Updates to L18, very preliminary L19

Lectures/L18_MazeTracingRobot/MazeTracingRobot.tex

-%\documentclass[13pt]{beamer} % some colour, looks good with logictheme style
-\documentclass[handout]{beamer} % for handout
-%\documentclass{beamer} % for slides using uncover
+%\documentclass[t,12pt,numbers,fleqn,handout]{beamer}
+\documentclass[t,12pt,numbers,fleqn]{beamer}
 
-\usepackage{logictheme}
-\usepackage{amsmath}
-\usepackage{bm}
-\usepackage{ulem}
-
-\usepackage{hhline}
-\usepackage{multirow}
-\usepackage{multicol}
-\usepackage{array}
+\usepackage{pgfpages} 
 \usepackage{hyperref}
+\hypersetup{colorlinks=true,
+    linkcolor=blue,
+    citecolor=blue,
+    filecolor=blue,
+    urlcolor=blue,
+    unicode=false}
+\urlstyle{same}
+
+\usepackage{booktabs}
+\usepackage{multirow}
 
-\usepackage{listings}
+\useoutertheme{split} %so the footline can be seen, without needing pgfpages
 
-\title[Maze Tracing Robot (slide \thepage)]{Maze Tracing Robot Example}
-%\subtitle{???}
-\author[Smith]{Dr.~Spencer Smith}
-\institute{Computing and Software Department, McMaster University}
-\date{\today}
-\pgfdeclareimage[height=0.5cm]{logo}{../McMasterLogo} %McMaster logo in one folder up
-\logo{\pgfuseimage{logo}}
+% \pgfpagesuselayout{resize to}[letterpaper,border
+% shrink=5mm,landscape] %if this is uncommented, the hyperref links do not work
 
-\setbeamercolor{alerted text}{fg=red!75!green!50!blue}
-%\setbeamerfont{alerted text}{series=\bfseries}
-\setbeamerfont{alerted text}{family=\rmfamily,series=\bfseries}
+\mode<presentation>{}
 
-%\setbeamertemplate{footline}{\insertpagenumber}  % only has the page number
+\input{../def-beamer}
 
-\newcounter{temp}
+\newcommand{\topic}{18 Maze Tracing Robot Example}
+
+\input{../titlepage}
 
 \begin{document}
 
-% ==================================================================================
-% Slide 1
-\maketitle
-% ==================================================================================
+\input{../footline}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \begin{frame}
 \frametitle{Maze Tracing Robot Example}
 
 \begin{itemize}
 \item Administrative details
-\item Dr.\ v.\ Mohrenschildt's maze tracing robot (see WebCT document)
+\item Index set example
+\item Solar water heating tank example
+\item Dr.\ v.\ Mohrenschildt's maze tracing robot (see GitLab)
 \item MIS for maze\_storage
 \end{itemize}
 
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
 \begin{frame}
 \frametitle{Administrative Details}
 
 \begin{itemize}
 
-\item Assignment 3 deadlines
+\item Assignment 2
 \begin{itemize}
-\item Minor modifications to posted file
-\item Code due by midnight Feb 23
-\item E-mail your partner your code by  Feb 24
-\item Lab report due by the beginning of class Mar 2
-\item Will discuss Assignment 3 during tutorial, time for questions
+\item {Files due by 11:59 pm Feb 19}
+\item {File automatically sent to partners on Feb 20}
+\item Lab report due by 11:59 pm Feb 27
+\item {When returning an object, you can either create a new object or
+    return a reference}
+\item {Remember: Deque is an Abstract Object, not an ADT}
 \end{itemize}
+
 \item Midterm exam
 \begin{itemize}
-\item March 4 during tutorial time
-\item In T29/105, not our usual classroom
+\item March 1, 7:00 pm, TSH/120
+\item 90 minute duration
+\item Multiple choice - 30--40 questions?
+\item Open book (any paper)
 \end{itemize}
+
 \end{itemize}
 
 \end{frame}
@@ -75,170 +78,151 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \begin{frame}
-\frametitle{Modules with External Interaction}
+\frametitle{Index Set}
 
