Merge branch 'master' of https://gitlab.cas.mcmaster.ca/smiths/se2aa4_cs2me3

Assignments/A2/A2.tex

@@ -201,6 +201,13 @@ on the first deadline will be the ones that are graded.
 
 Don't have to doxygen test driver program.
 
+Questions - rewrite isInBounds not assuming ascending
+- why isInBounds for Data, not for CurveT?
+
+- maybe add derivatives? integration?
+
+- explain index notation and notation for types
+
 \begin{enumerate}
 \item Your git repo will be organizes with the following directories at the
   top level: {\tt A1}, {\tt A2}, {\tt A3}, and {\tt A4}. 
@@ -244,7 +251,7 @@ Don't have to doxygen test driver program.
 \begin{itemize}
 \item The exceptions in the specification should be implemented via Python
   exceptions.  Your exceptions should have exactly the same name as given in the
-  specification (FULL, EMPTY).  Your exceptions should inherit from the
+  specification (Full, EMPTY).  Your exceptions should inherit from the
   Exception class and they should only be used with one argument, a string
   explaining what problem has occurred.
 \item For the Python implementation of the abstract module, your access programs
@@ -270,21 +277,21 @@ Don't have to doxygen test driver program.
 
 \newpage
 
-\section* {Point ADT Module}
+\section* {Curve Interpolation ADT Module}
 
 \subsection*{Template Module}
 
-pointADT
+CurveInterpADT
 
 \subsection* {Uses}
 
-N/A
+SeqServicesModule for isAscending, interp1d and index
 
 \subsection* {Syntax}
 
 \subsubsection* {Exported Types}
 
-PointT = ?
+CurveInterpT = ?
 
 \subsubsection* {Exported Access Programs}
 
@@ -292,204 +299,84 @@ PointT = ?
 \hline
 \textbf{Routine name} & \textbf{In} & \textbf{Out} & \textbf{Exceptions}\\
 \hline
-new PointT & real, real & PointT & ~\\
+new CurveInterpT & $X: \mathbb{R}^n$, $Y: \mathbb{R}^n$ & CurveInterpT & IndepVarNotAscending\\
 \hline
-xcrd & ~ & real & ~\\
+minD & ~ & $\mathbb{R}$ & ~\\
 \hline
-ycrd & ~ & real & ~\\
+maxD & ~ & $\mathbb{R}$ & ~\\
 \hline
-dist & PointT & real & ~\\
+eval & $x: \mathbb{R}$ & $\mathbb{R}$ & OutOfDomain\\
 \hline
-rot & real & ~ & ~\\
-\hline
-
 \end{tabular}
 
 \subsection* {Semantics}
 
 \subsubsection* {State Variables}
 
-$xc$: real\\
-$yc$: real
+minx: $\mathbb{R}$\\
+maxx: $\mathbb{R}$\\
+f: $\mathbb{R} \rightarrow \mathbb{R}$
 
 \subsubsection* {State Invariant}
-None
 
-\subsubsection* {Assumptions}
-None
-
-\subsubsection* {Access Routine Semantics}
-
-new PointT ($x, y$):
-\begin{itemize}
-\item transition: $xc, yc := x, y$
-\item output: $out := \mathit{self}$
-\item exception: none
-\end{itemize}
-
-\noindent xcrd:
-\begin{itemize}
-\item output: $out := xc$
-\item exception: none
-\end{itemize}
-
-\noindent ycrd:
-\begin{itemize}
-\item output: $out := yc$
-\item exception: none
-\end{itemize}
-
-\noindent dist($p$):
-\begin{itemize}
-\item output:
-  $out := \sqrt{(xc - p.\mbox{xcrd()})^2 + (yc - p.\mbox{ycrd()})^2}$
-\item exception: none
-\end{itemize}
-
-\noindent rot($\phi$):
-\begin{itemize}
-\item $\phi$ is in radians
-\item transition: 
-
-$$\left [
-\begin{array}{c}
-xc\\
-yc\\
-\end{array}
-\right ] :=
-\left [
-\begin{array}{r r}
-\cos \phi & - \sin \phi\\
-\sin \phi & \cos \phi\\
-\end{array}
-\right ]
-\left [
-\begin{array}{c}
-xc\\
-yc\\
-\end{array}
-\right ]
-$$
-
-\item exception: none
-\end{itemize}
-
-\newpage
-
-\section* {Line Module}
-
-\subsection* {Template Module}
-
-lineADT
-
-\subsection* {Uses}
-
-pointADT
-
-\subsection* {Syntax}
-
-\subsubsection* {Exported Types}
-
-LineT = ?
-
-\subsubsection* {Exported Access Programs}
-
-\begin{tabular}{| l | l | l | l |}
-\hline
-\textbf{Routine name} & \textbf{In} & \textbf{Out} & \textbf{Exceptions}\\
-\hline
-new LineT & PointT, PointT & LineT & ~\\
-\hline
-beg & ~ & PointT & ~\\
-\hline
-end & ~ & PointT & ~\\
-\hline 
-len & ~ & real & ~\\
-\hline
-mdpt & ~ & PointT & ~\\
-\hline
-rot & real & ~ & ~\\
-\hline
-\end{tabular}
-
-\subsection* {Semantics}
-
-\subsubsection* {State Variables}
-
-$b$: PointT\\
-$e$: PointT
-
-\subsubsection* {State Invariant}
 None
 
