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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; | 9.5078e+01 | 9.5078e+01 | 1.4211e-14 | 1.4947e-16 | |
| &#39;check&#39; | &#39;theta&#39; | 1.5121e+01 | 1.5121e+01 | 2.0592e-15 | 1.3618e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;check&#39; | &#39;v&#39; | 5.1922e+00 | 5.1922e+00 | 0.0000e+00 | 0.0000e+00 | |
| &#39;check&#39; | &#39;v&#39; | 3.2006e+00 | 3.2006e+00 | 2.2204e-16 | 6.9376e-17 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;vdot&#39; | &#39;theta&#39; | 1.5794e+01 | 1.5794e+01 | 4.4409e-16 | 2.8118e-17 | |
| &#39;vdot&#39; | &#39;theta&#39; | 1.7559e+01 | 1.7559e+01 | 2.5121e-15 | 1.4307e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;vdot&#39; | &#39;v&#39; | 0.0000e+00 | 0.0000e+00 | 0.0000e+00 | nan | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;xdot&#39; | &#39;theta&#39; | 7.6161e+00 | 7.6161e+00 | 9.9920e-16 | 1.3120e-16 | |
| &#39;xdot&#39; | &#39;theta&#39; | 6.2216e+00 | 6.2216e+00 | 0.0000e+00 | 0.0000e+00 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;xdot&#39; | &#39;v&#39; | 1.6105e+00 | 1.6105e+00 | 1.5944e-16 | 9.9002e-17 | |
| &#39;xdot&#39; | &#39;v&#39; | 1.7905e+00 | 1.7905e+00 | 0.0000e+00 | 0.0000e+00 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;ydot&#39; | &#39;theta&#39; | 1.0500e+01 | 1.0500e+01 | 2.2204e-16 | 2.1147e-17 | |
| &#39;ydot&#39; | &#39;theta&#39; | 1.2071e+01 | 1.2071e+01 | 4.4409e-16 | 3.6789e-17 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;ydot&#39; | &#39;v&#39; | 1.5512e+00 | 1.5512e+00 | 0.0000e+00 | 0.0000e+00 | |
| &#39;ydot&#39; | &#39;v&#39; | 1.3394e+00 | 1.3394e+00 | 1.1444e-16 | 8.5439e-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;check&#39; | &#39;theta&#39; | 9.5078e+01 | 9.5078e+01 | 1.4211e-14 | 1.4947e-16 |
| &#39;vdot&#39; | &#39;theta&#39; | 1.7559e+01 | 1.7559e+01 | 2.5121e-15 | 1.4307e-16 |
+-----------------+------------------+-------------+-------------+-------------+-------------+
</pre></div>
</div>
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70 changes: 34 additions & 36 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-21f8763d-24a5-4472-ab74-6ea939afe3db">
<span class="eqno">(21)<a class="headerlink" href="#equation-21f8763d-24a5-4472-ab74-6ea939afe3db" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-e2156145-491f-45ce-b4d0-1c8a27384765">
<span class="eqno">(21)<a class="headerlink" href="#equation-e2156145-491f-45ce-b4d0-1c8a27384765" 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-0f4c09f0-874d-4a6a-b3b2-29c9900371aa">
<span class="eqno">(22)<a class="headerlink" href="#equation-0f4c09f0-874d-4a6a-b3b2-29c9900371aa" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-13096672-c3de-40ca-98b1-77c999b13b60">
<span class="eqno">(22)<a class="headerlink" href="#equation-13096672-c3de-40ca-98b1-77c999b13b60" 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-a9067418-643c-4a7a-b57f-e3dd8b4fd3b4">
<span class="eqno">(23)<a class="headerlink" href="#equation-a9067418-643c-4a7a-b57f-e3dd8b4fd3b4" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-1d1408b7-3c74-4276-a1dc-e99f14514c7c">
<span class="eqno">(23)<a class="headerlink" href="#equation-1d1408b7-3c74-4276-a1dc-e99f14514c7c" 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-6236059f-e02f-41e7-a229-2662d54348e0">
<span class="eqno">(24)<a class="headerlink" href="#equation-6236059f-e02f-41e7-a229-2662d54348e0" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-0be39509-2b1c-4c84-ac75-3e1e03af28bb">
<span class="eqno">(24)<a class="headerlink" href="#equation-0be39509-2b1c-4c84-ac75-3e1e03af28bb" 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-79d5921b-8ce2-4de0-ae5c-306a989ab428">
<span class="eqno">(25)<a class="headerlink" href="#equation-79d5921b-8ce2-4de0-ae5c-306a989ab428" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-c5a7f62b-d230-4722-a238-95583053bf19">
<span class="eqno">(25)<a class="headerlink" href="#equation-c5a7f62b-d230-4722-a238-95583053bf19" 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-6d8ab040-0a7e-4ea5-9a75-8ec383281943">
<span class="eqno">(26)<a class="headerlink" href="#equation-6d8ab040-0a7e-4ea5-9a75-8ec383281943" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-f749e506-dd7e-483b-a398-4967020866f0">
<span class="eqno">(26)<a class="headerlink" href="#equation-f749e506-dd7e-483b-a398-4967020866f0" 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 0x7f43c842d410&gt;
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;dymos.phase.phase.Phase at 0x7f0545159810&gt;
</pre></div>
</div>
</div>
Expand Down Expand Up @@ -1721,15 +1721,14 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
</pre></div>
</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 BalancedFieldODEComp)
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Jacobian shape: (132, 60) (10.13% nonzero)

