Updates to L13 and A2

Assignments/A2/A2.tex

@@ -203,6 +203,8 @@ Don't have to doxygen test driver program.
 
 Questions - rewrite isInBounds not assuming ascending
 - why isInBounds for Data, not for CurveT?
+- question about what is needed for cubic
+- what is needed for regression?
 
 - maybe add derivatives? integration?
 
@@ -289,22 +291,29 @@ SeqServicesModule for isAscending, interp1d and index
 
 \subsection* {Syntax}
 
+\subsubsection* {Exported Constants}
+
+MAX\_ORDER = 2
+
 \subsubsection* {Exported Types}
 
 CurveInterpT = ?
 
 \subsubsection* {Exported Access Programs}
 
-\begin{tabular}{| l | l | l | l |}
+\begin{tabular}{| l | l | l | p{5cm} |}
 \hline
 \textbf{Routine name} & \textbf{In} & \textbf{Out} & \textbf{Exceptions}\\
 \hline
-new CurveInterpT & $X: \mathbb{R}^n$, $Y: \mathbb{R}^n$ & CurveInterpT & IndepVarNotAscending\\
+new CurveInterpT & $X: \mathbb{R}^n$, $Y: \mathbb{R}^n$, $i: \mathbb{N}$ &
+                                                                           CurveInterpT & IndepVarNotAscending,\newline InvalidInterpOrder\\
 \hline
 minD & ~ & $\mathbb{R}$ & ~\\
 \hline
 maxD & ~ & $\mathbb{R}$ & ~\\
 \hline
+order & ~ & $\mathbb{N}$ & ~\\
+\hline
 eval & $x: \mathbb{R}$ & $\mathbb{R}$ & OutOfDomain\\
 \hline
 \end{tabular}
@@ -315,6 +324,7 @@ eval & $x: \mathbb{R}$ & $\mathbb{R}$ & OutOfDomain\\
 
 minx: $\mathbb{R}$\\
 maxx: $\mathbb{R}$\\
+o: $\mathbb{N}$\\
 f: $\mathbb{R} \rightarrow \mathbb{R}$
 
 \subsubsection* {State Invariant}
@@ -329,11 +339,12 @@ None
 
 \noindent new CurveInterpT($X, Y$):
 \begin{itemize}
-\item transition: $\mbox{minx}, \mbox{maxx}, f := X_0, X_{|X|-1}, (\lambda v:
+\item transition: $\mbox{minx}, \mbox{maxx}, o, f := X_0, X_{|X|-1}, i, (\lambda v:
   \mbox{interp}(X, Y, v))$
 
 \item output: $out := \mbox{self}$
-\item exception: $(\neg \mbox{isAscending}(X) \Rightarrow \mbox{IndepVarNotAscending})$
+\item exception: $(\neg \mbox{isAscending}(X) \Rightarrow
+  \mbox{IndepVarNotAscending} | i \notin [1..\mbox{MAX\_ORDER}] \Rightarrow \mbox{InvalidInterpOrder})$
 \end{itemize}
 
 \noindent minD():
@@ -348,6 +359,12 @@ None
 \item exception: None
 \end{itemize}
 
+\noindent order():
+\begin{itemize}
+\item output: $out := \mbox{o}$
+\item exception: None
+\end{itemize}
+
 \noindent eval($x$):
 \begin{itemize}
 \item output: $out := f(x)$
@@ -356,9 +373,12 @@ None
 
 \subsection*{Local Functions}
 
-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 $i = \mbox{index}(X, v)$\\
+interp: $\mathbb{R}^n \times \mathbb{R}^n \times \mathbb{R} \times \mathbb{N}
+\rightarrow \mathbb{R}$\\
+
+\noindent interp($X$, $Y$, $v$, $o$) $$\equiv (o=1 \Rightarrow \mbox{interpLin}(X_i, Y_i,
+X_{i+1}, Y_{i+1}, v) | o = 2 \Rightarrow \mbox{interpQuad}(X_i, Y_i, X_{i+1},
+Y_{i+1}, v) )$$  where $i = \mbox{index}(X, v)$\\
 
 \newpage
 
@@ -507,7 +527,13 @@ None, unless noted with a particular access program
 \item exception: none
 \end{itemize}
 
-\noindent interp1d($x_1, y_1, x_2, y_2, x$) \textit{\# assuming isAscending is True}
+\noindent interpLin($x_1, y_1, x_2, y_2, x$) \textit{\# assuming isAscending is True}
+\begin{itemize}
+\item output: $out := \frac{(y_2 - y_1)}{(x_2-x_1)} (x - x_1) + y_1$
+\item exception: none
+\end{itemize}
+
+\noindent interpQuad($x_1, y_1, x_2, y_2, x$) \textit{\# assuming isAscending is True}
 \begin{itemize}
 \item output: $out := \frac{(y_2 - y_1)}{(x_2-x_1)} (x - x_1) + y_1$
 \item exception: none

Lectures/L13_ModuleDecomposition/ModuleDecomposition.tex

@@ -386,7 +386,7 @@ Example of raising the exception
 
 \begin{frame}
 
-\frametitle{Quality Criteria}
+\frametitle{Quality Criteria (H\&S Section 7.3.2)}
 
 \begin{itemize}
 \item Consistent