[build-bib, build-latex] Solver + consistency section, fix bug with backslash plague in bib file

.utils/biblatex_merger.py

@@ -102,12 +102,26 @@ def merge_bib(path):
     return filtered_bib_data
 
 
-def save_bib(bib_data, file):
-    bib_data.to_file(file, bib_format="bibtex")
+def save_bib(bib_data, file, manual_backslash_plague_fix=True):
+    if manual_backslash_plague_fix:
+        astr = bib_data.to_string(bib_format='bibtex')
+        astr = astr.replace("\\\\\\\&", "\&")
+        astr = astr.replace("\\\\\\&", "\&")
+        astr = astr.replace("\\\\\&", "\&")
+        astr = astr.replace("\\\\&", "\&")
+        astr = astr.replace("\\\&", "\&")
+        astr = astr.replace("\\&", "\&")
+        # astr = astr.replace("\_", "_")
+        # astr = astr.replace("\&", "&")
+        # astr = astr.replace("\%", "%")
+        with open(file, "w") as f_handle:
+            f_handle.write(astr)
+    else:
+        bib_data.to_file(file, bib_format="bibtex")
 
 
 if __name__ == "__main__":
     working_directory = sys.argv[1]
     output_file = sys.argv[2]
     filtered_bib_data = merge_bib(working_directory)
-    save_bib(filtered_bib_data, output_file)
+    save_bib(filtered_bib_data, output_file, manual_backslash_plague_fix=True)

tex/appendix/lagrangian.tex

@@ -20,7 +20,6 @@ \subsubsection{Discrete adjoint}
 Given that for every choice of the parameter $\theta$ we have $G(U; \theta) = 0$, we have that $I(U, \theta) = L(U, \theta)$.
 Then, the gradient of $L$ with respect to the vector parameter $\theta$ can be computed as 
 \begin{align}
-\begin{split}
     \frac{dL}{d\theta}
     = 
     \frac{dI}{d\theta}
@@ -33,9 +32,7 @@ \subsubsection{Discrete adjoint}
     &= 
     \frac{\partial L}{\partial \theta} + \lambda^T \frac{\partial G}{\partial U} 
     + 
-    \left( \frac{\partial L}{\partial \theta} + \lambda^T \frac{\partial G}{\partial U} \right) \frac{\partial U}{\partial \theta}.
-\end{split}
-\label{eq:appendix-discrete-adjoint}
+    \left( \frac{\partial L}{\partial \theta} + \lambda^T \frac{\partial G}{\partial U} \right) \frac{\partial U}{\partial \theta}. \label{eq:appendix-discrete-adjoint}
 \end{align}
 The important trick in the last term involved grouping all the terms involving the sensitivity $\frac{\partial U}{\partial \theta}$ together. 
 In order to avoid the computation of the sensitivity at all, we can define $\lambda$ as the vector that makes the last term in the right hand side of Equation \eqref{eq:appendix-discrete-adjoint} which results in the same results we obtained in Equation \eqref{eq:adjoint-state-equation} and \eqref{eq:def_adjoint}, that is,