 \subsubsection* {Assumptions}
+
 None
 
 \subsubsection* {Access Routine Semantics}
 
-\noindent new LineT ($p_1, p_2$):
+\noindent new CurveInterpT($X, Y$):
 \begin{itemize}
-\item transition: $b, e := p_1, p_2$
-\item output: $out := \mathit{self}$
-\item exception: none
-\end{itemize}
+\item transition: $\mbox{minx}, \mbox{maxx}, f := X_0, X_{|X|-1}, (\lambda v:
+  \mbox{interp}(X, Y, v))$
 
-\noindent beg:
-\begin{itemize}
-\item output: $out := b$
-\item exception: none
+\item output: $out := \mbox{self}$
+\item exception: $(\neg \mbox{isAscending}(X) \Rightarrow \mbox{IndepVarNotAscending})$
 \end{itemize}
 
-\noindent end:
+\noindent minD():
 \begin{itemize}
-\item output: $out := e$
-\item exception: none
+\item output: $out := \mbox{minx}$
+\item exception: None
 \end{itemize}
 
-\noindent len:
+\noindent maxD():
 \begin{itemize}
-\item output: $out := b.\mbox{dist}(e)$
-\item exception: none
+\item output: $out := \mbox{maxx}$
+\item exception: None
 \end{itemize}
 
-\noindent mdpt:
+\noindent eval($x$):
 \begin{itemize}
-\item output:
-  $$out := \mbox{new~} \mbox{PointT} (\mbox{avg}(b.\mbox{xcrd()},
-  e.\mbox{xcrd()}), \mbox{avg}(b.\mbox{ycrd()}, e.\mbox{ycrd()}))$$
-\item exception: none
+\item output: $out := f(x)$
+\item exception: $(\neg(\mbox{minx} \leq x \leq \mbox{maxx}) \Rightarrow \mbox{OutOfDomain}))$
 \end{itemize}
 
-\noindent rot ($\phi$):
-\begin{itemize}
-\item $\phi$ is in radians
-\item transition: $b.\mbox{rot}(\phi), e.\mbox{rot}(\phi)$
-\item exception: none
-\end{itemize}
+\subsection*{Local Functions}
 
-\subsubsection*{Local Functions}
-
-avg: real $\times$ real $\rightarrow$ real
-
-\noindent avg($x_1, x_2$) $\equiv \frac{x_1 + x_2}{2}$
+interp: $\mathbb{R}^n \times \mathbb{R}^n \rightarrow \mathbb{R}$\\
+interp($X$, $Y$, $v$) $\equiv \mbox{interp1d}(X_i, Y_i, X_{i+1}, Y_{i+1}, v)$
+where $i = \mbox{index}(X, v)$\\
 
