sec.
Time to compute coloring: 0.014845 sec.
Memory to compute coloring: 0.000000 MB.

Coloring for &#39;traj.phases.rotate.rhs_all&#39; (class BalancedFieldODEComp)
Expand All @@ -1461,8 +1460,8 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.3% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.020274 sec.
Time to compute coloring: 0.015171 sec.
Time to compute sparsity: 0.019450 sec.
Time to compute coloring: 0.014961 sec.
Memory to compute coloring: 0.000000 MB.
</pre></div>
</div>
Expand All @@ -1473,12 +1472,12 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 111 (85.6% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.041926 sec.
Time to compute coloring: 0.030395 sec.
Time to compute sparsity: 0.040187 sec.
Time to compute coloring: 0.029838 sec.
Memory to compute coloring: 0.000000 MB.
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Full total jacobian was computed 3 times, taking 1.383054 seconds.
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Full total jacobian was computed 3 times, taking 1.429048 seconds.
Total jacobian shape: (178, 166)


Expand All @@ -1487,8 +1486,8 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 12 vs 166 (92.8% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 1.383054 sec.
Time to compute coloring: 0.104511 sec.
Time to compute sparsity: 1.429048 sec.
Time to compute coloring: 0.102081 sec.
Memory to compute coloring: 0.000000 MB.
</pre></div>
</div>
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34 changes: 17 additions & 17 deletions examples/balanced_field/balanced_field_funccomp.html
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Expand Up @@ -988,14 +988,14 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Coloring for &#39;traj.phases.br_to_v1.rhs_all&#39; (class ExplicitFuncComp)

Jacobian shape: (132, 60) ( 9.81% nonzero)
Jacobian shape: (132, 60) ( 9.79% nonzero)
FWD solves: 16 REV solves: 0
Total colors vs. total size: 16 vs 60 (73.3% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.357813 sec.
Time to compute coloring: 0.076438 sec.
Memory to compute coloring: 0.000000 MB.
Time to compute sparsity: 0.345507 sec.
Time to compute coloring: 0.068077 sec.
Memory to compute coloring: 1.644531 MB.
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/core/system.py:1659: 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 @@ -1008,8 +1008,8 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.3% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.332938 sec.
Time to compute coloring: 0.075693 sec.
Time to compute sparsity: 0.326953 sec.
Time to compute coloring: 0.068471 sec.
Memory to compute coloring: 0.000000 MB.
</pre></div>
</div>
Expand All @@ -1023,8 +1023,8 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.3% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.327798 sec.
Time to compute coloring: 0.076807 sec.
Time to compute sparsity: 0.329144 sec.
Time to compute coloring: 0.069629 sec.
Memory to compute coloring: 0.000000 MB.
</pre></div>
</div>
Expand All @@ -1038,8 +1038,8 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.3% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.333193 sec.
Time to compute coloring: 0.077559 sec.
Time to compute sparsity: 0.330394 sec.
Time to compute coloring: 0.069712 sec.
Memory to compute coloring: 0.000000 MB.
</pre></div>
</div>
Expand All @@ -1053,12 +1053,12 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 111 (85.6% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.443164 sec.
Time to compute coloring: 0.173018 sec.
Memory to compute coloring: 1.406250 MB.
Time to compute sparsity: 0.435249 sec.
Time to compute coloring: 0.155184 sec.
Memory to compute coloring: 1.347656 MB.
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Full total jacobian was computed 3 times, taking 4.855364 seconds.
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Full total jacobian was computed 3 times, taking 4.719833 seconds.
Total jacobian shape: (178, 166)


Expand All @@ -1067,9 +1067,9 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 12 vs 166 (92.8% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 4.855364 sec.
Time to compute coloring: 0.112873 sec.
Memory to compute coloring: 0.285156 MB.
Time to compute sparsity: 4.719833 sec.
Time to compute coloring: 0.100876 sec.
Memory to compute coloring: 0.000000 MB.
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/core/total_jac.py:1782: DerivativesWarning:Constraints or objectives [(&#39;traj.phases.climb.timeseries.timeseries_comp.gam&#39;, inds=[(0, 0)])] cannot be impacted by the design variables of the problem.
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