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changed to inline equation default for mathjax
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+7
-23
@@ -48,22 +48,6 @@
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\newcommand{\I}{\vec{I}}
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.. raw:: html
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<script type="text/x-mathjax-config">
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MathJax.Hub.Config({
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extensions: ["tex2jax.js"],
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jax: ["input/TeX", "output/HTML-CSS"],
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tex2jax: {
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inlineMath: [ ['$','$'], ["\\(","\\)"] ],
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displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
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processEscapes: true
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},
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"HTML-CSS": { availableFonts: ["TeX"] },
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TeX: {extensions: ["color.js"]}
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});
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</script>
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Sensitivity Calculation
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***********************
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@@ -156,7 +140,7 @@ where
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\right]
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\end{align}
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For the fields $\u$, the measured data is given by
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For the fields \\(\\u\\), the measured data is given by
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.. math::
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@@ -173,7 +157,7 @@ The sensitivity matrix **J** is then defined as
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\end{align}
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Defining the function $\\c(m,\\u)$ to be
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Defining the function \\(\\c(m,\\u)\\) to be
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.. math::
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@@ -244,9 +228,9 @@ Implementing **J** times a vector
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Multiplying **J** onto a vector can be broken into three steps
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* Compute $\\vec{p} = \\mathbf{G}m$
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* Solve $\\hat{\\mathbf{A}} \\vec{y} = \\vec{p}$
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* Compute $\\vec{w} = -\\mathbf{Q} \\vec{y}$
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* Compute \\(\\vec{p} = \\mathbf{G}m\\)
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* Solve \\(\\hat{\\mathbf{A}} \\vec{y} = \\vec{p}\\)
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* Compute \\(\\vec{w} = -\\mathbf{Q} \\vec{y}\\)
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.. math::
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@@ -285,7 +269,7 @@ Remaining time steps:
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\begin{align}
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\dcurl \vec{y}_{e}^{(t+1)} + \frac{1}{\delta t} \vec{y}_{b}^{(t+1)}
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{\color{red}- \frac{1}{\delta t} \vec{y}_{b}^{(t)} }
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- \frac{1}{\delta t} \vec{y}_{b}^{(t)}
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= \vec{p}_b^{(t+1)} \\
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\dcurl^\top \MfMui \vec{y}_b^{(t+1)} - \MeSig \vec{y}_e^{(t+1)} = \vec{p}_e^{(t+1)}
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\end{align}
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@@ -296,7 +280,7 @@ and
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\begin{align}
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\left( \MfMui \dcurl \MeSig^{-1} \dcurl^\top \MfMui + \frac{1}{\delta t} \MfMui \right) \vec{y}_{b}^{(t+1)} =
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{\color{red} \frac{1}{\delta t} \MfMui \vec{y}_b^{(t)} }
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\frac{1}{\delta t} \MfMui \vec{y}_b^{(t)}
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+ \MfMui \dcurl \MeSig^{-1} \vec{p}_e^{(t+1)} + \MfMui \vec{p}_b^{(t+1)} \\
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\vec{y}_e^{(t+1)} = \MeSig^{-1} \dcurl^\top \MfMui \vec{y}_b^{(t+1)} - \MeSig^{-1} \vec{p}_e^{(t+1)}
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\end{align}
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