 \newpage
 
-\section* {Circle Module}
+\section* {Data Module}
 
-\subsection* {Template Module}
+\subsection* {Module}
 
-circleADT
+DataModule
 
 \subsection* {Uses}
 
-pointADT, lineADT
+CurveInterpT, SeqServicesModule for interp1d and index
 
 \subsection* {Syntax}
 
-\subsubsection* {Exported Types}
+\subsubsection* {Exported Constants}
 
-CircleT = ?
+MAX\_SIZE = 10
 
 \subsubsection* {Exported Access Programs}
 
@@ -497,19 +384,13 @@ CircleT = ?
 \hline
 \textbf{Routine name} & \textbf{In} & \textbf{Out} & \textbf{Exceptions}\\
 \hline
-new CircleT & PointT, real & CircleT & ~\\
+Data\_init & ~ & ~ & ~\\
 \hline
-cen & ~ & PointT & ~\\
+Data\_add & c: CurveInterpT, $z: \mathbb{R}$ & ~ & Full, IndepVarNotAscending\\
 \hline
-rad & ~ & real & ~\\
-\hline 
-area & ~ & real & ~\\
-\hline 
-intersect & CircleT & boolean & ~\\
+eval & $x: \mathbb{R}, z: \mathbb{R}$ & ~ & ~\\
 \hline
-connection & CircleT & LineT & ~\\
-\hline
-force & real $\rightarrow$ real & CircleT $\rightarrow$ real & ~\\
+slice & $x: \mathbb{R}$ & CurveInterpT & ~\\
 \hline
 
 \end{tabular}
@@ -518,83 +399,66 @@ force & real $\rightarrow$ real & CircleT $\rightarrow$ real & ~\\
 
 \subsubsection* {State Variables}
 
-$c$: PointT\\
-$r$: real
+$s$: sequence of CurveInterpT\\
+$Z$: sequence of $\mathbb{R}$
 
 \subsubsection* {State Invariant}
-None
 
-\subsubsection* {Assumptions}
-None
+$| s | \leq \mbox{MAX\_SIZE}$\\
+$| Z | \leq \mbox{MAX\_SIZE}$
 
-\subsubsection* {Access Routine Semantics}
+\subsubsection* {Assumptions}
 
-\noindent new CircleT ($\mathit{cin}, \mathit{rin}$):
-\begin{itemize}
-\item transition: $c, r := \mathit{cin}, \mathit{rin}$
-\item output: $out := \mathit{self}$
-\item exception: none
-\end{itemize}
+Data\_init() is called before any other access program.
 
-\noindent cen:
-\begin{itemize}
-\item output: $out := c$
-\item exception: none
-\end{itemize}
-
-\noindent rad:
-\begin{itemize}
-\item output: $out := r$
-\item exception: none
-\end{itemize}
+\subsubsection* {Access Routine Semantics}
 
-\noindent area:
+Data\_init():
 \begin{itemize}
-\item output: $out := \pi r^2$
+\item transition: $s, Z := < >, <>$
 \item exception: none
 \end{itemize}
 
-\noindent intersect($ci$):
+\noindent Data\_add($c, z$):
 \begin{itemize}
-\item output: $\exists ( p: \mbox{PointT} | \mbox{insideCircle}(p, ci) : \mbox{insideCircle}(p, \mathit{self}))$
-\item exception: none
+\item transition: $s, Z := s || <c>, Z || <z>$
+\item exception: $exc := (|s| = \mbox{MAX\_SIZE} \Rightarrow \mbox{Full} | z
+  \leq Z_{|Z|-1} \Rightarrow \mbox{IndepVarNotAscending})$
 \end{itemize}
 
-\noindent connection($ci$):
+\noindent Data\_eval($x, z$):
 \begin{itemize}
-\item output: $out := \mbox{new~} \mbox{LineT} (c, ci.\mathit{cen()})$
-\item exception: none
+\item output: $out := \mbox{interp1d}(z_j, s_j.\mbox{eval}(x), z_{j+1},
+  s_{j+1}.\mbox{eval}(x), z)$, where $j = \mbox{index}(Z, z)$
+\item exception:  $exc := (\neg \mbox{isInBounds}(Z, z) \Rightarrow \mbox{OutOfDomain})$
 \end{itemize}
 
-\noindent force($f$):
+\noindent Data\_slice($x$):
 \begin{itemize}
-\item output: $out := \lambda x \rightarrow \mathit{self}.\mbox{area()} \cdot
-  x.\mbox{area()} \cdot f(\mathit{self}.\mbox{connection}(x).\mbox{len}())$
-\item exception: none
+\item output: $out := \mbox{CurveInterpT}(Z, Y)$, where
+  $Y = ||(i: \mathbb{N}| i \in [0 .. |Z|-1] : \langle s_i.\mbox{eval}(x) \rangle
+  )$ or $Y = \mbox{ map } \mbox{eval}(x) \mbox{ } s$ \textit{\# in both cases
+    there is an abuse of notation}
+\item exception: None
 \end{itemize}
 