-\begin{itemize}
-\item In general, some modules may interact with the environment or other modules
-%\item The Display Point Masses Applet module does this
-\item Environment might include the keyboard, the screen, the file system, motors, sensors, etc.
-\item Sometimes the interaction is informally specified using prose (natural language)
-\item Can introduce an environment variable
-\begin{itemize}
-\item Name, type
-\item Interpretation
-\end{itemize}
-\item Environment variables include the screen, the state of a motor (on, direction of rotation, power level, etc.),
-the position of a robot
-
-\end{itemize}
+Write a function \texttt{indexSet(x, B)} that takes a value \texttt{x} and a
+list of values \texttt{B} and returns a list of indices where \texttt{B[i] =
+  x}.\\
+~\newline
+As a first step, how would you say this mathematically?
 
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \begin{frame}
-\frametitle{External Interaction Continued}
+\frametitle{Index Set}
 
-\begin{itemize}
-\item Some external interactions are hidden
-\begin{itemize}
-\item Present in the implementation, but not in the MIS
-\item An example might be OS memory allocation calls
-\end{itemize}
-\item External interaction described in the MIS
-\begin{itemize}
-\item Naming access programs of the other modules
-\item Specifying how the other module's state variables are changed
-\item The MIS should identify what external modules are used
-\end{itemize}
-\end{itemize}
+Write a function \texttt{indexSet(x, B)} that takes a value \texttt{x} and a
+list of values \texttt{B} and returns a list of indices where \texttt{B[i] =
+  x}.\\
+
+$$\mbox{indexSet}(x, B) \equiv \{i : \mathbb{N} | i \in [0 .. |B|-1] \wedge B_i =
+x : i\}$$
+
+How could you use \texttt{indexSet} to calculate \texttt{rank(x, A)}?
 
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}
-\frametitle{MIS for GUI Modules}
 
-\begin{itemize}
-\item Could introduce an environment variable
-\item window: sequence [RES\_H][RES\_V] of pixelT
-\begin{itemize}
-\item Where window[r][c] is the pixel located at row r and column c, with numbering zero-relative and beginning at the
-upper left corner
-\item Would still need to define pixelT
-\end{itemize}
-\item Could formally specify the environment variable transitions
-\item More often it is reasonable to specify the transition in prose
-\item In some cases the proposed GUI might be shown by rough sketches
-\end{itemize}
+\begin{frame}
+\frametitle{Anticipated Changes}
+
+\bi
+\item The specific hardware on which the software is to run
+\item The format of the initial input data
+\item The format of the input parameters
+\item The constraints on the input parameters
+\item The format of the output data
+\item The constraints on the output results
+\item How the governing ODEs are defined using the input parameters
+\item How the energy equations are defined using the input parameters
+\item How the overall control of the calculations is orchestrated
+\item The implementation of the sequence data structure
+\item The algorithm used for the ODE solver
+\item The implementation of plotting data
+\ei
 
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \begin{frame}
-\frametitle{Display Point Masses Module Syntax}
+\frametitle{Module Hierarchy by Secrets}
+\begin{table}[h!]
+\centering
+\begin{tabular}{p{0.3\textwidth} p{0.6\textwidth}}
+\toprule
+\textbf{Level 1} & \textbf{Level 2}\\
+\midrule
+
+{Hardware-Hiding Module} & ~ \\
+\midrule
+
+\multirow{6}{0.3\textwidth}{Behaviour-Hiding Module} & Input Format Module\\
+& Input Parameters Module\\
+& Output Format Module\\
+& Temperature ODEs Module\\
+& Energy Equations Module\\ 
+& Control Module\\
+\midrule
+
+\multirow{3}{0.3\textwidth}{Software Decision Module} & {Sequence Data Structure Module}\\
+& ODE Solver Module\\
+& Plotting Module\\
+\bottomrule
 
-\textbf{Exported Access Programs}\\
-~\newline
-\begin{tabular}{| l | l | l | l |}
-\hline
-\textbf{Routine name} & \textbf{In} & \textbf{Out} & \textbf{Exc.}\\
-\hline
-DisplayPointMassesApplet & ~ & DisplayPointMassesApplet & ~\\
-\hline
-paint & ~ & ~ & ~\\
-\hline
 \end{tabular}
-
+\caption{Module Hierarchy}
+\label{TblMH}
+\end{table}
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \begin{frame}
-\frametitle{Display Point Masses Module Semantics}
+\frametitle{Example Modules from SWHS}
 