Jacobian shape: (132, 60) (10.13% 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: 0.0155 sec
Time to compute coloring: 0.0103 sec
Time to compute sparsity: 0.0159 sec
Time to compute coloring: 0.0101 sec
Memory to compute coloring: 0.3750 MB
</pre></div>
</div>
Expand All @@ -1740,7 +1739,7 @@ <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: 0.0154 sec
Time to compute sparsity: 0.0158 sec
Time to compute coloring: 0.0098 sec
Memory to compute coloring: 0.0000 MB

Expand All @@ -1751,8 +1750,8 @@ <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: 0.0237 sec
Time to compute coloring: 0.0176 sec
Time to compute sparsity: 0.0157 sec
Time to compute coloring: 0.0098 sec
Memory to compute coloring: 0.0000 MB

Coloring for &#39;traj.phases.rotate.rhs_all&#39; (class BalancedFieldODEComp)
Expand All @@ -1762,24 +1761,23 @@ <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: 0.0231 sec
Time to compute coloring: 0.0156 sec
Time to compute sparsity: 0.0156 sec
Time to compute coloring: 0.0098 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.climb.rhs_all&#39; (class BalancedFieldODEComp)

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

Jacobian shape: (260, 111) (5.54% nonzero)
FWD solves: 16 REV solves: 0
Total colors vs. total size: 16 vs 111 (85.59% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.0573 sec
Time to compute coloring: 0.0256 sec
Memory to compute coloring: 0.1250 MB
Time to compute sparsity: 0.0327 sec
Time to compute coloring: 0.0188 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 1.0492951429999948 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 0.9843007159999502 seconds.
Total jacobian shape: (178, 166)


Expand All @@ -1788,10 +1786,10 @@ <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: 1.0493 sec
Time to compute coloring: 0.0679 sec
Time to compute sparsity: 0.9843 sec
Time to compute coloring: 0.0674 sec
Memory to compute coloring: 0.0000 MB
Coloring created on: 2024-11-01 00:50:59
Coloring created on: 2024-11-04 20:45:33
</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 @@ -1812,11 +1810,11 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Driver: pyOptSparseDriver
success : True
iterations : 25
runtime : 3.0591E+00 s
runtime : 2.9627E+00 s
model_evals : 25
model_time : 6.9377E-02 s
model_time : 6.5993E-02 s
deriv_evals : 24
deriv_time : 1.1451E+00 s
deriv_time : 1.1415E+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: 0.2304 sec
Time to compute sparsity: 0.2293 sec
Time to compute coloring: 0.0106 sec
Memory to compute coloring: 0.1250 MB
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: 0.1967 sec
Time to compute coloring: 0.0113 sec
Time to compute sparsity: 0.1899 sec
Time to compute coloring: 0.0114 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: 0.1924 sec
Time to compute coloring: 0.0119 sec
Time to compute sparsity: 0.1894 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: 0.2986 sec
Time to compute coloring: 0.0108 sec
Time to compute sparsity: 0.1925 sec
Time to compute coloring: 0.0115 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: 0.2738 sec
Time to compute coloring: 0.0197 sec
Time to compute sparsity: 0.2733 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 3.284827410000048 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 3.2551037000000065 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: 3.2848 sec
Time to compute coloring: 0.0685 sec
Memory to compute coloring: 0.2500 MB
Coloring created on: 2024-11-01 00:51:10
Time to compute sparsity: 3.2551 sec
Time to compute coloring: 0.0692 sec
Memory to compute coloring: 0.1250 MB
Coloring created on: 2024-11-04 20:45:45
</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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