-\subsubsection*{Local Functions}
-insideCircle: PointT $\times$ CircleT $\rightarrow$ boolean
-
-\noindent insideCircle($p, c$) $\equiv p.\mbox{dist}(c.\mbox{cen()}) \leq c.\mbox{rad()}$
-
-\newpage
+%\subsubsection*{Local Functions}
 
-\section* {Deque Of Circles Module}
+\section* {Sequence Services Module}
 
 \subsection* {Module}
 
-DequeCircleModule
+SeqServicesModule
 
 \subsection* {Uses}
 
-circleADT
+None
 
 \subsection* {Syntax}
 
 \subsubsection* {Exported Constants}
 
-MAX\_SIZE = 20
+None
 
 \subsubsection* {Exported Access Programs}
 
@@ -602,29 +466,15 @@ MAX\_SIZE = 20
 \hline
 \textbf{Routine name} & \textbf{In} & \textbf{Out} & \textbf{Exceptions}\\
 \hline
-Deq\_init & ~ & ~ & ~\\
-\hline
-Deq\_pushBack & CircleT & ~ & FULL\\
-\hline
-Deq\_pushFront & CircleT & ~ & FULL\\
-\hline
-Deq\_popBack & ~ & ~ & EMPTY\\
-\hline
-Deq\_popFront & ~ & ~ & EMPTY\\
-\hline
-Deq\_back & ~ & CircleT & EMPTY\\
-\hline
-Deq\_front & ~ & CircleT & EMPTY\\
-\hline
-Deq\_size & ~ & integer & ~\\
+isAscending & $x: \mathbb{R}^n$ & $\mathbb{B}$ & ~\\
 \hline
-Deq\_disjoint & ~ & boolean & EMPTY\\
+isInBounds & $x: \mathbb{R}^n, \mathbb{R}$ & $\mathbb{B}$ & ~\\
 \hline
-Deq\_sumFx & real $\rightarrow$ real & real & EMPTY\\
+interp1d & $x_1: \mathbb{R}, y_1: \mathbb{R}, x_2: \mathbb{R}, y_2: \mathbb{R},
+           x: \mathbb{R}$ & $\mathbb{R}$ & ~\\
 \hline
-Deq\_totalArea & ~ & real & EMPTY\\
-\hline
-Deq\_averageRadius & ~ & real & EMPTY\\
+index & $X: \mathbb{R}^n, x: \mathbb{R}$ & $\mathbb{N}$ & ~\\
+
 \hline
 
 \end{tabular}
@@ -632,107 +482,42 @@ Deq\_averageRadius & ~ & real & EMPTY\\
 \subsection* {Semantics}
 
 \subsubsection* {State Variables}
-$s$: sequence of CircleT
+
+None
 
 \subsubsection* {State Invariant}
-$| s | \leq \mbox{MAX\_SIZE}$
+
+None
 
 \subsubsection* {Assumptions}
-Deq\_init() is called before any other access program.
+
+None, unless noted with a particular access program
 
 \subsubsection* {Access Routine Semantics}
 
-Deq\_init():
+\noindent isAscending($x$)
 \begin{itemize}
-\item transition: $s := < >$
+\item output: $out := \exists(i | i \in [0..|x|-2] : x_{i+1} \leq x_i)$
 \item exception: none
 \end{itemize}
 