-\textbf{Environment Variables}\\
-$\mathit{win}:$ 2D sequence of pixels displayed within a web-browser \\
+\textbf{Hardware Hiding Modules}
 
-\noindent DisplayPointMassesApplet():
-\begin{itemize}
-\item transition: The state of the abstract object ListPointMasses is modified as follows:\\
-ListPointMasses.init()\\
-ListPointMasses.add(0, PointMassT(20, 20, 10)\\
-ListPointMasses.add(1, PointMassT(120, 200, 20)\\
-...
-\end{itemize}
-
-\noindent paint():
-\begin{itemize}
-\item transition $win := $ Modify window so that the point masses in ListPointMasses 
-are plotted as circles.  The centre of each circles should be the corresponding x and y coordinates and the radius should
-be the mass of the point mass.
-\end{itemize}
+\begin{description}
+\item[Secrets:]The data structure and algorithm used to implement the virtual
+  hardware.
+\item[Services:]Serves as a virtual hardware used by the rest of the
+  system. This module provides the interface between the hardware and the
+  software. So, the system can use it to display outputs or to accept inputs.
+\item[Implemented By:] OS
+\end{description}
 
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
 \begin{frame}
-\frametitle{Assignment 3 Vector Module}
+\frametitle{Example Modules from SWHS}
 
-\textbf {Exported Access Programs}\\
-~\newline
-\begin{tabular}{| l | l | l | p{0.75in} |}
-\hline
-\textbf{Routine name} & \textbf{In} & \textbf{Out} & \textbf{Exceptions}\\
-\hline
-new vectorT & real $\rightarrow$ real & vectorT & ~\\
-\hline
-getf & ~ & real $\rightarrow$ real & ~\\
-\hline
-eval & real, real, integer & sequence of real & deltaNeg, nstepsNeg\\
-\hline
-evalPrint & real, real, integer & ~ & deltaNeg, nstepsNeg\\
-\hline
-\end{tabular}
+\textbf{Input Verification Module}
+
+\begin{description}
+\item[Secrets:] The rules for the physical and software constraints.
+\item[Services:] Verifies that the input parameters comply with physical and
+  software constraints. Throws an error if a parameter violates a physical
+  constraint. Throws a warning if a parameter violates a software constraint.
+\item[Implemented By:] SWHS
+\end{description}
 
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \begin{frame}
-\frametitle{Vector Module Semantics}
+\frametitle{Example Modules from SWHS}
 
-\textbf{Environment Variables}\\
-$\mathit{screen}$ : two dimensional sequence of positions on the screen, which each position holding a character\\
-~\newline
-\textbf{State Variables}\\
-$f$: real $\rightarrow$ real\\
-~\newline
-\textbf{Access Routine Semantics}\\
-\noindent eval ($\mathit{startx}, \mathit{deltax}, \mathit{nsteps}$):
-\begin{itemize}
-\item output: $out := < f(\mathit{startx}), f(\mathit{startx} + \mathit{deltax}), f(\mathit{startx} + 2 \cdot \mathit{deltax}), ...
-, f(\mathit{startx} + \mathit{nsteps} \cdot \mathit{deltax})>$
-\item exception: $exc := ((\mathit{deltax} < 0) \Rightarrow  \mbox{deltaNeg} | (\mathit{nsteps} < 0) \Rightarrow
-\mbox{nstepsNeg})$
-\end{itemize}
+\textbf{ODE Solver Module}
+
+\begin{description}
+\item[Secrets:] The algorithm to solve a system of first order ODEs.
+\item[Services:] Provides solvers that take the governing equation, initial
+  conditions, and numerical parameters, and solve them.
+\item[Implemented By:] Matlab
+\end{description}
 
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-\begin{frame}
-\frametitle{Vector Module Semantics Continued}
+\begin{frame}[plain, fragile]
 
