resolve issue #35

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?
 
@@ -277,34 +279,41 @@ Questions - rewrite isInBounds not assuming ascending
 
 \newpage
 
-\section* {Curve Interpolation ADT Module}
+\section* {Curve ADT Module}
 
 \subsection*{Template Module}
 
-CurveInterpADT
+CurveADT
 
 \subsection* {Uses}
 
-SeqServicesModule for isAscending, interp1d and index
+SeqServicesModule
 
 \subsection* {Syntax}
 
+\subsubsection* {Exported Constants}
+
+MAX\_ORDER = 2
+
 \subsubsection* {Exported Types}
 
-CurveInterpT = ?
+CurveT = ?
 
 \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 CurveT & $X: \mathbb{R}^n$, $Y: \mathbb{R}^n$, $i: \mathbb{N}$ &
+                                                                           CurveT & 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}
@@ -323,17 +333,19 @@ None
 
 \subsubsection* {Assumptions}
 
-None
+The user will not request function evaluations that would cause the
+interpolation to select index values outside of where the function is defined.
 
 \subsubsection* {Access Routine Semantics}
 
-\noindent new CurveInterpT($X, Y$):
+\noindent new CurveT($X, Y$):
 \begin{itemize}
-\item transition: $\mbox{minx}, \mbox{maxx}, f := X_0, X_{|X|-1}, (\lambda v:
-  \mbox{interp}(X, Y, v))$
+\item transition: $\mbox{minx}, \mbox{maxx}, o, f := X_0, X_{|X|-1}, i, (\lambda v:
+  \mbox{interp}(X, Y, o, v))$
 
 \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 +360,12 @@ 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 +374,12 @@ 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: $\mathbb{R}^n \times \mathbb{R}^n \times \mathbb{N} \times \mathbb{R}
+\rightarrow \mathbb{R}$\\
+
+\noindent interp($X$, $Y$, $o$, $v$) $$\equiv (o=1 \Rightarrow \mbox{interpLin}(X_i, Y_i,
+X_{i+1}, Y_{i+1}, v) | o = 2 \Rightarrow \mbox{interpQuad}(X_{i-1}, Y_{i-1}, X_i, Y_i, X_{i+1},
+Y_{i+1}, v) )$$  where $i = \mbox{index}(X, v)$\\
 
 \newpage
 
@@ -366,11 +387,11 @@ where $i = \mbox{index}(X, v)$\\
 
 \subsection* {Module}
 
-DataModule
+Data
 
 \subsection* {Uses}
 
-CurveInterpT, SeqServicesModule for interp1d and index
+CurveADT for CurveT, SeqServices for interpLin and index
 
 \subsection* {Syntax}
 
@@ -386,11 +407,11 @@ MAX\_SIZE = 10
 \hline
 Data\_init & ~ & ~ & ~\\
 \hline
-Data\_add & c: CurveInterpT, $z: \mathbb{R}$ & ~ & Full, IndepVarNotAscending\\
+Data\_add & s: CurveT, $z: \mathbb{R}$ & ~ & Full, IndepVarNotAscending\\
 \hline
-eval & $x: \mathbb{R}, z: \mathbb{R}$ & ~ & ~\\
+Data\_eval & $x: \mathbb{R}, z: \mathbb{R}$ & ~ & ~\\
 \hline
-slice & $x: \mathbb{R}$ & CurveInterpT & ~\\
+Data\_slice & $x: \mathbb{R}$ & CurveT & ~\\
 \hline
 
 \end{tabular}
@@ -399,12 +420,12 @@ slice & $x: \mathbb{R}$ & CurveInterpT & ~\\
 
 \subsubsection* {State Variables}
 
-$s$: sequence of CurveInterpT\\
+$S$: sequence of CurveT\\
 $Z$: sequence of $\mathbb{R}$
 
 \subsubsection* {State Invariant}
 
-$| s | \leq \mbox{MAX\_SIZE}$\\
+$| S | \leq \mbox{MAX\_SIZE}$\\
 $| Z | \leq \mbox{MAX\_SIZE}$
 
 \subsubsection* {Assumptions}
@@ -415,29 +436,29 @@ Data\_init() is called before any other access program.
 
