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\title{TMA4320 --- Guide to Report Layout for Project \# 2}
\author{Jonas Blomberg Ghini \and Mariusz Eivind Gr{\o}tte}
\date{\today}

\begin{document}
	
	\maketitle
	
	\section{Introduction}
	In this document there will be specific instructions on how to write a report on Project 2 in TMA4320. Overall, the organization and structure of this particular report should not adhere to specific rules and layout of writing a standard technical report (i.e. you are mostly free to do whatever you want, but we fundamentally want you to explain your answers to questions). Most important is that students are able to answer the questions stated in the project description and that they show their thought process. This decision is made by all the course organizers and project instructors.
	
	Students are asked to follow these specific instructions when writing the report as a minimum effort but should not limit themselves to including material they believe are necessary. Finally, the report must be written in \LaTeX.
	
	\section{The report layout}
	Include the following for layout. For both options it is important for graders to illustrate your thought-process and substantiate your results. Justify your results in terms of understanding in Physics and explain the theory of mathematics in methodology. Important for all points is to include all the necessary code parts and explain these. It is NOT necessary to include the whole code in the report, although you are required to submit a .zip file with all of your code(s)!
	
	Please show your math in how to solve several of the questions, and answer the questions appropriately. Back up your thoughts, answers and procedure with code snippets if necessary.
	\\
	
	\textbf{Barebone layout}: Answers-to-questions report (Easy and sufficient). 
	\begin{itemize}
		\item Introduction and some theory. If you refer to equations please refer to them here.
		\item Answer, discussion and procedure to question 1
		\item Answer, discussion and procedure to question 2a
		\item Answer, discussion and procedure to question 2b
		\item Answer, discussion and procedure to question 3
		\item Answer, discussion and procedure to question 4
		\item Appendix: Relevant code with comments and explanation thereof. Key parts of your code should not only be included here, but also in the main body of the report, e.g. in answers-to-questions sections.
	\end{itemize}
	
	\section{What to include in the report (minimum)}
	\textbf{Question 1}:
	\begin{itemize}
		\item Full math, how did you achieve the result for $\mathbf{A}$ and $\mathbf{u}$ for $N=4$ used to calculate $\mathbf{x}$? 
		\item Explicitly show your linear system of equations $\mathbf{A}\mathbf{x}=\mathbf{u}$ for $N=4$. 
		\item What is your $\mathbf{x}$ when solved for the equation $\mathbf{A}\mathbf{x}=\mathbf{u}$?
	\end{itemize}
	\textbf{Question 2a}: 
	\begin{itemize}
		\item Plots showing both the numerical solution and the analytical one (to compare), as well as the plot(s) of the derivatives, with a short discussion of what the derivatives signify. Include relevant code.
	\end{itemize}
	\textbf{Question 2b}: 
	\begin{itemize}
		\item Show the calculation of $E_0$, be it analytic or with code.
		\item Show the solution of the system when using the DNA--specific material parameters.
		\item Comment on the validity of the model, given the calculated $\alpha$.
	\end{itemize}
	\textbf{Question 3}:
	\begin{itemize}
		\item Explain the algorithm, and show the relevant code that implements it.
		\item Plot the mean $\alpha$ values for several simulations of individual systems with several fibers.
		\item Comment on how the plots look for various $\beta$, and explain differences.
	\end{itemize} 
	\textbf{Question 4}: 
	\begin{itemize}
		\item Much the same as for \textbf{Question 3}, but also include how to define the sparse system; in what way does it differ from a dense system definition.
		\item Show the difference in computational time between a dense and a sparse solution approach.
	\end{itemize} 
	
	\section{How to include code}
	The following shows how to include code directly in the document.
	
	The environment to use is the one called ``python'', defined towards the top of the file (in the preamble). It is used in the following way:
	
	\begin{verbatim}
	\begin{lstlisting}[language=Python, caption=Python code example]
	import SomePythonModule as SPM
	
	if __name__ == "__main__":
	    Master_Flag = {
	    -1: 'TestSpace',
	    0: 'Some_other_name'
	    }[0]
	
	    if Master_Flag == 'Some_other_name':
	        SPM.main()
	\end{lstlisting}
	\end{verbatim}
	
	\begin{lstlisting}[language=Python, caption=Python code example]
		import SomePythonModule as SPM
		
		if __name__ == "__main__":
		    Master_Flag = {
			    -1: 'TestSpace',
			    0: 'Some_other_name'
		    }[0]
		
		    if Master_Flag == 'Some_other_name':
		    SPM.main()
	\end{lstlisting}
	
	The first mandatory argument (called ``caption'') is the caption of the code snippet, and should give a very brief description of what that snippet is about.
	
\end{document}