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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; | 5.2975e+01 | 5.2975e+01 | 3.5527e-15 | 6.7064e-17 | |
| &#39;check&#39; | &#39;theta&#39; | 9.3567e+05 | 9.3567e+05 | 1.1642e-10 | 1.2442e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;check&#39; | &#39;v&#39; | 4.1888e+00 | 4.1888e+00 | 0.0000e+00 | 0.0000e+00 | |
| &#39;check&#39; | &#39;v&#39; | 3.3758e+02 | 3.3758e+02 | 2.2204e-16 | 6.5776e-19 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;vdot&#39; | &#39;theta&#39; | 1.4221e+01 | 1.4221e+01 | 2.1756e-15 | 1.5298e-16 | |
| &#39;vdot&#39; | &#39;theta&#39; | 1.3676e+01 | 1.3676e+01 | 3.4694e-18 | 2.5369e-19 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;vdot&#39; | &#39;v&#39; | 0.0000e+00 | 0.0000e+00 | 0.0000e+00 | nan | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;xdot&#39; | &#39;theta&#39; | 1.0941e+01 | 1.0941e+01 | 9.9301e-16 | 9.0760e-17 | |
| &#39;xdot&#39; | &#39;theta&#39; | 1.1556e+01 | 1.1556e+01 | 4.4409e-16 | 3.8429e-17 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;xdot&#39; | &#39;v&#39; | 1.4502e+00 | 1.4502e+00 | 9.6148e-17 | 6.6301e-17 | |
| &#39;xdot&#39; | &#39;v&#39; | 1.3945e+00 | 1.3945e+00 | 1.1102e-16 | 7.9612e-17 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;ydot&#39; | &#39;theta&#39; | 9.9680e+00 | 9.9680e+00 | 1.0878e-15 | 1.0913e-16 | |
| &#39;ydot&#39; | &#39;theta&#39; | 9.4904e+00 | 9.4904e+00 | 1.3506e-15 | 1.4232e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;ydot&#39; | &#39;v&#39; | 1.7021e+00 | 1.7021e+00 | 1.5701e-16 | 9.2247e-17 | |
| &#39;ydot&#39; | &#39;v&#39; | 1.7479e+00 | 1.7479e+00 | 1.5701e-16 | 8.9826e-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; | 1.4221e+01 | 1.4221e+01 | 2.1756e-15 | 1.5298e-16 |
| &#39;ydot&#39; | &#39;theta&#39; | 9.4904e+00 | 9.4904e+00 | 1.3506e-15 | 1.4232e-16 |
+-----------------+------------------+-------------+-------------+-------------+-------------+
</pre></div>
</div>
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60 changes: 30 additions & 30 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-3228f40e-a586-447d-ab14-2e607fd5e6f5">
<span class="eqno">(21)<a class="headerlink" href="#equation-3228f40e-a586-447d-ab14-2e607fd5e6f5" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-5dc37eb0-6c59-45ed-b76a-73c9913cf673">
<span class="eqno">(21)<a class="headerlink" href="#equation-5dc37eb0-6c59-45ed-b76a-73c9913cf673" 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-ec5c7ed7-9b80-40cd-8286-c8f9a802e6e4">
<span class="eqno">(22)<a class="headerlink" href="#equation-ec5c7ed7-9b80-40cd-8286-c8f9a802e6e4" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-d0966c3d-4f73-42d6-b2d5-949de317ad2a">
<span class="eqno">(22)<a class="headerlink" href="#equation-d0966c3d-4f73-42d6-b2d5-949de317ad2a" 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-a7c34d59-09b7-498a-b5f2-8c3d78a8d9f8">
<span class="eqno">(23)<a class="headerlink" href="#equation-a7c34d59-09b7-498a-b5f2-8c3d78a8d9f8" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-53a0a72b-6435-46ea-b818-749b9c0b95ba">
<span class="eqno">(23)<a class="headerlink" href="#equation-53a0a72b-6435-46ea-b818-749b9c0b95ba" 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-3623ff3f-07af-45b2-a8b9-999f6551ec3d">
<span class="eqno">(24)<a class="headerlink" href="#equation-3623ff3f-07af-45b2-a8b9-999f6551ec3d" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-2bb9548c-1ebb-4233-9d0e-a37c4c91fe00">
<span class="eqno">(24)<a class="headerlink" href="#equation-2bb9548c-1ebb-4233-9d0e-a37c4c91fe00" 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-91cf6228-cb2d-46aa-a6ae-01b4dcb7879f">
<span class="eqno">(25)<a class="headerlink" href="#equation-91cf6228-cb2d-46aa-a6ae-01b4dcb7879f" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-5d9446ae-329e-443b-b049-1f074ba0f7f2">
<span class="eqno">(25)<a class="headerlink" href="#equation-5d9446ae-329e-443b-b049-1f074ba0f7f2" 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-186c72c1-b75f-45d0-bb2e-7c0a8ce7d143">
<span class="eqno">(26)<a class="headerlink" href="#equation-186c72c1-b75f-45d0-bb2e-7c0a8ce7d143" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-a34cb7c6-315c-4a2a-8cc5-3214c323df83">
<span class="eqno">(26)<a class="headerlink" href="#equation-a34cb7c6-315c-4a2a-8cc5-3214c323df83" 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 0x7ff84ac73ed0&gt;
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;dymos.phase.phase.Phase at 0x7f3c3de60410&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: 0.0160 sec
Time to compute coloring: 0.0103 sec
Time to compute sparsity: 0.0165 sec
Time to compute coloring: 0.0109 sec
Memory to compute coloring: 0.1250 MB

