Modifications to L16 on Funct Prog continued

Lectures/L16_FunctProgContinued/A2Examples.py

+from CurveADT import *
+from Data import *
+from Load import *
+from Plot import *
+
+X = range(11)
+Y = list(map(lambda x: x**2, X))
+
+c1 = CurveT(X, Y, 1)
+
+print(c1.eval(6.5))
+
+PlotCurve(c1, 50)
+
+c2 = CurveT(X, Y, 2)
+
+print(c2.eval(6.5))
+
+PlotCurve(c2, 5)
+#PlotCurve(c, 50) will look strange because of edge effects
+
+Load('glass.csv')
+
+c3 = Data.getC(9)
+PlotCurve(c3, 50)
+print(Data.eval(18, 34))
+
+c4 = Data.slice(18, 1)
+PlotCurve(c4, 50)
+print(c4.eval(34))
+

Lectures/L16_FunctProgContinued/FunctProgContinued.tex

@@ -56,7 +56,7 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-\begin{frame}
+\begin{frame}[fragile]
 \frametitle{Administrative Details}
 
 \ifDraft  
@@ -69,12 +69,20 @@ TBD
 \item Part 1: February 12, 2018
 \item Partner Files: February 18, 2018
 \item Part 2: March 2, 2018
+\item For floats remember to use pytests
+  \href{https://docs.pytest.org/en/latest/builtin.html#pytest.approx}{approx}
+\item Consider using
+  \href{https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.interp1d.html}
+  {interp1d} - the implementation does not have to follow the spec, it just has
+  to match the specified behaviour
+\item A2 demo
 \end{itemize}
 
 \item Midterm exam
 \begin{itemize}
 \item Wednesday, February 28, 7:00 pm
 \item 90 minute duration
+\item Next week's tutorial will cover a sample midterm
 \end{itemize}
 \end{itemize}
 }
@@ -84,16 +92,21 @@ TBD
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-\begin{frame}
+\begin{frame}[fragile]
 \frametitle{HW: Remove Everything but Uppercase}
 
 Write a function \texttt{removeNonUpperCase(st)} that takes a string
   \texttt{st} and returns the string that results by removing all non upper case
   letters\\
 ~\newline
-\structure<1>{How would you build the sequence of \texttt{['A', 'B', ..., 'Z']}?}\newline
-\uncover<2->{\texttt{[chr(i) for i in range(ord('A'),ord('Z')+1)]}}
-
+\structure<1>{How would you build the sequence of \texttt{['A','B',...,'Z']}?}\newline
+\uncover<2->{\texttt{[chr(i) for i in range(\structure<2>{?, ?})]}}\newline
+\uncover<3->{\texttt{[chr(i) for i in range(ord('A'),ord('Z')+1)]}}
+~\\
+\begin{verbatim}
+def removeNonUpperCase(st):
+   return [c for c in st if (c in upCase)]
+\end{verbatim}
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -151,15 +164,16 @@ list(map(add3, [1, 5, 3, 1, 6]))
 
 \bi
 \item \texttt{lamda} followed by list of arguments: expression
-\item \structure{Write code to add \texttt{'!'} to every string in a list of
+\item \structure<1>{Write code to add \texttt{'!'} to every string in a list of
     strings}
 \ei
-
+\uncover<1>{\structure<1>{\texttt{list(map(?, ["BIFF","BANG","POW"]))}}}\\
+\uncover<2>{\texttt{list(map(lambda s: s+'!', ["BIFF","BANG","POW"]))}}
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-\begin{frame}
+\begin{frame}[fragile]
 \frametitle{Introduce Partial Functions}
 
 \begin{itemize}
@@ -172,9 +186,12 @@ list(map(add3, [1, 5, 3, 1, 6]))
 \item $\mbox{rep}: t \times int \rightarrow [t]$
 \ei
 \item What if we could partially evaluate rep?
-
 \end{itemize}
 
+\begin{verbatim}
+def rep(x, n):
+    return [x for i in range(n)]
+\end{verbatim}
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -224,9 +241,12 @@ map (mapSqr, [[1,2], [3, 4, 5, 6], [7, 8]])
 \end{verbatim}
 
 \bi
-\item \structure{What is the type of \texttt{mapSqr}?}
+\item \structure<1>{What is the type of \texttt{mapSqr}?}\newline
+\uncover<2->{$\mbox{map}: (a \rightarrow b) \times [a] \rightarrow [b]$}\newline
+\uncover<3->{$\mbox{map}: (a \rightarrow b) \times [[int]] \rightarrow [[int]]$}\newline
+\uncover<4->{$\mbox{map}: ([int] \rightarrow [int]) \times [[int]] \rightarrow [[int]]$}\newline
 
