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thast committed Oct 2, 2019
2 parents 19c048f + b4d0102 commit 57cb51a
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10 changes: 6 additions & 4 deletions content/theory.rst
Original file line number Diff line number Diff line change
Expand Up @@ -249,11 +249,13 @@ where

.. math::
J_{ij} =
\left\{ \begin{array}{cl}
\frac{\partial \phi_i \left[ \sigma \right]}{\partial ln\sigma_j}, &\mathbf{d}=\phi_s\\
\left\{
\begin{array}{cl}
\frac{\partial \phi_i \left[ \sigma \right]}{\partial ln\sigma_j}, \mathbf{d}=\phi_s\\
\\
\frac{\partial ln\phi_i\left [ \sigma \right ]}{\partial ln\sigma_j},& \mathbf{d}=\eta_a
\frac{\partial ln\phi_i\left [ \sigma \right ]}{\partial ln\sigma_j}, \mathbf{d}=\eta_a
\end{array}
\right\}
:label: Jij
is the sensitivity matrix.
Expand All @@ -276,7 +278,7 @@ applying the transform to each row of :math:`\mathbf{J}` and forming a new matri
where :math:`\tilde{\mathbf{J}}` is the transformed matrix. The thresholding is applied to individual rows of :math:`\mathbf{J}` by the following rule to form the sparse representation :math:`\tilde{\mathbf{J}}^S`:

.. math::
{\tilde{f{J}}_{ij}}^s =
{\tilde{{J}}_{ij}}^s =
\left\{ \begin{array}{cl}
{\tilde{{J}}_{ij}} \text{ if } |{\tilde{{J}}_{ij}}| \geq \delta_i
\\
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