-\noindent evalPrint ($\mathit{startx}, \mathit{deltax}, \mathit{nsteps}$):
-\begin{itemize}
-\item transition: The state of $\mathit{screen}$ is modified so that the sequence returned by eval ($\mathit{startx}$,
-$\mathit{deltax}$, $\mathit{nsteps}$) is displayed.
-\item exception: $exc := ((\mathit{deltax} < 0) \Rightarrow  \mbox{deltaNeg} | (\mathit{nsteps} < 0) \Rightarrow
-\mbox{nstepsNeg})$
-\end{itemize}
+\frametitle{SWHS Uses Hierarchy}
+
+\begin{center}
+\includegraphics[scale=0.55]{UsesHierarchy.pdf}
+\end{center}
 
 \end{frame}
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \begin{frame}
 \frametitle{Dr.\ v.\ Mohrenschildt's Maze Tracing Robot Example}
@@ -254,7 +238,8 @@ $\mathit{deltax}$, $\mathit{nsteps}$) is displayed.
 \frametitle{Maze Tracing Robot Expected Changes}
 
 \begin{itemize}
-\item Changes to the geometry of the robot such that the mapping from a position to the robot inputs is different
+\item Changes to the geometry of the robot such that the mapping from a position
+  to the robot inputs is different
 \item Changes to the interface to the robot
 \item Changes to the format of the maze
 \item Changes to any constant values
@@ -306,20 +291,23 @@ $\mathit{deltax}$, $\mathit{nsteps}$) is displayed.
 \begin{itemize}
 \item \structure<1>{Module name:} control
 \begin{itemize}
-\item \structure<1>{Secret:} how the arm moves from position to position and how the buttons are checked
+\item \structure<1>{Secret:} how the arm moves from position to position and how
+  the buttons are checked
 \item \structure<1>{Service:} controls the movement of the arm
 \item \structure<1>{Module prefix:} cn\_
 \end{itemize}
 \item \structure<1>{Module name:} geometry
 \begin{itemize}
-\item \structure<1>{Secret:} how the calculations from cell coords to robot coords are performed
+\item \structure<1>{Secret:} how the calculations from cell coords to robot
+  coords are performed
 \item \structure<1>{Service:} handles geometric positioning of the arm
 \item \structure<1>{Module prefix:} gm\_
 \end{itemize}
 \item \structure<1>{Module name:} hardware
 \begin{itemize}
 \item \structure<1>{Secret:} how it interfaces with the robot
-\item \structure<1>{Service:} handles hardware aspects of arm (movement and button checking)
+\item \structure<1>{Service:} handles hardware aspects of arm (movement and
+  button checking)
 \item \structure<1>{Module prefix:} hw\_
 \end{itemize}
 \end{itemize}
@@ -332,8 +320,10 @@ $\mathit{deltax}$, $\mathit{nsteps}$) is displayed.
 \begin{itemize}
 \item \structure<1>{Module name:} types\_constants
 \begin{itemize}
-\item \structure<1>{Secret:} how the data structures are defined and constants defined
-\item \structure<1>{Service:} provides standard variable types and constants to modules
+\item \structure<1>{Secret:} how the data structures are defined and constants
+  defined
+\item \structure<1>{Service:} provides standard variable types and constants to
+  modules
 \end{itemize}
 \end{itemize}
 \end{frame}
@@ -410,8 +400,8 @@ cell = tuple of (x: integer, y: integer)
 % there could be one related to maximum size of the map
 ~\newline
 \textbf{Assumptions}\\
-~\newline
-ms\_get\_maze\_start and ms\_get\_maze\_end are not called until after the corresponding set routines have been called.
+~\newline ms\_get\_maze\_start and ms\_get\_maze\_end are not called until after
+the corresponding set routines have been called.
 
 \end{frame}
 
@@ -520,7 +510,6 @@ ms\_get\_maze\_start and ms\_get\_maze\_end are not called until after the corre
 \frametitle{Additional Specifications for Determining the Path}
 
 pathT = sequence of cell\\
-~\newline
 
 \noindent validPath : pathT $\rightarrow$ boolean
 \begin{itemize}