-\item \structure{Can you write a function of this type for \texttt{mapSqr}?}
+\item \structure<4>{Can you write a function of this type for \texttt{mapSqr}?}
 \ei
 
 \end{frame}
@@ -255,11 +275,19 @@ map (mapSqr, [[1,2], [3, 4, 5, 6], [7, 8]])
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-\begin{frame}
+\begin{frame}[fragile]
 \frametitle{Filter Example}
 
-Write a filter that takes a list of numbers and returns only the even numbers.
-%\texttt{filter(even, range(1, 11))}
+\structure<1>{Write a filter that takes a list of numbers from 1 to 10 and
+  returns only the even numbers.}
+
+\begin{verbatim}
+def even(x):
+    return x%2==0
+\end{verbatim}
+
+\texttt{filter(func, seq)}\\
+\uncover<2>{\texttt{filter(even, range(1, 11))}}
 
 \end{frame}
 
@@ -276,6 +304,7 @@ Write a filter that takes a list of numbers and returns only the even numbers.
   element
 \item Repeats until completely reduced
 \item \texttt{accum} is the initial value for the accumulator
+\item In Python 3 need \texttt{from functools import reduce}
 \item \structure{How would you use reduce to calculate the sum of the numbers
     from 1 to 100?}
 \item \structure{How about the product?}
@@ -285,6 +314,18 @@ Write a filter that takes a list of numbers and returns only the even numbers.
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \begin{frame}
+\frametitle{Understanding Reduce for Sum}
+
+\bi
+\item \texttt{reduce(lambda x, y: x+y, range(1, 5), 0)}
+\item \texttt{reduce(lambda x, y: x+y, [1, 2, 3, 4, 5], 0)}
+\item \texttt{((((0+1)+2)+3)+4)+5}
+\ei
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}[fragile]
 \frametitle{Standard Deviation}
 
 Write a function \texttt{stdDev(A)} that takes a list of numbers
@@ -292,54 +333,77 @@ Write a function \texttt{stdDev(A)} that takes a list of numbers
 
 $$\sigma = \sqrt{\frac{\sum_{i=0}^{|A|-1} (A_i - \mu)^2}{|A|}}$$
 
+\begin{verbatim}
+from math import sqrt
+from functools import reduce
+def stdDev(A):
+    add = lambda x, y: x+y
+    N = float(len(A))
+    mu = reduce(add, A, 0)/N
+    tot = reduce(add, [(a - mu)**2 for a in A], 0)
+    return sqrt(tot/N)
+
+print(stdDev([13, 23, 12, 44, 55]))
+\end{verbatim}
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-\begin{frame}
+\begin{frame}[fragile]
 \frametitle{And Series}
 
-Write a function \texttt{forall(A)} that takes a list of boolean values
-\texttt{A} and returns $\forall ( i:\mathbb{N} | i \in [0 ..|A|-1] : A_i)$
+\structure<1>{Write a function \texttt{forall(A)} that takes a list of boolean values
+\texttt{A} and returns $\forall ( i:\mathbb{N} | i \in [0 ..|A|-1] : A_i)$}
+
+\begin{verbatim}
+def forall(A):
+    return reduce(?, A, ?)
+
+print(forall([True, True, True, True]))
+print(forall([True, True, True, False]))
+\end{verbatim}
 
+\uncover<2->{\texttt{reduce(lambda x, y: x and y, A, True)}}
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-\begin{frame}
+\begin{frame}[fragile]
 \frametitle{Contains}
 
-Write a function \texttt{contains(x, xs)} that takes a value \texttt{x} and a
-list of values \texttt{xs} and returns $\exists ( y | y \in xs : y = x)$
+\structure<1>{Write a function \texttt{contains(x, xs)} that takes a value \texttt{x} and a
+list of values \texttt{xs} and returns $\exists ( y | y \in xs : y = x)$}
 
-\end{frame}
+\begin{verbatim}
+def contains(x, xs):
+    return reduce(func?, seq?, False)
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+adjectives = ["lazy", "grouchy", "scheming"]
 
-\begin{frame}
-\frametitle{Index Set}
+print(contains(4, [3, 4, 5, 6, 8]))
+print(contains("happy", adjectives))
 
-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{verbatim}
+
+\uncover<2->{\texttt{reduce(lambda a, b: a or b, [y==x for y in xs], False)}}
 
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \begin{frame}
-\frametitle{Index Set}
+\frametitle{Homework: Index Set}
 
 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
+\structure<1>{As a first step, how would you say this mathematically?}\\
 
-$$\mbox{indexSet}(x, B) \equiv \{i : \mathbb{N} | i \in [0 .. |B|-1] \wedge B_i =
-x : i\}$$
+\uncover<2->{$$\mbox{indexSet}(x, B) \equiv \{i : \mathbb{N} | i \in [0 .. |B|-1] \wedge B_i =
+x : i\}$$}\\
 