 Data\_init():
 \begin{itemize}
-\item transition: $s, Z := < >, <>$
+\item transition: $S, Z := < >, <>$
 \item exception: none
 \end{itemize}
 
-\noindent Data\_add($c, z$):
+\noindent Data\_add($s, z$):
 \begin{itemize}
-\item transition: $s, Z := s || <c>, Z || <z>$
-\item exception: $exc := (|s| = \mbox{MAX\_SIZE} \Rightarrow \mbox{Full} | z
+\item transition: $S, Z := S || <s>, Z || <z>$
+\item exception: $exc := (|S| = \mbox{MAX\_SIZE} \Rightarrow \mbox{Full} | z
   \leq Z_{|Z|-1} \Rightarrow \mbox{IndepVarNotAscending})$
 \end{itemize}
 
 \noindent Data\_eval($x, z$):
 \begin{itemize}
-\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 output: $out := \mbox{interpLin}(Z_j, S_j.\mbox{eval}(x), Z_{j+1},
+  S_{j+1}.\mbox{eval}(x), z)$, where $j = \mbox{index}(Z, z)$
 \item exception:  $exc := (\neg \mbox{isInBounds}(Z, z) \Rightarrow \mbox{OutOfDomain})$
 \end{itemize}
 
 \noindent Data\_slice($x$):
 \begin{itemize}
-\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
+\item output: $out := \mbox{CurveT}(Z, Y)$, 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}
@@ -448,7 +469,7 @@ Data\_init():
 
 \subsection* {Module}
 
-SeqServicesModule
+SeqServices
 
 \subsection* {Uses}
 
@@ -466,11 +487,15 @@ None
 \hline
 \textbf{Routine name} & \textbf{In} & \textbf{Out} & \textbf{Exceptions}\\
 \hline
-isAscending & $x: \mathbb{R}^n$ & $\mathbb{B}$ & ~\\
+isAscending & $X: \mathbb{R}^n$ & $\mathbb{B}$ & ~\\
 \hline
-isInBounds & $x: \mathbb{R}^n, \mathbb{R}$ & $\mathbb{B}$ & ~\\
+isInBounds & $X: \mathbb{R}^n, x: \mathbb{R}$ & $\mathbb{B}$ & ~\\
+\hline
+interpLin & $x_1: \mathbb{R}, y_1: \mathbb{R}, x_2: \mathbb{R}, y_2: \mathbb{R},
+           x: \mathbb{R}$ & $\mathbb{R}$ & ~\\
 \hline
-interp1d & $x_1: \mathbb{R}, y_1: \mathbb{R}, x_2: \mathbb{R}, y_2: \mathbb{R},
+interpQuad & $ x_0: \mathbb{R}, y_0: \mathbb{R},
+           x_1: \mathbb{R}, y_1: \mathbb{R}, x_2: \mathbb{R}, y_2: \mathbb{R},
            x: \mathbb{R}$ & $\mathbb{R}$ & ~\\
 \hline
 index & $X: \mathbb{R}^n, x: \mathbb{R}$ & $\mathbb{N}$ & ~\\
@@ -495,9 +520,9 @@ None, unless noted with a particular access program
 
 \subsubsection* {Access Routine Semantics}
 
-\noindent isAscending($x$)
+\noindent isAscending($X$)
 \begin{itemize}
-\item output: $out := \exists(i | i \in [0..|x|-2] : x_{i+1} \leq x_i)$
+\item output: $out := \neg \exists(i | i \in [0..|X|-2] : X_{i+1} \leq X_i)$
 \item exception: none
 \end{itemize}
 
@@ -507,12 +532,19 @@ 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($x_0, y_0, x_1, y_1, x_2, y_2, x$) \textit{\# assuming isAscending is True}
+\begin{itemize}
+\item output: $out := y_1 + \frac{y_2 - y_0}{x_2-x_0} (x - x_1) + \frac{y_2 - 2 y_1 + y_0}{2
+  (x_2-x_1)^2} (x - x_1)^2$
+\item exception: none
+\end{itemize}
+
 \noindent index($X, x$) \textit{\# assuming isAscending is True and isInBounds
   is True}
 \begin{itemize}

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

Tutorials/T05-PyUnit/src/test_circles.py

@@ -25,4 +25,4 @@ class TestCircles:
         assert self.circle.xcoord() == 1
 
     def test_xcoord_are_not_equal(self):
-        assert not(self.circle.xcoord() != 1)
\ No newline at end of file
+        assert self.circle.xcoord() != 2
\ No newline at end of file