Coloring for &#39;traj.phases.rto.rhs_all&#39; (class BalancedFieldODEComp)
Expand All @@ -1738,8 +1738,8 @@ <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: 0.0101 sec
Memory to compute coloring: 0.0000 MB

Coloring for &#39;traj.phases.v1_to_vr.rhs_all&#39; (class BalancedFieldODEComp)
Expand All @@ -1749,7 +1749,7 @@ <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 sparsity: 0.0159 sec
Time to compute coloring: 0.0100 sec
Memory to compute coloring: 0.0000 MB

Expand All @@ -1760,8 +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: 0.0159 sec
Time to compute coloring: 0.0098 sec
Time to compute sparsity: 0.0160 sec
Time to compute coloring: 0.0100 sec
Memory to compute coloring: 0.0000 MB

Coloring for &#39;traj.phases.climb.rhs_all&#39; (class BalancedFieldODEComp)
Expand All @@ -1771,12 +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: 0.0329 sec
Time to compute coloring: 0.0186 sec
Memory to compute coloring: 0.0000 MB
Time to compute sparsity: 0.0337 sec
Time to compute coloring: 0.0192 sec
Memory to compute coloring: 0.2500 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 0.9899345740000172 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 1.0049373029999629 seconds.
Total jacobian shape: (178, 166)


Expand All @@ -1785,10 +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: 0.9899 sec
Time to compute coloring: 0.0692 sec
Time to compute sparsity: 1.0049 sec
Time to compute coloring: 0.0695 sec
Memory to compute coloring: 0.0000 MB
Coloring created on: 2024-10-02 16:21:15
Coloring created on: 2024-10-02 16:45:39
</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 @@ -1809,11 +1809,11 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Driver: pyOptSparseDriver
success : True
iterations : 25
runtime : 3.0181E+00 s
runtime : 3.1027E+00 s
model_evals : 25
model_time : 7.1800E-02 s
model_time : 7.2978E-02 s
deriv_evals : 24
deriv_time : 1.1569E+00 s
deriv_time : 1.2133E+00 s
exit_status : SUCCESS
</pre></div>
</div>
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28 changes: 14 additions & 14 deletions examples/balanced_field/balanced_field_funccomp.html
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Expand Up @@ -1252,9 +1252,9 @@ <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: 0.2386 sec
Time to compute coloring: 0.0107 sec
Memory to compute coloring: 0.2500 MB
Time to compute sparsity: 0.2314 sec
Time to compute coloring: 0.0108 sec
Memory to compute coloring: 0.1250 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 @@ -1267,8 +1267,8 @@ <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: 0.1935 sec
Time to compute coloring: 0.0118 sec
Time to compute sparsity: 0.1949 sec
Time to compute coloring: 0.0112 sec
Memory to compute coloring: 0.0000 MB
</pre></div>
</div>
Expand All @@ -1282,7 +1282,7 @@ <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: 0.1918 sec
Time to compute sparsity: 0.1936 sec
Time to compute coloring: 0.0119 sec
Memory to compute coloring: 0.0000 MB
</pre></div>
Expand All @@ -1297,8 +1297,8 @@ <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: 0.1906 sec
Time to compute coloring: 0.0117 sec
Time to compute sparsity: 0.1963 sec
Time to compute coloring: 0.0114 sec
Memory to compute coloring: 0.0000 MB
</pre></div>
</div>
Expand All @@ -1312,12 +1312,12 @@ <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: 0.2778 sec
Time to compute coloring: 0.0194 sec
Time to compute sparsity: 0.2833 sec
Time to compute coloring: 0.0195 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 3.296542742999975 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 3.302916429999982 seconds.
Total jacobian shape: (178, 166)


Expand All @@ -1326,10 +1326,10 @@ <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: 3.2965 sec
Time to compute coloring: 0.0703 sec
Time to compute sparsity: 3.3029 sec
Time to compute coloring: 0.0697 sec
Memory to compute coloring: 0.2500 MB
Coloring created on: 2024-10-02 16:21:26
Coloring created on: 2024-10-02 16:45:51
</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 Down
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