-How could you use \texttt{indexSet} to calculate \texttt{rank(x, A)}?
+\uncover<3->{How could you use \texttt{indexSet} to calculate \texttt{rank(x, A)}?}\\
 
 \end{frame}
 

Lectures/L16_FunctProgContinued/FunctProgContinued.vrb

-\frametitle{Another Example with Map}
+\frametitle{Contains}
 
-Write a map that takes a 2D list of numbers and returns a 2D list where all
-elements are squared.
+\structure<1>{Write a function \texttt{contains(x, xs)} that takes a value \texttt{x} and a
+list of values \texttt{xs} and returns $\exists ( y | y \in xs : y = x)$}
 
 \begin{verbatim}
-map (mapSqr, [[1,2], [3, 4, 5, 6], [7, 8]])
-\end{verbatim}
+def contains(x, xs):
+    return reduce(func?, seq?, False)
+
+adjectives = ["lazy", "grouchy", "scheming"]
 
-\bi
-\item \structure{What is the type of \texttt{mapSqr}?}
+print(contains(4, [3, 4, 5, 6, 8]))
+print(contains("happy", adjectives))
+
+\end{verbatim}
 
-\item \structure{Can you write a function of this type for \texttt{mapSqr}?}
-\ei
+\uncover<2->{\texttt{reduce(lambda a, b: a or b, [y==x for y in xs], False)}}
 

Lectures/L16_FunctProgContinued/examples.py

@@ -25,8 +25,6 @@ L7 = list(map(lambda s: s+'!', ["BIFF", "BANG", "POW"]))
 
 # Partial Functions
 
-from functools import partial
-
 def power(base, exponent):
     return base ** exponent
 
@@ -60,10 +58,16 @@ def grt3(x):
 
 L8 = filter(grt3, [1,5,3,2,1,6,4,3,2,1])
 L9 = filter(lambda x: x==3, [1,5,3,2,1,6,4,3,2,1])
+
+def even(x):
+    return x%2==0
+
 L10 = filter(even, range(1, 11))
 
 # Reduce
 
+from functools import reduce
+
 reduce(lambda x, y: x+y, range(1, 101), 0)
 
 reduce(lambda x, y: x*y, range(1, 101), 1)
@@ -77,23 +81,25 @@ def stdDev(A):
     tot = reduce(add, [(a - mu)**2 for a in A], 0)
     return sqrt(tot/N)
 
-print stdDev([13, 23, 12, 44, 55])
+print(stdDev([13, 23, 12, 44, 55]))
 
 # And Series
 
 def forall(A):
     return reduce(lambda x, y: x and y, A, True)
 
-print forall([True, True, True, True])
-print forall([True, True, True, False])
+print(forall([True, True, True, True]))
+print(forall([True, True, True, False]))
 
 # Contains
 
 def contains(x, xs):
     return reduce(lambda a, b: a or b, [y==x for y in xs], False)
 
-print contains(4, [3, 4, 5, 6, 8])
-print contains("happy", adjectives)
+adjectives = ["lazy", "grouchy", "scheming"]
+
+print(contains(4, [3, 4, 5, 6, 8]))
+print(contains("happy", adjectives))
 
 def indexSet(x, B):
     return [i for i in range(len(B)) if B[i]==x]

Lectures/L16_FunctProgContinued/examplesPartial.py

@@ -60,9 +60,11 @@ L10 = filter(func?, seq?)
 
 # Reduce
 
-reduce(?)
+from functools import reduce
 
-reduce(?)
+reduce(func, seq, accum)
+
+reduce(func, seq, accum)
 
 # Standard Deviation
 
@@ -70,19 +72,19 @@ from math import sqrt
 def stdDev(A):
     add = lambda x, y: x+y
     N = float(len(A))
-    mu = reduce(?
-    tot = reduce(?
+    mu = reduce(func, seq, accum)
+    tot = reduce(func, seq, accum)
     return sqrt(tot/N)
 
-print stdDev([13, 23, 12, 44, 55])
+print(stdDev([13, 23, 12, 44, 55]))
 
 # And Series
 
 def forall(A):
-    return reduce(?)
+    return reduce(func, seq, accum)
 
-print forall([True, True, True, True])
-print forall([True, True, True, False])
+print(forall([True, True, True, True]))
+print(forall([True, True, True, False]))
 
 # Contains
 
@@ -91,8 +93,8 @@ def contains(x, xs):
 
 adjectives = ["lazy", "grouchy", "scheming"]
 
-print contains(4, [3, 4, 5, 6, 8])
-print contains("happy", adjectives)
+print(contains(4, [3, 4, 5, 6, 8]))
+print(contains("happy", adjectives))
 
 def indexSet(x, B):
     return [?]