-\noindent Deq\_pushBack($c$):
-\begin{itemize}
-\item transition: $s := s || <c>$
-\item exception: $exc := (|s| = \mbox{MAX\_SIZE} \Rightarrow  \mbox{FULL})$
-\end{itemize}
-
-\noindent Deq\_pushFront($c$):
-\begin{itemize}
-\item transition: $s := <c> || s $
-\item exception:  $exc := (|s| = \mbox{MAX\_SIZE} \Rightarrow  \mbox{FULL})$
-\end{itemize}
-
-\noindent Deq\_popBack():
-\begin{itemize}
-\item transition: $s := s[0..|s| - 2]$
-\item exception: $exc := (|s| = 0 \Rightarrow \mbox{EMPTY})$
-\end{itemize}
-
-\noindent Deq\_popFront():
-\begin{itemize}
-\item transition: $s := s[1..|s| - 1]$
-\item exception: $exc := (|s| = 0 \Rightarrow \mbox{EMPTY})$
-\end{itemize}
-
-\noindent Deq\_back():
+\noindent isInBounds($X, x$) \textit{\# assuming isAscending is True}
 \begin{itemize}
-\item output: $out := s[|s| - 1]$
-\item exception: $exc := (|s| = 0 \Rightarrow \mbox{EMPTY})$
-\end{itemize}
-
-\noindent Deq\_front():
-\begin{itemize}
-\item output: $out := s[0]$
-\item exception: $exc := (|s| = 0 \Rightarrow \mbox{EMPTY})$
-\end{itemize}
-
-\noindent Deq\_size():
-\begin{itemize}
-\item output: $out := | s |$
+\item output: $out := X_0 \leq x \leq X_{|X|-1}$
 \item exception: none
 \end{itemize}
 
-\noindent Deq\_disjoint():
-\begin{itemize}
-\item output $$out := \forall(i, j:\mathbb{N} | i \in [0 .. |s| -1] \wedge j \in [0 .. |s| -1] \wedge i \neq j:\neg  
-s[i].\mbox{intersect}(s[j]))$$
-\item exception: $exc := (|s| = 0 \Rightarrow \mbox{EMPTY})$
-\end{itemize}
-
-\noindent Deq\_sumFx(f):
+\noindent interp1d($x_1, y_1, x_2, y_2, x$) \textit{\# assuming isAscending is True}
 \begin{itemize}
-\item output $$out := +(i: \mathbb{N} | i \in ([1 .. |s|-1]):
-  \mbox{Fx}(f, s[i], s[0]))$$
-\item exception: $exc := (|s| = 0 \Rightarrow \mbox{EMPTY})$
-\end{itemize}
-
-\noindent Deq\_totalArea():
-\begin{itemize}
-\item output $$out := ?$$ [The total area is the sum of the area of all of the
-  circles in the deque.  You do not need to worry about overlap between
-  circles.  The assignment asks you to provide the missing
-  equation, but you do not have to implement this access program.]
-\item exception: $exc := (|s| = 0 \Rightarrow \mbox{EMPTY})$
+\item output: $out := \frac{(y_2 - y_1)}{(x_2-x_1)} (x - x_1) + y_1$
+\item exception: none
 \end{itemize}
 
-\noindent Deq\_averageRadius():
+\noindent index($X, x$) \textit{\# assuming isAscending is True and isInBounds
+  is True}
 \begin{itemize}
-\item output $$out := ?$$ [The assignment asks you to provide the missing
-  equation, but you do not have to implement this access program.]
-\item exception: $exc := (|s| = 0 \Rightarrow \mbox{EMPTY})$
+\item output: $out := i \mbox{ such that } X_i \leq x \leq X_{i+1}$
+\item exception: none
 \end{itemize}
 
-\subsubsection*{Local Functions}
-Fx: (real $\rightarrow$ real) $\times$ CircleT $\times$ CircleT $\rightarrow$ real
-
-\noindent Fx($f, ci, cj$) $\equiv \mbox{xcomp}(ci.\mbox{force}(f) (cj), ci, cj)$
-~\newline
-
-\noindent xcomp: real $\times$ CircleT $\times$ CircleT $\rightarrow$ real
-~\newline
-
-\noindent $$\mbox{xcomp}(F, ci, cj)
-\equiv F \left [ 
-\frac{ci.\mbox{cen()}.\mbox{xcrd()} -
-  cj.\mbox{cen()}.\mbox{xcrd()}} {ci.\mbox{connection}(cj).\mbox{len}()}
-\right ]$$
-
 \end {document}

Lectures/L13_ModuleDecomposition/ModuleDecomposition.tex

@@ -86,7 +86,7 @@ TBD
 
 \item Midterm exam
 \begin{itemize}
-\item Wednesday, February 29, 7:00 pm
+\item Wednesday, February 28, 7:00 pm
 \item 90 minute duration
 \item Multiple choice - 30--40 questions
 \end{itemize}